FRAGSTATS:

Spatial Pattern Analysis

Program for Quantifying

Landscape Structure

United States

Deparment of

Agriculture

Pacific Nrothwest

Research Station

General Technical

Report

PNW-GTR-351.

August 1995
Authors KEVIN MCGARIGAL was a research associate and BARBARA J. MARKS is a

research assistant, Forest Science Department, Oregon State University, College

of Forestry, Corvallis, OR 97331. McGarigal currently is a wildlife ecologist, 17590

County Road 27.7, Dolores, CO 81323-9998.

This paper is a product of the Coastal Oregon Productivity Enhancement Program

of which the Pacific Northwest Research Station (PNW) is a major partner. Members

of the Forest Ecosystem Team, the Andrews Forest Ecosystem Group, and the

Cascade Center for Ecosystem Management participated in development of this

software product. The Cascade Center for Ecosystem Management is a partnership

of researchers from PNW and Oregon State University and land managers from the

Willamette National Forest. Partial funding was also provided by the U.S. Department

of the Interior, Bureau of Land Management.
Abstract McGarigal, Kevin; Marks, Barbara J. 1995. FRAGSTATS: spatial pattern analysis

program for quantifying landscape structure. Gen. Tech. Rep. PNW-GTR-351.

Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest

Research Station. 122 p.

This report describes a program, FRAGSTATS, developed to quantify landscape

structure. FRAGSTATS offers a comprehensive choice of landscape metrics and

was designed to be as versatile as possible. The program is almost completely

automated and thus requires little technical training. Two separate versions of

FRAGSTATS exist: one for vector images and one for raster images. The vector

version is an Arc/Info AML that accepts Arc/Info polygon coverages. The raster

version is a C program that accepts ASCII image files, 8- or 16-bit binary image

files, Arc/Info SVF files, Erdas image files, and IDRISI image files. Both versions

of FRAGSTATS generate the same array of metrics, including a variety of area

metrics, patch density, size and variability metrics, edge metrics, shape metrics,

core area metrics, diversity metrics, and contagion and interspersion metrics. The

raster version also computes several nearest neighbor metrics.

In this report, each metric calculated by FRAGSTATS is described in terms of its

ecological application and limitations. Example landscapes are included, and a discussion is provided of each metric as it relates to the sample landscapes. Several

important concepts and definitions critical to the assessment of landscape structure

are discussed. The appendices include a complete list of algorithms, the units and

ranges of each metric, examples of the FRAGSTATS output files, and a users guide

describing how to install and run FRAGSTATS.

Keywords: Landscape ecology, landscape structure, landscape pattern, landscape

analysis, landscape metrics, spatial statistics.
As the authors of FRAGSTATS, we are very concerned about the potential for

misuse of this program. Like most tools, FRAGSTATS is only as good as the user.

FRAGSTATS crunches out a lot of numbers about the input landscape. These numbers can easily become “golden” in the hands of uninformed users. Unfortunately,

the garbage in-garbage out axiom applies here. We have done our best in the

documentation to stress the importance of defining landscape, patch, matrix, and

landscape context at a scale and in a manner relevant and meaningful to the

phenomenon under consideration. We have stressed the importance of understanding the exact meaning of each metric before it is used. These and other

important considerations in any landscape structural analysis are discussed in the

documentation. We strongly urge you to read the entire documentation, especially

the section, “Concepts and Definitions,” before running FRAGSTATS.

We welcome and encourage your criticisms and suggestions about the program,

as well as questions about how to run FRAGSTATS or interpret the output (after

you have read the entire documentation). We are interested in learning about how

others have applied FRAGSTATS in ecological investigations and management

applications. Therefore, we encourage you to contact us and describe your

application after using FRAGSTATS.

This release of FRAGSTATS (version 2.0) differs from the previous version in only

minor ways. Several bugs have been corrected. The most important change is the

added option to treat a specified proportion of the landscape boundary and background edge (instead of just all or none) as true edge in the edge metrics

(bound_wght option). This fraction also is used as the edge contrast weight for

landscape boundary and background edge segments in the calculation of edge

contrast metrics. In addition, the convention for naming the output file containing

patch IDs in the raster version has been modified to comply with DOS requirements

on a personal computer (PC) (id_image option). Similarly, the output file name

extensions in the PC raster version have been shortened and renamed to comply

with DOS requirements and to avoid conflicts with ERDAS conventions (out_file).

The nearest neighbor algorithm has been modified slightly to compute actual

edge-to-edge distance (previous version used cell midpoints rather than edge).

Finally, FRAGSTATS verifies that all interior and exterior background patches

have been classified correctly.

The FRAGSTATS software is available electronically from the following ftp site:

ftp.fsl.orst.edu. If you do not have Internet access, a diskette with the software can

be obtained by sending a 3.5 inch floppy diskette and a self-addressed, stamped

floppy disk mailer to:

Barbara Marks

Department of Forest Science

Oregon State University

Forest Science Lab 020

Corvallis, OR 97331-7501

Every effort has been made to ensure that FRAGSTATS was bug-free at the time of

distribution. If bugs should be discovered, they will be corrected and updated on the

ftp server only.

Preface and

Version 2.0

Upgrade

Information
The following procedure describes how to obtain the FRAGSTATS software

electronically:

1. Connect to the ftp server by issuing the following command:

ftp ftp.fsl.orst.edu

2. Enter “anonymous” when prompted for a log-in name.

3. Enter your e-mail address when prompted for a password.

4. Change the directory to pub/fragstats.2.0 with the following command:

cd pub/fragstats.2.0

The file changes.notes in this directory contains a record and description of all the

modifications made to the software. This file should be checked periodically.

5. If you are ftp’ing from a Unix machine, enter the following commands at the ftp

prompt:

binary

get frag.tar

quit

To extract the files, at your system prompt type:

tar xvf frag.tar

6. If you are ftp’ing from a DOS machine, enter the following commands at the ftp

prompt:

binary

get frag.zip

quit

To extract the files, at your system prompt type:

pkunzip -d frag.zip

(The program pkunzip is available in the fragstats.2.0 directory, if you need it).

We hope that FRAGSTATS is of great assistance in your work, and we look forward

to hearing about your applications.
Contents 1 Introduction

3 Concepts and Definitions

12 FRAGSTATS Overview

22 FRAGSTATS Metrics

22 General Considerations

23 Area Metrics

26 Patch Density, Size, and Variability Metrics

30 Edge Metrics

35 Shape Metrics

38 Core Area Metrics

45 Nearest Neighbor Metrics

49 Diversity Metrics

52 Contagion and Interspersion Metrics

54 Acknowledgments

54 Literature Cited

60 Appendix 1: FRAGSTATS Output File

72 Appendix 2: FRAGSTATS User Guidelines

80 Appendix 3: Definition and Description of FRAGSTATS Metrics
Introduction Growing concerns over the loss of biodiversity have spurred land managers to seek

better ways of managing landscapes at a variety of spatial and temporal scales.

Several developments have made possible the ability to analyze and manage entire

landscapes to meet multiresource objectives. The developing field of landscape

ecology has provided a strong conceptual and theoretical basis for understanding

landscape structure, function, and change (Forman and Godron 1986, Turner 1989,

Urban and others 1987). Growing evidence that habitat fragmentation is detrimental

to many species and may contribute substantially to the loss of regional and global

biodiversity (Harris 1984, Saunders and others 1991) has provided empirical justification for the need to manage entire landscapes, not just the components. The

development of GIS (geographical information systems) technology, in particular, has

made a variety of analytical tools available for analyzing and managing landscapes.

In response to this growing theoretical and empirical support and to technical capabilities, public land management agencies have begun to recognize the need to

manage natural resources at the landscape scale.

A good example of these changes is in wildlife science. Wildlife ecologists often have

assumed that the most important ecological processes affecting wildlife populations

and communities operate at local spatial scales (Dunning and others 1992). Vertebrate species richness and abundance, for example, often are considered functions

of variation in local resource availability, vegetation composition and structure, and

the size of the habitat patch (Cody 1985, MacArthur and MacArthur 1961, Willson

1974). Correspondingly, most wildlife research and management activities have

focused on the within-patch scale, typically small plots or forest stands. Wildlife

ecologists have become increasingly aware, however, that habitat variation and its

effects on ecological processes and vertebrate populations occur at many spatial

scales (Wiens 1989a, 1989b). In particular, there has been increasing awareness of

the potential importance of coarse-scale habitat patterns to wildlife populations and

a corresponding surge in landscape ecological investigations that examine vertebrate distributions and population dynamics over broad spatial scales (for example,

McGarigal and McComb, in press). The recent attention to metapopulation theory

(Gilpin and Hanski 1991) and the proliferation of mathematical models on dispersal

and spatially distributed populations (Kareiva 1990) are testimony to these changes.

Recent conservation efforts for the northern spotted owl (Strix occidentalis caurina)

demonstrate the willingness and ability of public land management agencies to

analyze and manage wildlife populations at the landscape scale (Interagency

Scientific Committee 1990, Lamberson and others 1992, Murphy and Noon 1992).

The emergence of landscape ecology to the forefront of ecology is testimony to the

growing recognition that ecological processes affect and are affected by the dynamic

interaction among ecosystems. This surge in interest in landscape ecology also is

shown in recent efforts to include a landscape perspective in policies and guidelines

for managing public lands. Landscape ecology embodies a way of thinking that many

see as very useful for organizing land management approaches. Specifically, landscape ecology focuses on three characteristics of the landscape (from Forman and

Godron 1986: 11):

1. Structure, the spatial relationships among the distinctive ecosystems or

“elements” present—more specifically, the distribution of energy, materials,

and species in relation to the sizes, shapes, numbers, kinds, and configurations of the ecosystems.

1
2. Function, the interactions among the spatial elements, that is, the flows

of energy, materials, and species among the component ecosystems.

3. Change, the alteration in the structure and function of the ecological

mosaic over time.

Thus, landscape ecology involves the study of landscape patterns, the interactions

among patches within a landscape mosaic, and how these patterns and interactions

change over time. In addition, landscape ecology involves applying these principles

to formulate and solve real-world problems. Landscape ecology considers the development and dynamics of spatial heterogeneity and its affects on ecological processes

and the management of spatial heterogeneity (Risser and others 1984).

Landscape ecology is largely founded on the idea that the patterning of landscape

elements (patches) strongly influences ecological characteristics, including vertebrate

populations. The ability to quantify landscape structure is prerequisite to the study of

landscape function and change. For this reason, much emphasis has been placed on

developing methods to quantify landscape structure (for example, Li 1990, O’Neill

and others 1988, Turner 1990b, Turner and Gardner 1991). Most efforts to date have

been tailored to meet the needs of specific research objectives and have employed

user-generated computer programs to perform the analyses. Such user-generated

programs allow the inclusion of customized analytical methods and easy linkages to

other programs, such as spatial simulation models, yet generally lack the advanced

graphics capabilities of commercially available GIS (Turner 1990b). Most usergenerated programs are limited to a particular hardware or are embedded within

a larger software package designed to accomplish a specific research objective

(for example, to model fire disturbance regimes). We are aware of only one other

published software program that offers a broad array of landscape metrics. The r.le

programs (Baker and Cai 1992), however, are intended to be part of the Geographical

Resources Analysis Support System (GRASS).

This report describes a program called FRAGSTATS1 that we developed to quantify

landscape structure. FRAGSTATS offers a comprehensive choice of landscape metrics and was designed to be as versatile as possible. The program is almost completely automated and thus requires little technical training. Two separate versions

of FRAGSTATS exist: one for vector images and one for raster images. The vector

1 This software is in the public domain, and the recipient may

not assert any proprietary rights thereto nor represent it to

anyone as other than an Oregon State University-produced

program. FRAGSTATS is provided “as-is” without warranty of

any kind, including, but not limited to, the implied warranties of

merchantability and fitness for a particular purpose. The user

assumes all responsibility for the accuracy and suitability of this

program for a specific application. In no event will the authors,

Oregon State University, or the USDA Forest Service be liable

for any damages, including lost profits, lost savings, or other

incidental or consequential damages, arising from the use of or

the inability to use this program.

2
version is an Arc/Info AML that accepts Arc/Info polygon coverages.2 The raster

version is a C program that accepts ASCII image files, 8- or 16-bit binary image

files, Arc/Info SVF files, Erdas image files, and IDRISI image files. Both versions of

FRAGSTATS generate the same array of metrics, although a few additional metrics

are computed in the raster version.

In this report, each metric calculated by FRAGSTATS is described by its ecological

application and limitations. Example landscapes are included as is a discussion of

each metric as it relates to the sample landscapes. In addition, several important

concepts and definitions critical to the assessment of landscape structure are discussed. The appendices include a complete list of algorithms, the units and ranges

of each metric, examples of the FRAGSTATS output files, and a users guide describing in detail how to install and run FRAGSTATS.

It is beyond the scope and purpose of this document to provide a glossary of terms

and a comprehensive discussion of the many concepts embodied in landscape

ecology. Instead, a few key terms and concepts essential to using FRAGSTATS

and to measuring spatial heterogeneity are defined and discussed; a thorough

understanding of these concepts is prerequisite to the effective use of

FRAGSTATS.

Landscape—What is a “landscape”? Surprisingly, there are many different interpretations of this well-used term. The disparity in definitions makes it difficult to

communicate clearly and even more difficult to establish consistent management

policies. Definitions invariably include an area of land containing a mosaic of patches

or landscape elements. Forman and Godron (1986: 11) define landscape as a

“heterogeneous land area composed of a cluster of interacting ecosystems that is

repeated in similar form throughout.” The concept differs from the traditional ecosystem concept in focusing on groups of ecosystems and the interactions among

them. There are many variants of the definition depending on the research or management context. From a wildlife perspective, for example, landscape might be

defined as an area of land containing a mosaic of habitat patches, within which a

particular “focal” or “target” habitat patch often is embedded (Dunning and others

1992). Because habitat patches can be defined only relative to a particular organism’s perception of the environment (that is, each organism defines habitat patches

differently and at different scales), landscape size would differ among organisms

(Wiens 1976); however, landscapes generally occupy some spatial scale intermediate between an organism’s normal home range and its regional distribution. In

other words, because each organism scales the environment differently (for example,

a salamander and a hawk view their environment on different scales), there is no

absolute size for a landscape; from an organism-centered perspective, the size of

a landscape differs depending on what constitutes a mosaic of habitat or resource

patches meaningful to that particular organism (fig. 1).

2 The use of trade or firm names in this publication is for

reader information and does not imply endorsement by the

U.S. Department of Agriculture of any product or service.

Concepts and

Definitions

3
This definition contrasts with the more anthropocentric definition that a landscape

corresponds to an area of land equal to or larger than, say, a large basin (several

thousand hectares). Indeed, Forman and Godron (1986) suggest a lower limit for

landscapes at a “few kilometers in diameter,” although they recognize that most of

the principles of landscape ecology apply to ecological mosaics at any scale. This

may be a more pragmatic definition than the organism-centered definition and

perhaps corresponds to our human perception of the environment, but it has limited

use in managing wildlife populations if it is accepted that each organism scales the

environment differently. From an organism-centered perspective, a landscape could

range in absolute scale from an area smaller than a single forest stand (for example,

an individual log) to an entire ecoregion. If this organism-centered definition of a

landscape is accepted, then a logical consequence of this is a mandate to manage

wildlife habitats across the full range of spatial scales; each scale, whether stand or

watershed, or some other scale, will likely be important for a subset of species, and

each species will likely respond to more than one scale.

Figure 1—Multiscale view of “landscape” from an organism-centered perspective. Because the eagle,

cardinal, and butterfly perceive their environments differently and at different scales, what constitutes a

single habitat patch for the eagle may constitute an entire landscape or patch-mosaic for the cardinal,

and a single habitat patch for the cardinal may comprise an entire landscape for the butterfly that perceives patches on an even finer scale.

4
KEY

POINT

It is not our intent to argue for a single definition of landscape, but

rather to suggest that there are many appropriate ways to define landscape, depending on the situation being considered. The important

point is that a landscape is not necessarily defined by its size but by

an interacting mosaic of patches relevant to the phenomenon under

consideration (at any scale). The investigator or manager must define

landscape appropriately; this is the first step in any landscape-level

research or management endeavor.

Patch—Landscapes are composed of a mosaic of patches (Urban and others 1987).

Landscape ecologists have used several terms to refer to the basic elements or units

that make up a landscape, including ecotope, biotope, landscape component, landscape element, landscape unit, landscape cell, geotope, facies, habitat, and site

(Forman and Godron 1986). We prefer the term “patch”; but any of these terms,

when defined, are satisfactory according to the preference of the investigator. Like

the landscape, patches comprising the landscape are not self-evident; patches must

be defined relative to the given situation. From a timber management perspective,

for example, a patch may correspond to the forest stand; however, the stand may

not function as a patch from a particular organism’s perspective. From an ecological

perspective, patches represent relatively discrete areas (spatial domain) or periods

(temporal domain) of relatively homogeneous environmental conditions, where the

patch boundaries are distinguished by discontinuities in environmental character

states from their surroundings of magnitudes that are perceived by or relevant to

the organism or ecological phenomenon under consideration (Wiens 1976). From

a strictly organism-centered view, patches may be defined as environmental units

between which fitness prospects or, “quality,” differ; although, in practice, patches

may be more appropriately defined by nonrandom distribution of activity or resource

utilization among environmental units, as recognized in the concept of “grain

response” (Wiens 1976).

Patches are dynamic and occur on many spatial and temporal scales that, from an

organism-centered perspective, differ as a function of each animal’s perceptions

(Wiens 1976, 1989a; Wiens and Milne 1989). A patch at any given scale has an

internal structure reflecting patchiness at finer scales, and the mosaic containing that

patch has a structure determined by patchiness at broader scales (Kotliar and Wiens

1990). Thus, regardless of the basis for defining patches, a landscape does not

contain a single patch mosaic but contains a hierarchy of patch mosaics across a

range of scales. From an organism-centered perspective, the smallest scale at which

an organism perceives and responds to patch structure is its “grain” (Kotliar and

Wiens 1990). This lower threshold of heterogeneity is the level of resolution where

the patch size becomes so fine that the individual or species stops responding to it,

even though patch structure may actually exist at a finer resolution (Kolasa and Rollo

1991). The lower limit to grain is set by the physiological and perceptual abilities of

the organism and therefore differs among species. Similarly, “extent” is the coarsest

scale of heterogeneity, or upper threshold of heterogeneity, to which an organism

5
responds (Kolasa and Rollo 1991, Kotliar and Wiens 1990). At the level of the individual, extent is determined by the lifetime home range of the individual (Kotliar and

Wiens 1990) and differs among individuals and species. More generally, however,

extent differs with the organizational level (individual, population, metapopulation)

under consideration; for example, the upper threshold of patchiness for the population would probably greatly exceed that of the individual. From an organismcentered perspective, patches therefore can be defined hierarchically in scales

ranging between the grain and extent for the individual, deme, population, or

range of each species.

Patch boundaries are artificially imposed and are in fact meaningful only when

referenced to a particular scale (grain size and extent). Even a relatively discrete

patch boundary, for example between an aquatic surface (a lake) and a terrestrial

surface, becomes more and more like a continuous gradient as one progresses to

a finer and finer resolution. Most environmental dimensions possess one or more

“domains of scale” (Wiens 1989a) at which the individual spatial or temporal patches

can be treated as functionally homogeneous; at intermediate scales, the environmental dimensions appear more as gradients of continuous variation in character

states. Thus, as one moves from a finer resolution to coarser resolution, patches

may be distinct at some scales (that is, domains of scale) but not at others.

KEY

POINT

It is not our intent to argue for a particular definition of patch. Rather,

we wish to point out that (1) patch must be defined relative to the

phenomenon under investigation or its management; (2) regardless of

the phenomenon under consideration (for example, a species or

geomorphological disturbance), patches are dynamic and occur at

multiple scales; and (3) patch boundaries are only meaningful when

referenced to a particular scale. The investigator or manager must

establish the basis for delineating among patches (that is, patch type

classification system) and a scale appropriate to the phenomenon

under consideration.

Matrix—A landscape is composed typically of several types of landscape elements

(patches). Of these, the matrix is the most extensive and most connected landscape

element type and therefore plays the dominant role in the functioning of the landscape (Forman and Godron 1986). In a large contiguous area of mature forest

embedded with numerous small disturbance patches (for example, timber harvest

patches), the mature forest constitutes the matrix element type because it is greatest

in areal extent, is mostly connected, and exerts a dominant influence on the area

flora and fauna and ecological processes. In most landscapes, the matrix type is

obvious to the investigator or manager. But in some landscapes, or at a certain point

in time during the trajectory of a landscape, the matrix element will not be obvious,

and it may not be appropriate to consider any element as the matrix. The designation

of a matrix element depends mainly on the phenomenon under consideration. In a

study of geomorphological processes, the geological substrate may serve to define

the matrix and patches; in a study of vertebrate populations, vegetation structure may

serve to define the matrix and patches. What constitutes the matrix also depends on

the scale of investigation or management. At a particular scale, mature forest may be

the matrix with disturbance patches embedded within; whereas at a coarser scale,

agricultural land may be the matrix with mature forest patches embedded within.

6
KEY

POINT

The investigator or manager must determine whether a matrix element

exists and should be designated given the scale and phenomenon

under consideration. This should be done before the analysis of

landscape structure, because this decision will influence the choice

and interpretation of landscape metrics.

Scale—The pattern detected in any ecological mosaic is a function of scale, and

the ecological concept of spatial scale encompasses both extent and grain (Forman

and Godron 1986, Turner and others 1989, Wiens 1989a). Extent is the overall area

encompassed by an investigation or the area included within the landscape boundary. From a statistical perspective, the spatial extent of an investigation is the area

defining the population to be sampled. Grain is the size of the individual units of observation. For example, a fine-grained map might structure information into 1-hectare

units, whereas a map with resolution an order of magnitude coarser would have information structured into 10-hectare units (Turner and others 1989). Extent and grain

define the upper and lower limits of resolution of a study and any inferences about

scale-dependency in a system are constrained by the extent and grain of investigation

(Wiens 1989a). From a statistical perspective, we can neither extrapolate beyond the

population sample nor infer differences among objects smaller than the experimental

units. Likewise, in the assessment of landscape structure, we cannot detect pattern

beyond the extent of the landscape or below the resolution of the grain (Wiens

1989a).

As with the concept of landscape and patch, it may be more ecologically meaningful to define scale from the perspective of the organism or ecological phenomenon

under consideration. From an organism-centered perspective, grain and extent may

be defined as the degree of acuity of a stationary organism with respect to shortand long-range perceptual ability (Kolasa and Rollo 1991). Thus, grain is the finest

component of the environment that can be differentiated up close by the organism,

and extent is the range at which a relevant object can be distinguished from a fixed

vantage point by the organism (Kolasa and Rollo 1991). Unfortunately, while this is

ecologically an ideal way to define scale, it is not very pragmatic. In practice, extent

and grain are often dictated by the scale of the imagery being used (for example,

aerial photo scale) or the technical capabilities of the computing environment.

It is critical that extent and grain be defined for a particular study and represent, to

the greatest possible degree, the ecological phenomenon or organism under study;

otherwise, the landscape patterns detected will have little meaning and there is a

good chance of reaching erroneous conclusions. It would be meaningless, for

example, to define grain as 1-hectare units if the organism under consideration

perceives and responds to habitat patches at a resolution of 1 square meter. A

strong landscape pattern at 1-hectare resolution may have no significance to the

organism under study. The reverse is also true; that is, defining grain as 1-squaremeter units if the organism under consideration perceives habitat patches at a

resolution of 1 hectare. Typically, however, we do not know what the appropriate

resolution should be. In this case, it is much safer to choose a finer grain than is

believed to be important. Remember, the grain sets the minimum resolution of

investigation. Once set, we can always dissolve to a coarser grain. In addition, we

can always specify a minimum mapping unit coarser than the grain; that is, we can

specify the minimum patch size to be represented in a landscape, and this can

easily be manipulated above the resolution of the data. Unfortunately, the technical

7
capabilities of GIS for image resolution may far exceed the technical capabilities of

the remote sensing equipment; thus it is possible to generate GIS images at too

fine a resolution for the spatial data being represented, resulting in a more complex

representation of the landscape than can accurately be generated from the data.

Information may be available at several scales, and it may be necessary to extrapolate information from one scale to another. It also may be necessary to integrate

data represented at different spatial scales. It is suggested that information can be

transferred across scales if both grain and extent are specified (Allen and others

1987), yet it is unclear how observed landscape patterns differ in response to

changes in grain and extent and whether landscape metrics obtained at different

scales can be compared. The limited work on this topic suggests that landscape

metrics differ in their sensitivity to changes in scale and that qualitative and quantitative changes in measurements across spatial scales will differ depending on how

scale is defined (Turner and others 1989). Until more is learned, it is critical that

attempts to compare landscapes measured at different scales be done cautiously

in investigations of landscape structure.

KEY

POINT

The most important considerations in any landscape ecological

investigation or landscape structural analysis are (1) to explicitly

define the scale of the investigation or analysis, (2) to describe

any observed patterns or relations relative to the scale of the investigation, and (3) to be especially cautious when attempting to compare

landscapes measured at different scales.

Landscape context—Landscapes do not exist in isolation. Landscapes are nested

within larger landscapes, that are nested within larger landscapes, and so on. In

other words, each landscape has a context or regional setting, regardless of scale

and how the landscape is defined. The landscape context may constrain processes

operating within the landscape. Landscapes are “open” systems; energy, materials,

and organisms move into and out of the landscape. This is especially true in practice,

where landscapes are often somewhat arbitrarily delineated. That broad-scale processes act to constrain or influence finer scale phenomena is one of the key principles

of hierarchy theory (Allen and Star 1982) and supply-side ecology (Roughgarden and

others 1987). The importance of the landscape context depends on the phenomenon

of interest, but typically differs with “openness” of the landscape. The openness

depends not only on the phenomenon under consideration but also on the basis

used for delineating the landscape boundary. From a geomorphological or hydrological perspective, for example, the watershed forms a natural landscape, and a

landscape defined in this manner might be considered relatively “closed.” Of course,

energy and materials flow out of this landscape, and the landscape context influences

the input of energy and materials by affecting climate and so forth, but the system is

nevertheless relatively closed. Conversely, from the perspective of a bird population,

topographic boundaries may have little ecological relevance, and the landscape

defined by watershed boundaries might be considered a relatively “open” system.

Local bird abundance patterns may be produced not only by local processes or

events operating within the designated landscape but also by the dynamics of

regional populations or events elsewhere in the species’ range (Haila and others

1987; Ricklefs 1987; Vaisanen and others 1986; Wiens 1981, 1989b).

8
Landscape metrics quantify the structure of the landscape only within the designated

landscape boundary. Consequently, the interpretation of these metrics and their ecological significance requires an acute awareness of the landscape context and the

openness of the landscape relative to the phenomenon under consideration. These

concerns are particularly important for nearest neighbor metrics. Nearest neighbor

distances are computed solely from patches contained within the landscape boundary. If the landscape extent is small relative to the scale of the organism or ecological

processes under consideration, and the landscape is an open system relative to that

organism or process, then nearest neighbor results can be misleading. Consider a

small subpopulation of a species occupying a patch near the boundary of a somewhat

arbitrarily defined (from the organism’s perspective) landscape. The nearest neighbor

within the landscape boundary might be quite far away, yet in reality the closest

patch might be very close, but just outside the landscape boundary. The magnitude

of this problem is a function of scale. Increasing the size of the landscape relative to

the scale at which the organism under investigation perceives and responds to the

environment will generally decrease the severity of this problem. In general, the

larger the ratio of extent to grain (that is, the larger the landscape relative to the

average patch size), the less likely these and other metrics will be dominated by

boundary effects.

KEY

POINT

The important point is that a landscape should be defined relative

to both the patch mosaic within the landscape and the landscape

context. Consideration always should be given to the landscape

context and the openness of the landscape relative to the phenomenon under consideration when choosing and interpreting landscape

metrics.

Landscape structure—Landscapes are distinguished by spatial relations among

component parts. A landscape can be characterized by both its composition and

configuration (sometimes referred to as landscape physiognomy or landscape

pattern) (Dunning and others 1992, Turner 1989), and these two aspects of a

landscape can independently or in combination affect ecological processes and

organisms. The difference between landscape composition and configuration is

analogous to the difference between floristics (for example, the types of plant

species present) and vegetation structure (for example, foliage height diversity)

so commonly considered in wildlife-habitat studies at the within-patch scale.

Landscape composition refers to features associated with the presence and amount

of each patch type within the landscape but without being spatially explicit. In other

words, landscape composition encompasses the variety and abundance of patch

types within a landscape but not the placement or location of patches within the landscape mosaic. Landscape composition is important to many ecological processes

and organisms. For example, many vertebrate species require specific habitat types,

and the total amount of suitable habitat (a function of landscape composition) likely

influences the occurrence and abundance of these vertebrate species. There have

been many attempts to model animal populations within landscapes based on landscape composition alone; such models have been referred to as “island models” by

Kareiva (1990). Island models represent the discrete patchwork mosaic of the landscape; the key feature of these models is population subdivision. Yet these models

do not specify the relative distances among patches or their positions relative to each

9
other. Thus, although these models provide strong analytical solutions, they may be

overly simplified for most natural populations; but we have learned much about population dynamics in spatially complex environments based on models of landscape

composition alone (Kareiva 1990).

There are many quantitative measures of landscape composition, including the proportion of the landscape in each patch type, patch richness, patch evenness, and

patch diversity. Indeed, because of the many ways to measure diversity, there are

literally hundreds of possible ways to quantify landscape composition. The investigator or manager must choose the formulation best representing their concerns.

Landscape configuration refers to the physical distribution or spatial character of

patches within the landscape. Some aspects of configuration, such as patch isolation

or patch contagion, are measures of the placement of patch types relative to other

patch types, the landscape boundary, or other features of interest. Other aspects of

configuration, such as shape and core area, are measures of the spatial character

of the patches. Many attempts have been made to explicitly incorporate landscape

configuration into models of ecological processes and population dynamics within

heterogeneous landscapes; such models have been referred to as “stepping-stone

models” by Kareiva (1990). In contrast to island models, stepping-stone models have

an explicit spatial dimension and can account for dispersal distances and environmental variability with a spatial structure. Recently, we have seen dramatic increases

in the level of sophistication in stepping-stone models, and some results have had

profound effects on the design of managed landscapes (for example, Lamberson and

others 1992, McKelvey and others 1992).

There are many aspects to landscape configuration with much literature available

on methods and indices developed for representing them. Landscape configuration

can be quantified by using statistics in terms of the landscape unit itself (that is, the

patch). The spatial pattern being represented is the spatial character of the individual

patches. The location of patches relative to each other in the landscape (the configuration of patches within the landscape) is not explicitly represented. Landscape

metrics quantified in terms of the individual patches (for example, mean patch core

area or mean patch shape) are spatially explicit at the level of the individual patch.

Such metrics represent a recognition that the ecological properties of a patch are

influenced by the surrounding neighborhood (for example, edge effects) and that the

magnitude of these influences are affected by patch size and shape. These metrics

simply quantify, for the landscape as a whole, the average patch characteristics or

some measure of variability in patch characteristics. Although these metrics are not

spatially explicit at the landscape level, they have clear ecological relevance when

considered from a patch dynamics standpoint (Pickett and White 1985). As an

example, a number of bird species are sensitive to patch core area (a function of

patch size and shape) because of negative intrusions from the surrounding landscape (for example, Robbins and others 1989, Temple 1986). Quantifying mean

patch core area across the landscape could provide a good index to landscape

suitability for such species.

Landscape metrics quantified in terms of the spatial relation of patches and matrix

comprising the landscape (for example, nearest neighbor, contagion) are spatially

explicit at the landscape level because the relative location of individual patches

10
within the landscape is represented in some way. Such metrics represent a recognition that ecological processes and organisms are affected by the interspersion

and juxtaposition of patch types within the landscape. For example, the population

dynamics of species with limited dispersal ability are likely affected by the distribution

of suitable habitat patches. Both the distance between suitable patches and the

spatial arrangement of suitable patches can influence population dynamics (Kareiva

1990, Lamberson and others 1992, McKelvey and others 1992). Likewise, patch

juxtaposition is especially important to organisms that require two or more habitat

types because the close proximity of resources provided by different patch types is

critical for their survival and reproduction. Patch juxtaposition also is important for

species adversely affected by edges, because the types of patches juxtaposed along

an edge will influence the character of that edge.

A number of landscape configuration metrics can be formulated either by individual

patches or by the whole landscape, depending on the emphasis sought. For example,

fractal dimension is a measure of shape complexity (Burrough 1986, Mandelbrot

1982, Milne 1988) that can be computed for each patch and then averaged for the

landscape, or it can be computed from the landscape as a whole (by using the

box-count method [Morse and others 1985]). Similarly, core area can be computed

for each patch and then represented as mean patch core area for the landscape, or

it can be computed simply as total core area in the landscape. Obviously, one form

can be derived from the other if the number of patches is known, and so they are

largely redundant; the choice of formulations depends on user preference or the

emphasis sought (patch or landscape). The same is true for several other common

landscape metrics. Typically, these metrics are spatially explicit at the patch level but

not at the landscape level.

Not all landscape metrics can be classified easily as representing landscape

composition or landscape configuration. Landscape metrics, such as mean patch

size and patch density, are not really spatially explicit at either the patch or landscape level because they do not depend explicitly on the spatial character of the

patches or their relative location. Moreover, mean patch size and patch density of

a particular patch type reflect both the amount of a patch type present (composition)

and its spatial distribution (configuration). Because mean patch size and patch density

differ with spatial heterogeneity of the landscape, it often is more appropriate to

consider them as indices of landscape configuration. In addition, some landscape

metrics clearly represent spatial heterogeneity but are not spatially explicit at all.

These metrics differ with the heterogeneity of the landscape but do not depend

explicitly on the relative location of patches within the landscape or their individual

spatial character. For example, total edge or edge density is a function of the amount

of border between patches. For a given edge density there could be 2 patches or

10 patches, they could be clustered or maximally dispersed, or they could be skewed

to one side of the landscape or in the middle. It is not important that all metrics be

classified by the simple composition versus configuration dichotomy. What is important, however, is that the investigator or manager recognize that landscape structure

consists of both composition and configuration and that various metrics have been

developed to represent these aspects of landscape structure separately or in

combination.

11
Finally, it is important to understand how measures of landscape structure are influenced by the designation of a matrix element. If an element is designated as matrix

and therefore presumed to function as such (that is, has a dominant influence on

landscape dynamics), then it should not be included as another patch type in any

metric that simply averages some characteristic (for example, mean patch size or

mean patch shape) across all patches. Otherwise, the matrix will dominate the metric

and serve more to characterize the matrix than the patches within the landscape,

although this may itself be meaningful in some applications. From a practical standpoint, it is important to recognize this because in FRAGSTATS the matrix can be

excluded from calculations by designating its class value as background. If the matrix

is not excluded from the calculations, it may be more meaningful to use the classlevel statistics for each patch type and ignore the patch type designated as the

matrix. From a conceptual standpoint, it is important to recognize that the choice

and interpretation of landscape metrics must ultimately be evaluated in terms of

their ecological meaningfulness, which depends on how the landscape is defined,

including the choice of patch types and the designation of a matrix.

KEY

POINT

The importance of fully understanding each landscape metric before it

is used cannot be emphasized enough. Specifically, these questions

should be asked of each metric before it is used: Does it represent

landscape composition, configuration, or both? What aspect of configuration does it represent? What scale, if any, is spatially explicit? How

is it affected by the designation of a matrix element? Based on answers

to these questions, does the metric represent landscape structure in a

manner ecologically meaningful to the phenomenon under consideration? Only after answering these questions should one attempt to

draw conclusions about the structure of the landscape analyzed.

FRAGSTATS is a spatial pattern analysis program for quantifying landscape structure. The landscape subject to analysis is user defined and can represent any spatial

phenomenon. FRAGSTATS quantifies the areal extent and spatial distribution of

patches (that is, polygons on a map coverage) within a landscape; the user must

establish a sound basis for defining and scaling the landscape (including the extent

and grain of the landscape) and the scheme by which patches within the landscape

are classified and delineated (we strongly recommend reading the preceding section,

“Concepts and Definitions”). The output from FRAGSTATS is meaningful only if the

landscape mosaic is meaningful for the phenomenon under consideration.

FRAGSTATS does not limit the scale (extent or grain) of the landscape subject to

analysis. But, the distance- and area-based metrics computed in FRAGSTATS are

reported in meters and hectares, respectively, and thus landscapes of extreme extent

or resolution may result in rather cumbersome numbers and be subject to rounding

errors. FRAGSTATS, however, outputs data files in ASCII format that can be manipulated with any database management program to rescale metrics or to convert

them to other units (for example, converting hectares to acres).

There are two versions of FRAGSTATS: one accepts Arc/Info polygon coverages

(vector), and one accepts a raster image in various formats. The vector version of

FRAGSTATS is an Arc/Info AML developed on a SUN workstation running Arc/Info

FRAGSTATS

Overview

12
version 6.1; it will not run with earlier versions of Arc/Info. Because of limitations in

Arc/Info, the AML calls several C programs developed in a Unix environment and

compiled with the GNU C compiler (they may not compile with other compilers). The

raster version of FRAGSTATS also was developed on a SUN workstation in the Unix

operating environment. It is written in C and also compiled with the GNU C compiler.

Both versions of FRAGSTATS respond to command line input or allow the user to

answer a series of prompts. Both versions of FRAGSTATS generate the same array

of metrics (see table 1), although a few additional metrics (that is, nearest neighbor

metrics and contagion) are computed in the raster version, and the format of the

output files is exactly the same. The raster version of FRAGSTATS also has been

compiled to run in the DOS environment on a personal computer (PC). The directions for running the DOS version on a PC are exactly the same as the Unix version.

It is important to realize that vector and raster images depict edges differently. Vector

images portray a line in the form it is digitized. Raster images, however, portray lines

in stairstep fashion. Consequently, the measurement of edge length is biased upward

in raster images; that is, measured edge length is always more than the true edge

length. The magnitude of this bias depends on the grain or resolution of the image

(cell size), and the consequences of this bias in use and interpretation of edge-based

metrics must be weighed relative to the phenomenon under investigation. Because

of this bias, the vector and raster versions of FRAGSTATS will not produce identical

results for a landscape.

In some investigations, it may be desirable or necessary to create a raster image

from the initial vector image and run the raster version of FRAGSTATS. It is critical

that great care be taken during the rasterization process and that the resulting raster

image be carefully scrutinized for accurate representation of the original image.

During the rasterization process, it is possible for disjunct patches to join or for a

contiguous patch to be subdivided. This problem can be quite severe (for example,

resulting in numerous one-cell patches) if the cell size chosen is too large relative

to the minimum patch dimension in the vector image.

FRAGSTATS accepts images in several forms, including images that contain

background and a landscape border (figs. 2 and 3). Every image will include a

landscape boundary that defines the perimeter of the landscape and surrounds

the patch mosaic of interest. Every patch within the landscape boundary must have

a positive patch type code, whereas every patch outside the landscape boundary

(border or background, see below) must have a negative patch type code. An

image may include background (also referred to as “mask”), an undefined area

either interior or exterior to the landscape of interest. Background can exist as

“holes” in the landscape, can partially or completely surround the landscape of

interest, and can occur on the edge of the designated landscape of interest and

span the landscape boundary (that is, be broken into two pieces, one inside the

landscape boundary and one outside). The background value can be any nonpatch

code; background patches within the landscape boundary must e positive and those

outside the landscape boundary must be negative, like all other patch types. The

background class is ignored in all metrics but those involving edge. The user specifies

how boundary and background edge segments should be handled (see below). An

13
Table 1—Metrics computed in FRAGSTATS, grouped by subject areaa

Scale Acronym Metric (units)

Area metrics:

Patch AREA Area (ha)

Patch LSIM Landscape similarity index (percent)

Class CA Class area (ha)

Class %LAND Percentage of landscape

Class/landscape TA Total landscape area (ha)

Class/landscape LPI Largest patch index (percent)

Patch density, patch size and variability metrics:

Class/landscape NP Number of patches

Class/landscape PD Patch density (number/100 ha)

Class/landscape MPS Mean patch size (ha)

Class/landscape PSSD Patch size standard deviation (ha)

Class/landscape PSCV Patch size coefficient of variation (percent)

Edge metrics:

Patch PERIM Perimeter (m)

Patch EDCON Edge contrast index (percent)

Class/landscape TE Total edge (m)

Class/landscape ED Edge density (m/ha)

Class/landscape CWED Contrast-weighted edge density (m/ha)

Class/landscape TECI Total edge contrast index (percent)

Class/landscape MECI Mean edge contrast index (percent)

Class/landscape AWMECI Area-weighted mean edge contrast index (percent)

Shape metrics:

Patch SHAPE Shape index

Patch FRACT Fractal dimension

Class/landscape LSI Landscape shape index

Class/landscape MSI Mean shape index

Class/landscape AWMSI Area-weighted mean shape index

Class/landscape DLFD Double log fractal dimension

Class/landscape MPFD Mean patch fractal dimension

Class/landscape AWMPFD Area-weighted mean patch fractal dimension

Core area metrics:

Patch CORE Core area (ha)

Patch NCORE Number of core areas

Patch CAI Core area index (percent)

Class C%LAND Core area percentage of landscape

Class/landscape TCA Total core area (ha)

Class/landscape NCA Number of core areas

Class/landscape CAD Core area density (number/100 ha)

Class/landscape MCA1 Mean core area per patch (ha)

Class/landscape CASD1 Patch core area standard deviation (ha)

Class/landscape CACV1 Patch core area coefficient of variation (percent)

Class/landscape MCA2 Mean area per disjunct core (ha)

Class/landscape CASD2 Disjunct core area standard deviation (ha)

Class/landscape CACV2 Disjunct core area coefficient of variation (percent)

Class/landscape TCAI Total core area index (percent)

Class/landscape MCAI Mean core area index (percent)

14
image also may include a landscape border—a strip of land surrounding the landscape of interest (that is, outside the landscape boundary) within which patches have

been delineated and classified. Patches in the border must be set to the negative of

the appropriate patch type code. If a border patch is a patch type of code 34, then its

label must be -34. The border can be any width and provides information on patch

type adjacency for patches on the edge of the landscape. It is ignored in all but the

edge contrast, interspersion, and contagion metrics.

The convention described above for classifying interior and exterior background

patches is often hard to adhere to with raster images. The raster version of

FRAGSTATS will accept images in which all background patches have been set

to the same patch type code. When reading the image, FRAGSTATS notes if any

interior (positive) or exterior (negative) background patches are present. If the

landscape contains both positively and negatively classified background patches,

FRAGSTATS assumes the user has followed the convention stated above. If

only one type of background was found (only interior or only exterior), however,

FRAGSTATS will verify that each background patch was classified correctly. If

FRAGSTATS finds that an interior background patch was incorrectly classified as

exterior background, it will be reclassified as interior background, and a message

will be issued. Incorrectly classified exterior background patches also will be reclassified as exterior, if necessary. A warning will be issued if FRAGSTATS finds

background patches along the boundary and a border is present. It is impossible to

tell whether these patches should be interior or exterior. Be aware that if background

patches are not classified correctly, the following indices may not be calculated correctly at the class and landscape level: landscape shape index, total edge, edge

density, contrast weighted edge density, and total edge contrast index.

Table 1—Metrics computed in FRAGSTATS, grouped by subject areaa

(continued)

Scale Acronym Metric (units)

Nearest neighbor metrics:

Patch NEAR Nearest neighbor distance (m)

Patch PROXIM Proximity index

Class/landscape MNN Mean nearest neighbor distance(m)

Class/landscape NNSD Nearest neighbor standard deviation (m)

Class/landscape NNCV Nearest neighbor coefficient of variation (percent)

Class/landscape MPI Mean proximity index

Diversity metrics:

Landscape SHDI Shannon’s diversity index

Landscape SIDI Simpson’s diversity index

Landscape MSIDI Modified Simpson’s diversity index

Landscape PR Patch richness (number)

Landscape PRD Patch richness density (number/100 ha)

Landscape RPR Relative patch richness (percent)

Landscape SHEI Shannon’s evenness index

Landscape SIEI Simpson’s evenness index

Landscape MSIEI Modified Simpson’s evenness index

Contagion and interspersion metrics:

Class/landscape IJI Interspersion and Juxtaposition index (percent)

Landscape CONTAG Contagion index (percent)

a See appendix 3 for mathematical definitions of the metrics.

15
Under most circumstances, it is probably not valid to assume that all edges function

the same. Indeed, there is good evidence that edges differ in their effects on ecological processes and organisms depending on the nature of the edge (for example,

type of adjacent patches, degree of structural contrast, orientation) (Hansen and

di Castri 1992). Accordingly, the user can specify a file containing edge contrast

weights for each combination of patch types (classes). These weights represent the

magnitude of edge contrast between adjacent patch types and must range between 0

(no contrast) and 1 (maximum contrast). Edge contrast weights are used to compute

several edge-based metrics (see “Edge Metrics,” below). If this weight file is not

provided, these edge contrast metrics are not computed and are reported as “NA”

or “.” in the output files (see below). Generally, if a landscape border is designated,

a weight file will be specified also, because the main reason for specifying a border

is when information on edge contrast is deemed important. However, a border is

also useful for determining patch type adjacency for the interspersion and contagion

indices. Any scheme can be used to establish weights as long as it is meaningful to

the phenomenon under investigation.

Regardless of the image format (figs. 2 and 3), the user must specify how the landscape boundary and any edge segments bordering a specified background class

should be treated relative to the edge metrics. This has various effects depending

on whether a contrast weight file is specified, whether a landscape border is present,

Figure 2—Alternative image formats accepted in the vector version of FRAGSTATS. Landscape boundary,

background, and border are defined in the text.

16
and whether a background class is designated. If a contrast weight file is specified,

then all patch edges are evaluated for edge contrast based on the weight file and the

edge contrast metrics (see “Edge Metrics,” below) are computed. In this scenario, if a

landscape border is present, then edge segments along the landscape boundary are

evaluated for edge contrast based on the weight file. Conversely, if a landscape

border is absent, then edge segments along the landscape boundary are treated as

either maximum-contrast edge (weight = 1), no-contrast edge (weight = 0), or some

intermediate, average-contrast edge (weight = user specified), depending on how

the user decides to handle boundary and background edge. Regardless of whether

a landscape border is present or not, if a background class is specified, then edge

segments bordering the background class are treated according to the user-specified

edge contrast. In other words, it is possible for a landscape border to be present and

still have a background class designated. The background may occur as “holes” in

the landscape or along the landscape boundary. In either case, edge segments

bordering background are treated according to the decision regarding boundary and

background edge. Note, however, that the presence of a landscape border and a

background class and the decision on how to treat these edges will have no effect

on the edge contrast metrics if a contrast weight file is not specified—because these

metrics will not be computed.

Figure 3—Alternative image formats accepted in the raster version of FRAGSTATS. Landscape

boundary, background, and border are defined in the text.

17
Regardless of whether an edge contrast weight file is specified, the presence of a

landscape border, the specification of a background class, and the decision regarding

how to treat the boundary and background edge will affect metrics based on patch

type adjacency as well as those based on edge length. Metrics based on patch type

adjacency (for example, interspersion and contagion indices) consider only edge

segments with adjacent patch information. Therefore, if a landscape border is

present, then edge segments along the border are considered in these calculations.

Conversely, if a landscape border is absent, then the entire landscape boundary is

ignored in these calculations. Similarly, if a background class is specified, then edge

segments bordering background are ignored in these calculations. Metrics based on

edge length (for example, total edge or edge density) are affected by these considerations as well. If a landscape border is present, then edge segments along the

border are evaluated to determine which segments represent true edge and which

do not. Conversely, if a landscape border is absent, then a user-specified proportion

of the landscape boundary is treated as true edge and the remainder is ignored. As

an example, if the user specifies that 50 percent of the landscape boundary or background should be treated as true edge, then 50 percent of the landscape boundary

will be incorporated into the edge length metrics. Regardless of whether a landscape

border is present or not, if a background class is specified, then a user-specified

proportion of edge bordering background is treated as true edge and the remainder

is ignored.

We recommend including a landscape border, especially if edge contrast or patch

type adjacency is deemed important. In most cases, some portions of the landscape

boundary will constitute true edge (an edge with a contrast weight greater than 0)

and others will not, and it will be difficult to estimate the proportion of the landscape

boundary representing true edge. It also will be difficult to estimate the average edge

contrast weight for the entire landscape boundary. Thus, the decision on how to treat

the landscape boundary will be somewhat subjective and may not accurately represent the landscape. In the absence of a landscape border, the effects of the decision

for treating the landscape boundary on the landscape metrics will depend on landscape extent and heterogeneity. Larger and more heterogeneous landscapes will

have a greater internal edge-to-boundary ratio, and therefore the boundary will have

less influence on the landscape metrics. Of course, only those metrics based on

edge lengths and types are affected by the presence of a landscape border and the

decision of how to treat the landscape boundary. When edge-based metrics are of

particular importance to the investigation and the landscapes are small in extent and

relatively homogeneous, the inclusion of a landscape border and the decision on the

landscape boundary should be considered carefully. In addition, unless there is a

strong ecological reason for designating a background class, we recommend that

background not be included because it only complicates the calculation and interpretation of edge-based metrics. Ideally, a landscape should have a border and contain

no background.

18
FRAGSTATS computes three groups of metrics. For a given landscape mosaic,

FRAGSTATS computes several statistics for (1) each patch in the mosaic (fig. 4);

(2) each patch type (class) in the mosaic (fig. 5); and (3) the landscape mosaic as

a whole (fig. 6) (see table 1 for a description of the acronyms for each metric). In the

assessment of landscape structure, patch indices serve primarily as the computational

basis for several of the landscape metrics; the individual patch indices may have little

interpretive value. But sometimes patch indices can be important and informative in

landscape-level investigations. Many vertebrates, for example, require suitable habitat

patches larger than some minimum size (for example, Robbins and others 1989), so

it would be useful to know the size of each patch in the landscape. Similarly, some

species are adversely affected by edges and are more closely associated with patch

interiors (for example, Temple 1986), so it would be useful to know the size of the

core area for each patch in the landscape. The probability of occupancy and persistence of an organism in a patch may be related to patch insularity (see Kareiva 1990),

so it would be useful to know the nearest neighbor of each patch and the degree of

contrast between the patch and its neighborhood. The utility of the patch characteristic information ultimately will depend on the objectives of the investigation.

Figure 4—Example of FRAGSTATS patch indices for three sample patches drawn from a sample landscape. See text and appendix 3 for descriptions and definitions of the metrics. Indices with an asterisk were

computed from the raster version of FRAGSTATS.

19
In many landscape ecological applications, the primary interest is in the amount and

distribution of a particular patch type (class). A good example is in the study of forest

fragmentation. Forest fragmentation is a landscape-level process in which forest tracts

are progressively subdivided into smaller, geometrically more complex (initially but

not necessarily ultimately), and more isolated forest fragments as a result of both

natural processes and human land use activities (Harris 1984). This process involves

changes in landscape composition, structure, and function and occurs on a backdrop

of a natural patch mosaic created by changing landforms and natural disturbances.

Forest fragmentation is the prevalent landscape change in several human-dominated

forest regions of the world, and is increasingly recognized as a major cause of declining biodiversity (Terborgh 1989, Whitcomb and others 1981). Class indices separately

quantify the amount and distribution of each patch type in the landscape and thus

can be considered indices of fragmentation for each patch type.

In other landscape ecological applications, the primary interest is in the structure

(composition and configuration) of the entire landscape(s). A good example is in the

study of landscape diversity. Leopold (1933) noted that wildlife diversity is greater in

more diverse landscapes. Thus, the quantification of landscape diversity has assumed

Figure 5—Example of FRAGSTATS class indices for the mixed, large sawtimber (MLS) patch type in three

sample landscapes. See text and appendix 3 for descriptions and definitions of the metrics. Indices with an

asterisk were computed from the raster version of FRAGSTATS.

20
a preeminent role in landscape ecology. A major focus of landscape ecology is on

quantifying the relations between landscape structure and ecological processes.

Consequently, much emphasis has been placed on developing methods to quantify

landscape structure (for example, Li 1990, O’Neill and others 1988, Turner 1990b,

Turner and Gardner 1991) and a great variety of landscape structural indices have

been developed for this purpose. Many of these published indices have been incorporated into FRAGSTATS, although sometimes in modified form.

By default, FRAGSTATS creates four output files. The user supplies a basename for

the output files, and FRAGSTATS appends the extensions .full, .patch, .class, and

.land to the basename. All files created are ASCII and viewable. However, only the

basename.full file is in a format intended for displaying results. The basename.full file

contains all the patch, class, and landscape metrics calculated for an input landscape

(see appendix 1 for an example of the basename.full file). The name of each metric

is spelled out along with its value and units. This file’s main utility is for viewing

results; its format is not intended for input to other data management or analysis

programs.

Figure 6—Example of FRAGSTATS landscape indices for three sample landscapes. See text and appendix

3 for descriptions and definitions of the metrics. Indices with an asterisk were computed from the raster

version of FRAGSTATS.

21
The other three files are formatted to facilitate input into database management programs. The basename.patch file contains the patch metrics for a landscape; the file

contains one record for each patch in the landscape. Similarly, the basename.class

file contains the class metrics; the file contains one record for each class in the landscape. Finally, the basename.land file contains the landscape metrics; the file contains one record for the landscape. The first record in all these files is a header consisting of the acronyms for all the metrics that follow. The user has the option of suppressing the output of the patch or class metrics, or both. If these metrics are suppressed, the corresponding basename ASCII file is not created and the metrics are

not included in the basename.full file.

FRAGSTATS Metrics This section provides a general overview and discussion of the various metrics computed in FRAGSTATS; detailed mathematical definitions and descriptions of each

metric, including the units and range in values, are provided in appendix 3. Metrics

are grouped in logical fashion by the aspect of landscape structure measured; for

example, the core area metrics (those based on core area measurements) computed

at the patch, class, and landscape levels are discussed together. For each group, the

general applicability of the metrics to landscape ecological investigations and some

of their limitations are discussed. In addition, the results presented in figures 4 to 6

are discussed relative to each group of metrics at the end of each section (in reduced

font size on a shaded background).

General Considerations Metrics involving standard deviation employ the population standard deviation formula,

not the sample formula, because all patches in the landscape (or class) are included

in the calculations. In other words, the landscape is considered a population of patches and every patch is counted; FRAGSTATS does not sample patches from the landscape, it censuses the entire landscape. Even if each landscape represents a sample

from a larger region, it is still more appropriate to compute the standard deviation for

each landscape by using the population formula. In this case, it is appropriate to use

the sample formula when calculating the variation among landscapes by using the

FRAGSTATS output for each landscape. The difference between the population and

sample formulas is insignificant when sample sizes (number of patches) are large

(greater than 20). However, when quantifying landscapes with few patches, the differences can be significant.

FRAGSTATS computes several statistics for each patch and class in the landscape

and for the landscape as a whole. At the class and landscape level, some of the

metrics quantify landscape composition, and others quantify landscape configuration.

As previously discussed, composition and configuration can affect ecological processes independently and interactively. Thus, it is especially important to understand

for each metric what aspect of landscape structure is being quantified. In addition,

many of the metrics are partially or completely redundant; that is, they quantify a

similar or identical aspect of landscape structure. In most cases, redundant metrics

will be very highly or even perfectly correlated; at the landscape level, patch density

(PD) and mean patch size (MPS), for example, will be perfectly correlated because

they represent the same information. These redundant metrics are alternate ways of

22
representing the same information; they are included in FRAGSTATS because the

preferred form of representing a particular aspect of landscape structure will differ

among applications and users. The user needs to understand these redundancies,

because in most applications only one of each set of redundant metrics should be

employed. In particular applications, some metrics may be empirically redundant; not

because they measure the same aspect of landscape structure, but because for the

particular landscapes under investigation, different aspects of landscape structure

are statistically correlated. The distinction between this form of redundancy and the

former is important, because little can be learned by interpreting inherently redundant

metrics, but much can be learned about landscapes by interpreting empirically redundant metrics.

Many of the patch indices have counterparts at the class and landscape levels; for

example, many of the class indices (such as, mean shape index) represent the same

basic information as the corresponding patch indices (patch shape index), but instead

of considering a single patch, they consider all patches of a particular type simultaneously. Likewise, many of the landscape indices are derived from patch or class characteristics. Consequently, many of the class and landscape indices are computed

from patch and class statistics by summing or averaging over all patches or classes.

Even though many of the class and landscape indices represent the same fundamental information, the algorithms of course differ slightly (see appendix 3). Class

indices represent the spatial distribution and pattern within a landscape of a single

patch type; landscape indices represent the spatial pattern of the entire landscape

mosaic, considering all patch types simultaneously. Thus, even though many of the

indices have counterparts at the class and landscape levels, their interpretations may

be somewhat different. Most of the class indices can be interpreted as fragmentation

indices because they measure the fragmentation of a particular patch type; most of

the landscape indices can be interpreted more broadly as landscape heterogeneity

indices because they measure the overall landscape structure. Hence, it is important

to interpret each index in a manner appropriate to its scale (patch, class, or landscape).

Area Metrics FRAGSTATS computes several simple statistics representing area at the patch,

class, and landscape levels (table 1). Area metrics quantify landscape composition,

not landscape configuration. The area (AREA) of each patch comprising a landscape

mosaic is perhaps the single most important and useful piece of information contained

in the landscape. Not only is this information the basis for many of the patch, class,

and landscape indices, but patch area has a great deal of ecological utility in its own

right. There is considerable evidence, for example, that bird species richness and the

occurrence and abundance of some species are strongly correlated with patch size

(Robbins and others 1989). Thus, patch size information alone could be used to

model species richness, patch occupancy, and species distribution patterns in a

landscape, given the appropriate empirical relations derived from field studies.

23
Class area (CA) is a measure of landscape composition; specifically, how much of

the landscape is comprised of a particular patch type. This is an important measure

in several ecological applications. For example, an important by-product of habitat

fragmentation is quantitative habitat loss. In the study of forest fragmentation, it is

therefore important to know how much of the target patch type (habitat) exists within

the landscape. In addition, although many vertebrate species specializing on a particular habitat have minimum area requirements (Robbins and others 1989), not all

species require that the suitable habitat be present in one contiguous patch. Northern

spotted owls, for example, have minimum area requirements for late-seral forest that

differs geographically; yet, individual spotted owls use late-seral forest that may be

distributed among many patches (Forsman and others 1984). For this species, lateseral forest area might be a good index of habitat suitability within landscapes the

size of spotted owl home ranges (Lehmkuhl and Raphael 1993). In addition to its

direct interpretive value, class area is used in the computations for many of the class

and landscape metrics.

Total landscape area (TA) often does not have a great deal of interpretive value for

evaluating landscape structure, but it is important because it defines the extent of the

landscape. Total landscape area also is used in the computations for many of the

class and landscape metrics. Total landscape area is included as both a class and

landscape index (and included in the corresponding output files) because it is important regardless of whether the primary interest is in class or landscape indices.

These metrics quantify area in absolute terms (hectares), but it often is desirable to

quantify area in relative terms as a percentage of total landscape area. Therefore,

at the class level, FRAGSTATS computes the percentage of landscape (%LAND)

occupied by each patch type. At the patch level, the landscape similarity index

(LSIM) equals the percentage of the landscape occupied by the same patch type

as the patch (and is equivalent to %LAND). It is included as a patch characteristic

because some ecological properties of a patch can be influenced by the abundance

of similar patches in the surrounding landscape. For example, island biogeographic

theory predicts that the probability of patch occupancy for some species or species

richness is a function of both patch size and isolation (MacArthur and Wilson 1967).

One aspect of isolation is the amount of similar habitat within a specified distance.

Thus, the dynamics of a local population contained within a patch are likely to be

influenced by the size of the metapopulation occupying the entire landscape. Indeed,

there is some evidence that regional habitat availability has a strong influence

on local bird populations at the patch level (Askins and Philbrick 1987). Finally,

FRAGSTATS computes a largest patch index (LPI) at the class and landscape

levels that quantifies the percentage of total landscape area comprised by the

largest patch.

Area metrics have limitations imposed by the scale of investigation. Minimum patch

size and landscape extent set the lower and upper limits of these area metrics,

respectively. These are critical limits to recognize because they establish the lower

and upper limits of resolution for the analysis of landscape composition and pattern.

Otherwise, these area metrics have few limitations.

24
Patch-level example—Figure 4 depicts three patches extracted from a sample landscape that

differ in size and landscape similarity. Roughly 50 percent of the landscape is similar to patch

A (LSIM) and thus comprised of mixed, large sawtimber (MLS). In contrast, patches B and

C represent relatively rare patch types, because only 8 percent of the landscape is comprised

of these patch types. Thus, patch A is less insular than patches B and C. The dynamics of

some ecological processes are likely to be different among patches A, B, and C. An organism

inhabiting patch A and dependent on mixed, large sawtimber is likely to experience a different

population dynamic than a similar organism occupying either patch B or C because of the

larger regional population size and probable increased interaction among individuals inhabiting

the landscape. On the other hand, because of their rarity, patches B and C probably would

contribute more to faunal species richness than would patch A.

Class-level example—Figure 5 depicts three sample landscapes that differ in the amount

and pattern of mixed, large sawtimber habitat. According to class area (CA), landscapes B

and C have more than 10 times as much mixed, large sawtimber as landscape A. Roughly

50 percent of landscapes B and C are mixed, large sawtimber, in contrast to only 5 percent

of landscape A, according to the percentage of landscape (%LAND) measure. Thus, the

dynamics of some ecological processes are likely to be quite different in landscape A than

in either B or C. Populations of organisms associated with mixed, large sawtimber habitat,

for example, are likely to be much smaller in landscape A and perhaps subject to a higher

probability of local extinction than in either B or C. On the other hand, the mixed, large

sawtimber habitat in landscape A probably contributes proportionately more to landscape

diversity and species richness than in either B or C.

In addition, although class area and percentage of landscape indicate that landscapes B

and C are similar in composition with respect to mixed, large sawtimber habitat, other indices

suggest that they differ greatly in configuration. For example, the largest patch index (LPI)

represents the three landscapes along a continuum from most to least fragmented and clearly

distinguishes between landscapes B and C in terms of landscape configuration. The largest

patch in landscape B comprises only 17 percent of the landscape, whereas in landscape C

it comprises 47 percent of the landscape. Thus, although mixed, large sawtimber is equally

abundant in both landscapes, the largest patch index indicates that it is fragmented into

smaller patches in landscape B than in landscape C.

Landscape-level example—Figure 6 depicts three sample landscapes that differ in composition

and pattern. The largest patch index (LPI) indicates that almost half of landscape C, the least

heterogeneous landscape, is comprised of a single patch. However, the largest patch in landscape A comprises much more of the landscape than the largest patch in landscape B, even

though landscape A is considerably more heterogeneous than B. If a single large patch comprising more than 25 percent is important for the presence of a particular species, then landscape A could include suitable habitat but landscape B would not. This illustrates both the

potential usefulness of this index in particular applications and the limitations of this index

as a measure of overall heterogeneity.

25
FRAGSTATS computes several simple statistics representing the number or density

of patches, the average size of patches, and the variation in patch size at the class

and landscape levels (table 1). These metrics usually are best considered as representing landscape configuration, even though they are not spatially explicit measures.

Number of patches (NP) of a particular habitat type may affect a variety of ecological

processes, depending on the landscape context; for example, the number of patches

may determine the number of subpopulations in a spatially dispersed population, or

metapopulation, for species exclusively associated with that habitat type. The number

of subpopulations could influence the dynamics and persistence of the metapopulation

(Gilpin and Hanski 1991). The number of patches also can alter the stability of species interactions and opportunities for coexistence in both predator-prey and competitive systems (Kareiva 1990). In addition, habitat subdivision, as indexed by the

number of patches, may affect the propagation of disturbances across a landscape

(Franklin and Forman 1987). Specifically, a highly subdivided patch type may be

more resistent to the propagation of some disturbances (for example, disease, fire),

and thus more likely to persist in a landscape than a patch type that is contiguous.

Conversely, habitat fragments may suffer higher rates of disturbance for some disturbance types (for example, windthrow) than do contiguous habitats. The number

of patches in a landscape mosaic (pooled across patch types) can have the same

ecological applicability but more often serves as an index of spatial heterogeneity of

the entire landscape mosaic. A landscape with more patches has a finer grain; that

is, the spatial heterogeneity occurs at a finer resolution. Although the number of

patches in a class or landscape may be fundamentally important to various ecological processes, often it does not have any interpretive value by itself because it

conveys no information about area, distribution, or density of patches. Of course,

if total landscape area and class area are held constant, then number of patches

conveys the same information as patch density or mean patch size and it could be

a useful index to interpret. Number of patches is probably most valuable, however,

as the basis for computing other, more interpretable metrics.

Patch density (PD) is a limited, fundamental aspect of landscape structure. Patch

density has the same basic utility as an index as does the number of patches, except

that the former expresses number of patches by per unit area, which facilitates comparisons among landscapes of various sizes. Of course, if total landscape area is

held constant, then patch density and number of patches convey the same information. If numbers of patches, not their area or distribution, is particularly meaningful,

then patch density for a particular patch type could serve as a good fragmentation

index. If class area is held constant, then a landscape with a greater density of patches of a target patch type would be considered more fragmented than a landscape

with a lower density of patches of that patch type. Similarly, the density of patches in

the entire landscape mosaic could serve as a good heterogeneity index because a

landscape with greater patch density would have more spatial heterogeneity.

Another class and landscape index based on the number of patches is mean patch

size (MPS). As discussed previously, the area of each patch comprising a landscape

mosaic is perhaps the single most important and useful piece of information contained

in the landscape. The area comprised by each patch type (class) is equally important;

Patch Density, Size, and

Variability Metrics

26
for example, progressive reduction in the size of habitat fragments is a key component of habitat fragmentation. Thus, a landscape with a smaller mean patch size for

the target patch type than another landscape might be considered more fragmented.

Similarly, within a single landscape, a patch type with a smaller mean patch size than

another patch type might be considered more fragmented. Thus, mean patch size

can serve as a habitat fragmentation index, although the limitations discussed below

may reduce its utility in this respect.

Like patch area, the range in mean patch size is ultimately constrained by the grain

and extent of the image and minimum patch size; relations cannot be detected beyond these lower and upper limits of resolution. Mean patch size at the class level is

a function of the number of patches in the class and total class area. In contrast,

patch density is a function of total landscape area. Therefore, at the class level,

these two indices represent slightly different aspects of class structure. For example,

two landscapes could have the same number and size distribution of patches for a

given class and thus have the same mean patch size; yet, if total landscape area

differed, patch density could be very different between the landscapes. Or two landscapes could have the same number of patches and total landscape area and thus

have the same patch density; yet, if class area differed, mean patch size could be

very different between landscapes. These differences should be kept in mind when

class metrics are selected for a particular application. In addition, although mean

patch size is derived from the number of patches, it does not convey any information

about how many patches are present. A mean patch size of 10 hectares could represent 1 or 100 patches, and the difference could have profound ecological implications.

Furthermore, mean patch size represents the average condition. Variation in patch

size may convey more useful information. For example, a mean patch size of 10 hectares could represent a class with five 10-hectare patches or a class with 2-, 3-, 5-,

10-, and 30-hectare patches, and this difference could be important ecologically. For

these reasons, mean patch size is probably best interpreted in conjunction with total

class area, patch density (or number of patches), and patch size variability.

At the landscape level, mean patch size and patch density are both functions of number of patches and total landscape area. In contrast to the class level, these indices

are completely redundant. Although both indices may be useful for “describing” one

or more landscapes, they would never be used simultaneously in a statistical analysis of landscape structure. Including both of these indices in a discriminant analysis, for example, would cause a singularity in the correlation matrix and inhibit the

eigenanalysis.

In many ecological applications, second-order statistics, such as the variation in patch

size, may convey more useful information than first-order statistics, such as mean

patch size. Variability in patch size measures a key aspect of landscape heterogeneity

not captured by mean patch size and other first-order statistics. Consider two landscapes with the same patch density and mean patch size, but with very different

levels of variation in patch size: Greater variability indicates less uniformity in pattern,

either at the class or landscape level, and may reflect differences in underlying processes affecting the landscapes. Variability is a difficult thing to summarize in a single

metric. FRAGSTATS computes two of the simplest measures of variability—standard

deviation and coefficient of variation.

27
Patch size standard deviation (PSSD) is a measure of absolute variation; it is a function of the mean patch size and the difference in size among patches. Thus, although

patch size standard deviation conveys information about patch size variability, it is a

difficult parameter to interpret without doing so in conjunction with mean patch size,

because the absolute variation depends on mean patch size. Two landscapes may

have the same patch size standard deviation; for example, 10 hectares. Yet, one

landscape may have a mean patch size of 10 hectares, while the other may have

a mean patch size of 100 hectares. In this case, the interpretations of landscape

structure would be very different, even though absolute variation is the same. Specifically, the former landscape has greatly differing and smaller patch sizes, and the

latter has more uniformly sized, larger patches. For this reason, patch size coefficient

of variation (PSCV) is generally preferable to standard deviation for comparing variability among landscapes. Patch size coefficient of variation measures relative variability about the mean (that is, variability as a percentage of the mean), not absolute

variability; thus, it is not necessary to know mean patch size to interpret the coefficient

of variation. Patch size coefficient of variation nevertheless can be misleading regarding landscape structure in the absence of information on the number of patches or

patch density and other structural characteristics. Two landscapes may have the

same PSCV, but one landscape may have 100 patches with a mean patch size of

10 hectares, while the other may have 10 patches with a mean patch size of 100 hectares. In such a case, the interpretations of landscape structure could be very different, even though the coefficient of variation is the same. The choice of standard

deviation or coefficient of variation ultimately will depend on whether absolute or

relative variation is more meaningful in a particular application. Because these

measures are not wholly redundant, interpreting both may be appropriate in some

applications.

It is important to keep in mind that both standard deviation and coefficient of variation

assume a normal distribution about the mean. In a real landscape, the distribution of

patch sizes may be highly irregular. It may be more informative to inspect the actual

distribution itself, rather than relying on summary statistics that make assumptions

about the distribution and therefore can be misleading. Also, note that patch size

standard deviation and coefficient of variation can equal 0 under two different conditions: (1) when there is only one patch in the landscape, and (2) when there is

more than one patch, but they are all the same size. In both cases, there is no

variability in patch size, yet the ecological interpretations could be different.

Class-level example—Figure 5 depicts three sample landscapes that differ in the amount and

pattern of mixed, large sawtimber habitat. Because total landscape area (TA) is similar among

the landscapes, number of patches (NP) and patch density (PD) convey the same information.

Although the three landscapes differ considerably in amount and distribution of mixed, large

sawtimber, neither number of patches nor patch density capture these landscape structural

differences very well. For example, landscapes A and B differ dramatically in amounts of this

patch type yet have about the same number and density of patches. The number and density

of patches do indicate, however, that the mixed, large sawtimber is more subdivided in landscape B than in landscape C, and because class area (CA) is similar among landscapes,

landscape B can be considered more fragmented than landscape C.

28
In contrast to the previous indices, mean patch size (MPS) does a good job of ranking

the three landscapes with respect to mixed, large sawtimber fragmentation (A being most

fragmented, C least). Mean patch size is most informative, however, when interpreted in

conjunction with class area, patch density, and patch size variability. Patch size standard

deviation (PSSD) measures absolute variation in patch size and is affected by the average

patch size. Patch size standard deviation in landscape A is several times smaller than in

landscape B, thereby reflecting the smaller patch sizes in landscape A. But according to

patch size coefficient of variation (PSCV), these two landscapes have similar variability in

patch sizes relative to their respective mean patch sizes (standard deviation roughly equivalent to the mean in both landscapes). The greater patch size coefficient of variation in

landscape C compared to the other landscapes indicates a much larger relative variation

in patch size.

According to these area metrics, landscape A contains several small and similar-sized, mixed,

large sawtimber patches. Landscape B also contains several similar-sized, mixed, large sawtimber patches, but the patches are much larger. Thus, the mixed, large sawtimber in landscapes A and B is fragmented to a similar degree, but landscape A has lost more of this

habitat than has landscape B. Overall, landscape A is much farther along in the fragmentation

process than landscape B. Similarly, landscapes B and C contain the same amount of mixed,

large sawtimber, but the habitat is fragmented into a greater number of smaller fragments in

landscape B because of past timber management activities. Thus, the mixed, large sawtimber

habitat is more fragmented in landscape B than in landscape C, although they have both

undergone the same degree of habitat loss. Finally, landscapes A and B have been subject to

more human disturbance in the form of timber management activities than has landscape C.

Differences in patch size variability suggest that the human-altered landscapes contain more

uniformity in patch size than the unaltered landscape.

Landscape-level example—Figure 6 depicts three sample landscapes that differ in composition

and pattern. Because total landscape area (TA) is similar among the landscapes, number of

patches (NP), patch density (PD), and mean patch size (MPS) all convey the same information. All three metrics do a good job of representing the strong landscape diversity or heterogeneity gradient among landscapes. Although these metrics indicate that the habitat patterns

in landscape A are much finer grained than those in B and C, they do not indicate anything

about the number of different patch types present or their relative abundance and spatial

distribution. Thus, these metrics are more meaningful when considered in conjunction with

other indices.

According to patch size standard deviation (PSSD), patch size in landscape A is much less

variable than in landscape C in absolute terms. Sixty-five percent of the patches in landscape

A are within 20 hectares in size (± 1 standard deviation); whereas 65 percent of the patches

in landscape C are within 100 hectares in size. Based on standard deviation, the variation in

patch size therefore is much greater in landscape C than in landscape A. However, according

to patch size coefficient of variation (PSCV), relative to mean patch size, the patches in landscape A are actually much more variable in size than those in landscape C. Depending on

whether you view variation in absolute (PSSD) or relative (PSCV) terms, you can reach very

different conclusions regarding these landscapes. The choice between measures will depend

on the application, but in most cases coefficient of variation is more meaningful.

29
Edge Metrics FRAGSTATS computes several statistics representing the amount of edge or degree

of edge contrast at the patch, class, and landscape levels (table 1). Edge metrics

usually are best considered as representing landscape configuration, even though

they are not spatially explicit at all. Total amount of edge in a landscape is important

to many ecological phenomena. In particular, a great deal of attention has been given

to wildlife-edge relations (Logan and others 1985; Morgan and Gates 1982; Strelke

and Dickson 1980; Thomas and others 1978, 1979). In landscape ecological investigations, much of the presumed importance of spatial pattern is related to edge

effects. The forest edge effect, for example, results primarily from differences in wind

and light intensity and quality reaching a forest patch that alter microclimate and disturbance rates (Chen and Franklin 1990, Gratkowski 1956, Ranney and others 1981).

These changes, combined with changes in seed dispersal and herbivory, can influence vegetation composition and structure (Ranney and others 1981). The proportion

of a forest patch affected in this manner depends, therefore, on patch shape and

orientation and on adjacent land cover. A large but convoluted patch, for example,

could be entirely edge habitat. It is now widely accepted that edge effects must be

viewed from an organism-centered perspective because edge effects influence organisms differently; some species have an affinity for edges, some are unaffected, and

others are adversely affected.

Early wildlife management efforts focused on maximizing edge habitat because it

was believed that most species favored habitat conditions created by edges and that

the juxtaposition of different habitats would increase species diversity (Leopold 1933).

This concept of edge as a positive influence has guided land management practices

until recently. Recent studies have suggested, though, that changes in vegetation,

invertebrate populations, predation, brood parasitism, and competition along forest

edges has resulted in the population declines of several vertebrate species dependent

upon forest interior conditions (Brittingham and Temple 1983, Kroodsma 1982, Noss

1988, Robbins and others 1989, Strelke and Dickson 1980, Temple 1986, Wilcove

1985, Yahner and Scott 1988). Forest interior species, therefore, may be sensitive to

patch shape because for a given patch size, the more complex the shape, the larger

the edge-to-interior ratio. Most of the adverse effects of forest fragmentation on organisms seem to be either directly or indirectly related to edge effects. Total class edge

in a landscape, therefore, often is the most critical piece of information in the study of

fragmentation, and many of the class indices directly or indirectly reflect the amount

of class edge. Similarly, the total amount of edge in a landscape is directly related to

the degree of spatial heterogeneity in that landscape.

At the patch level, edge is a function of patch perimeter (PERIM). The edge effect on

a patch can be indexed by using the perimeter-to-area ratio employed in the shape

indices discussed below. At the class and landscape levels, edge can be quantified

in other ways. Total edge (TE) is an absolute measure of total edge length of a particular patch type (class level) or of all patch types (landscape level). In applications

involving comparisons of landscapes of different sizes, this index may not be useful.

Edge density (ED) standardizes edge to a per unit area basis that facilitates comparisons among landscapes of various sizes. In comparisons of landscapes of identical

size, total edge and edge density are completely redundant.

30
These edge indices are affected by the resolution of the image. Generally, the finer

the resolution (the greater the detail with which edges are delineated), the greater the

edge length. At coarse resolutions, edges may appear as relatively straight lines; at

finer resolutions, edges may appear as highly convoluted lines. Thus, values calculated for edge metrics should not be compared among images with different resolutions. In addition, vector and raster images portray lines differently. Patch perimeter

and the length of edges will be biased upward in raster images because of the stairstep patch outline, and this will affect all edge indices. The magnitude of this bias will

vary in relation to the grain or resolution of the image, and the consequences of this

bias for the use and interpretation of these indices must be weighed relative to the

phenomenon under investigation.

The contrast between a patch and its neighborhood can influence a number of important ecological processes (Forman and Godron 1986). The edge effects described

previously are influenced by the degree of contrast between patches. Microclimatic

changes (for example, wind, light intensity and quality) likely will extend farther into

a patch along an edge with high structural contrast than along an edge with low

structural contrast (Ranney and others 1981). Similarly, the adverse effects of

brown-headed cowbird (Molothrus ater) nest parasitism on some forest-dwelling

neotropical migratory bird species are likely to be greatest along high-contrast forest

edges (between mature forest patches and grassland), because cowbirds prefer to

forage in early-seral habitats and parasitize nests in late-seral habitats (Brittingham

and Temple 1983). Because of edge effects, the interface between some patch types

can have sufficiently distinctive characteristics to be considered a separate type of

habitat (Reese and Ratti 1988).

Patch insularity is a function of many things, including distance between the patch

and its nearest neighbor, age of the patch or its duration of isolation, connectivity of

the patch with neighbors (for example, through corridors), and the character of the

intervening landscape. The permeability of a landscape for some organisms may

depend on the character of the intervening landscape. The degree of contrast between the focal habitat patch and the surrounding landscape may influence dispersal

patterns and survival and thus indirectly affect the degree of patch isolation. Similarly,

an organism’s ability to use the resources in adjacent patches, as in the process of

landscape supplementation (Dunning and others 1992), depends on the nature of the

boundary between the patches. The boundary between patches can function as a

barrier to movement, a differentially permeable membrane that facilitates some ecological flows but impedes others, or as a semipermeable membrane that partially

impairs flows (Hansen and di Castri 1992, Wiens and others 1985). High-contrast

edges may prohibit or inhibit some organisms from seeking supplementary resources

in surrounding patches. Conversely, some species (for example, great horned owl,

Bubo virginianus) seem to prefer the juxtaposition of patch types with high contrast,

as in the process of landscape complementation (Dunning and others 1992).

31
Clearly, edge contrast can assume various meanings for different ecological processes. Contrast therefore can be defined in several ways, but it always reflects the

magnitude of difference between patches for one or more ecological attributes at a

given scale that are important to the phenomenon under investigation (Kotliar and

Wiens 1990, Wiens and others 1985). Similar to Romme (1982), FRAGSTATS

employs weights to represent the magnitude of edge contrast between adjacent

patch types; weights must range between 0 (no contrast) and 1 (maximum contrast).

Under most circumstances, it probably is not valid to assume that all edges function

similarly. Often there will not be a strong empirical basis for establishing a weighting

scheme, but a reasoned guess based on a theoretical understanding of the phenomenon probably is better than assuming all edges are alike. From an avian habitat-use

standpoint, for example, we might weight edges somewhat subjectively by the degree

of structural and floristic contrast between adjacent patches, because a number of

studies have shown these features to be important to many bird species (Logan

and others 1985; Thomas and others 1978, 1979).

FRAGSTATS computes several indices based on edge contrast at the patch,

class, and landscape levels (table 1). At the patch level, the edge contrast index

(EDGECON) measures the degree of contrast between a patch and its immediate

neighborhood. Each segment of the patch perimeter is weighted by the degree of

contrast with the adjacent patch. Total patch perimeter is reduced proportionate to

the degree of contrast in the perimeter and reported as a percentage of the total

perimeter. A patch with a 10-percent edge contrast index has very little contrast

with its neighborhood; it has the equivalent of 10 percent of its perimeter in

maximum-contrast edge. A patch with a 90-percent edge contrast index has high

contrast with its neighborhood. At the class and landscape levels, FRAGSTATS

computes a total edge contrast index (TECI). Like its patch-level counterpart, this

index quantifies edge contrast as a percentage of maximum possible. This index

ignores patch distinctions; it quantifies edge contrast for the landscape as a whole,

thereby focusing on the landscape condition, not the average patch condition, as

does the mean edge contrast index (MECI). This latter index quantifies the average

edge contrast for patches of a particular patch type (class level) or for all patches in

the landscape. FRAGSTATS also computes an area-weighted mean edge contrast

index (AWMECI) by weighting patches according to their size. Larger patches are

weighted more heavily than smaller patches in calculating the average patch edge

contrast for the class or landscape. This area-weighted index may be more appropriate than the unweighted mean index in cases where larger patches play a dominant role in the landscape dynamics relative to the phenomenon under consideration. In such cases, it may make sense to weight larger patches more heavily

when characterizing landscape structure. Otherwise, small patches will have an

equal effect on the average edge contrast index, when in fact they play a disproportionately small role in the overall landscape function.

These edge contrast indices are relative measures. Given any amount or density

of edge, they measure the degree of contrast in that edge. For this reason, these

indices are probably best interpreted in conjunction with total edge or edge density.

32
High values of these indices mean that the edge present, regardless of whether it is

10 meters or 1000 meters, is of high contrast, and vice versa. Note that these indices

consider landscape boundary segments even if they have a contrast of zero (the

patch extends beyond the landscape boundary). These zero-contrast boundary

segments are included in the calculation of these indices because we believe that

boundary segments should be treated equal to internal edge segments in determining the degree of contrast in the patch, class, or landscape. Similarly, background edges are included in the calculation of these indices as well. Therefore, if

a landscape border is absent, the choice of how to treat the landscape boundary

and background edge (that is, user-specified average edge contrast) could have

significant effects on these indices, depending on the size and heterogeneity of the

landscape. If a landscape border is present, this decision can still have significant

effects on these indices if there is a large amount of background edge.

FRAGSTATS also computes an index that incorporates both edge density and edge

contrast in a single index. Contrast-weighted edge density (CWED) standardizes

edge to a per unit area basis that facilitates comparison among landscapes of different sizes. Unlike edge density, however, this index reduces the length of each

edge segment proportionate to the degree of contrast. Thus, 100 meters per hectare

of maximum-contrast edge (weight = 1) is unaffected; but 100 meters per hectare of

edge with a contrast weight of 0.2 is reduced by 80 percent to 20 meters per hectare

of contrast-weighted edge. This index measures the equivalent maximum-contrast

edge density. An edge density of 100 means that there are 100 meters of edge per

hectare in the landscape. A contrast-weighted edge density of 80 for the same

landscape means that the equivalent of 80 meters of maximum-contrast edge per

hectare exist in the landscape. A landscape with 100 meters per hectare of edge

and an average contrast weight of 0.8 would have twice the contrast-weighted edge

density (80 m/ha) as a landscape with only 50 meters per hectare of edge but with

the same average contrast weight (40 m/ha). Thus, both edge density and edge

contrast are reflected in this index. For many ecological phenomena, edge types

function differently. Consequently, comparing total edge density among landscapes

may be misleading because of differences in edge types. This contrast-weighted

edge density index attempts to quantify edge from the perspective of its functional

significance. Thus, landscapes with the same contrast-weighted edge density are

presumed to have the same total magnitude of edge effects from a functional

perspective.

Edge contrast indices are limited by the considerations discussed above for metrics

based on total edge length. These indices are calculated and reported in the output

files only if an edge contrast weight file is specified. The usefulness of these indices

is directly related to the meaningfulness of the weighting scheme used to quantify

edge contrast. Careful consideration should be given to devising weights that reflect

any empirical and theoretical knowledge and understanding of the phenomenon

under consideration. If the weighting scheme does not accurately represent the

phenomenon under investigation, then the results will be spurious.

33
Patch-level example—Figure 4 depicts three patches extracted from a sample landscape that

differ in edge contrast. According to the edge contrast index (EDGECON), patch A has the

least contrast with its neighborhood, where contrast represents the degree of difference in

floristic and vegetation structure among patches. This is because patch A is a mixed, large

sawtimber patch surrounded mainly by conifer and hardwood, large sawtimber patches. Thus,

the differences in vegetation composition and structure along the patch perimeter are relatively

subtle; moreover, the ecotones between patch A and these other large sawtimber patches

are probably gradual. Consequently, although there are important differences between these

adjacent patches that warrant their discrimination, the contrast between them is very low. An

animal dispersing from patch A, for example, might not be impeded at all by the low-contrast

boundary of patch A. In contrast, patch C is a mixed grass and forb (MGF) patch surrounded

mostly by large sawtimber patches. Hence, the degree of structural contrast between patch C

and its neighborhood is very high. The edge contrast index indicates that the perimeter of

patch C has the equivalent of 80 percent of its perimeter in maximum-contrast edge, whereas

the perimeter of patch A has the equivalent of only 17 percent of its perimeter in maximumcontrast edge. The edge contrast index seems to do a good job of quantifying differences in

insularity among these patches.

Class-level example—Figure 5 depicts three sample landscapes that differ in the amount and

pattern of mixed, large sawtimber habitat. Because these landscapes are similar in size, total

edge (TE) and edge density (ED) are largely redundant. Both indices are highest for landscape B and lowest for landscape A. Depending on the application, the interpretation of these

differences may change. The process of habitat fragmentation, for example, involves both

habitat loss and changes in habitat pattern. Over the course of fragmentation, the proportion

of the landscape composed of the target habitat type would go from 100 percent to 0 percent.

The total amount of class edge would be expected to peak when roughly 50 percent of the

landscape is comprised of this habitat type, depending on the pattern of habitat loss (Franklin

and Forman 1987). Thus, from a fragmentation perspective, total edge and edge density are

best interpreted in conjunction with the percent of landscape index. In this case, although

landscapes B and C have undergone the same amount of mixed, large sawtimber loss (that

is, have similar %LAND values), total edge and edge density indicate that this habitat in

landscape B is more highly fragmented than in landscape C. Alternatively, consider a species

that requires mixed, large sawtimber edge habitat. Total edge or edge density might be used

to model habitat suitability. In this case, landscape A would be least suitable and landscape B

most suitable.

If edge contrast is deemed important, then the edge contrast indices may lead to a slightly

different interpretation of the mixed, large sawtimber habitat context in these landscapes.

Contrast-weighted edge density (CWED) indicates that although landscape C has roughly

33 meters of mixed, large sawtimber edge per hectare, it has the equivalent of less than 2

meters of maximum-contrast edge per hectare. Thus, mixed, large sawtimber habitat in landscape C is not very insular; it is surrounded by patches similar in structure, and any edge

effects on this habitat (or organisms inhabiting it) are likely to be relatively weak. Contrastweighted edge density indicates that landscape C has the least equivalent maximum-contrast

edge density. This differs from the results of total edge and edge density, which both indicate

that landscape A has the least edge. If the contrast-weighting scheme used here is particularly

meaningful, then contrast-weighted edge density may be a more insightful index of edge

effects than either total edge or edge density.

Edge contrast also can be measured in relative terms by using the total edge contrast index

(TECI), mean edge contrast index (MECI), and area-weighted mean edge contrast index

(AWMECI). These three indices are largely redundant in the sample landscapes and therefore

lead to the same conclusions. The total edge contrast index indicates that the mixed, large

sawtimber edge present in landscape C has very low contrast; specifically, every 100 meters

of edge has a maximum-contrast equivalent of only 4 meters. In contrast, the mixed, large

34
Shape Metrics FRAGSTATS computes several statistics that quantify landscape configuration by

complexity of patch shape at the patch, class, and landscape levels (table 1). The

interaction of patch shape and size can influence a number of important ecological

processes. Patch shape has been shown to influence interpatch processes such as

small mammal migration (Buechner 1989) and woody plant colonization (Hardt and

Forman 1989) and may influence animal foraging strategies (Forman and Godron

1986). However, the primary significance of shape in determining the nature of

patches in a landscape seems to be related to the “edge effect” (see discussion

of edge effects for edge metrics).

Shape is a difficult parameter to quantify concisely in a metric. FRAGSTATS computes two types of shape indices; both are based on perimeter-area relations. Patton

(1975) proposed a diversity index based on shape for quantifying habitat edge for

wildlife species and as a means for comparing alternative habitat improvement efforts

(for example, wildlife clearings). This shape index (SHAPE) measures the complexity

of patch shape compared to a standard shape. In the vector version of FRAGSTATS,

patch shape is evaluated with a circular standard; shape index is minimum for circular patches and increases as patches become increasingly noncircular. Similarly, in

the raster version of FRAGSTATS, patch shape is evaluated with a square standard.

Although there are other means of quantifying patch shape (Lee and Sallee 1970),

this shape index is widely applicable and used in landscape ecological research

(Forman and Godron 1986). This shape index can be applied at the class and landscape levels as well. Mean shape index (MSI) measures the average patch shape,

or the average perimeter-to-area ratio, for a particular patch type (class) or for all

patches in the landscape. FRAGSTATS also computes an area-weighted mean

shape index (AWMSI) of patches at the class and landscape levels by weighting

patches according to their size. Specifically, larger patches are weighted more

heavily than smaller patches in calculating the average patch shape for the class or

landscape. This index may be more appropriate than the unweighted mean shape

index in cases where larger patches play a dominant role in the landscape function

relative to the phenomenon under consideration. The difference between the unweighted and weighted mean shape indices can be particularly noticeable when

sample sizes are small (only a few patches).

sawtimber edge in landscape A has much higher contrast; every 100 meters of edge has a

maximum-contrast equivalent of 40 meters. Although landscape A has the lowest total edge

and edge density, all three relative contrast indices indicate that its edge contrast is the

greatest. Similarly, although landscape B has the greatest amount of mixed, large sawtimber edge, the contrast is moderate relative to landscapes A and C.

Landscape-level example—Figure 6 depicts three sample landscapes that differ in composition

and pattern. Because these landscapes are similar in size, total edge (TE) and edge density

(ED) are largely redundant. Both indices are highest for landscape A and lowest for landscape

C, corresponding to the overall magnitude of spatial heterogeneity in these landscapes. Conclusions regarding the overall ranking of landscapes based on contrast-weighted edge density

(CWED) are similar; although, it is apparent that landscape C contains low-contrast edges

amounting to an equivalent of only 3.7 meters per hectare of maximum-contrast edge. Landscape B has roughly twice as much total edge as landscape C, but roughly 6 times more

equivalent maximum-contrast edge. Likewise, the conclusions based on the total edge

contrast index (TECI), mean edge contrast index (MECI), and area-weighted mean edge

contrast index (AWMECI) are similar, although edge contrast is reported in relative terms.

35
An alternative to these patch shape indices based on the “average” patch characteristics at the class and landscape levels is the landscape shape index (LSI). This

index measures the perimeter-to-area ratio for the landscape as a whole. This index

is identical to the habitat diversity index proposed by Patton (1975), except that we

apply the index at the class level as well. This index quantifies the amount of edge

present in a landscape relative to what would be present in a landscape of the same

size but with a simple geometric shape (circle in vector, square in raster) and no internal edge (landscapes comprised of a single circular or square patch). Landscape

shape index is identical to the shape index at the patch level (SHAPE), except that

the former treats the entire landscape as if it were one patch and any patch edges

(or class edges) as though they belong to the perimeter. The landscape boundary

must be included as edge in the calculation to use a circle or square standard for

comparison. Unfortunately, this may not be meaningful in cases where the landscape

boundary does not represent true edge or the actual shape of the landscape is of no

particular interest. In this case, the total amount of true edge, or some other index

based on edge, probably would be more meaningful. If the landscape boundary represents true edge or the shape of the landscape is particularly important, then the landscape shape index can be a useful index, especially when comparing a range of

landscape sizes.

These shape indices have important limitations. First, vector and raster images

use different shapes as standards. Thus, the absolute value of these indices differs

between vector and raster images. The implications of this difference should be

considered relative to the phenomenon under investigation. Second, these shape

indices are limited in the same manner as the edge indices discussed above in the

differences between how lines are portrayed in vector and raster images. Perimeter

length will be biased upward in raster images because of the stair-stepping pattern

of line segments, and the magnitude of this bias will differ in relation to the grain or

resolution of the image. Third, as an index of shape, the perimeter-to-area ratio

method is relatively insensitive to differences in patch morphology. Thus, although

patches may possess quite different shapes, they may have identical areas and

perimeters and shape indexes. For this reason, these shape indices are not useful

as measures of patch morphology; they are best considered as measures of overall

shape complexity. Finally, the mean shape index and area-weighted mean shape

index are subject to the limitations of first-order statistics (for example, the average

patch shape for a class or the landscape may not be very meaningful if the distribution of patch shapes is complex).

The other basic type of shape index computed by FRAGSTATS is the fractal dimension. In landscape ecological research, patch shapes are frequently characterized via

the fractal dimension (Iverson 1989, Krummel and others 1987, Milne 1988, Ripple

and others 1991, Turner and Ruscher 1988). The appeal of fractal analysis is that it

can be applied to spatial features over a wide variety of scales. Mandelbrot (1977,

1982) introduced the concept of fractal, a geometric form that exhibits structure at

all spatial scales, and proposed a perimeter-area method to calculate the fractal dimension of natural planar shapes. The perimeter-area method quantifies the degree

of complexity of the planar shapes. The degree of complexity of a polygon is characterized by the fractal dimension (D), such that the perimeter (P) of a patch is related

to the area (A) of the same patch by P ≈ √Α D (that is, log P ≈ 1/2D log A). For simple

36
Euclidean shapes (circles, rectangles, and so forth), P ≈ √Α and D = 1 (the dimension of a line). As the polygons become more complex, the perimeter becomes increasingly plane filling and P ≈ A with D → 2. Although fractal analysis typically has

not been used to characterize individual patches in landscape ecological research,

we use this relationship to calculate the fractal dimension (FRACT) of each patch

separately. The value of the fractal dimension calculated in this manner depends

on patch size or the units used, or both (Rogers 1993). Caution therefore should

be exercised when using this fractal dimension index as a measure of patch shape

complexity.

Fractal analysis usually is applied to the entire landscape mosaic by using the

perimeter-area relationship A = k P2/D, where k is a constant (Burrough 1986). If

sufficient data are available, the slope of the line obtained by regressing log(P) on

log(A) is equal to 2/D (Burrough 1986). Note, fractal dimension using this perimeterarea method is equal to 2 divided by the slope; D is neither equal to the slope

(Krummel and others 1987) nor to 2 times the slope (Gustafson and Parker 1992,

O’Neill and others 1988), as reported by some authors. We refer to this index as the

double log fractal dimension (DLFD) in FRAGSTATS. Because this index employs

regression analysis, it is subject to spurious results when sample sizes are small.

In landscapes with only a few patches, it is not unusual to get values that greatly

exceed the theoretical limits of this index. Thus, this index is probably only useful

if sample sizes are large (n is greater than 20). If insufficient data are available,

an alternative to the regression approach is to calculate the mean patch fractal

dimension (MPFD) based on the fractal dimension of each patch. FRAGSTATS

also computes an area-weighted mean patch fractal dimension (AWMPFD) at the

class and landscape levels by weighting patches according to their size, similar to

the area-weighted mean shape index. These latter two indices may be particularly

meaningful if the focus of the analysis is on patch characteristics; that is, when

patch-level phenomena are deemed most important and patch shape is particularly

meaningful.

Because the method used to calculate these fractal indices involves perimeter-area

calculations, these fractal indices are subject to some of the same limitations as the

shape indices discussed above. Perhaps the greatest limitation of the fractal indices

is the difficulty in conceptualizing fractal dimension. Even though fractal dimension

is increasingly being used in landscape ecological research, it remains an abstract

concept to many and may easily be used inappropriately.

Patch-level example—Figure 4 depicts three patches extracted from a sample landscape and

differing in shape. In particular, patch A has a much more complex shape than either patch B

or C. Accordingly, the shape index (SHAPE) for patch A is almost twice as large as that for

the other two patches. The fractal dimension (FRACT) results are consistent with the shape

index; however, the magnitude of differences among patches in fractal dimension is notably

less than shape index values. In addition, the subtle difference in shape complexity between

patch B and C is reflected in a rather small difference in their shape indices. Overall, these

shape indices do a good job of quantifying obvious differences in shape complexity among

these patches, but fractal dimension appears to be less sensitive to differences than is the

shape index.

37
FRAGSTATS computes several statistics based on core area at the patch, class,

and landscape levels (table 1). Core area is defined as the area within a patch

beyond some specified edge distance or buffer width. Core area metrics reflect both

landscape composition and landscape configuration. Most of the indices dealing with

number or density of patches, size of patches, and differences in patch size have

corresponding core area indices computed in the same manner after eliminating the

edge or buffer from all patches. Like patch shape, the primary significance of core

area in determining the nature of patches in a landscape appears to be related to

the “edge effect.” As discussed previously, edge effects result from a combination

of biotic and abiotic factors that alter environmental conditions along patch edges

compared to patch interiors. The nature of the edge effect differs among organisms

Class-level example—Figure 5 depicts three sample landscapes that differ in the amount and

pattern of mixed, large sawtimber habitat. In this case, the landscape boundary does not all

represent mixed, large sawtimber edge. Therefore, the landscape shape index (LSI) is not

particularly meaningful because it treats the entire landscape boundary as edge. The mean

shape index (MSI) values for all three landscapes are greater than 1, indicating that the average patch shape in all three landscapes is noncircular. The mixed, large sawtimber patches in

landscape A (most fragmented) are least irregular in shape, whereas the patches in landscape

C (least fragmented) are most irregular. The area-weighted mean shape index (AWMSI) supports these conclusions. In addition, the area-weighted values for all three landscapes are

greater than the unweighted values, indicating that the larger patches in each landscape are

more irregular in shape than the average. These results indicate that human-induced fragmentation in landscapes A and B caused a simplification in patch shapes compared to the

geometrically complex patch shapes found in the natural, unaltered landscape (C).

Because of the small sample sizes, double log fractal dimension (DLFD) is probably not a

reliable index for these three landscapes. Mean patch fractal dimension (MPFD) values do

agree in rank order with mean shape index values. According to the latter index, landscape A

contains the simplest average patch shape, but according to mean patch fractal dimension,

the opposite is true. The reason for the discrepancy between these indices is not clear;

however, the mean shape index is more consistent with the results of other indices and

therefore is probably more reliable in this case.

Landscape-level example—Figure 6 depicts three sample landscapes that differ in composition

and pattern. In this case, even though the landscape boundary does not represent totally true

edge, the landscape shape index (LSI) still ranks the landscapes along an intuitive gradient

from least to most heterogeneous. The mean shape index (MSI) values for all three landscapes

are greater than 1, indicating that the average patch shape in all three landscapes is noncircular. The patches in landscape A are least irregular in shape, whereas the patches in landscape

C are most irregular in shape. The area-weighted mean shape index (AWMSI) supports these

conclusions. In addition, the area-weighted values for all three landscapes are greater than the

unweighted values, indicating that the larger patches in each landscape are more irregular in

shape than the average. These results reflect the simple shapes of management units in

landscape A compared to the natural shapes of patches in the undisturbed landscape C.

Because of the small sample size in landscape C, double log fractal dimension (DLFD) is

probably not a reliable index for this landscape. The index compares nicely, however, with the

mean shape index and area-weighted mean shape index for landscapes A and B. As in the

class-level example, the rank order of mean patch fractal dimension (MPFD) values do not

agree with the other shape indices. The reason for the discrepancy between these indices is

not clear; however, because all other shape indices are consistent with each other, mean

patch fractal dimension is probably less reliable in this case.

Core Area Metrics

38
and ecological processes (Hansen and di Castri 1992). For example, some bird

species are adversely affected by predation, competition, brood parasitism, and

perhaps other factors along forest edges (see discussion, “Edge metrics,” for

citations). Core area has been found to be a much better predictor of habitat quality

than patch area for these forest interior specialists (Temple 1986). Unlike patch area,

core area is affected by patch shape. Thus, while a patch may be large enough to

support a given species, it still may not contain enough suitable core area to support

the species.

For ecological processes or organisms adversely affected by edge, it seems likely

that core area would better characterize a patch than total area would. In addition, it

seems likely that edge effects would differ with the type and nature of the edge (the

degree of floristic and structural contrast and orientation). Unfortunately, in most

cases, there is insufficient empirical support (or none) for designating separate edge

widths for each unique edge type. Accordingly, the user must specify a single edge

width for all edge types in FRAGSTATS.

In raster images, there are different ways to determine core area. FRAGSTATS

employs a method in which the four parallel neighbors of a cell are evaluated for

similarity; diagonal neighbors are ignored. This method tends to slightly overestimate

the true core area. Other methods can seriously underestimate core area. For more

details on the algorithm, see the “patch.c” routine in the source files.

Patch area, class area, total landscape area, and the percentage of landscape in

each patch type all have counterparts computed after eliminating edge area defined

by the specified edge width; these are core area (CORE) at the patch level, total

core area (TCA) at the class and landscape levels, and core area percentage of

landscape (C%LAND) at the class level. The latter index quantifies the core area in

each patch type as a percentage of total landscape area. For organisms strongly

associated with patch interiors, this index may provide a better measure of habitat

availability than its counterpart. In contrast to their counterparts, these core area

indices integrate into a single measure the effects of patch area, patch shape, and

edge effect distance. Therefore, although they quantify landscape composition, they

are affected by landscape configuration. For this reason, these metrics at the class

level may be useful in the study of habitat fragmentation, because fragmentation

affects both habitat area and configuration. On the other hand, these indices

confound the effects of habitat area and configuration; for example, if the core area

percentage of a landscape is small, it indicates that very little core area is available,

but it does not discriminate between a small amount of the patch type (area effect)

and a large amount of the patch type in a highly fragmented configuration. Thus, like

many indices summarizing more than one feature (for example, diversity indices),

these indices are best interpreted in conjunction with other indices to provide a more

complete description of landscape structure.

39
From an organism-centered perspective, a single patch may contain several disjunct

patches of suitable interior habitat, and considering disjunct core areas as separate

patches may be appropriate. For this reason, FRAGSTATS computes the number of

core areas (disjunct) in each patch (NCORE), as well as the number in each class

and the landscape as a whole (NCA). If core area is deemed more important than

total area, then these indices may be more applicable than their counterparts, but

they are subject to the same limitations as their counterparts (number of patches)

because they are not standardized for area. Although these metrics are not particularly useful in most cases, they are used to compute other landscape metrics

based on core area.

Number of core areas can be reported on a per unit area basis (core area density,

CAD) that has the same ecological applicability as its counterpart (patch density),

except that all edge area is eliminated from consideration. Alternatively, this information can be represented as mean core area. Like their counterparts, there is a

difference between core area density and mean core area at the class level. Specifically, core area density is based on total landscape area, and mean core area is

based on total core area for the class. In contrast, at the landscape level, they are

both based on total landscape area and therefore are completely redundant. Furthermore, mean core area can be defined in two ways. First, mean core area can be

defined as the mean core area per patch (MCA1). Patches with no core area are

included in the average, and the total core area in a patch is considered as one

observation, regardless of whether the core area is contiguous or divided into two or

more disjunct areas within the patch. Mean core area also can be defined as the

mean area per disjunct core (MCA2). The distinction between these two ways of

defining mean core area should be noted.

FRAGSTATS also computes several relative core area indices that quantify core

area as a percentage of total area. The core area index (CAI) at the patch level

quantifies the percentage of the patch that is comprised of core area. Similarly, the

total core area index (TCAI) at the class and landscape levels quantifies core area

for the entire class or landscape as a percentage of total class or landscape area,

respectively. At the class and landscape levels, FRAGSTATS also computes the

mean core area index (MCAI) of patches comprising the class or landscape. Note

that the total core area index is equivalent to an area-weighted mean core area

index; thus, the latter is not computed.

These core area indices are basically edge-to-interior ratios like the shape indices

discussed previously, the main difference being that the core area indices treat edge

as an area of varying width and not as a line (perimeter) around each patch. In

addition, these core area indices are relative measures. They do not reflect patch

size, class area, or total landscape area; they quantify the percentage of available

area, whether 10 hectares or 1000 hectares, comprised of core. These indices do

40
not confound area and configuration like the previous core area indices; rather, they

isolate the configuration effect. For this reason, these core area indices are probably

best interpreted in conjunction with total area at the corresponding scale. In conjunction with total class area, these indices could serve as effective fragmentation

indices for a particular class.

Variation in core area size may convey more useful information than mean core area

does. Like variation in patch size, FRAGSTATS computes corresponding measures

of variability among patches in core area size. Core area standard deviation and

core area coefficient of variation have the same ecological applicability as patch

size standard deviation and patch size coefficient of variation, except that all edge

area is eliminated from consideration. FRAGSTATS computes both the patch core

area standard deviation (CASD1) and patch core area coefficient of variation

(CACV1), which represent the variation in core area per patch (associated with

MCA1), as well as the disjunct core area standard deviation (CASD2) and disjunct

core area coefficient of variation (CACV2), which represent the variation in the size

of disjunct core areas (associated with MCA2). In contrast to their counterparts, these

core area metrics reflect the interaction of patch size and shape and edge width

and, therefore, may serve as better heterogeneity indices when edge width can be

meaningfully specified and edge effects are of particular interest. Standard deviation

can be difficult to interpret without doing so in conjunction with other statistics (for

example, mean patch size or mean core area). For this reason, core area coefficient

of variation usually is preferable to core area standard deviation. Also, note that

core area standard deviation and coefficient of variation can equal 0 under three

conditions: (1) when there is only one core area in the landscape; (2) when there is

more than one core area greater than 0 in size, but they are all the same size; and

(3) when there is more than one patch, but none has a core area (CORE = 0). In all

three cases, there is no variability in core area size; yet, the ecological implications

could be quite different.

All the core area indices are affected by the interaction of patch size, patch shape,

and the specified edge width. Increasing edge width will decrease core area, and

vice versa; therefore, these indices are meaningful only if the specified edge width

is relevant and meaningful to the phenomenon under investigation. In many cases,

there is no empirical basis for specifying any particular edge width, and so it must be

chosen somewhat arbitrarily. The usefulness of these metrics is directly related to the

arbitrariness in the specified edge width, and this should be clearly understood when

using these metrics. The utility of core area indices compared to their area-based

counterparts depends on the resolution, minimum patch dimensions, and edge widths

employed. Given, for example, a landscape with a resolution of 1 square meter and

minimum patch dimensions of 100 by 100 meters, if an edge width of 1 meter is

specified, then the core area indices and their counterparts will be nearly identical

and the core area indices will be relatively insensitive to differences in patch size

and shape. In this case, core area indices will offer little over their counterparts in

terms of unique characterization of landscape structure.

41
Patch-level example—Figure 4 depicts three patches extracted from a sample landscape that

differ in core area based on a 100-meter edge width for all edge types. Although patch A is

almost three times larger than patch C, it has less than twice the core area (CORE). This is

because patch A has a more complex shape than patch C and therefore a greater edge-tointerior ratio. Although patches B and C are almost equal in size, patch B has half the core

area of patch C because of the interaction among patch size, patch shape, and edge width.

With a 100-meter edge width, the subtle difference in shape between patch B and C results in

a large difference in core area. A much larger edge width (for example, 200 m) would result in

both patches having no core area because of their small size, and a much smaller edge width

(10 m) would result in both patches having similar core areas. Thus, the affect of patch shape

on core area depends on both patch size and edge width.

According to the number of core areas (NCORE), patches B and C both contain one core

area because of their simple shapes. Patch A, however, contains two core areas because

it is narrower than 200 meters in the middle and widens on both sides. Thus, under certain

conditions, it may be more meaningful to treat patch A as two separate patches. If an organism avoids edge habitat for 100 meters, then from the organism’s perspective, patch A may

actually contain two separate suitable habitat patches. Like core area, though, number of core

areas is affected by the interaction of patch size, patch shape, and edge width. With a much

larger edge width (say, 200 m) or much smaller edge width (10 m), patch A would contain

only one core area.

Although patch A is almost three times larger than patch B and has a more complex shape,

it has roughly the same core area index (CAI) as patch B. Thus, these two patches have

about the same proportion of core area, even though they differ markedly in absolute size and

shape. In contrast, the core area index of patch B is about half that of patch C, even though

they are similar in size. Because of the interaction of patch size, patch shape, and edge width,

the slightly more complex shape of patch B results in disproportionately less core area and

therefore a much smaller core area index than patch C. Again, note the affect of the interaction among patch size, patch shape, and edge width on this index.

Class-level example—Figure 5 depicts three sample landscapes that differ in the amount and

pattern of mixed, large sawtimber habitat based on a 100-meter edge width for all edge types.

According to the percentage of landscape (%LAND) in this patch type, roughly 50 percent of

landscapes B and C are mixed, large sawtimber. According to the core area percentage of

landscape (C%LAND), however, only 10 percent of this habitat type in landscape B is core

area, whereas 23 percent of this habitat type in landscape C is core area. Thus, the core area

percentage of landscape clearly indicates that landscape B is fragmented to a much greater

degree than landscape C. But inspection of this index alone does not indicate whether differences in the amount of core area are from differences in total habitat area or habitat configuration, or both. Nevertheless, for an organism requiring interior mixed, large sawtimber habitat,

the core area percentage of landscape suggests that landscape C contains twice the suitable

habitat as landscape B. This would not necessarily be true if landscapes B and C were greatly

different in size because this index is a relative measure. All core area indices are affected by

the interaction of patch size, patch shape, and edge width. Given either a much larger edge

width (200 m) or much smaller edge width (10 m), the index values change dramatically,

especially in landscapes A and B, because of the size and shapes of the mixed, large

sawtimber patches in these landscapes.

Total core area (TCA) indicates that although landscape A contains four mixed, large sawtimber patches totaling 13 hectares, there is no core area (that is, no point in these patches is

more than 100 meters from the patch perimeter). Although landscapes B and C have similar

amounts of mixed, large sawtimber, total core area indicates that landscape B has much less

core area, suggesting a much more fragmented (greater edge-to-interior ratio) configuration of

habitat in landscape B than in C.

42
Number of core areas (NCA) indicates that although landscape B has less than half as much

mixed, large sawtimber core area as landscape C, it has more than three times as many

disjunct core areas. Note also the difference between number of patches (NP) and number

of core areas. The difference between landscape B and C is more pronounced with the latter

index, thereby indicating that the habitat in landscape B is indeed more fragmented than in

landscape C.

Compared to patch density (PD), core area density (CAD) does a much better job of characterizing the differences in landscape structure among landscapes. In our example, landscapes

A and B have similar patch densities, but core area density differs dramatically between them.

Landscape A has no core areas, indicating that the habitat is highly fragmented into very small

patches; whereas, landscape B has a comparatively high core area density. Similarly, although

landscapes B and C have similar amounts of mixed, large sawtimber habitat, the core area in

landscape B is fragmented into several disjunct areas, whereas in landscape C it is more contiguous. Although the three landscapes differ considerably in both amount and distribution of

mixed, large sawtimber habitat, it is difficult to interpret these landscape structural differences

by core area density alone; this index is best interpreted in conjunction with other indices such

as class area (CA). Also, because total landscape area is similar among the landscapes, core

area density and number of core areas convey the same information.

Although mean patch size (MPS) does a good job of ranking the three landscapes by mixed,

large sawtimber fragmentation (A being most fragmented, C being least), mean core area per

patch (MCA1) distinguishes the different stages of fragmentation even more effectively. Like

mean patch size, mean core area per patch is most informative when interpreted in conjunction with other indices such as class area, patch density (PD), and patch size variability (PSSD

or PSCV). It is difficult to tell from MCA1 alone if differences between landscapes B and C are

because of differences in habitat area or habitat configuration; by interpreting both class area

and mean core area per patch it becomes clear that the differences are due solely to configuration. Mean area per disjunct core (MCA2) is consistent with mean core area per patch, but

note the differences due to the differences in number of patches and number of disjunct core

areas.

Variation in the amount of core area per patch or disjunct core often is of greater interest than

the average condition. Patch core area standard deviation (CASD1) and disjunct core area

standard deviation (CASD2) indicate that the absolute variation in core area size per patch

and per disjunct core area, respectively, is six times greater in landscape C than in B. These

indices alone do not say much about differences in structure among the three landscapes,

however, unless the user simultaneously considers the mean core area per patch or mean

area per disjunct core, respectively. Patch core area coefficient of variation (CACV1) measures relative variability and indicates that core area variability decreases progressively from

the least (C) to the most (A) fragmented landscape. This suggests that timber management

activities have tended to produce greater homogeneity in core areas for this habitat type.

Disjunct core area coefficient of variation (CACV2) measures relative variability among

disjunct core areas and indicates that the disjunct core areas in landscape B are slightly

more variable than in landscape C. The choice between the coefficient of variation measures depends on the application.

43
The total core area index (TCAI) represents the landscapes along a continuum from most to

least fragmented. According to this index, only 20 percent of the mixed, large sawtimber in

landscape B is “interior” habitat; the remaining 80 percent is “edge” habitat. Without any other

information, it could be deduced that this habitat type is highly fragmented in landscape B.

When total core area index is interpreted in conjunction with class area or the percentage

of landscape, it becomes quite clear that landscapes B and C differ exclusively in habitat

configuration and not habitat area, and that landscape B is indeed more fragmented than

landscape C. The mean core area index (MCAI) indicates that the mixed, large sawtimber

habitat in all three landscapes is highly fragmented (that is, all have high edge-to-interior ratios).

According to this index, however, the mixed, large sawtimber patches in landscapes B and C

have roughly the same average core area index. Yet, the total core area index and other

indices clearly indicate that landscape B is in fact more fragmented than landscape C. These

differences illustrate some important differences between the total and mean core area indices.

The mean core area index represents the average patch characteristic and may not necessarily

represent the overall landscape structural condition very well. This may be appropriate and meaningful when the focus of the application is on patch-level phenomena. When

the focus is on landscape structure, however, the mean patch condition may be misleading. For

example, the mean core area index for landscape C is affected by the great variation in core

area index among the three patches. The large core area index of the largest patch is offset by

the 0 core area index of the smallest patch and the very small core area index of the midsized

patch. This bias is characteristic of first-order statistics, such as the mean, and is particularly

pronounced in this case because of the small sample size (n = 3 patches) in landscape C.

Landscape-level example—Figure 6 depicts three sample landscapes that differ in composition

and pattern based on a 100-meter edge width for all edge types. Total core area (TCA) indicates that landscapes A, B, and C contain progressively more core area, and because total

landscape area (TA) is similar, they represent a continuum from most to least patchy. All core

area indices are affected by the interaction of patch size, patch shape, and edge width. With

a much larger (say, 200 m) or smaller edge width (10 m), the index values change dramatically, especially in landscapes A and B, because of the size and shapes of the mixed, large

sawtimber patches in these landscapes.

Number of core areas (NCA) indicates that although landscape A has the greatest number

of patches (NP), it does not have the greatest number of core areas, because many of the

patches in landscape A do not have any core area. Because total landscape area is similar

among landscapes, number of core areas and core area density (CAD) are largely redundant.

Note that although landscapes A and B have fewer core areas than patches, landscape C has

more core areas than patches. The rank order of landscapes based on number of core areas

is different than that based on number of patches and total core area. This reversal occurs

because of the relation between patch sizes and shapes in these landscapes and the designated edge width of 100 meters. With a much larger edge width (say, 200 m) or smaller edge

width (10 m), number of core areas changes dramatically, especially in landscapes A and B,

because of the size and shapes of the patches in those landscapes. For this reason, particular

attention should be given to the interpretation of number of core areas, core area density, and

total core area because they can lead to a different rank ordering of landscapes along a

gradient in landscape heterogeneity.

Although mean patch size (MPS) does a good job of ranking the three landscapes by their

spatial heterogeneity, mean core area per patch (MCA1) distinguishes among these landscapes even more distinctly. Because mean core area per patch is affected by patch shape,

it captures an aspect of spatial pattern not captured by mean patch size. Like mean patch

size, mean core area per patch is most informative when interpreted in conjunction with other

indices such as total landscape area, patch density (PD), and patch size variability (PSSD or

PSCV). Mean area per disjunct core (MCA2) is consistent with mean core area per patch, but

note the differences due to the differences in number of patches and number of disjunct core

areas, especially in landscape A.

44
FRAGSTATS computes a few statistics based on nearest neighbor distance at the

patch, class, and landscape levels (table 1) for the raster version only. Nearest

neighbor distance is defined as the distance from a patch to the nearest neighboring

patch of the same type, based on edge-to-edge distance. Nearest neighbor metrics

quantify landscape configuration. Nearest neighbor distance can influence a number

of important ecological processes. For example, there has been a proliferation of

mathematical models on population dynamics and species interactions in spatially

subdivided populations (Kareiva 1990), and results suggest that the dynamics of

local plant and animal populations in a patch are influenced by their proximity to

other subpopulations of the same or competing species. Several authors have

claimed, for example, that patch isolation explains why fragmented habitats often

contain fewer bird species than contiguous habitats (Dickman 1987, Forman and

others 1976, Hayden and others 1985, Helliwell 1976, Moore and Hooper 1975,

Whitcomb and others 1981). Opdam (1991) reviewed a number of studies empirically

demonstrating an isolation effect on bird communities in various habitat patches.

Interpatch distance plays a critical role in island biogeographic theory (MacArthur

and Wilson 1967) and metapopulation theory (Gilpin and Hanski 1991, Levins 1970)

and has been discussed in the context of conservation biology (for example, Burkey

1989). The role of interpatch distance in metapopulations has had a preeminent role

in recent conservation efforts for endangered species (Lamberson and others 1992,

McKelvey and others 1992). Nearest neighbor distance clearly can be an important

characteristic of the landscape, depending on the phenomenon under investigation.

Patch core area standard deviation (CASD1) and disjunct core area standard deviation

(CASD2) indicate that the absolute variation in core area size per patch and per disjunct core

area, respectively, decreases progressively from landscape C to A, and in this manner they

mimic the results of patch size standard deviation. These indices alone do not tell us much

about differences in structure among the three landscapes unless the mean core area per

patch or mean area per disjunct core, respectively, also is considered. Patch core area

coefficient of variation (CACV1) measures relative variability and, in contrast to the standard

deviation, indicates that core area variability increases progressively from the least (C) to the

most (A) patchy landscape. Thus, although patch core area varies less in absolute terms in

landscape A than C, it varies much more in relative terms. Hence, timber management

activities have tended to produce smaller, but more variable, core areas. Disjunct core area

coefficient of variation (CACV2) measures relative variability among disjunct core areas. This

index indicates that in landscape A the disjunct core areas are much less variable than the

core areas per patch. The choice between coefficient of variation measures depends on the

particular application.

The total core area index (TCAI) represents the three landscapes along a continuum from

most to least patchy. According to this index, only 10 percent of landscape A is “interior”

habitat, the remaining 90 percent is “edge” habitat. Without any other information on landscape A, it might be deduced that landscape A contains a great deal of spatial heterogeneity.

However, the total core area index does not indicate how much total core area exists or how

many patches the core area is distributed among and, in this respect, it is best interpreted in

conjunction with other indices. The mean core area index (MCAI) mimics the results of the

total core area index, although the values are smaller because patches in each landscape

with 0 core area contribute equally to the mean and reduce the average value.

Nearest Neighbor

Metrics

45
FRAGSTATS computes the nearest neighbor distance (NEAR) and proximity index

(PROXIM) for each patch. The proximity index was developed by Gustafson and

Parker (1992) (see also, Gustafson and Parker, in press; Gustafson and others, in

press; Whitcomb and others 1981) and considers the size and proximity distance

of all patches having edges within a specified search radius of the focal patch. The

index is computed as the sum, over all patches of the corresponding patch type

whose edges are within the search radius of the focal patch, of each patch size

divided by the square of its distance from the focal patch. We used the distance

between the focal patch and each of the other patches within the search radius,

similar to the isolation index of Whitcomb and others (1981), rather than the nearest

neighbor distance of each patch within the search radius (which could be to a patch

other than the focal patch), as in Gustafson and Parker (1992). According to the

authors, the proximity index quantifies the spatial context of a habitat patch in relation

to its neighbors; specifically, the index distinguishes sparse distributions of small

habitat patches from configurations where the habitat forms a complex cluster of

larger patches. All other things being equal, a patch located in a neighborhood

(defined by the search radius) containing more of the corresponding patch type than

another patch will have a larger index value. Similarly, all other things being equal, a

patch located in a neighborhood in which the corresponding patch type is distributed

in larger, more contiguous, or closer patches than another patch will have a larger

index value. Thus, the proximity index measures both the degree of patch isolation

and the degree of fragmentation of the corresponding patch type within the specified

neighborhood of the focal patch. The index is dimensionless (has no units), and

therefore the absolute value of the index has little interpretive value; instead it is

used as a comparative index.

At the class and landscape levels, FRAGSTATS computes the mean proximity

index (MPI) for patches comprising the class or for all patches in the landscape.

At the class level, the mean proximity index measures the degree of isolation and

fragmentation of the corresponding patch type, and the performance of the index

under various scenarios is described in detail by Gustafson and Parker (in press).

We also compute the mean proximity index at the landscape level by averaging the

proximity index across all patches and patch types in the landscape, although the

performance of this index as a measure of overall landscape structural complexity

has not been evaluated quantitatively.

At the class and landscape levels, FRAGSTATS computes the mean nearest

neighbor distance (MNN) for patches comprising the class or for all patches in

the landscape. At the class level, mean nearest neighbor distance can be computed

only if at least two patches of the corresponding type occur. At the landscape level,

mean nearest neighbor distance considers only patches having neighbors. Thus,

there could be 10 patches in the landscape, but 8 of them might belong to separate

patch types and therefore have no neighbor within the landscape. In this case, mean

nearest neighbor distance would be based on the distance between the two patches

of the same type, whether close together or far apart. In either case, the mean nearest neighbor distance for this landscape might not characterize the entire landscape

very well. For this reason, this index should be interpreted carefully when landscapes

contain rare patch types.

46
Mean nearest neighbor distance is a first-order statistic and may not be meaningful if

the distribution is complex. Variability in nearest neighbor distance measures a key

aspect of landscape heterogeneity not captured by mean nearest neighbor distance.

Nearest neighbor standard deviation (NNSD) is a measure of patch dispersion; a

small standard deviation relative to the mean implies a fairly uniform or regular distribution of patches across landscapes, whereas a large standard deviation relative to

the mean implies a more irregular or uneven distribution of patches. The distribution

of patches may reflect underlying natural processes or human-caused disturbance

patterns. In absolute terms, the magnitude of nearest neighbor standard deviation is

a function of the mean nearest neighbor distance and variation in nearest neighbor

distance among patches. Thus, even though the standard deviation conveys information about nearest neighbor variability, it is a difficult parameter to interpret without

doing so in conjunction with the mean nearest neighbor distance. Two landscapes

may have the same nearest neighbor standard deviation, 100 meters; yet one landscape may have a mean nearest neighbor distance of 100 meters, and the other a

mean nearest neighbor distance of 1000 meters. In this case, the interpretations of

landscape structure would be very different, even though the absolute variation is the

same. Specifically, the former landscape has a more irregular but concentrated pattern of patches, and the latter has a more regular but dispersed pattern of patches.

In addition, standard deviation assumes a normal distribution about the mean. In a

real landscape, nearest neighbor distribution may be highly irregular. In this case, it

may be more informative to inspect the actual distribution itself (for example, plot a

histogram of the nearest neighbor distances for the corresponding patches), rather

than relying on summary statistics such as standard deviation that make assumptions

about the distribution and therefore can be misleading.

Coefficient of variation often is preferable to standard deviation for comparing variability among landscapes. Nearest neighbor coefficient of variation (NNCV) measures

relative variability about the mean (that is, variability as a percentage of the mean),

not absolute variability. Thus, it is not necessary to know the mean nearest neighbor

distance to interpret this metric. Even so, nearest neighbor coefficient of variation can

be misleading for landscape structure when the number of patches or patch density

and other structural characteristics is not also known. Two landscapes may have the

same nearest neighbor coefficient of variation, say, 100 percent; yet one landscape

may have 100 patches with a mean nearest neighbor distance of 100 meters, and

the other 10 patches with a mean nearest neighbor distance of 1000 meters. In this

case, the interpretations of overall landscape structure could be very different, even

though nearest neighbor coefficient of variation is the same; although the identical

coefficients of variation values indicate that both landscapes have the same regularity

or uniformity in patch distribution.

Because of limitations in Arc/Info (inability to calculate edge-to-edge distances), the

vector version of FRAGSTATS does not calculate nearest neighbor metrics. To compute these indices from a vector image, the image must be rasterized first and then

analyzed with the raster version of FRAGSTATS. During the rasterization process,

depending on the cell size selected, polygons can merge or divide. Indeed, this problem can be quite severe and lead to erroneous results for metrics based on the number and size of patches. Therefore, considerable care should be exercised when rasterizing a vector image to ensure the desired results. The most important limitation of

47
these nearest neighbor indices is that nearest neighbor distances are computed solely

from patches contained within the landscape boundary. If the landscape extent is

small relative to the scale of the organism or ecological process under consideration and the landscape is an “open” system relative to that organism or process,

then nearest neighbor results can be misleading. Consider, for example, a small

subpopulation of a bird species occupying a patch near the boundary of a somewhat

arbitrarily defined (from a bird’s perspective) landscape. The nearest neighbor within

the landscape boundary might be quite far away; yet, in reality, the closest patch

might be very close but just outside the designated landscape boundary. The magnitude of this problem is a function of scale. Increasing the size of the landscape

relative to the scale that the organism under investigation perceives and responds

to the environment will decrease the severity of this problem. Similarly, the proximity

index sums the distance-weighted area of all patches whose edges are within the

specified search radius of the focal patch but only considers patches within the landscape boundary. Thus, the proximity index may be biased low for patches located

within the search radius distance from the landscape boundary because a portion of

the search area will be outside the area under consideration. The magnitude of this

problem is also a function of scale. Increasing the size of the landscape relative to

the average patch size or decreasing the search radius, or both, will decrease the

severity of this problem at the class and landscape levels. However, at the patch

level, regardless of scale, individual patches located within the search radius of the

boundary will have a biased proximity index. The proximity index also evaluates the

landscape context of patches at a specific scale of analysis defined by the size of the

search radius. Therefore, this index is only meaningful if the specified search radius

has some ecological justification given the phenomenon under consideration. Otherwise, the results of the proximity index will be arbitrary and therefore meaningless.

Although these scaling issues are a critical consideration for all landscape metrics,

they are particularly problematic for these nearest neighbor indices.

Patch-level example—Figure 4 depicts three patches extracted from a sample landscape

that differ in their neighborhood context. Patch A has the smallest nearest neighbor distance

(NEAR), followed by patches B and C. Similarly, patch A has the largest proximity index

(PROXIM) based on a 200-meter search radius, followed by patches B and C. Note the

inverse relationship between nearest neighbor distance and the proximity index. These

indices support the conclusion drawn from the landscape similarity index (LSIM) that patch A

is the least insular of the three patches. Patch A contains a closer neighbor and a greater

amount of similar habitat within its immediate neighborhood than either patch B or C does.

Because of the relatively small landscape extent relative to patch size, nearest neighbor

distances are probably not very meaningful in this sample landscape.

Class-level example—Figure 5 depicts three sample landscapes that differ in the amount

and pattern of mixed, large sawtimber habitat. Mean nearest neighbor distance (MNN) is

greatest in landscape A, suggesting that mixed, large sawtimber patches are most isolated

in this landscape, although the differences among landscapes are relatively small. Nearest

neighbor standard deviation (NNSD) and nearest neighbor coefficient of variation (NNCV) are

greatest in landscape B, suggesting that the dispersion of mixed, large sawtimber patches is

least regular in this landscape. The mean proximity index (MPI) is inversely related to mean

nearest neighbor distance based on a 200-meter search radius and indicates that mixed,

48
Diversity Metrics FRAGSTATS computes several statistics that quantify diversity at the landscape

level (table 1). These metrics quantify landscape composition. Diversity measures

have been used extensively in a variety of ecological applications. They originally

gained popularity as measures of plant and animal species diversity. FRAGSTATS

computes three diversity indices. These diversity measures are influenced by two

components—richness and evenness. Richness refers to the number of patch types

present; evenness refers to the distribution of area among different types. Richness

and evenness are generally referred to as the compositional and structural components of diversity, respectively. Some indices (for example, Shannon’s diversity index

[Shannon and Weaver 1949]) are more sensitive to richness than evenness. Thus,

rare types have a disproportionately large influence on the magnitude of the index.

Other indices (for example, Simpson’s diversity index [Simpson 1949]) are relatively

less sensitive to richness and thus place more weight on the common species. These

diversity indices have been applied by landscape ecologists to measure one aspect

of landscape structure—landscape composition (see O’Neill and others 1988, Romme

1982, Turner 1990b).

The most popular diversity index is Shannon’s diversity index (SHDI), which is based

on information theory (Shannon and Weaver 1949). The value of this index represents

the amount of “information” per individual (or patch, in this case). Information is a

somewhat abstract mathematical concept that we will not attempt to define. The absolute magnitude of Shannon’s diversity index is not particularly meaningful; therefore,

it is used as a relative index for comparing different landscapes or the same landscape at different times. Simpson’s diversity index (SIDI) is another popular diversity

measure not based on information theory (Simpson 1949). Simpson’s index is less

sensitive to the presence of rare types and has an interpretation that is much more

intuitive than Shannon’s index. The value of Simpson’s index represents the probability that any two patches selected at random will be different types; the higher the

value, the greater the diversity. Because Simpson’s index is a probability, it can be

interpreted in both absolute and relative terms. FRAGSTATS also computes a modified Simpson’s diversity index (MSIDI) based on Pielou’s (1975) modification of

large sawtimber in landscape A is most fragmented and insular. These nearest neighbor

indices indicate that mixed, large sawtimber is less fragmented in landscape B than in C; yet,

most other fragmentation indices indicate the opposite. These differences likely reflect the

relatively small extent of these landscapes relative to patch size. Under these conditions,

nearest neighbor indices are not particularly meaningful and their interpretations can be

misleading.

Landscape-level example—Figure 6 depicts three sample landscapes that differ in composition and pattern. Mean nearest neighbor distance (MNN) is smallest in landscape C, suggesting that patches are least insular in this landscape. Nearest neighbor standard deviation

(NNSD) and nearest neighbor coefficient of variation (NNCV) are greatest in landscape A,

suggesting that the dispersion of patches is least regular in this landscape. The mean proximity index (MPI) is smallest in landscape A, based on a 200-meter search radius, and

indicates that patches are most fragmented and insular in this landscape, although the

interpretation of this index at the landscape level is somewhat difficult. Because of the

relatively small extent of these landscapes, nearest neighbor indices are not particularly

meaningful.

49
Simpson’s diversity index; this index was used by Romme (1982). The modification

eliminates the intuitive interpretation of Simpson’s index as a probability but transforms the index into one in a general class of diversity indices to which Shannon’s

diversity index also belongs (Pielou 1975). The modified Simpson’s and Shannon’s

diversity indices are similar in many respects and have the same applicability.

The use of diversity measures in community ecology has been heavily criticized

because diversity conveys no information on the actual species composition of a

community. Species diversity is a summary measure of a community that does not

take into account the uniqueness or potential ecological, social, or economical importance of individual species. A community may have high species diversity yet be comprised mainly of common or undesirable species. Conversely, a community may have

low species diversity yet be comprised of especially unique, rare, or highly desired

species. Although these criticisms have not been discussed explicitly regarding the

landscape ecological application of diversity measures, these criticisms are equally

valid when diversity measures are applied to patch types instead of species. In

addition, these diversity indices combine richness and evenness components into a

single measure, even though it usually is more informative to evaluate richness and

evenness independently.

Patch richness (PR) measures the number of patch types present; it is not affected

by the relative abundance of each patch type or the spatial arrangement of patches.

Two landscapes may have very different structure yet have the same richness; for

example, one landscape may be 96 percent in patch type A and 1 percent each of

patch types B through E, whereas another landscape may have 20 percent each of

patch types A through E. Patch richness would be the same, but the functioning of

these landscapes and the structure of the animal and plant communities likely would

be quite different. Because richness does not account for relative abundance of each

patch type, rare patch types and common patch types contribute equally to richness.

Patch richness, nevertheless is a key element of landscape structure because the

variety of landscape elements present in a landscape can have an important influence on several ecological processes. Because many organisms are associated with

a single patch type, patch richness often correlates well with species richness.

3

Richness is partially a function of scale. Larger areas are generally richer because

of the greater heterogeneity over large areas than over comparable smaller areas.

This contributes to the species-area relation predicted by island biogeographic theory

(MacArthur and Wilson 1967). Therefore, comparing richness among landscapes differing in size can be problematic. Patch richness density (PRD) standardizes richness

to a per area basis that facilitates comparison among landscapes, although it does

not correct for this interaction with scale. FRAGSTATS also computes a relative richness index. Relative patch richness (RPR) is similar to patch richness, but it represents richness as a percentage of the maximum potential richness as specified by

the user (Romme 1982). In some applications, this form may have more interpretive

value than absolute richness or richness density. Relative patch richness and patch

richness are completely redundant and would not be used simultaneously in any

subsequent statistical analysis. 3 Unpublished data. McGarigal, K.; McComb, W.C. On file with:

Forest Science Data Bank, a partnership between the Department of Forest Science, Oregon State University, and the U.S.

Department of Agriculture, Forest Service, Pacific Northwest

Research Station, 3200 Jefferson Way, Corvallis, OR 97331.

50
Evenness measures the other aspect of landscape diversity—the distribution

of area among patch types. There are numerous ways to quantify evenness and

most diversity indices have a corresponding evenness index derived from them.

In addition, evenness can be expressed as its compliment—dominance (that is,

evenness = 1 − dominance). Indeed, dominance often has been the chosen form

in landscape ecological investigations (for example, O’Neill and others 1988, Turner

1990b, Turner and others 1989), although we prefer evenness because larger values

imply greater landscape diversity. FRAGSTATS computes three evenness indices

(Shannon’s evenness index, SHEI; Simpson’s evenness index, SIEI; and modified

Simpson’s evenness index, MSIEI) corresponding to the three diversity indices. Each

evenness index isolates the evenness component of diversity by controlling for the

contribution of richness to the diversity index. Evenness is expressed as the observed level of diversity divided by the maximum possible diversity for a given patch

richness. Maximum diversity for any level of richness is based on an equal

distribution among patch types. Therefore, the observed diversity divided by the

maximum diversity (that is, equal distribution) for a given number of patch types

represents the proportional reduction in the diversity index attributed to lack of perfect

evenness. As the evenness index approaches 1, the observed diversity approaches

perfect evenness.

Because evenness is represented as a proportion of maximum evenness, Shannon’s

evenness index does not suffer from the limitation of Shannon’s diversity index in interpretability. Evenness, like richness and diversity, does not convey any information

about which patch types are most or least abundant or which may be of greater ecological significance.

Landscape-level example—Figure 6 depicts three sample landscapes that differ in composition and pattern. Shannon’s diversity index (SHDI), Simpson’s diversity index (SIDI), and the

modified Simpson’s diversity index (MSIDI) mainly reflect differences in patch richness and

represent the landscapes along a continuum from most (A) to least (C) diverse. In landscape

A, Simpson’s diversity index indicates a 79-percent probability that two randomly chosen

patches will represent different patch types. According to patch richness (PR), the number of

different patch types ranges from 10 in landscape A to 3 in landscape C. Because these landscapes are similar in area and the maximum possible number of patch types is a constant,

patch richness density (PRD), relative patch richness (RPR), and patch richness are largely

redundant. On the average, landscape A contains three and one-half different patch types

within a 100-hectare area and contains 37 percent of the potential number of patch types.

Although landscape C is the least diverse based on the diversity and richness indices, it has

the most even area distribution among patch types, according to Shannon’s evenness index

(SHEI), Simpson’s evenness index (SIEI), and the modified Simpson’s evenness index (MSIEI).

These three indices indicate that the distribution of area among patch types is 84 to 91 percent

of the maximum evenness in landscape C, depending on which index is interpreted. This

illustrates the potential importance of interpreting richness and evenness independently and

the importance of interpreting evenness separate from diversity, which is influenced strongly

by richness. Differences in evenness among landscapes based on Simpson’s evenness index

are less pronounced than with the other two evenness indices, perhaps because Simpson’s

metric is less influenced by rare patch types.

51
FRAGSTATS computes two indices representing patch interspersion and juxtaposition

at the class and landscape levels, although one index applies only to the landscape

level (table 1). These metrics quantify landscape configuration. A contagion index

was proposed first by O’Neill and others (1988), and subsequently, it has been

widely used (Graham and others 1991; Gustafson and Parker 1992; Turner 1989,

1990a, 1990b; Turner and others 1989; Turner and Ruscher 1988). Li and Reynolds

(in press) show that the original formula was incorrect; they introduce two forms of an

alternative contagion index that correct this error and improve performance. Both

contagion indices are designed for raster images in which each cell is individually

evaluated for adjacency, and like adjacencies (cells not on a patch perimeter) are

considered. Both indices have been applied at the landscape level to measure

landscape structure.

FRAGSTATS computes one of the contagion indices proposed by Li and Reynolds

(in press). This contagion index (CONTAG) is applicable only to raster images at the

landscape level; it is based on raster “cell” adjacencies—not “patch” adjacencies.

This contagion index consists of the sum, over patch types, of the product of two

probabilities: (1) the probability that a randomly chosen cell belongs to patch type i

(estimated by the proportional abundance of patch type i); and (2) the conditional

probability that given a cell is of patch type i, one of its neighboring cells belongs to

patch type j (estimated by the proportional abundance of patch type i adjacencies

involving patch type j). The product of these probabilities equals the probability that

two randomly chosen adjacent cells belong to patch types i and j. This contagion

index is appealing because of the straightforward and intuitive interpretation of this

probability. Contagion measures both patch type interspersion (the intermixing of

units of different patch types) as well as patch dispersion (the spatial distribution of

a patch type). All other things being equal, a landscape with well-interspersed patch

types will have lower contagion than a landscape with poorly interspersed patch

types. According to Li and Reynolds (in press), contagion measures the extent to

which landscape elements (patch types) are aggregated or clumped (dispersion);

higher values of contagion may result from landscapes with a few large, contiguous

patches, whereas lower values generally characterize landscapes with many small,

dispersed patches. Thus, holding interspersion constant, a landscape in which the

patch types are aggregated into larger, contiguous patches will have greater contagion than a landscape where patch types are fragmented into many small patches.

Contagion measures dispersion in addition to patch type interspersion because cells,

not patches, are evaluated for adjacency. Landscapes consisting of large, contiguous

patches have a majority of internal cells with like adjacencies. In this case, contagion

is high because of the large proportion of total cell adjacencies comprised of like

adjacencies and the uneven distribution of adjacencies among edge types. The

contagion index represents the observed level of contagion as a percentage of the

maximum possible, given the total number of patch types.

Contagion and

Interspersion Metrics

52
We present a new interspersion and juxtaposition index (IJI) that is compatible with

both vector and raster images and applicable at both the class and landscape levels.

Unlike the earlier contagion indices based on raster “cell” adjacencies, our index is

based on “patch” adjacencies. Each patch is evaluated for adjacency with all other

patch types; like adjacencies are not possible because a patch cannot be adjacent to

a patch of the same type. For raster images, internal cells are ignored; only the patch

perimeters are considered in determining the total length of each unique edge type.

Because this index is a measure of “patch” adjacency and not “cell” adjacency, the

interpretation is somewhat different than the contagion index. The interspersion index

measures the extent to which patch types are interspersed (not necessarily dispersed); higher values result from landscapes in which the patch types are well

interspersed (equally adjacent to each other), whereas lower values characterize

landscapes in which the patch types are poorly interspersed (disproportionate distribution of patch type adjacencies). The interspersion index is not directly affected

by the number, size, contiguity, or dispersion of patches per se, as is the contagion

index. A landscape containing four large patches, each a different patch type, and a

landscape of the same extent containing 100 small patches of four patch types will

have the same index value if the patch types are equally interspersed (or adjacent to

each other based on the proportion of total edge length in each edge type); the value

of contagion would be quite different. Like the contagion index, the interspersion

index is a relative index representing the observed level of interspersion as a

percentage of the maximum possible given the total number of patch types.

Unlike the contagion index, the interspersion and juxtaposition index can be applied

at both the class and landscape levels. At the class level, this index measures the

juxtapositioning of a focal patch type with all others and does not reflect the interspersion of other patch types. Again, the index is not affected by the dispersion of

the focal patch type per se, except that a well-dispersed patch type is more likely to

be well interspersed as well. For example, the focal patch type could be aggregated

in one portion of the landscape or maximally dispersed, and the value of the index

would be the same if the proportion of total edge length involving the focal patch and

each other patch type is the same.

The differences between the contagion index and the interspersion and juxtaposition

index are important. Contagion is affected by both interspersion and dispersion. The

interspersion and juxtaposition index, in contrast, is affected only by patch type interspersion and juxtaposition and not necessarily by the size, contiguity, or dispersion of

patches. Thus, although often indirectly affected by dispersion, the interspersion and

juxtaposition index directly measures patch type interspersion, whereas contagion

measures a combination of both patch type interspersion and dispersion. In addition,

contagion and interspersion are inversely related to each other. Higher contagion generally corresponds to lower interspersion and vice versa. Finally, in contrast to the

interspersion and juxtaposition index, the contagion index is strongly affected by the

grain size or resolution of the image. Given a particular patch mosaic, a smaller grain

size will result in greater contagion because of the proportional increase in like adjacencies from internal cells. The interspersion and juxtaposition index is not affected

because it considers only patch edges. This scale effect should be carefully considered when results from different studies are compared.

53
Acknowledgments Many individuals provided valuable feedback during the development and revisions

of the software, including Steve Garman, Eric Gustafson, Jeff Nighbert, Tom Moore,

Catherine Rogers, and David Wallin. We are especially grateful to Catherine Rogers

and Eric Gustafson for their comprehensive and detailed testing of the program and

their many useful suggestions. We thank Jim Kiser for conducting the photogrammetry and digitization work on the landscapes used in the documentation examples

and Tom Moore for porting FRAGSTATS to the DOS environment. Initial funding

for this project was provided through the Coastal Oregon Productivity Enhancement

(COPE) program; COPE is a cooperative research and technology transfer effort

among Oregon State University, U.S. Department of Agriculture Forest Service, U.S.

Department of the Interior Bureau of Land Management, other state and Federal

agencies, forest industry, county governments, and resource protection organizations.

Subsequent funding for the completion of this documentation was provided by the

Bureau of Land Management Cooperative Research Unit and the USDA Forest

Service, Pacific Northwest Research Station, Corvallis, Oregon.

Literature Cited Allen, T.F.H.; O’Neill, R.V.; Hoekstra, T.W. 1987. Interlevel relations in ecological

research and management: some working principles from hierarchy theory.

Journal of Applied Systems Analysis. 14: 63-79.

Allen, T.F.H.; Starr, T.B. 1982. Hierarchy: perspectives for ecological complexity.

Chicago: University of Chicago Press. 310 p.

Askins, R.A.; Philbrick, M.J. 1987. Effect of changes in regional forest abundance

on the decline and recovery of a forest bird community. Wilson Bulletin. 99: 7-21.

Baker, W.L.; Cai, Y. 1992. The r.le programs for multiscale analysis of landscape

structure using the GRASS geographical information system. Landscape Ecology.

7: 291-302.

Brittingham, M.C.; Temple, S.A. 1983. Have cowbirds caused forest songbirds to

decline? Bio-Science. 33: 31-35.

Buechner, M. 1989. Are small-scale landscape features important factors for field

studies of small mammal dispersal sinks? Landscape Ecology. 2: 191-199.

Class-level example—Figure 5 depicts three sample landscapes that differ in the amount

and pattern of mixed, large sawtimber habitat. The interspersion and juxtaposition index (IJI)

indicates that the mixed, large sawtimber edge present in landscape B is more equitably distributed among patch types than in either landscape A or C. Although landscapes A and C

contain different numbers of patch types (10 vs. 3), the interspersion and juxtaposition index

is roughly the same, indicating that the mixed, large sawtimber edge is distributed among the

available patch types at about 50 percent of the maximum possible equitable distribution in

both landscapes, even though the absolute amounts of edge and proportions associated with

each edge type clearly are quite different.

Landscape-level example—Figure 6 depicts three sample landscapes that differ in composition and pattern. The interspersion and juxtaposition index (IJI) indicates that the interspersion

of available patch types is greatest in landscape A and least in landscape C. This occurs

because landscape C contains two patch types that are present only in the landscape border,

and the amount of edge involving these two types is very small. Thus, the distribution of edge

lengths among unique types is very uneven. Accordingly, the contagion index (CONTAG) is

greatest in landscape C and least in landscape A. This reflects both the interspersion of patch

types as discussed above as well as the larger, more contiguous patches in landscape C

compared to landscape A.

54
Burkey, T.V. 1989. Extinction in nature reserves: the effect of fragmentation and

the importance of migration between reserve fragments. Oikos. 55: 75-81.

Burrough, P.A. 1986. Principles of geographical information systems for land

resources assessment. Oxford: Clarendon Press. 193 p.

Chen, J.; Franklin, J.F. 1990. Microclimatic pattern and basic biological responses

at the clearcut edges of old-growth Douglas-fir stands. Northwest Environmental

Journal. 6: 424-425.

Cody, M.L., ed. 1985. Habitat selection in birds. San Diego: Academic Press. 558 p.

Dickman, C.R. 1987. Habitat fragmentation and vertebrate species richness in an

urban environment. Journal of Applied Ecology. 24: 337-351.

Dunning, J.B.; Danielson, B.J.; Pulliam, H.R. 1992. Ecological processes that

affect populations in complex landscapes. Oikos. 65: 169-175.

Forman, R.T.T.; Galli, A.E.; Leck, C.F. 1976. Forest size and avian diversity in

New Jersey woodlots with some land use implications. Oecologia. 26: 1-8.

Forman, R.T.T.; Godron, M. 1986. Landscape ecology. New York: John Wiley &

Sons. 619 p.

Forsman, E.D.; Meslow, E.C.; Wight, H.M. 1984. Distribution and biology of the

spotted owl in Oregon. Wildlife Monograph. 87: 64.

Franklin, J.F.; Forman, R.T.T. 1987. Creating landscape pattern by forest cutting:

ecological consequences and principles. Landscape Ecology. 1: 5-18.

Gilpin, M.E.; Hanski, I., eds. 1991. Metapopulation dynamics: empirical and

theoretical investigations. San Diego: Academic Press. 336 p.

Graham, R.L.; Hunsaker, C.T.; O’Neill, R.V.; Jackson, B. 1991. Ecological risk

assessment at the regional scale. Ecological Applications. 1: 196-206.

Gratkowski, H.J. 1956. Windthrow around staggered settings in old-growth

Douglas-fir. Forest Science. 2: 60-74.

Gustafson, E.J.; Parker, G.R. 1992. Relationships between landcover proportion

and indices of landscape spatial pattern. Landscape Ecology. 7: 101-110.

Gustafson, E.J.; Parker, G.R. [In press]. Using an index of habitat patch proximity

for landscape design. Landscape and Urban Planning.

Gustafson, E.J.; Parker, G.R.; Backs, S.E. [In press]. Evaluating spatial pattern

of wildlife habitat: a case study of the wild turkey (Meleagris gallopavo). American

Midland Naturalist.

Haila, Y.; Hanski, I.K.; Raivio, S. 1987. Breeding bird distribution in fragmented

coniferous taiga in southern Finland. Ornis Fennica. 64: 90-106.

Hansen, A.; di Castri, F., eds. 1992. Landscape boundaries. New York: Springer.

452 p.

Hardt, R.A.; Forman, R.T.T. 1989. Boundary form effects on woody colonization

of reclaimed surface mines. Ecology. 70: 1252-1260.

Harris, L.D. 1984. The fragmented forest: island biogeographic theory and the

preservation of biotic diversity. Chicago: University of Chicago Press. 211 p.

55
Hayden, I.J.; Faaborg, J.; Clawson, R.L. 1985. Estimates of minimum area requirements for Missouri forest birds. Missouri Academy of Science. 19: 11-22.

Helliwell, D.R. 1976. The effects of size and isolation on the conservation value of

wooded sites in Britain. Journal of Biogeography. 3: 407-416.

Interagency Scientific Committee. 1990. A conservation strategy for the northern

spotted owl. Portland, OR: [Publisher unknown]. 427 p.

Iverson, L.R. 1989. Land use changes in Illinois, USA: the influence of landscape

attributes on current and historic land use. Landscape Ecology. 2: 45-61.

Kareiva, P. 1990. Population dynamics in spatially complex environments: theory

and data. Philosophical Transactions of the Royal Society of London. B(330):

175-190.

Kolasa, J.; Rollo, C.D. 1991. Introduction: the heterogeneity of heterogeneity: a

glossary. In: Kolasa, J.; Pickett, S.T.A., eds. Ecological heterogeneity. New York:

Springer-Verlag: 1-23.

Kotliar, N.B.; Wiens, J.A. 1990. Multiple scales of patchiness and patch structure:

a hierarchical framework for the study of heterogeneity. Oikos. 59: 253-260.

Kroodsma, R.L. 1982. Edge effect on breeding forest birds along a power-line

corridor. Journal of Applied Ecology. 19: 361-370.

Krummel, J.R.; Gardner, R.H.; Sugihara, G. [and others]. 1987. Landscape

patterns in a disturbed environment. Oikos. 48: 321-324.

Lamberson, R.H.; McKelvey, R.; Noon, B.R.; Voss, C. 1992. A dynamic analysis

of northern spotted owl viability in a fragmented forest landscape. Conservation

Biology. 6(4): 1-8.

Lee, D.R.; Sallee, G.T. 1970. A method of measuring shape. Geographical Review.

60: 555-563.

Lehmkuhl, J.F.; Raphael, M.G. 1993. Habitat pattern around northern spotted owl

locations on the Olympic Peninsula, Washington. Journal of Wildlife Management.

57: 302-315.

Leopold, A. 1933. Game management. New York: Charles Scribners. 481 p.

Levins, R. 1970. Extinctions. In: Gertenhaber, M., ed. Some mathematical questions

in biology. Vol. 2: Lectures on mathematics in the life sciences. Providence, RI:

American Mathematical Society: 77-107.

Li, H. 1990. Spatio-temporal pattern analysis of managed forest landscapes: a simulation approach. Corvallis, OR: Oregon State University. 166 p. Ph.D. thesis.

Li, H.; Reynolds, J.F. [In press]. A new contagion index to quantify spatial patterns

of landscapes. Landscape Ecology.

Logan, W.; Brown, E.R.; Longrie, D.; Herb, G. [and others]. 1985. Edges. In:

Brown, E.R., tech. ed. Management of wildlife and fish habitats in forests of

western Oregon and Washington. R6-F&WL-192-1985. [Portland, OR]: U.S.

Department of Agriculture, Forest Service, [Pacific Nothwest Region]: 115-127.

MacArthur, R.H.; MacArthur, J.W. 1961. On bird species diversity. Ecology.

42: 597-598.

56
MacArthur, R.H.; Wilson, E.O. 1967. The theory of island biogeography. Princeton:

Princeton University Press. 203 p.

Mandelbrot, B.B. 1977. Fractals, form, chance and dimension. New York: W.H.

Freeman and Co. 365 p.

Mandelbrot, B.B. 1982. The fractal geometry of nature. New York: W.H. Freeman

and Co. 460 p.

McGarigal, K.; McComb, W.C. In press. Relationships between landscape structure

and breeding birds in Oregon Coast Range. Ecological Monographs.

McKelvey, K.; Noon, B.R.; Lamberson, R. 1992. Conservation planning for species

occupying fragmented landscapes: the case of the northern spotted owl. In:

Kingsolver, J.; Kareiva, P.; Hyey, R., eds. Biotic interactions and global change.

Sunderland, MA: Sinauer Associates: 338-357.

Milne, B.T. 1988. Measuring the fractal geometry of landscapes. Applied

Mathematics and Computation. 27: 67-79.

Moore, N.W.; Hooper, M.D. 1975. On the number of bird species in British woods.

Biological Conservation. 8: 239-250.

Morgan, K.A.; Gates, J.E. 1982. Bird population patterns in forest edge and strip

vegetation at Remington Farms, Maryland. Journal of Wildlife Management.

46: 933-944.

Morse, D.R.; Lawton, J.H.; Dodson, M.M. 1985. Fractal dimension of vegetation

and the distribution of arthropod body lengths. Nature. 314: 731-733.

Murphy, D.D.; Noon, B.R. 1992. Integrating scientific methods with habitat

conservation planning: reserve design for northern spotted owls. Ecological

Applications. 2(1): 3-17.

Noss, R.F. 1988. Effects of edge and internal patchiness on habitat use by birds

in a Florida hardwood forest. Gainesville, FL: University of Florida. 109 p. Ph.D.

thesis.

O’Neill, R.V.; Krummel, J.R.; Gardner, R.H. [and others]. 1988. Indices of

landscape pattern. Landscape Ecology. 1: 153-162.

Opdam, P. 1991. Metapopulation theory and habitat fragmentation: a review of

holarctic breeding bird studies. Landscape Ecology. 5: 93-106.

Patton, D.R. 1975. A diversity index for quantifying habitat “edge.” Wildlife Society

Bulletin. 3: 171-173.

Pickett, S.T.A.; White, P.S., eds. 1985. The ecology of natural disturbances and

patch dynamics. Orlando, FL: Academic Press. 472 p.

Pielou, E.C. 1975. Ecological diversity. New York: Wiley-Interscience. 165 p.

Ranney, J.W.; Bruner, M.C.; Levenson, J.B. 1981. The importance of edge in the

structure and dynamics of forest islands. In: Burgess, R.L.; Sharpe, D.M., eds.

Forest island dynamics in man-dominated landscapes. New York: Springer-Verlag:

67-94.

Reese, K.P.; Ratti, J.T. 1988. Edge effect: a concept under scrutiny. Transactions

of the North American Wildlife and Natural Resources Conference. 53: 127-136.

57
Ricklefs, R.E. 1987. Community diversity: relative roles of local and regional

processes. Science. 235: 167-171.

Ripple, W.J.; Bradshaw, G.A.; Spies, T.A. 1991. Measuring landscape pattern in

the Cascade Range of Oregon, USA. Biological Conservation. 57: 73-88.

Risser, P.G.; Karr, J.R.; Forman, R.T.T. 1984. Landscape ecology: directions and

approaches. Spec. Publ. 2. Champaign, IL: Illinois Natural History Survey. 18 p.

Robbins, C.S.; Dawson, D.K.; Dowell, B.A. 1989. Habitat area requirements of

breeding forest birds of the middle Atlantic states. Wildlife Monograph. 103: 34.

Rogers, C.A. 1993. Describing landscapes: indices of structure. Burnaby, BC: Simon

Fraser University. 170 p. M.S. thesis.

Romme, W.H. 1982. Fire and landscape diversity in subalpine forests of Yellowstone

National Park. Ecological Monograph. 52: 199-221.

Roughgarden, J.; Gaines, S.D.; Pacala, S.W. 1987. Supply side ecology: the role

of physical transport processes. In: Gee, J.H.R.; Giller, P.S., eds. Organization of

communities past and present. Oxford: Blackwell Scientific Publications: 491-518.

Saunders, D.; Hobbs, R.J.; Margules, C.R. 1991. Biological consequences of

ecosystem fragmentation: a review. Conservation Biology. 5: 18-32.

Shannon, C.; Weaver, W. 1949. The mathematical theory of communication. Urbana:

University of Illinois Press. 117 p.

Simpson, E.H. 1949. Measurement of diversity. Nature. 163: 688.

Strelke, W.K.; Dickson, J.G. 1980. Effect of forest clearcut edge on breeding birds

in Texas. Journal of Wildlife Management. 44: 559-567.

Temple, S.A. 1986. Predicting impacts of habitat fragmentation on forest birds: a

comparison of two models. In: Verner, J.; Morrison, M.L.; Ralph, C.J., eds. Wildlife

2000: modeling habitat relationships of terrestrial vertebrates. Madison, WI: University of Wisconsin Press: 301-304.

Terborgh, J. 1989. Where have all the birds gone? New Jersey: Princeton University

Press. 207 p.

Thomas, J.W.; Maser, C.; Rodiek, J.E. 1978. Edges—their interspersion, resulting

diversity, and its measurement. In: Degraff, R.M., tech. coord. Proceedings of the

workshop on nongame bird habitat management in the coniferous forests of the

Western United States; [Dates of meeting unknown]; [Location of meeting unknown]. Gen. Tech. Rep. PNW-64. Portland, OR: U.S. Department of Agriculture,

Forest Service, Pacific Northwest Forest and Range Experiment Station: 91-100.

Thomas, J.W.; Maser, C.; Rodiek, J.E. 1979. Edges. In: Thomas, J.W., tech. ed.

Wildlife habitats in managed forests, the Blue Mountains of Oregon and Washington. Agric. Handb. 553. Washington, DC: U.S. Department of Agriculture: 48-59.

Turner, M.G. 1989. Landscape ecology: the effect of pattern on process. Annual

Review of Ecological Systems. 20: 171-197.

Turner, M.G. 1990a. Landscape changes in nine rural counties of Georgia. Photogrammetric Engineering and Remote Sensing. 56: 379-386.

58
Turner, M.G. 1990b. Spatial and temporal analysis of landscape patterns. Landscape Ecology. 4: 21-30.

Turner, M.G.; Gardner. R.H., eds. 1991. Quantitative methods in landscape ecology. New York: Springer. 536 p.

Turner, M.G.; O’Neill, R.V.; Gardner, R.H.; Milne, B.T. 1989. Effects of changing

spatial scale on the analysis of landscape pattern. Landscape Ecology. 3: 153-162.

Turner, M.G.; Ruscher, C.L. 1988. Changes in the spatial patterns of lands use in

Georgia. Landscape Ecology. 1: 241-251.

Urban, D.L.; O’Neill, R.V.; Shugart, Jr., H.H. 1987. Landscape ecology: a hierarchical perspective can help scientist understand spatial patterns. BioScience.

37: 119-127.

Vaisanen, R.A.; Jarvinen, O.; Rauhala, P. 1986. How are extensive, human-caused

habitat alterations expressed on the scale of local bird populations in boreal forest?

Ornis Scandinavica. 17: 282-292.

Whitcomb, R.F.; Robbins, C.S.; Lynch, J.F. [and others]. 1981. Effects of forest

fragmentation on avifauna of the eastern deciduous forest. In: Burgess, R.L.;

Sharpe, D.M., eds. Forest island dynamics in man-dominated landscapes. New

York: Springer-Verlag: 125-205.

Wiens, J.A. 1976. Population response to patchy environments. Annual Review of

Ecological Systems. 7: 81-129.

Wiens, J.A. 1981. Scale problems in avian censusing. Studies in Avian Biology.

6: 513-521.

Wiens, J.A. 1989a. Spatial scaling in ecology. Functional Ecology. 3: 385-397.

Wiens, J.A. 1989b. The ecology of bird communities: volume 2, processes and

variations. Cambridge: Cambridge University Press. 316 p.

Wiens, J.A.; Crawford, C.S.; Gosz, J.R. 1985. Boundary dynamics: a conceptual

framework for studying landscape ecosystems. Oikos. 45: 421-427.

Wiens, J.A.; Milne, B.T. 1989. Scaling of ‘landscapes’ in landscape ecology, or,

landscape ecology from a beetle’s perspective. Landscape Ecology. 3: 87-96.

Wilcove, D.S. 1985. Nest predation in forest tracts and the decline of migratory

songbirds. Ecology. 66: 1211-1214.

Willson, M.F. 1974. Avian community organization and habitat structure. Ecology.

55: 1017-1029.

Yahner, R.H.; D.P. Scott. 1988. Effects of forest fragmentation on depredation of

artificial nests. Journal of Wildlife Management. 52: 158-161.

59
Following is an example of the FRAGSTATS output file formatted exclusively for display purposes (that is, “basename”.full). Each run of FRAGSTATS for a landscape

produces an output file like this one. The results reported here correspond to the

landscape displayed in figure 6 (landscape B). The results obtained by using the

vector and raster versions of FRAGSTATS are included separately; note the differences in indices involving edge lengths and patch perimeters.

Vector Version

Date: 07 Oct 93 13:39:26 Thursday

Coverage: ncveg

Basename For Output Files: ncveg

Patch Type Attribute: class Edge Dist: 100

Background Class: NONE

Max Patch Types Possible: 27

Weight File: contrast.new

Patch ID Attribute: patchid Class Names Attribute: classdesc

Input Landscape Contains a Landscape Border

Proportion of Boundary/Background to Count as Edge: 0.00

Write Patch Indices: YES Write Class Indices: YES

AML/Program Directory: /gis/giswork/barbara/vector/

Appendix 1:

FRAGSTATS Output

File

PATCH INDICES

Patch ID: 700 Patch Type: W

Area (ha): 1.118 Landscape Similarity (%): 0.378

Perimeter (m): 437.399 Edge Contrast (%): 6.695

Shape Index: 1.167 Fractal Dimension: 1.305

Core Area (ha): 0.000 Num Core Areas: 0

Core Area Index (%): 0.000

CLASS INDICES

Patch Type: W Class Area (ha): 1.118

Total Area (ha): 296.073 Percent of Landscape (%): 0.378

Largest Patch Index (%): 0.378 Number Patches: 1

Patch Density (#/100 ha): 0.338 Mean Patch Size (ha): 1.118

Patch Size SD (ha): 0.000 Patch Size CV (%): 0.000

Total Edge (m): 437.399 Edge Den (m/ha): 1.477

Con-Wght Edge Den (m/ha): 0.099 Total Edge Contrast (%): 6.695

Mean Edge Contrast (%): 6.695 Area-Wt Mean Edge Con (%): 6.695

Landscape Shape Index: 1.243 Mean Shape Index: 1.167

Area-Weighted Mean Shape: 1.167 Double Log Fractal Index: NA

Mean Patch Fractal: 1.305 Area-Weighted Mean Fractal: 1.305

Core % of Landscape (%): 0.000 Total Core Area (ha): 0.000

Number Core Areas: 0 Core Area Den (#/100 ha): 0.000

Mean Core Area 1 (ha): 0.000 Core Area SD 1 (ha): 0.000

Core Area CV 1 (%): 0.000 Mean Core Area 2 (ha): 0.000

Core Area SD 2 (ha): 0.000 Core Area CV 2 (%): 0.000

Total Core Area Index (%): 0.000 Mean Core Area Index (%): 0.000

Intersper/Juxtapos (%): 13.711

PATCH INDICES

Patch ID: 200 Patch Type: MGF

Area (ha): 18.586 Landscape Similarity (%): 8.413

Perimeter (m): 1907.330 Edge Contrast (%): 80.049

Shape Index: 1.248 Fractal Dimension: 1.245

Core Area (ha): 4.622 Num Core Areas: 1

Core Area Index (%): 24.868

60
Patch ID: 500 Patch Type: MGF

Area (ha): 6.323 Landscape Similarity (%): 8.413

Perimeter (m): 1046.888 Edge Contrast (%): 91.000

Shape Index: 1.174 Fractal Dimension: 1.258

Core Area (ha): 0.016 Num Core Areas: 1

Core Area Index (%): 0.248

CLASS INDICES

Patch Type: MGF Class Area (ha): 24.908

Total Area (ha): 296.073 Percent of Landscape (%): 8.413

Largest Patch Index (%): 6.277 Number Patches: 2

Patch Density (#/100 ha): 0.676 Mean Patch Size (ha): 12.454

Patch Size SD (ha): 6.131 Patch Size CV (%): 49.232

Total Edge (m): 2954.219 Edge Den (m/ha): 9.978

Con-Wght Edge Den (m/ha): 8.375 Total Edge Contrast (%): 83.930

Mean Edge Contrast (%): 85.525 Area-Wt Mean Edge Con (%): 82.829

Landscape Shape Index: 1.655 Mean Shape Index: 1.211

Area-Weighted Mean Shape: 1.229 Double Log Fractal Index: 1.113

Mean Patch Fractal: 1.252 Area-Weighted Mean Fractal: 1.248

Core % of Landscape (%): 1.566 Total Core Area (ha): 4.638

Number Core Areas: 2 Core Area Den (#/100 ha): 0.676

Mean Core Area 1 (ha): 2.319 Core Area SD 1 (ha): 2.303

Core Area CV 1 (%): 99.324 Mean Core Area 2 (ha): 2.319

Core Area SD 2 (ha): 2.303 Core Area CV 2 (%): 99.324

Total Core Area Index (%): 18.619 Mean Core Area Index (%): 12.558

Intersper/Juxtapos (%): 62.578

PATCH INDICES

Patch ID: 600 Patch Type: MSH

Area (ha): 18.008 Landscape Similarity (%): 6.082

Perimeter (m): 1712.001 Edge Contrast (%): 74.276

Shape Index: 1.138 Fractal Dimension: 1.231

Core Area (ha): 4.612 Num Core Areas: 1

Core Area Index (%): 25.610

CLASS INDICES

Patch Type: MSH Class Area (ha): 18.008

Total Area (ha): 296.073 Percent of Landscape (%): 6.082

Largest Patch Index (%): 6.082 Number Patches: 1

Patch Density (#/100 ha): 0.338 Mean Patch Size (ha): 18.008

Patch Size SD (ha): 0.000 Patch Size CV (%): 0.000

Total Edge (m): 2355.761 Edge Den (m/ha): 7.957

Con-Wght Edge Den (m/ha): 5.882 Total Edge Contrast (%): 73.927

Mean Edge Contrast (%): 74.276 Area-Wt Mean Edge Con (%): 74.276

Landscape Shape Index: 1.452 Mean Shape Index: 1.138

Area-Weighted Mean Shape: 1.138 Double Log Fractal Index: NA

Mean Patch Fractal: 1.231 Area-Weighted Mean Fractal: 1.231

Core % of Landscape (%): 1.558 Total Core Area (ha): 4.612

Number Core Areas: 1 Core Area Den (#/100 ha): 0.338

Mean Core Area 1 (ha): 4.612 Core Area SD 1 (ha): 0.000

Core Area CV 1 (%): 0.000 Mean Core Area 2 (ha): 4.612

Core Area SD 2 (ha): 0.000 Core Area CV 2 (%): 0.000

Total Core Area Index (%): 25.610 Mean Core Area Index (%): 25.610

Intersper/Juxtapos (%): 30.221

PATCH INDICES

Patch ID: 102 Patch Type: MLS

Area (ha): 28.318 Landscape Similarity (%): 48.802

Perimeter (m): 2430.356 Edge Contrast (%): 18.807

Shape Index: 1.288 Fractal Dimension: 1.242

61
Core Area (ha): 8.769 Num Core Areas: 1

Core Area Index (%): 30.965

Patch ID: 110 Patch Type: MLS

Area (ha): 51.288 Landscape Similarity (%): 48.802

Perimeter (m): 4544.994 Edge Contrast (%): 24.408

Shape Index: 1.790 Fractal Dimension: 1.281

Core Area (ha): 12.336 Num Core Areas: 3

Core Area Index (%): 24.052

Patch ID: 104 Patch Type: MLS

Area (ha): 51.332 Landscape Similarity (%): 48.802

Perimeter (m): 6230.153 Edge Contrast (%): 16.959

Shape Index: 2.453 Fractal Dimension: 1.329

Core Area (ha): 8.459 Num Core Areas: 2

Core Area Index (%): 16.478

Patch ID: 108 Patch Type: MLS

Area (ha): 8.255 Landscape Similarity (%): 48.802

Perimeter (m): 1893.036 Edge Contrast (%): 25.391

Shape Index: 1.859 Fractal Dimension: 1.333

Core Area (ha): 0.000 Num Core Areas: 0

Core Area Index (%): 0.000

Patch ID: 107 Patch Type: MLS

Area (ha): 5.298 Landscape Similarity (%): 48.802

Perimeter (m): 912.608 Edge Contrast (%): 21.105

Shape Index: 1.118 Fractal Dimension: 1.253

Core Area (ha): 0.010 Num Core Areas: 1

Core Area Index (%): 0.189

CLASS INDICES

Patch Type: MLS Class Area (ha): 144.491

Total Area (ha): 296.073 Percent of Landscape (%): 48.802

Largest Patch Index (%): 17.338 Number Patches: 5

Patch Density (#/100 ha): 1.689 Mean Patch Size (ha): 28.898

Patch Size SD (ha): 19.940 Patch Size CV (%): 69.001

Total Edge (m): 15198.311 Edge Den (m/ha): 51.333

Con-Wght Edge Den (m/ha): 11.374 Total Edge Contrast (%): 19.311

Mean Edge Contrast (%): 21.334 Area-Wt Mean Edge Con (%): 20.599

Landscape Shape Index: 3.218 Mean Shape Index: 1.702

Area-Weighted Mean Shape: 1.907 Double Log Fractal Index: 1.519

Mean Patch Fractal: 1.288 Area-Weighted Mean Fractal: 1.292

Core % of Landscape (%): 9.988 Total Core Area (ha): 29.573

Number Core Areas: 7 Core Area Den (#/100 ha): 2.364

Mean Core Area 1 (ha): 5.915 Core Area SD 1 (ha): 5.014

Core Area CV 1 (%): 84.772 Mean Core Area 2 (ha): 4.225

Core Area SD 2 (ha): 5.010 Core Area CV 2 (%): 118.578

Total Core Area Index (%): 20.467 Mean Core Area Index (%): 14.337

Intersper/Juxtapos (%): 75.666

PATCH INDICES

Patch ID: 101 Patch Type: HLS

Area (ha): 33.096 Landscape Similarity (%): 14.474

Perimeter (m): 5744.522 Edge Contrast (%): 35.092

Shape Index: 2.817 Fractal Dimension: 1.362

Core Area (ha): 0.370 Num Core Areas: 1

Core Area Index (%): 1.118

Patch ID: 106 Patch Type: HLS

Area (ha): 9.757 Landscape Similarity (%): 14.474

Perimeter (m): 1937.990 Edge Contrast (%): 5.734

62
Shape Index: 1.750 Fractal Dimension: 1.318

Core Area (ha): 0.014 Num Core Areas: 1

Core Area Index (%): 0.146

CLASS INDICES

Patch Type: HLS Class Area (ha): 42.853

Total Area (ha): 296.073 Percent of Landscape (%): 14.474

Largest Patch Index (%): 11.178 Number Patches: 2

Patch Density (#/100 ha): 0.676 Mean Patch Size (ha): 21.427

Patch Size SD (ha): 11.670 Patch Size CV (%): 54.463

Total Edge (m): 7541.288 Edge Den (m/ha): 25.471

Con-Wght Edge Den (m/ha): 7.216 Total Edge Contrast (%): 27.136

Mean Edge Contrast (%): 20.413 Area-Wt Mean Edge Con (%): 28.407

Landscape Shape Index: 2.256 Mean Shape Index: 2.284

Area-Weighted Mean Shape: 2.574 Double Log Fractal Index: 1.779

Mean Patch Fractal: 1.340 Area-Weighted Mean Fractal: 1.352

Core % of Landscape (%): 0.130 Total Core Area (ha): 0.384

Number Core Areas: 2 Core Area Den (#/100 ha): 0.676

Mean Core Area 1 (ha): 0.192 Core Area SD 1 (ha): 0.178

Core Area CV 1 (%): 92.580 Mean Core Area 2 (ha): 0.192

Core Area SD 2 (ha): 0.178 Core Area CV 2 (%): 92.580

Total Core Area Index (%): 0.897 Mean Core Area Index (%): 0.632

Intersper/Juxtapos (%): 48.750

PATCH INDICES

Patch ID: 300 Patch Type: COS

Area (ha): 5.733 Landscape Similarity (%): 7.622

Perimeter (m): 1291.624 Edge Contrast (%): 51.324

Shape Index: 1.522 Fractal Dimension: 1.308

Core Area (ha): 0.000 Num Core Areas: 0

Core Area Index (%): 0.000

Patch ID: 400 Patch Type: COS

Area (ha): 16.833 Landscape Similarity (%): 7.622

Perimeter (m): 1922.240 Edge Contrast (%): 42.022

Shape Index: 1.322 Fractal Dimension: 1.257

Core Area (ha): 2.347 Num Core Areas: 1

Core Area Index (%): 13.944

CLASS INDICES

Patch Type: COS Class Area (ha): 22.567

Total Area (ha): 296.073 Percent of Landscape (%): 7.622

Largest Patch Index (%): 5.685 Number Patches: 2

Patch Density (#/100 ha): 0.676 Mean Patch Size (ha): 11.283

Patch Size SD (ha): 5.550 Patch Size CV (%): 49.186

Total Edge (m): 2895.564 Edge Den (m/ha): 9.780

Con-Wght Edge Den (m/ha): 5.296 Total Edge Contrast (%): 46.407

Mean Edge Contrast (%): 46.673 Area-Wt Mean Edge Con (%): 44.386

Landscape Shape Index: 1.520 Mean Shape Index: 1.422

Area-Weighted Mean Shape: 1.372 Double Log Fractal Index: 0.738

Mean Patch Fractal: 1.282 Area-Weighted Mean Fractal: 1.270

Core % of Landscape (%): 0.793 Total Core Area (ha): 2.347

Number Core Areas: 1 Core Area Den (#/100 ha): 0.338

Mean Core Area 1 (ha): 1.174 Core Area SD 1 (ha): 1.174

Core Area CV 1 (%): 100.000 Mean Core Area 2 (ha): 2.347

Core Area SD 2 (ha): 0.000 Core Area CV 2 (%): 0.000

Total Core Area Index (%): 10.401 Mean Core Area Index (%): 6.972

Intersper/Juxtapos (%): 55.228

63
PATCH INDICES

Patch ID: 103 Patch Type: CLS

Area (ha): 11.882 Landscape Similarity (%): 14.229

Perimeter (m): 2454.529 Edge Contrast (%): 4.720

Shape Index: 2.009 Fractal Dimension: 1.336

Core Area (ha): 0.000 Num Core Areas: 0

Core Area Index (%): 0.000

Patch ID: 111 Patch Type: CLS

Area (ha): 2.386 Landscape Similarity (%): 14.229

Perimeter (m): 608.411 Edge Contrast (%): 12.854

Shape Index: 1.111 Fractal Dimension: 1.272

Core Area (ha): 0.000 Num Core Areas: 0

Core Area Index (%): 0.000

Patch ID: 105 Patch Type: CLS

Area (ha): 20.633 Landscape Similarity (%): 14.229

Perimeter (m): 3059.747 Edge Contrast (%): 3.612

Shape Index: 1.900 Fractal Dimension: 1.312

Core Area (ha): 1.308 Num Core Areas: 1

Core Area Index (%): 6.341

Patch ID: 109 Patch Type: CLS

Area (ha): 7.227 Landscape Similarity (%): 14.229

Perimeter (m): 2034.829 Edge Contrast (%): 27.785

Shape Index: 2.135 Fractal Dimension: 1.362

Core Area (ha): 0.000 Num Core Areas: 0

Core Area Index (%): 0.000

CLASS INDICES

Patch Type: CLS Class Area (ha): 42.129

Total Area (ha): 296.073 Percent of Landscape (%): 14.229

Largest Patch Index (%): 6.969 Number Patches: 4

Patch Density (#/100 ha): 1.351 Mean Patch Size (ha): 10.532

Patch Size SD (ha): 6.729 Patch Size CV (%): 63.894

Total Edge (m): 8261.122 Edge Den (m/ha): 27.902

Con-Wght Edge Den (m/ha): 4.099 Total Edge Contrast (%): 13.426

Mean Edge Contrast (%): 12.243 Area-Wt Mean Edge Con (%): 8.595

Landscape Shape Index: 2.267 Mean Shape Index: 1.789

Area-Weighted Mean Shape: 1.926 Double Log Fractal Index: 1.626

Mean Patch Fractal: 1.320 Area-Weighted Mean Fractal: 1.325

Core % of Landscape (%): 0.442 Total Core Area (ha): 1.308

Number Core Areas: 1 Core Area Den (#/100 ha): 0.338

Mean Core Area 1 (ha): 0.327 Core Area SD 1 (ha): 0.567

Core Area CV 1 (%): 173.205 Mean Core Area 2 (ha): 1.308

Core Area SD 2 (ha): 0.000 Core Area CV 2 (%): 0.000

Total Core Area Index (%): 3.106 Mean Core Area Index (%): 1.585

Intersper/Juxtapos (%): 46.744

LANDSCAPE INDICES

Total Area (ha): 296.073

Largest Patch Index(%): 17.338

Number of patches: 17

Patch Density (#/100 ha): 5.742

Mean Patch Size (ha): 17.416

Patch Size Standard Dev (ha): 15.048

Patch Size Coeff of Variation (%): 86.404

Total Edge (m): 19821.830

Edge Density (m/ha): 66.949

Contrast-Weight Edge Density (m/ha): 21.170

Total Edge Contrast Index (%): 26.497

64
Date: Tue Oct 26 12:41:29 1993

Image Name: ncveg.svf

Basename For Output Files: ncveg

Rows: 473 Cols: 465 Cellsize: 5.0 Data Type: 1

Edge Dist: 100.0 Max Patch Types Possible: 27

Background Class: -9999

Weight File: contrast.new

ID Image: ncvegid.svf

Descriptor File: classnames.dat

Image Includes a Landscape Border

Proportion of Boundary/Background to Count as Edge: 0.00

Diagonals Used; Proximity Dist (m): 200.0

Nearest Neighbor Calcs

Write Patch Indices; Write Class Indices

Mean Edge Contrast Index (%): 31.872

Area-Wght Mean Class Edge Contrast (%): 30.281

Landscape Shape Index: 3.878

Mean Shape Index: 1.635

Area-Weighted Mean Shape Index: 1.859

Double Log Fractal Dimension: 1.489

Mean Patch Fractal Dimension: 1.294

Area-Weighted Mean Fractal Dimension: 1.296

Total Core Area (ha): 42.862

Number of Core Areas: 14

Core Area Density (#/100 ha): 4.729

Mean Core Area 1 (ha): 2.521

Core Area Standard Dev 1 (ha): 6.931

Core Area Coeff of Variation 1 (%): 274.894

Mean Core Area 2 (ha): 3.062

Core Area Standard Dev 2 (ha): 7.528

Core Area Coeff of Variation 2 (%): 245.900

Total Core Area Index (%): 14.477

Mean Core Area Index (%): 8.468

Shannon’s Diversity Index: 1.503

Simpson’s Diversity Index: 0.704

Modified Simpson’s Diversity Index: 1.218

Patch Richness: 7

Patch Richness Density (#/100 ha): 2.364

Relative Patch Richness (%): 25.926

Shannon’s Evenness Index: 0.772

Simpson’s Evenness Index: 0.821

Modified Simpson’s Evenness Index: 0.626

Interspersion/Juxtaposition (%): 64.713

PATCH INDICES

Patch ID: 700 Patch Type: W

Area (ha): 1.117 Landscape Similarity (%): 0.377

Perimeter (m): 550.000 Edge Contrast (%): 6.364

Shape Index: 1.301 Fractal Dimension: 1.056

Core Area (ha): 0.000 Num Core Areas: 0

Core Area Index (%): 0.000 Near Neigh Dist (m): NONE

Proximity Index: 0.000

65
CLASS INDICES

Patch Type: W Class Area (ha): 1.117

Total Area (ha): 296.068 Percent of Landscape (%): 0.377

Largest Patch Index (%): 0.377 Number Patches: 1

Patch Density (#/100 ha): 0.338 Mean Patch Size (ha): 1.117

Patch Size SD (ha): 0.000 Patch Size CV (%): 0.000

Total Edge (m): 550.000 Edge Den (m/ha): 1.858

Con-Wght Edge Den (m/ha): 0.118 Total Edge Contrast (%): 6.364

Mean Edge Contrast (%): 6.364 Area-Wt Mean Edge Con(%): 6.364

Landscape Shape Index: 1.353 Mean Shape Index: 1.301

Area-Weighted Mean Shape: 1.301 Double Log Fractal Index: NA

Mean Patch Fractal: 1.056 Area-Weighted Mean Fractal: 1.056

Core % of Landscape (%): 0.000 Total Core Area (ha): 0.000

Number Core Areas: 0 Core Area Den (#/100 ha): 0.000

Mean Core Area 1 (ha): 0.000 Core Area SD 1 (ha): 0.000

Core Area CV 1 (%): 0.000 Mean Core Area 2 (ha): 0.000

Core Area SD 2 (ha): 0.000 Core Area CV 2 (%): 0.000

Total Core Area Index (%): 0.000 Mean Core Area Index (%): 0.000

Mean NearNeigh Dist(m): NONE Near Neighor SD (m): NA

Nearest Neighbor CV (%): NA Mean Prox Index: 0.000

Intersper/Juxtapos (%): 13.219

PATCH INDICES

Patch ID: 200 Patch Type: MGF

Area (ha): 18.595 Landscape Similarity (%): 8.410

Perimeter (m): 2320.000 Edge Contrast (%): 80.925

Shape Index: 1.345 Fractal Dimension: 1.049

Core Area (ha): 5.513 Num Core Areas: 1

Core Area Index (%): 29.645 Near Neigh Dist (m): 216.910

Proximity Index: 0.000

Patch ID: 500 Patch Type: MGF

Area (ha): 6.305 Landscape Similarity (%): 8.410

Perimeter (m): 1340.000 Edge Contrast (%): 91.000

Shape Index: 1.334 Fractal Dimension: 1.052

Core Area (ha): 0.310 Num Core Areas: 1

Core Area Index (%): 4.917 Near Neigh Dist (m): 216.910

Proximity Index: 0.000

CLASS INDICES

Patch Type: MGF Class Area (ha): 24.900

Total Area (ha): 296.068 Percent of Landscape (%): 8.410

Largest Patch Index (%): 6.281 Number Patches: 2

Patch Density (#/100 ha): 0.676 Mean Patch Size (ha): 12.450

Patch Size SD (ha): 6.145 Patch Size CV (%): 49.357

Total Edge (m): 3660.000 Edge Den (m/ha): 12.362

Con-Wght Edge Den (m/ha): 10.460 Total Edge Contrast (%): 84.613

Mean Edge Contrast (%): 85.962 Area-Wt Mean Edge Con(%): 83.476

Landscape Shape Index: 1.805 Mean Shape Index: 1.340

Area-Weighted Mean Shape: 1.342 Double Log Fractal: 1.015

Mean Patch Fractal: 1.051 Area-Weighted Mean Fractal: 1.050

Core % of Landscape (%): 1.967 Total Core Area (ha): 5.822

Number Core Areas: 2 Core Area Den (#/100 ha): 0.676

Mean Core Area 1 (ha): 2.911 Core Area SD 1 (ha): 2.601

Core Area CV 1 (%): 89.352 Mean Core Area 2 (ha): 2.911

Core Area SD 2 (ha): 2.601 Core Area CV 2 (%): 89.352

Total Core Area Index (%): 23.384 Mean Core Area Index (%): 17.281

Mean NearNeigh Dist (m): 216.910 Nearest Neighbor SD (m): 0.000

Nearest Neighbor CV (%): 0.000 Mean Prox Index: 0.000

Intersper/Juxtapos (%): 61.481

66
PATCH INDICES

Patch ID: 600 Patch Type: MSH

Area (ha): 18.010 Landscape Similarity (%): 6.083

Perimeter (m): 2150.000 Edge Contrast (%): 74.247

Shape Index: 1.267 Fractal Dimension: 1.039

Core Area (ha): 5.553 Num Core Areas: 1

Core Area Index (%): 30.830 Near Neigh Dist (m): NONE

Proximity Index: 0.000

CLASS INDICES

Patch Type: MSH Class Area (ha): 18.010

Total Area (ha): 296.068 Percent of Landscape (%): 6.083

Largest Patch Index (%): 6.083 Number Patches: 1

Patch Density (#/100 ha): 0.338 Mean Patch Size (ha): 18.010

Patch Size SD (ha): 0.000 Patch Size CV (%): 0.000

Total Edge (m): 2975.000 Edge Den (m/ha): 10.048

Con-Wght Edge Den (m/ha): 7.426 Total Edge Contrast (%): 73.901

Mean Edge Contrast (%): 74.247 Area-Wt Mean Edge Con(%): 74.247

Landscape Shape Index: 1.585 Mean Shape Index: 1.267

Area-Weighted Mean Shape: 1.267 Double Log Fractal Index: NA

Mean Patch Fractal: 1.039 Area-Weighted Mean Fractal: 1.039

Core % of Landscape (%): 1.875 Total Core Area (ha): 5.553

Number Core Areas: 1 Core Area Den (#/100 ha): 0.338

Mean Core Area 1 (ha): 5.552 Core Area SD 1 (ha): 0.000

Core Area CV 1 (%): 0.000 Mean Core Area 2 (ha): 5.552

Core Area SD 2 (ha): 0.000 Core Area CV 2 (%): 0.000

Total Core Area Index (%): 30.830 Mean Core Area Index (%): 30.830

Mean NearNeigh Dist(m): NONE Near Neighor SD (m): NA

Nearest Neighbor CV (%): NA Mean Prox Index: 0.000

Intersper/Juxtapos (%): 29.771

PATCH INDICES

Patch ID: 102 Patch Type: MLS

Area (ha): 28.317 Landscape Similarity (%): 48.806

Perimeter (m): 3100.000 Edge Contrast (%): 19.137

Shape Index: 1.456 Fractal Dimension: 1.060

Core Area (ha): 10.977 Num Core Areas: 1

Core Area Index (%): 38.766 Near Neigh Dist (m): 49.497

Proximity Index: 285.044

Patch ID: 110 Patch Type: MLS

Area (ha): 51.273 Landscape Similarity (%): 48.806

Perimeter (m): 5720.000 Edge Contrast (%): 24.814

Shape Index: 1.997 Fractal Dimension: 1.105

Core Area (ha): 16.308 Num Core Areas: 2

Core Area Index (%): 31.806 Near Neigh Dist (m): 82.462

Proximity Index: 52.460

Patch ID: 104 Patch Type: MLS

Area (ha): 51.362 Landscape Similarity (%): 48.806

Perimeter (m): 7810.000 Edge Contrast (%): 17.213

Shape Index: 2.724 Fractal Dimension: 1.152

Core Area (ha): 11.623 Num Core Areas: 2

Core Area Index (%): 22.628 Near Neigh Dist (m): 25.000

Proximity Index: 200.342

Patch ID: 108 Patch Type: MLS

Area (ha): 8.248 Landscape Similarity (%): 48.806

Perimeter (m): 2390.000 Edge Contrast (%): 24.791

Shape Index: 2.081 Fractal Dimension: 1.129

Core Area (ha): 0.000 Num Core Areas: 0

67
Core Area Index (%): 0.000 Near Neigh Dist (m): 87.321

Proximity Index: 74.190

Patch ID: 107 Patch Type: MLS

Area (ha): 5.298 Landscape Similarity (%): 48.806

Perimeter (m): 1090.000 Edge Contrast (%): 20.578

Shape Index: 1.184 Fractal Dimension: 1.031

Core Area (ha): 0.255 Num Core Areas: 1

Core Area Index (%): 4.814 Near Neigh Dist (m): 25.000

Proximity Index: 832.616

CLASS INDICES

Patch Type: MLS Class Area (ha): 144.498

Total Area (ha): 296.068 Percent of Landscape (%): 48.806

Largest Patch Index (%): 17.348 Number Patches: 5

Patch Density (#/100 ha): 1.689 Mean Patch Size (ha): 28.899

Patch Size SD (ha): 19.945 Patch Size CV (%): 69.015

Total Edge (m): 19115.000 Edge Den (m/ha): 64.563

Con-Wght Edge Den (m/ha): 14.399 Total Edge Contrast (%): 19.470

Mean Edge Contrast (%): 21.307 Area-Wt Mean Edge Con(%): 20.843

Landscape Shape Index: 3.565 Mean Shape Index: 1.888

Area-Weighted Mean Shape: 2.125 Double Log Fractal: 1.551

Mean Patch Fractal: 1.096 Area-Weighted Mean Fractal: 1.112

Core % of Landscape (%): 13.228 Total Core Area (ha): 39.163

Number Core Areas: 6 Core Area Den (#/100 ha): 2.027

Mean Core Area 1 (ha): 7.832 Core Area SD 1 (ha): 6.555

Core Area CV 1 (%): 83.691 Mean Core Area 2 (ha): 6.527

Core Area SD 2 (ha): 6.658 Core Area CV 2 (%): 102.005

Total Core Area Index (%): 27.103 Mean Core Area Index (%): 19.603

Mean NearNeigh Dist (m): 53.856 Nearest Neighbor SD (m): 26.917

Nearest Neighbor CV (%): 49.979 Mean Prox Index: 288.930

Intersper/Juxtapos (%): 75.795

PATCH INDICES

Patch ID: 101 Patch Type: HLS

Area (ha): 33.065 Landscape Similarity (%): 14.464

Perimeter (m): 7190.000 Edge Contrast (%): 35.184

Shape Index: 3.126 Fractal Dimension: 1.179

Core Area (ha): 0.900 Num Core Areas: 1

Core Area Index (%): 2.722 Near Neigh Dist (m): 125.000

Proximity Index: 6.245

Patch ID: 106 Patch Type: HLS

Area (ha): 9.758 Landscape Similarity (%): 14.464

Perimeter (m): 2410.000 Edge Contrast (%): 5.747

Shape Index: 1.929 Fractal Dimension: 1.114

Core Area (ha): 0.275 Num Core Areas: 1

Core Area Index (%): 2.818 Near Neigh Dist (m): 125.000

Proximity Index: 21.162

CLASS INDICES

Patch Type: HLS Class Area (ha): 42.822

Total Area (ha): 296.068 Percent of Landscape (%): 14.464

Largest Patch Index (%): 11.168 Number Patches: 2

Patch Density (#/100 ha): 0.676 Mean Patch Size (ha): 21.411

Patch Size SD (ha): 11.654 Patch Size CV (%): 54.428

Total Edge (m): 9405.000 Edge Den (m/ha): 31.766

Con-Wght Edge Den (m/ha): 9.048 Total Edge Contrast (%): 27.294

Mean Edge Contrast (%): 20.465 Area-Wt Mean Edge Con(%): 28.476

Landscape Shape Index: 2.472 Mean Shape Index: 2.527

Area-Weighted Mean Shape: 2.853 Double Log Fractal: 1.791

68
Mean Patch Fractal: 1.147 Area-Weighted Mean Fractal: 1.165

Core % of Landscape (%): 0.397 Total Core Area (ha): 1.175

Number Core Areas: 2 Core Area Den (#/100 ha): 0.676

Mean Core Area 1 (ha): 0.587 Core Area SD 1 (ha): 0.312

Core Area CV 1 (%): 53.191 Mean Core Area 2 (ha): 0.587

Core Area SD 2 (ha): 0.312 Core Area CV 2 (%): 53.191

Total Core Area Index (%): 2.744 Mean Core Area Index (%): 2.770

Mean NearNeigh Dist (m): 125.000 Nearest Neighbor SD (m): 0.000

Nearest Neighbor CV (%): 0.000 Mean Prox Index: 13.703

Intersper/Juxtapos (%): 48.817

PATCH INDICES

Patch ID: 300 Patch Type: COS

Area (ha): 5.725 Landscape Similarity (%): 7.627

Perimeter (m): 1580.000 Edge Contrast (%): 51.902

Shape Index: 1.651 Fractal Dimension: 1.092

Core Area (ha): 0.000 Num Core Areas: 0

Core Area Index (%): 0.000 Near Neigh Dist (m): 155.081

Proximity Index: 7.008

Patch ID: 400 Patch Type: COS

Area (ha): 16.855 Landscape Similarity (%): 7.627

Perimeter (m): 2420.000 Edge Contrast (%): 43.157

Shape Index: 1.474 Fractal Dimension: 1.064

Core Area (ha): 3.830 Num Core Areas: 1

Core Area Index (%): 22.723 Near Neigh Dist (m): 155.081

Proximity Index: 2.380

CLASS INDICES

Patch Type: COS Class Area (ha): 22.580

Total Area (ha): 296.068 Percent of Landscape (%): 7.627

Largest Patch Index (%): 5.693 Number Patches: 2

Patch Density (#/100 ha): 0.676 Mean Patch Size (ha): 11.290

Patch Size SD (ha): 5.565 Patch Size CV (%): 49.291

Total Edge (m): 3630.000 Edge Den (m/ha): 12.261

Con-Wght Edge Den (m/ha): 6.676 Total Edge Contrast (%): 47.173

Mean Edge Contrast (%): 47.529 Area-Wt Mean Edge Con(%): 45.374

Landscape Shape Index: 1.659 Mean Shape Index: 1.562

Area-Weighted Mean Shape: 1.519 Double Log Fractal: 0.790

Mean Patch Fractal: 1.078 Area-Weighted Mean Fractal: 1.071

Core % of Landscape (%): 1.294 Total Core Area (ha): 3.830

Number Core Areas: 1 Core Area Den (#/100 ha): 0.338

Mean Core Area 1 (ha): 1.915 Core Area SD 1 (ha): 1.915

Core Area CV 1 (%): 100.000 Mean Core Area 2 (ha): 3.830

Core Area SD 2 (ha): 0.000 Core Area CV 2 (%): 0.000

Total Core Area Index (%): 16.962 Mean Core Area Index (%): 11.362

Mean NearNeigh Dist (m): 155.081 Nearest Neighbor SD (m): 0.000

Nearest Neighbor CV (%): 0.000 Mean Prox Index: 4.694

Intersper/Juxtapos (%): 54.242

PATCH INDICES

Patch ID: 103 Patch Type: CLS

Area (ha): 11.883 Landscape Similarity (%): 14.233

Perimeter (m): 3100.000 Edge Contrast (%): 4.742

Shape Index: 2.248 Fractal Dimension: 1.139

Core Area (ha): 0.000 Num Core Areas: 0

Core Area Index (%): 0.000 Near Neigh Dist (m): 220.511

Proximity Index: 0.000

Patch ID: 111 Patch Type: CLS

Area (ha): 2.390 Landscape Similarity (%): 14.233

69
Perimeter (m): 780.000 Edge Contrast (%): 13.269

Shape Index: 1.261 Fractal Dimension: 1.046

Core Area (ha): 0.000 Num Core Areas: 0

Core Area Index (%): 0.000 Near Neigh Dist (m): 313.050

Proximity Index: 0.000

Patch ID: 105 Patch Type: CLS

Area (ha): 20.610 Landscape Similarity (%): 14.233

Perimeter (m): 3810.000 Edge Contrast (%): 3.675

Shape Index: 2.098 Fractal Dimension: 1.121

Core Area (ha): 2.022 Num Core Areas: 1

Core Area Index (%): 9.813 Near Neigh Dist (m): 220.511

Proximity Index: 0.000

Patch ID: 109 Patch Type: CLS

Area (ha): 7.258 Landscape Similarity (%): 14.233

Perimeter (m): 2530.000 Edge Contrast (%): 27.419

Shape Index: 2.348 Fractal Dimension: 1.153

Core Area (ha): 0.000 Num Core Areas: 0

Core Area Index (%): 0.000 Near Neigh Dist (m): 313.050

Proximity Index: 0.000

CLASS INDICES

Patch Type: CLS Class Area (ha): 42.140

Total Area (ha): 296.068 Percent of Landscape (%): 14.233

Largest Patch Index (%): 6.961 Number Patches: 4

Patch Density (#/100 ha): 1.351 Mean Patch Size (ha): 10.535

Patch Size SD (ha): 6.716 Patch Size CV (%): 63.747

Total Edge (m): 10425.000 Edge Den (m/ha): 35.212

Con-Wght Edge Den (m/ha): 5.165 Total Edge Contrast (%): 13.509

Mean Edge Contrast (%): 12.276 Area-Wt Mean Edge Con(%): 8.609

Landscape Shape Index: 2.504 Mean Shape Index: 1.989

Area-Weighted Mean Shape: 2.136 Double Log Fractal: 1.598

Mean Patch Fractal: 1.115 Area-Weighted Mean Fractal: 1.127

Core % of Landscape (%): 0.683 Total Core Area (ha): 2.022

Number Core Areas: 1 Core Area Den (#/100 ha): 0.338

Mean Core Area 1 (ha): 0.506 Core Area SD 1 (ha): 0.876

Core Area CV 1 (%): 173.205 Mean Core Area 2 (ha): 2.023

Core Area SD 2 (ha): 0.000 Core Area CV 2 (%): 0.000

Total Core Area Index (%): 4.799 Mean Core Area Index (%): 2.453

Mean NearNeigh Dist (m): 266.780 Nearest Neighbor SD (m): 46.269

Nearest Neighbor CV (%): 17.344 Mean Prox Index: 0.000

Intersper/Juxtapos (%): 46.635

LANDSCAPE INDICES

Total Area (ha): 296.067

Largest Patch Index(%): 17.348

Number of patches: 17

Patch Density (#/100 ha): 5.742

Mean Patch Size (ha): 17.416

Patch Size Standard Dev (ha): 15.048

Patch Size Coeff of Variation (%): 86.405

Total Edge (m): 24880.000

Edge Density (m/ha): 84.035

Contrast-Weight Edge Density (m/ha): 26.647

Total Edge Contrast Index (%): 26.721

Mean Edge Contrast Index (%): 32.010

Area-Wght Mean Class Edge Contrast (%): 30.538

Landscape Shape Index: 4.290

Mean Shape Index: 1.813

Area-Weighted Mean Shape Index: 2.064

70
Double Log Fractal Dimension: 1.491

Mean Patch Fractal Dimension: 1.093

Area-Weighted Mean Fractal Dimension: 1.109

Total Core Area (ha): 57.565

Number of Core Areas: 13

Core Area Density (#/100 ha): 4.391

Mean Core Area 1 (ha): 3.386

Core Area Standard Dev 1 (ha): 4.897

Core Area Coeff of Variation 1 (%): 144.609

Mean Core Area 2 (ha): 4.428

Core Area Standard Dev 2 (ha): 5.171

Core Area Coeff of Variation 2 (%): 152.717

Total Core Area Index (%): 19.443

Mean Core Area Index (%): 11.852

Mean Nearest Neighbor (m): 155.359

Nearest Neighbor Standard Dev (m): 90.473

Nearest Neigh Coeff of Variation (%): 58.235

Mean Proximity Index: 87.144

Shannon’s Diversity Index: 1.503

Simpson’s Diversity Index: 0.704

Modified Simpson’s Diversity Index: 1.217

Patch Richness: 7

Patch Richness Density (#/100 ha): 2.364

Relative Patch Richness (%): 25.926

Shannon’s Evenness Index: 0.772

Simpson’s Evenness Index: 0.821

Modified Simpson’s Evenness Index: 0.626

Interspersion/Juxtaposition Index (%): 64.587

Contagion (%): 41.358

71
The following instructions provide the information required to install and run the vector

and raster versions of FRAGSTATS. The input parameters are described only briefly

here; read “FRAGSTATS Overview” to fully understand these guidelines and some

of the options. These instructions assume that users have working knowledge of the

UNIX operating environment.

Vector Version Requirements and limitations—The vector version of the program is an Arc/Info

AML. It was developed on a SUN workstation in a UNIX operating environment

using Arc/Info version 6.1; it will not run with earlier versions of Arc/Info. The AML

calls several C programs to perform functions that either are not available in AML

or are difficult to implement in AML. These C programs were compiled with the GNU

C compiler and may not compile with other compilers. Many loops in this AML go

from the minimum to the maximum patch type value. Is it, therefore, most efficient

if the patch type codes are sequential; for example, a coverage with 50 patch type

codes ranging from 1 to 50 would process much faster than one with 50 codes

scattered throughout the range 1000 to 2000. Because of limitations in Arc/Info (it

cannot calculate edge-to-edge distances), the vector version of FRAGSTATS does

not calculate nearest neighbor metrics. To compute these indices from a vector

image, the image must be rasterized first and then analyzed with the raster version of

FRAGSTATS. During the rasterization process, depending on the cell size selected, it

is possible for polygons to merge or divide. Considerable care, therefore, should be

exercised when rasterizing a vector image to ensure meaningful results. The

following instructions assume that users have working knowledge of Arc/Info.

Installation—To install FRAGSTATS from the DOS compatible diskette:

1. In DOS, load the FRAGSTATS diskette in your floppy drive, move to the directory

you want to install FRAGSTATS in, then type:

pkunzip -d a:\frag.zip

where “a:” should be replaced with the name of your 3.5-inch floppy drive. If your

system does not have a copy of the program “pkunzip,” copy the program from the

FRAGSTATS diskette, then issue the above command.

2. Three subdirectories will be created: vector, raster, and pcver. Move all the files

in the vector directory to the UNIX environment by using FTP or some other file

transfer utility.

3. In UNIX, move to the vector directory and rename the files fragstat.aml to

fragstats.aml (mv fragstat.aml fragstats.aml). (DOS shortens file names to eight

characters.)

4. In UNIX, rename the file fragstat.doc to fragstats.doc (mv fragstat.doc

fragstats.doc). This file contains the user guidelines for the vector version of

FRAGSTATS.

5. In UNIX, run the script “makeall” to build the C programs required by the

FRAGSTATS amls.

Running FRAGSTATS—To run FRAGSTATS in Arc/Info there is a single command

line, consisting of several arguments (each described below), issued from the arc

prompt as follows:

Appendix 2:

FRAGSTATS User

Guidelines

72
&run fragstats coverage out_file patchtype edge_dist [background]

[max_classes] [weight_file] [patch_id] [descriptor] [bound_wght]

[write_patch] [write_class] [path]

NOTE: If fragstats is run without the command line arguments, the user will be

prompted for all the necessary inputs.

NOTE: The first four parameters are required; the remaining nine parameters

in square brackets are optional; use a # in place of skipped OPTIONAL parameters; enter a carriage return for defaults.

NOTE: If an index is not calculated, a dot (“.”) will be output to the “basename.patch”, “basename.class”, and “basename.land” files. The abbreviation

“NA” will be output to the “basename.full” file.

Coverage {char}: The name of the input Arc/Info coverage. The coverage must be

built for polygons and lines. Acceptable landscape formats are discussed in

“FRAGSTATS Overview” (see fig. 2).

Out_file {char}: The basename for the output ASCII files. The extensions “.patch”,

“.class”, “.land”, and “.full” will be added to the basename. The output files contain

the following information:

basename.patch: each record contains all the patch indices for a given patch

separated by spaces.

basename.class: each record contains all the class indices for a given class

separated by spaces.

basename.land: each record contains all the landscape indices for a given

landscape separated by spaces.

basename.full: a file containing patch, class, and landscape indices for a given

landscape. This file is formatted for displaying results.

NOTE: The “basename.patch”, “basename.class”, and “basename.land” files are

in a format that should facilitate input to database management programs; they are

not intended for viewing results (records are very long). Also note that if the files

already exist, the information for a given landscape will be appended to the

existing files.

Patchtype {char}: The name of the numeric attribute containing patch type codes

(for example, an attribute “class” defined as 4,4,b that contains patch type codes

ranging from 1 to 50). Polygons with patch type codes greater than or equal to

zero are considered to be the landscape of interest. Polygons surrounding the

landscape can be included so that indices requiring adjacency information can

be calculated for polygons bordering the landscape boundary. These landscape

border polygons should be set to a negative patch type value (see fig. 2).

Edge_dist {float}: The distance from patch edge in meters to use for determining core

area (interior habitat). The core area of a patch is the area remaining after a buffer

“edge_dist” wide is removed from the edge of a patch.

73
Background {integer}: Optional; the patch type (class) value of patches to be ignored

in the input landscape [default is NONE]. Background polygons inside the landscape must have a positive patch type code. Background polygons in the landscape border must be set to the negative of the code used for the correponding

interior background polygons.

Max_classes {integer}: Optional; the maximum number of patch types (classes) that

could be present in the landscape [default is NONE]. This is needed for calculating

relative patch richness. If a value is not provided, relate patch richness will not be

calculated.

Weight_file {char}: Optional; the name of an ASCII file containing weights for each

combination of patch types (classes) [default is NONE]. Each record should

contain the numeric representation of two patch types and a weight, separated

by commas or spaces. For example:

1,2,.25

1,3,.32

2,3,.45 and so forth.

Weights represent the magnitude of edge contrast between adjacent patch types

and must range between 0 and 1 (0 = no contrast, 1 = maximum contrast). Edge

contrast weights are used to calculate several edge contrast indices. If the weight

file is not provided, these indices are not calculated. Background patch type codes

should not be included in this file.

Patch_id {char}: Optional; the name of an attribute that contains unique ID’s for each

polygon [default is “coverage”#]. If an attribute is not provided, the “coverage”#

attribute will be used.

Descriptor {char}: Optional; the name of an attribute that contains character descriptors for each patch type code (class) [default is NONE]. This attribute must be

defined as 10 characters or less and may not contain spaces. If provided, the

character descriptors will be written to the output files. Otherwise, the numeric

patch type codes will be written to the output files.

Bound_wght {float}: Optional; what proportion (equivalent to contrast weight) of the

landscape boundary and background class edges should be considered edge

[default is 0]? This affects all edge indices.

(0) none; do not count any boundary/background as edge (weight = 0).

(1) all; count all boundary/background as maximum-contrast edge (weight = 1).

(2) other; specify a fraction between 0 and 1.

If you specify a fraction between 0 and 1, then that proportion of the total edge

length involving the landscape boundary and any background class will be

included as edge in the metrics based on edge length (for example, total edge,

edge density). Also, that same fraction will be used as the edge contrast weight for

all edge segments involving the landscape boundary and background class in the

edge contrast metrics. See “FRAGSTATS Overview” for a more detailed

discussion.

74
Write_patch {y/n}: Optional; should patch indices be written to the output files [default

is YES]? If not, the “basename.patch” file will not be created and the patch indices

will not be written to the “basename.full” file.

Write_class {y/n}: Optional; should class indices be written to the output files [default

is YES]? If not, the “basename.class” file will not be created and the class indices

will not be written to the “basename.full” file.

Path {char}: Optional; the name of the directory containing the FRAGSTATS AML’s

and C programs [default is the current directory]. If these are in a directory other

than the one the user is running FRAGSTATS from, the user must set

&AMLPATH prior to running FRAGSTATS.

Raster Version Requirements and limitations—The raster version of the program was developed

on a SUN workstation in the UNIX operating environment. It is written in C and

compiled with the GNU C compiler and may not compile with other C compilers. In

this version of FRAGSTATS the input landscape file and the patch ID file are stored

as signed shorts (16 bits). A landscape, therefore, may not contain more than 32,767

different patch types (this shouldn’t be a problem!). The input (or output) patch ID

image is also limited to 32,767 unique ID’s. On DEC or IBM machines, the option

of inputting an Arc/Info SVF file (see below) does not work, owing to the different

architectures of these machines and SUNs.

The UNIX raster version of FRAGSTATS also has been compiled to run in the DOS

environment on a personal computer (PC). The PC version of FRAGSTATS will run

only on a 386 or better machine. A math coprocessor also is required. It should run

under DOS or Windows. FRAGSTATS will use disk space to allocate virtual memory.

The environmental variable TEMP must be set to tell the program where to allocate

the swap file (for example, SET TEMP=C:\tmp). Otherwise, the PC version of

FRAGSTATS is run exactly the same way as the UNIX version (see guidelines

below). Be aware that the PC version of FRAGSTATS may not run successfully

on very large and complex landscapes owing to memory limitations of the PC.

Installation—To install FRAGSTATS from the DOS compatible diskette:

1. In DOS, load the FRAGSTATS diskette in your floppy drive, move to the directory

you want to install FRAGSTATS in, then type:

pkunzip -d a:\frag.zip

where “a:” should be replaced with the name of your 3.5-inch floppy drive. If your

system does not have a copy of the program “pkunzip,” copy the program from the

FRAGSTATS diskette, then issue the above command.

2. Three subdirectories will be created: vector, raster, and pcver. Move all the files in

the raster directory to the UNIX environment by using FTP or some other file transfer

utility.

3. In UNIX, move to the raster directory and rename the file fragstat.c to fragstats.c

(mv fragstat.c fragstats.c). (DOS shortens file names to eight characters.)

4. In UNIX, rename the file fragstat.doc to fragstats.doc (mv fragstat.doc

fragstats.doc). This file contains the user guidelines for the raster version of

FRAGSTATS.

75
5. In UNIX, rename the file fragstat.mak to fragstats.make (mv fragstat.mak

fragstats.make).

6. In UNIX, build FRAGSTATS with the command “make -f fragstats.make.”

NOTE: The DOS version of FRAGSTATS does not require any installation.

Running FRAGSTATS—To run FRAGSTATS there is a single command line,

consisting of several arguments (each described below), issued from the prompt,

as follows:

fragstats in_image out_file cellsize edge_dist data_type [rows] [cols]

[background] [max_classes] [weight_file] [id_image] [desc_file]

[bound_wght] [diags] [prox_dist] [nndist] [patch_stats] [class_stats]

NOTE: If fragstats is run without the command line arguments, the user will

be prompted for all the necessary inputs.

NOTE: The first five parameters are required; the remaining 13 parameters

in square parentheses are optional; use a $ in place of skipped OPTIONAL

parameters.

NOTE: If an index is not calculated, a dot (“.”) will be output to the

“basename.patch”, “basename.class”, and “basename.land” files. The

abbreviation “NA” will be output to the “basename.full” file. For nearest

neighbor distance, if a patch has no neighbors, “NONE” will be output to

“basename.full” and a dot to the other files.

In_image {char}: The name of the input landscape file. File formats are discussed

under data_type below and in “FRAGSTATS Overview” (see fig. 3). Patches outside the landscape boundary can be included so that indices requiring adjacency

information can be calculated for patches bordering the landscape boundary; these

landscape border patches should be set to a negative class value.

Out_file {char}: Basename for output ASCII files. The extensions .patch, .class, .land,

and .full will be added to the basename. Note that in the PC version, the

extensions have been shortened to .pat, .cla, .lnd (not .lan to avoid conflict with

ERDAS file name extensions), and .ful to comply with DOS requirements. The

output files contain the following information:

basename.patch: each record contains all the patch indices for a given patch

separated by spaces.

basename.class: each record contains all the class indices for a given class

separated by spaces.

basename.land: each record contains all the landscape indices for a given

landscape separated by spaces.

basename.full: a file containing patch, class, and landscape indices for a given

landscape. This file is formatted for displaying results.

NOTE: The “basename.patch”, “basename.class” and “basename.land” files are

in a format that should facilitate input to database management programs; they are

not intended for viewing results (records are very long). Also note that if the files

already exist, the information for a given landscape will be appended to the

existing files.

76
Cellsize {float}: The size of cells in meters in the input image. Cells must be square.

The length of one side of a cell should be input.

Edge_dist {float}: The distance from patch edge in meters used to determine core

area (interior habitat). The core area of a patch is the area remaining after a buffer

“edge_dist” wide is removed from the edge of a patch.

Data_type {integer}: The type of input image file, as follows:

1. SVF file; this is a file created with the Arc/Info “gridsvf” command.

2. ASCII file, no header. Each record should contain one image row. Cell values

should be separated by a comma or a space(s).

3. 8-bit binary file, no header.

4. 16-bit binary file, no header.

5. ERDAS image files (4, 8, or 16 bit), not IMAGINE images.

6. IDRISI image files.

Rows {integer}: Optional; the number of rows in the input image. This is only required

if data_type is 2, 3, or 4.

Cols {integer}: Optional; the number of columns in the input image. This is only

required if data_type is 2, 3, or 4.

Background {integer}: Optional; the value of background cells [default is NONE]. This

is required only if there are cells interior or exterior to the landscape of interest that

should be ignored (see fig. 3).

Background patch cells inside the landscape should have a positive patch type

value. Background cells in the landscape border and outside the area of interest

should be set to a negative patch type value (the negative of the value used for

interior background patch cells). The user must enter a positive value for background even if the landscape contains only exterior (negative) background cells.

Sometimes this convention is difficult to follow. If only one type of background

is found in the image (only interior [positive] or only exterior [negative]),

FRAGSTATS will verify that each patch has been classified correctly. If

FRAGSTATS finds that an interior background patch has been classified

incorrectly as exterior background, it will be reclassified as interior background,

and a message will be issued. Incorrectly classified exterior background patches

also will be reclassified as exterior, if necessary. A warning will be issued about

any questionable patches (for example, background patches along the landscape

boundary).

If background patches along the landscape boundary are not classified correctly,

the following class and landscape indices may not be calculated accurately: landscape shape index, total edge, edge density, contrast weighted edge density, and

total edge contrast index.

Max_classes {integer}: Optional; the maximum number of patch types (classes) that

could be present in the landscape [default is NONE]. This is needed for calculating

relative patch richness. If a value is not provided, relative patch richness will not

be calculated.

77
Weight_file {char}: Optional; the name of an ASCII file containing weights for each

combination of patch types (classes) [default is NONE]. Each record should

contain the numeric representation of two patch types and a weight, separated

by commas or spaces. For example:

1,2,.25

1,3,.32

2,3,.45 and so forth.

Weights represent the magnitude of edge contrast between adjacent patch types

and must range between 0 and 1 (0 = no contrast, 1 = maximum contrast). Edge

contrast weights are used to calculate several edge contrast indices. If the weight

file is not provided, these indices are not calculated. Background patch type codes

should not be included in this file.

Id_image: Optional {char}; the method for assigning patch ID’s to each patch in the

landscape [default is 2]. Input 1, 2, or the name of a file, as follows:

1. Create and output an image that contains unique ID’s for each patch. This

allows the user to relate a set of patch statistics to a specific patch in the

landscape, if another user-specified ID image is not specified (option 3). This

file is named “in_image”.ID and is the same “data_type” as “in_image”.

2. Do not output an ID image (because it is not important to relate a set of patch

statistics to a specific patch in the landscape).

3. The name of an ID image to read. The ID associated with each patch in this

image will be written to the output files. The “data_type” of this file must be the

same as “in_image”.

Desc_file: Optional {char}; the name of an ASCII file containing character descriptors

for each patch type (class) [default is NONE]. Each record in the file should

contain a numeric patch type value and the character descriptor for that patch

type, separated by a comma or space(s). For example:

1 shrubs

2 conifers

3 deciduous

Descriptive names cannot contain spaces. Use an underscore (“_”) or a hyphen

(“-”) in place of blanks. The parameter max_label_length, in the file stats.h,

controls the printed length of labels in the output files. FRAGSTATS is distributed

with max_label_length set to 10. To change this, edit the file stats.h, change the

parameter to the desired length, then rebuild FRAGSTATS. If max_label_length

exceeds 22, the columns will not be aligned in the file “basename”.full. If this

descriptor file is provided, the character descriptors will be written to the output

files. Otherwise, the numeric patch type codes will be written to the output files.

78
Bound_wght {float}: Optional; what proportion (equivalent to contrast weight) of the

landscape boundary and background class edges should be considered edge

[default is 0]? This affects all edge indices.

(0) none; do not count any boundary/background as edge (weight = 0).

(1) all; count all boundary/background as maximum-contrast edge (weight = 1).

(2) other; specify a fraction between 0 and 1.

If you specify a fraction between 0 and 1, then that proportion of the total edge

length involving the landscape boundary and any background class will be

included as edge in the metrics based on edge length (for example, total edge,

edge density). Also, that same fraction will be used as the edge contrast weight for

all edge segments involving the landscape boundary and background class

in the edge contrast metrics. See “FRAGSTATS Overview” for a more detailed

discussion.

Diags: Optional {y/n}; should diagonal neighbors be evaluated when finding the

cells that make up a patch [default is YES]? If not, then the four cells (not eight)

surrounding the cell of interest will be evaluated.

Prox_dist: Optional {float}; the search radius in meters to use for calculating the proximity indices [default is NONE]. If a value is not provided, the proximity indices will

not be calculated. Note that “nndist” (below) must be “yes” if the proximity indices

are to be calculated because they require the same calculations.

Nndist: Optional {y/n}; should indices based on nearest neighbor distance be calculated [default in YES]? This can be very time consuming for landscapes with

hundreds of patches per class. This parameter must be “yes” if the proximity

indices are to be calculated because they require the same calculations.

Patch_stats: Optional {y/n}; should patch indices be written to the output files [default

is YES]? If not, the “basename.patch” file will not be created and the patch indices

will not be written to the “basename.full” file.

Class_stats: Optional {y/n}; should class indices be written to the output files [default

is YES]? If not, the “basename.class” file will not be created and the class indices

will not be written to the “basename.full” file.

79
In this section, each metric computed in FRAGSTATS is described. Metrics are

grouped into patch, class, and landscape indices. Within each group, metrics are

ordered in logical fashion according to the aspect of landscape structure measured.

For example, the core area metrics (that is, those based on core area measurements)

are grouped together. Each metric is defined in mathematical terms, and the measurement units and theoretical range in values are reported. The acronym for the

metric given on the left side of the equation is the field name used in the ASCII

output files. Where the vector and raster algorithms differ, we define both. A single

notation scheme is used consistently for all metrics (table 2). To facilitate interpretation of the algorithm, we intentionally separate from each equation any constants

used to rescale the metric. For example, in many cases the right side of the equation

is multiplied by 100 to convert a proportion to a percentage, or multiplied or divided

by 10,000 to convert square meters to hectares. These conversion factors are

separated out by parentheses even though they may be factored into the equation

differently in the computational form of the algorithm. For each metric, the mathematical formula is described in narrative terms to facilitate interpretation of the

formula.

Appendix 3:

Definition and

Description of

FRAGSTATS Metrics

Table 2—Notation used in FRAGSTATS algorithms

Term Definition

Subscripts:

i 1, ... , m or m′ patch types (classes)

j 1, ... , n patches

k 1, ... , m or m′ patch types (classes)

q 1, ... , p disjunct core areas

s 1, ... , n patches, within specified neighborhood

Symbols:

A Total landscape area (m2

)

aij Area (m2

) of patch ij

aijs Area (m2

) of patch ijs within specified neighborhood (m) of patch ij

aij

c Core area (m2

) of patch ij based on specified buffer width (m)

aijqc Area (m2

) of disjunct core area q in patch ij based on specified buffer

width (m)

pij Perimeter (m) of patch ij

pijk Length (m) of edge of patch ij adjacent to patch type (class) k

E Total length (m) of edge in landscape; includes landscape boundary

and background edge segments if the user decides to treat boundary

and background as edge; otherwise, only boundary segments representing true edge are included

80
Table 2—Notation used in FRAGSTATS algorithms (continued)

Term Definition

E′ Total length (m) of edge in landscape; includes entire landscape

boundary and background edge segments regardless of whether they

represent true edge

eik Total length (m) of edge in landscape between patch types (classes) i

and k; includes landscape boundary segments representing tree edge

only involving patch type i

e′ik Total length (m) of edge in landscape between patch types (classes) i

and k; includes all landscape boundary and background edge segments

involving patch type i, regardless of whether they represent true edge

e′′ik Total length (m) of edge in landscape between patch types (classes) i

and k; includes the entire landscape boundary and background edge

segments, regardless of whether they represent true edge

dik Dissimilarity (edge contrast weight) between patch types i and k

N Total number of patches in the landscape, excluding any background

patches

N′ Total number of patches in the landscape that have nearest neighbors

n=ni Number of patches in the landscape of patch type (class) i

n′ = n′i Number of patches in the landscape of patch type (class) i that have

nearest neighbors

nij

c Number of disjunct core areas in patch ij based on specified buffer

width (m)

m Number of patch types (classes) present in the landscape, excluding

the landscape border if present

m′ Number of patch types (classes) present in the landscape, including the

landscape border if present

mmax Maximum number of patch types (classes) present in a landscape

hij Distance (m) from patch ij to nearest neighboring patch of the same

type (class), based on edge-to-edge distance

hijs Distance (m) between patch ijs [located within specified neighborhood

distance (m) of patch ij] and patch ij, based on edge-to-edge distance

gik Number of adjacencies (joins) between pixels of patch types (classes)

i and k

Pi Proportion of the landscape occupied by patch type (class) i

81
Patch Indices (P1) Landscape ID

The first field in the patch output file is landscape ID (LID). Landscape ID is set to

the name of the input coverage (coverage) in the vector version and the name of

the input image (in_image) in the raster version.

(P2) Patch ID

The second field in the patch output file is patch ID (PID). The vector version of

FRAGSTATS contains an option (patch_id) to name an attribute that contains

unique ID’s for each patch. If an attribute is not specified, the “coverage” # attribute

is used. Likewise, the raster version of FRAGSTATS contains an option (id_image)

to name an image that contains unique ID’s for each patch. If an image is not specified, FRAGSTATS will create unique ID’s for each patch and optionally produce an

image that contains patch ID’s that correspond to the FRAGSTATS output.

(P3) Patch Type

The third field in the patch output file is patch type (TYPE). The vector version

of FRAGSTATS contains an option (descriptor) to name an attribute that contains character descriptors for each patch type. Likewise, the raster version of

FRAGSTATS contains an option (desc_file) to name an ASCII file that contains

character descriptors for each patch type. In both versions, if the patch type options

are not used, FRAGSTATS will write the numeric patch type codes to TYPE.

(P4) Area

Vector/Raster

AREA = aij







1

10,000







Units: Hectares.

Range: AREA > 0, without limit.

The range in AREA is limited by the grain and extent of the image, and in a particular application, AREA may be further limited by the specification of a minimum

patch size that is larger than the grain.

Description: AREA equals the area (m2

) of the patch, divided by 10,000 (to convert

to hectares).

(P5) Landscape Similarity Index

Vector/Raster

LSIM = Pi =

∑

j=1

n

aij

A (100)

Units: Percent.

Range: 0 < LSIM ≤ 100.

LSIM approaches 0 when the corresponding patch type (class) becomes increasingly

rare in the landscape. LSIM = 100 when the entire landscape consists of the corresponding patch type; that is, when the entire image is comprised of a single patch.

82
Description: LSIM equals total class area (m2

) divided by total landscape area (m2),

multiplied by 100 (to convert to a percentage); in other words, LSIM equals the

percentage of the landscape comprised of the corresponding patch type. Note that

LSIM is equivalent to %LAND at the class level.

(P6) Perimeter

Vector/Raster

PERIM = pij

Units: Meters.

Range: PERIM > 0, without limit.

Description: PERIM equals the perimeter (m) of the patch, including any internal

holes in the patch.

(P7) Edge Contrast Index

Vector/Raster

EDGECON =

∑

k=1

m′

(pijk o dik)

pij (100)

Units: Percent.

Range: 0 ≤ EDGECON ≤ 100.

EDGECON = 0 if the landscape consists of only 1 patch and either the landscape

boundary contains no edge (when a border is present) or the boundary is not to be

treated as edge (when a border is absent). Also, EDGECON = 0 when all the patch

perimeter segments involve patch type adjacencies that have been given a zerocontrast weight in the edge contrast weight file. EDGECON = 100 when the entire

patch perimeter is maximum-contrast edge (d = 1). EDGECON < 100 when a portion

of the patch perimeter is less than maximum-contrast edge (d < 1). EDGECON is

reported as “NA” in the “basename”.full file and a dot “.” in the “basename”.patch

file if a contrast weight file is not specified by the user.

Description: EDGECON equals the sum of the patch perimeter segment lengths (m)

multiplied by their corresponding contrast weights, divided by total patch perimeter

(m), multiplied by 100 (to convert to a percentage). Any perimeter segment along the

landscape boundary (if a border is absent) or bordering background is assigned the

edge contrast weight specified by the user (see bound_wght option).

(P8) Shape Index

Vector Raster

SHAPE = pij

2√ π o aij

SHAPE = 0.25 pij

√aij

Units: None.

Range: SHAPE ≥ 1, without limit.

SHAPE = 1 when the patch is circular (vector) or square (raster) and increases

without limit as patch shape becomes more irregular.

83
Description: SHAPE equals patch perimeter (m) divided by the square root of patch

area (m2), adjusted by a constant to adjust for a circular standard (vector) or square

standard (raster).

(P9) Fractal Dimension

Vector Raster

FRACT = 2 In pij

In aij

FRACT = 2 In (0.25 pij)

In aij

Units: None.

Range: 1 ≤ FRACT ≤ 2.

A fractal dimension greater than 1 for a 2-dimensional patch indicates a departure

from euclidean geometry (that is, an increase in shape complexity). FRACT approaches 1 for shapes with very simple perimeters such as circles or squares, and

approaches 2 for shapes with highly convoluted, plane-filling perimeters. If patch

area is 1 m2 (thus, the denominator is 0) and the perimeter is 3.545 m in vector

and 4 m in raster, then FRACT = 1; otherwise, FRACT is reported as “NA” in the

“basename”.full file and as a dot “.” in the “basename”.patch file.

Description: FRACT equals 2 times the logarithm of patch perimeter (m) divided

by the logarithm of patch area (m2

); the raster formula is adjusted to correct for the

bias in perimeter (Li 1990).

(P10) Core Area

Vector/Raster

CORE = aij

c 





1

10,000







Units: Hectares.

Range: CORE ≥ 0, without limit.

CORE = 0 when every location within the patch is within the specified edge distance from the patch perimeter (that is, edge width). CORE approaches AREA as

the specified edge distance decreases and as patch shape is simplified.

Description: CORE equals the area (m2

) within the patch that is further than the

specified edge distance from the patch perimeter, divided by 10,000 (to convert to

hectares). Note that raster version of FRAGSTATS employs the 4-neighbor approach

when determining which cells are core and which are in the edge buffer.

(P11) Number of Core Areas

Vector/Raster

NCORE = nij

c

Units: None.

Range: NCORE ≥ 0, without limit.

NCORE = 0 when CORE = 0 (that is, every location within the patch is within the

specified edge distance from the patch perimeter [edge width]). NCORE > 1 when,

because of shape, the patch contains disjunct core areas.

84
Description: NCORE equals the number of disjunct core areas contained within the

patch boundary.

(P12) Core Area Index

Vector/Raster

CAI = aij

c

aij (100)

Units: Percent.

Range: 0 ≤ CAI < 100.

CAI = 0 when CORE = 0 (that is, every location within the patch is within the specified edge distance from the patch perimeter [edge width]); that is, when the patch

contains no core area. CAI approaches 100 when the patch, because of size, shape,

and edge width, contains mostly core area.

Description: CAI equals the patch core area (m2

) divided by total patch area (m2),

multiplied by 100 (to convert to a percentage); in other words, CAI equals the

percentage of a patch that is core area.

(P13) Nearest Neighbor Distance

Raster

NEAR = hij

Units: Meters.

Range: NEAR > 0, without limit.

NEAR is reported as “None” in the “basename.full” output file and a dot in the

“basename.patch” output file if no other patch of the same type exists in the

landscape.

Description: NEAR equals the distance (m) to the nearest neighboring patch of

the same type, based on shortest edge-to-edge distance.

(P14) Proximity Index

Raster

PROXIM = ∑

s=1

n aijs

hijs

2

Units: None.

Range: PROXIM ≥ 0.

PROXIM = 0 if a patch has no neighbors of the same patch type within the specified

search radius. PROXIM increases as the neighborhood (defined by the specified

search radius) is increasingly occupied by patches of the same type and as those

patches become closer and more contiguous and less fragmented in distribution.

The upper limit of PROXIM is affected by the search radius and minimum distance

between patches. PROXIM is reported as “NA” in the “basename”.full file and a dot

“.” in the “basename”.patch file if a search radius is not specified by the user.

85
Description: PROXIM equals the sum of patch area (m2

) divided by the nearest

edge-to-edge distance squared (m2) between the patch and the focal patch of all

patches of the corresponding patch type whose edges are within a specified distance

(m) of the focal patch. Note, when the search buffer extends beyond the landscape

boundary, only patches contained within the landscape are considered in the

computations.

Class Indices (C1) Landscape ID (LID)

The first field in the class output file is landscape ID (LID); it is defined as in the

patch output file (see previous discussion).

(C2) Patch Type (TYPE)

The second field in the class output file is patch type (TYPE); it is defined as in the

patch output file (see previous discussion).

(C3) Class Area

Vector/Raster

CA = ∑

j=1

n

aij







1

10,000







Units: Hectares.

Range: CA > 0, without limit.

CA approaches 0 as the patch type becomes increasing rare in the landscape. CA =

TA when the entire landscape consists of a single patch type; that is, when the entire

image is comprised of a single patch.

Description: CA equals the sum of the areas (m2

) of all patches of the corresponding

patch type, divided by 10,000 (to convert to hectares); that is, total class area.

(C4) Total Landscape Area

Vector/Raster

TA = A





1

10,000







Units: Hectares.

Range: TA > 0, without limit.

Description: TA equals the area (m2

) of the landscape, divided by 10,000 (to convert

to hectares). TA excludes the area of any background patches within the landscape.

(C5) Percentage of Landscape

Vector/Raster

%LAND = Pi =

∑

j=1

n

aij

A (100)

Units: Percent.

86
Range: 0 < %LAND ≤ 100.

%LAND approaches 0 when the corresponding patch type (class) becomes increasingly rare in the landscape. %LAND = 100 when the entire landscape consists of a

single patch type; that is, when the entire image is comprised of a single patch.

Description: %LAND equals the sum of the areas (m2

) of all patches of the corresponding patch type, divided by total landscape area (m2

), multiplied by 100 (to

convert to a percentage); in other words, %LAND equals the percentage the landscape comprised of the corresponding patch type. Note that %LAND is equivalent

to LSIM at the patch level.

(C6) Largest Patch Index

Vector/Raster

LPI =

n

max(aij)

j=1

A (100)

Units: Percent.

Range: 0 < LPI ≤ 100.

LPI approaches 0 when the largest patch of the corresponding patch type becomes

increasingly smaller. LPI = 100 when the entire landscape consists of a single patch

of the corresponding patch type; that is, when the largest patch comprises 100% of

the landscape.

Description: LPI equals the area (m2

) of the largest patch of the corresponding

patch type divided by total landscape area (m2

), multiplied by 100 (to convert to a

percentage); in other words, LPI equals the percentage of the landscape comprised

by the largest patch.

(C7) Number of Patches

Vector/Raster

NP = ni

Units: None.

Range: NP ≥ 1, without limit.

NP = 1 when the landscape contains only 1 patch of the corresponding patch type;

that is, when the class consists of a single patch.

Description: NP equals the number of patches of the corresponding patch type

(class).

(C8) Patch Density

Vector/Raster

PD = ni

A (10,000)(100)

Units: Number per 100 hectares.

Range: PD > 0, without limit.

87
Description: PD equals the number of patches of the corresponding patch type (NP)

divided by total landscape area, multiplied by 10,000 and 100 (to convert to 100

hectares).

(C9) Mean Patch Size

Vector/Raster

MPS =

∑

j=1

n

aij

ni







1

10,000







Units: Hectares.

Range: MPS > 0, without limit.

The range in MPS is limited by the grain and extent of the image and the minimum

patch size in the same manner as patch area (AREA).

Description: MPS equals the sum of the areas (m2

) of all patches of the corresponding patch type, divided by the number of patches of the same type, divided

by 10,000 (to convert to hectares).

(C10) Patch Size Standard Deviation

Vector/Raster

Units: Hectares.

Range: PSSD ≥ 0, without limit.

PSSD = 0 when all patches in the class are the same size or when there is only

1 patch (that is, no variability in patch size).

Description: PSSD equals the square root of the sum of the squared deviations of

each patch area (m2

) from the mean patch size of the corresponding patch type,

divided by the number of patches of the same type, divided by 10,000 (to convert

to hectares); that is, the root mean squared error (deviation from the mean) in patch

size. This is the population standard deviation, not the sample standard deviation.

(C11) Patch Size Coefficient of Variation

Vector/Raster

PSCV = PSSD

MPS (100)

Units: Percent.

Range: PSCV ≥ 0, without limit.

PSSD

a

a

n

n

1

10,000

ij

ij

j 1

n

i j 1

n

2

i

=

−

F

H

G

G

G

G

G

I

K

J

J

J

J

J

L

N

M

M

M

M

M

M

O

Q

P

P

P

P

P

P F

H

G I

K

J

=

=

∑

∑

88
Description: PSCV equals the standard deviation in patch size (PSSD) divided by

the mean patch size of the corresponding patch type (MPS), multiplied by 100 (to

convert to percent); that is, the variability in patch size relative to the mean patch

size. This is the population coefficient of variation, not the sample coefficient of

variation.

(C12) Total Edge

Vector/Raster

TE = ∑

k=1

m′

eik

Units: Meters.

Range: TE ≥ 0, without limit.

TE = 0 when there is no class edge in the landscape; that is, when the entire landscape, and landscape border, if present, consists of the corresponding patch type

and the user specifies that none of the landscape boundary and background edge

be treated as edge.

Description: TE equals the sum of the lengths (m) of all edge segments involving the

corresponding patch type. If a landscape border is present, TE includes landscape

boundary segments involving the corresponding patch type and representing true

edge only (that is, contrast weight > 0). If a landscape border is absent, TE includes

a user-specified proportion of landscape boundary segments involving the corresponding patch type. Regardless of whether a landscape border is present or not,

TE includes a user-specified proportion of background edge segments involving the

corresponding patch type.

(C13) Edge Density

Vector/Raster

ED =

∑

k=1

m′

eik

A (10,000)

Units: Meters per hectare.

Range: ED ≥ 0, without limit.

ED = 0 when there is no class edge in the landscape; that is, when the entire

landscape and landscape border, if present, consists of the corresponding patch

type and the user specifies that none of the landscape boundary and background

edge be treated as edge.

Description: ED equals the sum of the lengths (m) of all edge segments involving

the corresponding patch type, divided by the total landscape area (m2

), multiplied

by 10,000 (to convert to hectares). If a landscape border is present, ED includes

landscape boundary segments involving the corresponding patch type and representing true edge only (that is, contrast weight > 0). If a landscape border is absent,

89
ED includes a user-specified proportion of landscape boundary segments involving

the corresponding patch type. Regardless of whether a landscape border is present

or not, ED includes a user-specified proportion of background edge segments

involving the corresponding patch type.

(C14) Contrast-Weighted Edge Density

Vector/Raster

CWED =

∑

k=1

m′

(eik o dik)

A (10,000)

Units: Meters per hectare.

Range: CWED ≥ 0, without limit.

CWED = 0 when there is no class edge in the landscape; that is, when the entire

landscape and landscape border, if present, consists of the corresponding patch type

and the user specifies that none of the landscape boundary and background edge

be treated as edge. CWED increases as the amount of class edge in the landscape

increases or as the contrast in edges involving the corresponding patch type increases (that is, contrast weight approaches 1), or both. CWED is reported as “NA”

in the “basename”.full file and as a dot “.” in the “basename”.class file if a contrast

weight file is not specified by the user.

Description: CWED equals the sum of the lengths (m) of each edge segment involving the corresponding patch type multiplied by the corresponding contrast weight,

divided by the total landscape area (m2

), multiplied by 10,000 (to convert to hectares). If a landscape border is present, CWED includes landscape boundary segments involving the corresponding patch type and representing true edge only (that

is, contrast weight > 0). If a landscape border is absent, all landscape boundary edge

segments involving the corresponding patch type are assigned the edge contrast

weight specified by the user (see bound_wght option). This is equivalent to treating

the specified proportion of all boundary edge segments involving the corresponding

patch type as maximum-contrast edge. Regardless of whether a landscape border is

present or not, all background edge segments involving the corresponding patch type

are assigned the edge contrast weight specified by the user. Again, this is equivalent

to treating the specified proportion of all background edge segments involving the

corresponding patch type as maximum-contrast edge.

(C15) Total Edge Contrast Index

Vector/Raster

TECI =

∑

k=1

m′

(eik o dik)

∑

k=1

m′

eik

′

(100)

Units: Percent.

Range: 0 ≤ TECI ≤ 100.

90
TECI = 0 when there is no class edge in the landscape; that is, when the entire

landscape and landscape border, if present, consists of the corresponding patch

type and the user specifies that none of the landscape boundary and background

edge be treated as edge. TECI approaches 0 as the contrast in edges involving the

corresponding patch type lessen (that is, contrast weight approaches 0). TECI = 100

when all class edge is maximum contrast (that is, contrast weight = 1). TECI is reported as “NA” in the “basename”.full file and as a dot “.” in the “basename”.class

file if a contrast weight file is not specified by the user.

Description: TECI equals the sum of the lengths (m) of each edge segment involving

the corresponding patch type multiplied by the corresponding contrast weight, divided

by the sum of the lengths (m) of all edge segments involving the same type, multiplied by 100 (to convert to a percentage). In the numerator, if a landscape border is

present, all edge segments along the landscape boundary involving the corresponding

patch type are treated according to their edge contrast weights as designated in the

contrast weight file. If a landscape border is absent, all landscape boundary segments

involving the corresponding patch type are assigned the edge contrast weight specified by the user (see bound_wght option). This is equivalent to treating the specified

proportion of all boundary edge segments involving the corresponding patch type as

maximum-contrast edge and the remainder as zero-contrast edge. Regardless of

whether a landscape border is present or not, all background edge segments involving the corresponding patch type are assigned the edge contrast weight specified

by the user. Again, note that this is equivalent to treating the specified proportion of

all background edge segments involving the corresponding patch type as maximumcontrast edge and the remainder as zero-contrast edge. In the denominator, all edges

involving the corresponding patch type are included, including the landscape boundary and background edge segments, regardless of whether they represent true edge

or not or how the user chooses to handle boundary and background edges.

(C16) Mean Edge Contrast Index

Vector/Raster

MECI =

∑

j=1

n















∑

k=1

m′

(pijk o dik)

pij















ni (100)

Units: Percent.

Range: 0 ≤ MECI ≤ 100.

MECI = 0 when there is no class edge in the landscape; that is, when the entire

landscape, and landscape border, if present, consists of the corresponding patch

type and the user specifies that none of the landscape boundary and background

edge be treated as edge. MECI approaches 0 as the contrast in edges involving the

corresponding patch type lessen (that is, contrast weight approaches 0). MECI =

100 when all class edge is maximum contrast (that is, contrast weight = 1). MECI is

reported as “NA” in the “basename”.full file and as a dot “.” in the “basename”.class

file if a contrast weight file is not specified by the user.

91
Description: MECI equals the sum of the segment lengths (m) of each patches’

perimeter multiplied by their corresponding contrast weights, divided by total patch

perimeter (m), summed across all patches of the corresponding patch type, divided

by the number of patches of the same type, multiplied by 100 (to convert to a percentage). If a landscape border is present, any patch perimeter segments along the

landscape boundary are treated according to their edge contrast weights as designated in the contrast weight file. If a landscape border is absent, any patch perimeter

segments along the landscape boundary are assigned the edge contrast weight

specified by the user (see bound_wght option). Regardless of whether a landscape

border is present or not, all patch perimeter segments bordering background are

assigned the edge contrast weight specified by the user.

(C17) Area-Weighted Mean Edge Contrast Index

Vector/Raster

AWMECI = ∑

j=1

n

































∑

k=1

m′

(pijk o dik)

pij





























aij

∑

j=1

n

aij

































(100)

Units: Percent.

Range: 0 ≤ AWMECI ≤ 100.

AWMECI = 0 when there is no class edge in the landscape; that is, when the entire

landscape, and landscape border, if present, consists of the corresponding patch

type and the user specifies that none of the landscape boundary and background

edge be treated as edge. AWMECI approaches 0 as the contrast in edges involving the corresponding patch type lessen (that is, contrast weight approaches 0).

AWMECI = 100 when all class edge is maximum contrast (that is, contrast weight

= 1). AWMECI is reported as “NA” in the “basename”.full file and as a dot “.” in the

“basename”.class file if a contrast weight file is not specified by the user.

Description: AWMECI equals the sum of the segment lengths (m) of each patches’

perimeter multiplied by their corresponding contrast weights, divided by total patch

perimeter (m), multiplied by patch area (m2

) divided by the sum of patch areas,

summed across all patches of the corresponding patch type, multiplied by 100 (to

convert to a percentage). If a landscape border is present, any patch perimeter segments along the landscape boundary are treated according to their edge contrast

weights as designated in the contrast weight file. If a landscape border is absent

any patch perimeter segments along the landscape boundary are assigned the

edge contrast weight specified by the user (see bound_wght option). Regardless

of whether a landscape border is present or not, all patch perimeter segments

bordering background are assigned the edge contrast weight specified by the

user. AWMECI is similar to MECI except that each patch weighted by its size in

computing the average patch edge contrast index.

92
(C18) Landscape Shape Index

Vector Raster

LSI =

∑

k=1

m

eik

′′

2√ π oA LSI =

0.25∑

k=1

m

eik

′′

√A

Units: None.

Range: LSI ≥ 1, without limit.

LSI = 1 when the landscape consists of a single patch of the corresponding type and

is circular (vector) or square (raster); LSI increases without limit as landscape shape

becomes more irregular or as the length of edge within the landscape of the corresponding patch type increases, or both.

Description: LSI equals the sum of the landscape boundary (regardless of whether

it represents true edge or not) and all edge segments (m) within the landscape

boundary involving the corresponding patch type (including those bordering background), divided by the square root of the total landscape area (m2

), adjusted by a

constant for a circular standard (vector) or square standard (raster).

(C19) Mean Shape Index

Vector Raster

MSI =

∑

j=1

n







pij

2√π o aij







ni

MSI =

∑

j=1

n







0.25pij

√aij







ni

Units: None.

Range: MSI ≥ 1, without limit.

MSI = 1 when all patches of the corresponding patch type are circular (vector) or

square (raster); MSI increases without limit as the patch shapes become more

irregular.

Description: MSI equals the sum of the patch perimeter (m) divided by the square

root of patch area (m2

) for each patch of the corresponding patch type, adjusted by a

constant to adjust for a circular standard (vector) or square standard (raster), divided

by the number of patches of the same type; in other words, MSI equals the average

shape index (SHAPE) of patches of the corresponding patch type.

(C20) Area-Weighted Mean Shape Index

Vector Raster

AWMSI = ∑

j=1

n 



















pij

2√ π o aij





















aij

∑

j=1

n

aij





























AWMSI = ∑

j=1

n 



















0.25pij

√aij





















aij

∑

j=1

n

aij





























Units: None.

Range: AWMSI ≥ 1, without limit.

93
AWMSI = 1 when all patches of the corresponding patch type are circular (vector) or

square (raster); AWMSI increases without limit as the patch shapes become more

irregular.

Description: AWMSI equals the sum, across all patches of the corresponding patch

type, of each patch perimeter (m) divided by the square root of patch area (m2

),

adjusted by a constant to adjust for a circular standard (vector) or square standard

(raster), multiplied by the patch area (m2

) divided by total class area (sum of patch

area for each patch of the corresponding patch type). In other words, AWMSI equals

the average shape index (SHAPE) of patches of the corresponding patch type,

weighted by patch area so that larger patches weigh more than smaller patches.

(C21) Double Log Fractal Dimension

Vector/Raster

DLFD = 2





























ni∑

j=1

n

(lnpij o lnaij)











−





















∑

j=1

n

ln pij





















∑

j=1

n

ln aij































ni∑

j=1

n

ln pij

2











−











∑

j=1

n

ln pij











2



















Units: None.

Range: 1 ≤ DLFD ≤ 2.

A fractal dimension greater than 1 for a 2-dimensional landscape mosaic indicates

a departure from a euclidean geometry (that is, an increase in patch shape complexity). DLFD approaches 1 for shapes with very simple perimeters such as circles

or squares, and approaches 2 for shapes with highly convoluted, plane-filling

perimeters. DLFD employs regression techniques and is subject to small sample

problems. Specifically, DLFD may greatly exceed the theoretical range in values

when the number of patches is small (for example, <10), and its use should be

avoided in such cases. In addition, DLFD requires patches to vary in size. Thus,

DLFD is undefined and reported as “NA” in the “basename”.full file and as a dot “.”

in the “basename”.class file if all patches are the same size or there is only 1 patch.

Description: DLFD equals 2 divided by the slope of regression line obtained by

regressing the logarithm of patch area (m2

) against the logarithm of patch perimeter

(m).

(C22) Mean Patch Fractal Dimension

Vector Raster

MPFD =

∑

j=1

n







2ln pij

ln aij







ni

MPFD =

∑

j=1

n







2ln(0.25pij)

lnaij







ni

Units: None.

Range: 1 ≤ MPFD ≤ 2.

94
A fractal dimension greater than 1 for a 2-dimensional landscape mosaic indicates a

departure from a euclidean geometry (that is, an increase in patch shape complexity).

MPFD approaches 1 for shapes with very simple perimeters, such as circles or

squares, and approaches 2 for shapes with highly convoluted, plane-filling perimeters.

Description: MPFD equals the sum of 2 times the logarithm of patch perimeter (m)

divided by the logarithm of patch area (m2

) for each patch of the corresponding

patch type, divided by the number of patches of the same type; the raster formula is

adjusted to correct for the bias in perimeter (Li 1990).

(C23) Area-Weighted Mean Patch Fractal Dimension

Vector Raster

AWMPFD = ∑

j=1

n





















2lnpij

lnaij





















aij

∑

j=1

n

aij





























AWMPFD = ∑

j=1

n





















2ln(0.25pij)

lnaij





















aij

∑

j=1

n

aij





























Units: None.

Range: 1 ≤ AWMPFD ≤ 2.

A fractal dimension greater than 1 for a 2-dimensional landscape mosaic indicates a

departure from a euclidean geometry (that is, an increase in patch shape complexity).

AWMPFD approaches 1 for shapes with very simple perimeters, such as circles or

squares, and approaches 2 for shapes with highly convoluted, plane-filling perimeters.

Description: AWMPFD equals the sum, across all patches of the corresponding patch

type, of 2 times the logarithm of patch perimeter (m) divided by the logarithm of patch

area (m2

), multiplied by the patch area (m2) divided by total class area (sum of patch

area for each patch of the corresponding patch type); the raster formula is adjusted

to correct for the bias in perimeter (Li 1990). In other words, AWMPFD equals the

average patch fractal dimension (FRACT) of patches of the corresponding patch

type, weighted by patch area so that larger patches weigh more than smaller patches.

(C24) Core Area Percentage of Landscape

Vector/Raster

C%LAND =

∑

j=1

n

aij

c

A (100)

Units: Percent.

Range: 0 ≤ C%LAND < 100.

C%LAND approaches 0 when core area of the corresponding patch type (class)

becomes increasingly rare in the landscape, because of smaller patches or more

convoluted patch shapes, or both. C%LAND approaches 100 when the entire

landscape consists of a single patch type (when the entire image is comprised

of a single patch) and the specified edge width approaches 0.

95
Description: C%LAND equals the sum of the core areas of each patch (m2

) of the

corresponding patch type, divided by total landscape area (m2), multiplied by 100

(to convert to a percentage); in other words, C%LAND equals the percentage of the

landscape comprised of core area of the corresponding patch type.

(C25) Total Core Area

Vector/Raster

TCA = ∑

j=1

n

aij

c 





1

10,000







Units: Hectares.

Range: TCA ≥ 0, without limit.

TCA = 0 when every location within each patch of the corresponding patch type is

within the specified edge distance from the patch perimeters. TCA approaches CA

as the specified edge distance decreases and as patch shapes are simplified.

Description: TCA equals the sum of the core areas of each patch (m2

) of the

corresponding patch type, divided by 10,000 (to convert to hectares).

(C26) Number of Core Areas

Vector/Raster

NCA = ∑

j=1

n

nij

c

Units: None.

Range: NCA ≥ 0, without limit.

NCA = 0 when TCA = 0 (that is, every location within patches of the corresponding

patch type are within the specified edge distance from the patch perimeters). NCA >

1 when, because of patch shape complexity, a patch contains more than 1 core area.

Description: NCA equals the sum of the number of disjunct core areas contained

within each patch of the corresponding patch type; that is, the number of disjunct

core areas contained within the class.

(C27) Core Area Density

Vector/Raster

CAD =

∑

j=1

n

nij

c

A (10,000) (100)

Units: Number per 100 hectares.

Range: CAD ≥ 0, without limit.

CAD = 0 when TCA = 0 (that is, every location within patches of the corresponding

patch type are within the specified edge distance from the patch perimeters); in other

words, when there are no core areas.

96
Description: CAD equals the sum of number of disjunct core areas contained within

each patch of the corresponding patch type, divided by total landscape area, multiplied by 10,000 and 100 (to convert to 100 hectares).

(C28) Mean Core Area Per Patch

Vector/Raster

MCA1 =

∑

j=1

n

aij

c

ni







1

10,000







Units: Hectares.

Range: MCA1 ≥ 0, without limit.

Ultimately, the range in MCA1 is limited by the grain and extent of the image and the

minimum patch size in the same manner as mean patch size (MPS), but MCA1 is

also effected by the specified edge width. MCA1 = 0 when total core area = 0 (every

location within patches of the corresponding patch type are within the specified edge

distance from the patch perimeters); in other words, when there are no core areas.

MCA1 approaches MPS as the specified edge width decreases and as patch shapes

are simplified.

Description: MCA1 equals the sum of the core areas of each patch (m2

) of the corresponding patch type, divided by the number of patches of the same type, divided

by 10,000 (to convert to hectares). Note that MCA1 equals the average core area per

patch, not the average size of disjunct core areas, as in MCA2.

(C29) Patch Core Area Standard Deviation

Vector/Raster

Units: Hectares.

Range: CASD1 ≥ 0, without limit.

CASD1 = 0 when all patches in the class have the same core area or when there is

only 1 patch (that is, no variability in core area).

Description: CASD1 equals the square root of the sum of the squared deviations

of each patch core area (m2

) from the mean core area per patch (MCA1) of the

corresponding patch type, divided by the number of patches of the same type,

divided by 10,000 (to convert to hectares); that is, the root mean squared error

(deviation from the mean) in patch core area. This is the population standard

deviation, not the sample standard deviation, and CASD1 represents the variation

in core area among patches, not among disjunct core areas as in CASD2.

CASD1=

a

a

n

n

ij

ij

j=1

n

i j=1

n

i

c

c

−

F

H

G

G

G

G

G

I

K

J

J

J

J

J

L

N

M

M

M

M

M

M

O

Q

P

P

P

P

P

P F

H

G I

K

J

∑

∑

2

1

10 000 ,

97
(C30) Patch Core Area Coefficient of Variation

Vector/Raster

CACV1 = CASD1

MCA1 (100)

Units: Percent.

Range: CACV1 ≥ 0, without limit.

CACV1 = 0 when all patches in the class have the same core area or when there is

only 1 patch (that is, no variability in core area).

Description: CACV1 equals the standard deviation in core area of patches (CASD1)

divided by the mean core area per patch (MCA1) of the corresponding patch type,

multiplied by 100 (to convert to percent); that is, the variability in core area relative

to the mean core area. This is the population coefficient of variation, not the sample

coefficient of variation, and CACV1 represents the variation in core area among

patches, not among disjunct core areas as in CACV2.

(C31) Mean Area Per Disjunct Core

Vector/Raster

MCA2 =

∑

j=1

n

∑

q=1

p

aijqc

∑

j=1

n

nij

c







1

10,000







Units: Hectares.

Range: MCA2 ≥ 0, without limit.

Ultimately, the range in MCA2 is limited by the grain and extent of the image and the

minimum patch size in the same manner as mean patch size (MPS), but MCA2 is

also effected by the specified edge width. MCA2 = 0 when total core area = 0 (every

location within patches of the corresponding patch type are within the specified edge

distance from the patch perimeters); in other words, when there are no core areas.

MCA2 approaches MPS as the specified edge width decreases and as patch shapes

are simplified.

Description: MCA2 equals the sum of the disjunct core areas of each patch (m2

) of

the corresponding patch type, divided by the number of disjunct core areas of the

same type, divided by 10,000 (to convert to hectares). Note that MCA2 equals the

average size of disjunct core areas, not the average core area per patch, as in

MCA1.

98
(C32) Disjunct Core Area Standard Deviation

Vector/Raster

Units: Hectares.

Range: CASD2 ≥ 0, without limit.

CASD2 = 0 when all disjunct core areas are the same size or when there is only

1 core area (that is, no variability in core area).

Description: CASD2 equals the square root of the sum of the squared deviations

of each disjunct core area (m2

) from the mean size of disjunct core areas (MCA2)

of the corresponding patch type, divided by the number of disjunct core areas of the

same type, divided by 10,000 (to convert to hectares); that is, the root mean squared

error (deviation from the mean) in the size of disjunct core areas. This is the population standard deviation, not the sample standard deviation, and CASD2 represents

the variation in size of disjunct core areas, not patch core areas as in CASD1.

(C33) Disjunct Core Area Coefficient of Variation

Vector/Raster

CACV2 = CASD2

MCA2 (100)

Units: Percent.

Range: CACV2 ≥ 0, without limit.

CACV2 = 0 when all disjunct core areas are the same size or when there is only

1 core area (that is, no variability in core area).

Description: CACV2 equals the standard deviation in the size of disjunct core areas

(CASD2) divided by the mean size of disjunct core areas (MCA2) of the corresponding patch type, multiplied by 100 (to convert to percent); that is, the variability in core

area relative to the mean core area. This is the population coefficient of variation, not

the sample coefficient of variation, and CACV2 represents the variation in size of

disjunct core areas, not patch core areas as in CACV1.

CASD2 =

a

a

n

n

ijq

ijq

q

p

j

n

ij

j=1

n

q 1

p

j 1

n

ij

j=1

n

c

c

c

c

−

F

H

G

G

G

G

G

I

K

J

J

J

J

J

L

N

M

M

M

M

M

M

O

Q

P

P

P

P

P

P F

H

G I

K

J

= =

= =

∑∑

∑

∑∑

∑

1 1

1

10 000 ,

99
(C34) Total Core Area Index

Vector/Raster

TCAI =

∑

j=1

n

aij

c

∑

j=1

n

aij

(100)

Units: Percent.

Range: 0 ≤ TCAI < 100.

TCAI = 0 when none of the patches of the corresponding patch type contains any

core area (CORE = 0 for every patch); that is, when the landscape contains no core

area for the corresponding patch type. TCAI approaches 100 when the patches of

the corresponding patch type, because of size, shape, and edge width, contain

mostly core area.

Description: TCAI equals the sum of the core areas of each patch (m2

) of the corresponding patch type, divided by the sum of the areas of each patch (m2

) of the same

type, multiplied by 100 (to convert to a percentage); that is, TCAI equals the percentage of a patch type in the landscape that is core area based on a specified edge

width.

(C35) Mean Core Area Index

Vector/Raster

MCAI =

∑

j=1

n 





aij

c

aij







ni (100)

Units: Percent.

Range: 0 ≤ MCAI < 100.

MCAI = 0 when none of the patches of the corresponding patch type contain any

core area (CORE = 0 for every patch); that is, when the landscape contains no core

area for the corresponding patch type. MCAI approaches 100 when the patches of

the corresponding patch type, because of size, shape, and edge width, contain

mostly core area.

Description: MCAI equals the sum of the proportion of each patch that is core area

(core area of each patch [m2

] divided by the area of each patch [m2]) of the corresponding patch type, divided by the number of patches of the same type, multiplied

by 100 (to convert to a percentage); in other words, MCAI equals the average percentage of a patch of the corresponding patch type in the landscape that is core area

based on a specified edge width.

100
(C36) Mean Nearest Neighbor Distance

Raster

MNN =

∑

j=1

n′

hij

n′i

Units: Meters.

Range: MNN > 0, without limit.

MNN is reported as “None” in the “basename”.full file and as a dot “.” in the

“basename”.class file if there is only 1 patch of the corresponding patch type.

Similarly, MNN is reported as “NA” in the “basename”.full file and a dot “.” in the

“basename”.class file if the user chooses not to calculate nearest neighbor distance.

Description: MNN equals the sum of the distance (m) to the nearest neighboring

patch of the same type, based on nearest edge-to-edge distance, for each patch of

the corresponding patch type, divided by the number of patches of the same type.

(C37) Nearest Neighbor Standard Deviation

Raster

Units: Meters.

Range: NNSD ≥ 0, without limit.

NNSD = 0 when there are only 2 patches in the class or all patches have the same

nearest neighbor distance (no variability in nearest neighbor distance). NNSD is

reported as “NA” in the “basename”.full file and as a dot “.” in the “basename”.class

file if there is only 1 patch of the corresponding patch type. Similarly, NNSD is

reported as “NA” in the “basename”.full file and as a dot “.” in the “basename”.class

file if the user chooses not to calculate nearest neighbor distance.

Description: NNSD equals the square root of the sum of the squared deviations

of each patches’ nearest neighbor distance (m) from the mean nearest neighbor

distance (MNN) of the corresponding patch type, divided by the number of patches

of the same type; that is, the root mean squared error (deviation from the mean) in

patch nearest neighbor distance. This is the population standard deviation, not the

sample standard deviation.

NNSD

h

h

n

n

ij

ij

j 1

n

i j 1

n

i

2

=

− ′

F

H

G

G

G

G

G

I

K

J

J

J

J

J

L

N

M

M

M

M

M

M

O

Q

P

P

P

P

P

P ′

=

′

=

′ ∑

∑

101
(C38) Nearest Neighbor Coefficient of Variation

Raster

NNCV = NNSD

MNN (100)

Units: Percent.

Range: NNCV ≥ 0, without limit.

NNCV = 0 when there are only 2 patches in the class or all patches have the

same nearest neighbor distance (no variability in nearest neighbor distance; NNSD

= 0). NNCV is reported as “NA” in the “basename”.full file and as a dot “.” in the

“basename”.class file if there is only 1 patch of the corresponding patch type.

Similarly, NNCV is reported as “NA” in the “basename”.full file and as a dot “.” in

the “basename”.class file if the user chooses not to calculate nearest neighbor

distance.

Description: NNCV equals the standard deviation in nearest neighbor distances

(NNSD) divided by the mean nearest neighbor distance (MNN) of the corresponding

patch type, multiplied by 100 (to convert to percent); that is, the variability in nearest

neighbor distance relative to the mean nearest neighbor distance. This is the population coefficient of variation, not the sample coefficient of variation.

(C39) Mean Proximity Index

Raster

MPI =

∑

j=1

n

∑

s=1

n

aijs

hijs

2

ni

Units: None.

Range: MPI ≥ 0.

MPI = 0 if all patches of the corresponding patch type have no neighbors of the

same type within the specified search radius. MPI increases as patches of the

corresponding patch type become less isolated and the patch type becomes less

fragmented in distribution. The upper limit of MPI is determined by the search

radius and minimum distance between patches. MPI is reported as “NA” in the

“basename”.full file and as a dot “.” in the “basename”.class file if the user chooses

not to calculate the proximity index.

Description: MPI equals the sum of patch area (m2

) divided by the nearest edge-toedge distance squared (m2

) between the patch and the focal patch of all patches of

the corresponding patch type whose edges are within a specified distance (m) of the

focal patch, summed across all patches of the same type and divided by the total

number of patches in the class. In other words, MPI equals the average proximity

index for patches in the class. When the search buffer extends beyond the

landscape boundary for focal patches near the boundary, only patches contained

within the landscape are considered in the computations.

102
(C40) Interspersion and Juxtaposition Index

Vector/Raster

IJI =

− ∑

k=1

m′





























eik

∑

k=1

m′

eik















ln 













eik

∑

k=1

m′

eik





























ln (m′ − 1) (100)

Units: Percent.

Range: 0 < IJI ≤ 100.

IJI approaches 0 when the corresponding patch type is adjacent to only 1 other

patch type and the number of patch types increases. IJI = 100 when the corresponding patch type is equally adjacent to all other patch types (maximally

interspersed and juxtaposed to other patch types). IJI is undefined and reported

as “NA” in the “basename”.full file and as a dot “.” in the “basename”.class file

if the number of patch types is less than 3.

Description: IJI equals minus the sum of the length (m) of each unique edge type

involving the corresponding patch type divided by the total length (m) of edge (m)

involving the same type, multiplied by the logarithm of the same quantity, summed

over each unique edge type; divided by the logarithm of the number of patch types

minus 1; multiplied by 100 (to convert to a percentage). In other words, the observed

interspersion over the maximum possible interspersion for the given number of patch

types. IJI considers all patch types present on an image, including any present in the

landscape border.

Landscape Indices

(L1) Landscape ID (LID)

The first field in the landscape output file is landscape ID (LID); it is defined as in the

patch output file (see previous discussion).

(L2) Total Area

Vector/Raster

TA = A 





1

10,000







Units: Hectares.

Range: TA > 0, without limit.

Description: TA equals the total area (m2

) of the landscape, divided by 10,000 (to

convert to hectares). TA excludes the area of any background patches within the

landscape.

103
(L3) Largest Patch Index

Vector/Raster

LPI =

max

j=1

n

(aij)

A (100)

Units: Percent.

Range: 0 < LPI ≤ 100.

LPI approaches 0 when the largest patch in the landscape is increasingly small. LPI

= 100 when the entire landscape consists of a single patch; that is, when the largest

patch comprises 100 percent of the landscape.

Description: LPI equals the area (m2

) of the largest patch in the landscape divided

by total landscape area (m2

), multiplied by 100 (to convert to a percentage); in other

words, LPI equals the percentage of the landscape that the largest patch comprises.

(L4) Number of Patches

Vector/Raster

NP = N

Units: None.

Range: NP ≥ 1, without limit.

NP = 1 when the landscape contains only 1 patch.

Description: NP equals the number of patches in the landscape. NP does not include

any background patches within the landscape or patches in the landscape border.

(L5) Patch Density

Vector/Raster

PD = N

A (10,000)(100)

Units: Number per 100 hectares.

Range: PD > 0, without limit.

Description: PD equals the number of patches in the landscape divided by total

landscape area, multiplied by 10,000 and 100 (to convert to 100 hectares).

(L6) Mean patch Size

Vector/Raster

MPS = A

N







1

10,000







Units: Hectares.

Range: MPS > 0, without limit.

The range in MPS is limited by the grain and extent of the image and the minimum

patch size in the same manner as patch area (AREA).

104
Description: MPS equals the total landscape area (m 2) , divided by the total number of

patches, divided by 10,000 (to convert to hectares).

(L7) Patch Size Standard Deviation

Vector/Raster

Units: Hectares.

Range: PSSD ≥ 0, without limit.

PSSD = 0 when all patches in the landscape are the same size or when there is

only 1 patch (no variability in patch size).

Description: PSSD equals the square root of the sum of the squared deviations

of each patch area (m2

) from the mean patch size, divided by the total number of

patches, divided by 10,000 (to convert to hectares); that is, the root mean squared

error (deviation from the mean) in patch size. This is the population standard

deviation, not the sample standard deviation.

(L8) Patch Size Coefficient of Variation

Vector/Raster

PSCV = PSSD

MPS (100)

Units: Percent.

Range: PSCV ≥ 0, without limit.

PSCV = 0 when all patches in the landscape are the same size or when there is

only 1 patch (no variability in patch size).

Description: PSCV equals the standard deviation in patch size (PSSD) divided by

the mean patch size (MPS), multiplied by 100 (to convert to percent); that is, the

variability in patch size relative to the mean patch size. This is the population

coefficient of variation, not the sample coefficient of variation.

(L9) Total Edge

Vector/Raster

TE = E

Units: Meters.

Range: TE ≥ 0, without limit.

TE = 0 when there is no edge in the landscape; that is, when the entire landscape

and landscape border, if present, consists of a single patch and the user specifies

that none of the landscape boundary and background edge be treated as edge.

PSSD

a

A

N

N

1

10,000

ij

j 1

n

i 1

m 2

=

− F

H

G I

K

J L

N

M O

Q

P F

H

G I

K

J = =

∑∑

105
Description: TE equals the sum of the lengths (m) of all edge segments in the landscape. If a landscape border is present, TE includes landscape boundary segments

representing true edge only (that is, contrast weight > 0). If a landscape border is

absent, TE includes a user-specified proportion of the landscape boundary. Regardless of whether a landscape border is present or not, TE includes a user-specified

proportion of background edge.

(L10) Edge Density

Vector/Raster

ED = E

A (10,000)

Units: Meters per hectare.

Range: ED ≥ 0, without limit.

ED = 0 when there is no edge in the landscape; that is, when the entire landscape

and landscape border, if present, consists of a single patch and the user specifies

that none of the landscape boundary and background edge be treated as edge.

Description: ED equals the sum of the lengths (m) of all edge segments in the landscape, divided by the total landscape area (m2

), multiplied by 10,000 (to convert to

hectares). If a landscape border is present, ED includes landscape boundary segments representing true edge only (that is, contrast weight 0). If a landscape border

is absent, ED includes a user-specified proportion of the landscape boundary.

Regardless of whether a landscape border is present or not, ED includes a userspecified proportion of background edge.

(L11) Contrast-Weighted Edge Density

Vector/Raster

CWED =

∑

i=1

m′

∑

k=i+1

m′

(eik o dik)

A (10,000)

Units: Meters per hectare.

Range: CWED ≥ 0, without limit.

CWED = 0 when there is no edge in the landscape; that is, when the entire landscape and landscape border, if present, consists of a single patch and the user

specifies that none of the landscape boundary and background edge be treated as

edge. CWED increases as the amount of edge in the landscape increases or as the

contrast in edges increases (contrast weight approaches 1). CWED is reported as

“NA” in the “basename”.full file and as a dot “.” in the “basename”.land file if a

contrast weight file is not specified by the user.

106
Description: CWED equals the sum of the lengths (m) of each edge segment in the

landscape multiplied by the corresponding contrast weight, divided by the total landscape area (m2

), multiplied by 10,000 (to convert to hectares). If a landscape border

is present, CWED includes landscape boundary segments representing true edge

only (contrast weight > 0). If a landscape border is absent, all landscape boundary

edge segments are assigned the edge contrast weight specified by the user (see

bound_wght option). This is equivalent to treating the specified proportion of all

boundary edge segments as maximum-contrast edge. Regardless of whether a

landscape border is present or not, all background edge segments are assigned the

edge contrast weight specified by the user. Again, this is equivalent to treating the

specified proportion of all background edge segments as maximum-contrast edge.

(L12) Total Edge Contrast Index

Vector/Raster

TECI =

∑

i=1

m′

∑

k=i+1

m′

(eik o dik)

E′ (100)

Units: Percent.

Range: 0 ≤ TECI ≤ 100.

TECI = 0 when there is no edge in the landscape; that is, when the entire landscape

and landscape border, if present, consist of a single patch and the user specifies that

none of the landscape boundary and background edge be treated as edge. TECI

approaches 0 as the contrast in edges lessen (contrast weight approaches 0). TECI

= 100 when all edge is maximum contrast (contrast weight = 1). TECI is reported

as “NA” in the “basename”.full file and as a dot “.” in the “basename”.land file if a

contrast weight file is not specified by the user.

Description: TECI equals the sum of the lengths (m) of each edge segment in the

landscape multiplied by the corresponding contrast weight, divided by the total length

(m) of edge in the landscape, multiplied by 100 (to convert to a percentage). In the

numerator, if a landscape border is present, all edge segments along the landscape

boundary are treated according to their edge contrast weights as designated in the

contrast weight file. If a landscape border is absent, all landscape boundary segments

are assigned the edge contrast weight specified by the user (see bound_wght option).

Note that this is equivalent to treating the specified proportion of the landscape

boundary as maximum-contrast edge and the remainder as zero-contrast edge.

Regardless of whether a landscape border is present or not, all background edge

segments are assigned the edge contrast weight specified by the user. This is

equivalent to treating the specified proportion of all background edge as maximumcontrast edge and the remainder as zero-contrast edge. In the denominator, all

edges are included, including the landscape boundary and background edge segments, regardless of whether they represent true edge or how the user chooses to

handle boundary and background edges.

107
(L13) Mean Edge Contrast Index

Vector/Raster

MECI =

∑

i=1

m

∑

j=1

n















∑

k=1

m′

(pijk o dik)

pij















N (100)

Units: Percent.

Range: 0 ≤ MECI ≤ 100.

MECI = 0 when there is no edge in the landscape; that is, when the entire landscape

and landscape border, if present, consist of a single patch type and the user specifies

that none of the landscape boundary and background edge be treated as edge. MECI

approaches 0 as the contrast in edges lessen (contrast weight approaches 0). MECI

= 100 when all edge is maximum contrast (contrast weight = 1). MECI is reported as

“NA” in the “basename”.full file and as a dot “.” in the “basename”.land file if a contrast weight file is not specified by the user.

Description: MECI equals the sum of the segment lengths (m) of each patches’

perimeter multiplied by their corresponding contrast weights, divided by total patch

perimeter (m), divided by the total number of patches, multiplied by 100 (to convert

to a percentage). If a landscape border is present, any patch perimeter segments

along the landscape boundary are treated according to their edge contrast weights

as designated in the contrast weight file. If a landscape border is absent, any patch

perimeter segments along the landscape boundary are assigned the edge contrast

weight specified by the user (see bound_wght option). Regardless of whether a

landscape border is present or not, all patch perimeter segments bordering background are assigned the edge contrast weight specified by the user.

(L14) Area-Weighted Mean Edge Contrast Index

Vector/Raster

AWMECI = ∑

i=1

m

∑

j=1

n





























∑

k=1

m′

(pijk o dik)

pij





















aij

A



















 (100)

Units: Percent.

Range: 0 ≤ AWMECI ≤ 100.

AWMECI = 0 when there is no edge in the landscape; that is, when the entire landscape and landscape border, if present, consist of a single patch type and the user

specifies that none of the landscape boundary and background edge be treated as

edge. AWMECI approaches 0 as the contrast in edges lessen (contrast weight

approaches 0). AWMECI = 100 when all edge is maximum contrast (contrast weight

= 1). AWMECI is reported as “NA” in the “basename”.full file and as a dot “.” in the

“basename”.land file if a contrast weight file is not specified by the user.

108
Description: AWMECI equals the sum of the segment lengths (m) of each patches’

perimeter multiplied by their corresponding contrast weights, divided by total patch

perimeter (m), multiplied by patch area (m2

), divided by total landscape area (m2),

summed across all patches in the landscape, multiplied by 100 (to convert to a

percentage). If a landscape border is present, any patch perimeter segments along

the landscape boundary are treated according to their edge contrast weights as

designated in the contrast weight file. If a landscape border is absent, any patch

perimeter segments along the landscape boundary are assigned the edge contrast

weight specified by the user (see bound_wght option). Regardless of whether a

landscape border is present or not, all patch perimeter segments bordering background are assigned the edge contrast weight specified by the user. AWMECI is

similar to MECI except that each patch weighted by its size in computing the

average patch edge contrast index.

(L15) Landscape Shape Index

Vector Raster

LSI = E′

2√ π oA LSI = 0.25 E′√A

Units: None.

Range: LSI ≥ 1, without limit.

LSI = 1 when the landscape consists of a single circular (vector) or square (raster)

patch; LSI increases without limit as landscape shape becomes more irregular or

as the length of edge within the landscape increases, or both.

Description: LSI equals the sum of the landscape boundary (regardless of whether

it represents true edge) and all edge segments (m) within the landscape boundary

(including those bordering background), divided by the square root of the total

landscape area (m2

), adjusted by a constant for a circular standard (vector) or

square standard (raster).

(L16) Mean Shape Index

Vector Raster

MSI =

∑

i=1

m

∑

j=1

n







pij

2√ π o aij







N MSI =

∑

i=1

m

∑

j=1

n







0.25pij

√aij







N

Units: None.

Range: MSI ≥ 1, without limit.

MSI = 1 when all patches in the landscape are circular (vector) or square (raster);

MSI increases without limit as the patch shapes become more irregular.

Description: MSI equals the sum of the patch perimeter (m) divided by the square

root of patch area (m2

) for each patch in the landscape, adjusted by a constant for

a circular standard (vector) or square standard (raster), divided by the number of

patches (NP); in other words, MSI equals the average shape index (SHAPE) of

patches in the landscape.

109
(L17) Area-Weighted Mean Shape Index

Vector Raster

AWMSI = ∑

i=1

m

∑

j=1

n













pij

2√ π o aij













aij

A













AWMSI = ∑

i=1

m

∑

j=1

n













0.25pij

√aij













aij

A













Units: None.

Range: AWMSI ≥ 1, without limit.

AWMSI = 1 when all patches in the landscape are circular (vector) or square (raster);

AWMSI increases without limit as the patch shapes become more irregular.

Description: AWMSI equals the sum, across all patches, of each patch perimeter (m)

divided by the square root of patch area (m2

), adjusted by a constant to adjust for a

circular standard (vector) or square standard (raster), multiplied by the patch area

(m2

) divided by total landscape area. In other words, AWMSI equals the average

shape index (SHAPE) of patches, weighted by patch area so that larger patches

weigh more than smaller ones.

(L18) Double Log Fractal Dimension

Vector/Raster

DLFD = 2





























N ∑

i=1

m

∑

j=1

n

(ln pij o ln aij)











−





















∑

i=1

m

∑

j=1

n

ln pij





















∑

i=1

m

∑

j=1

n

ln aij































N ∑

i=1

m

∑

j=1

n

ln pij

2











−











∑

i=1

m

∑

j=1

n

ln pij











2



















Units: None.

Range: 1 ≥ DLFD ≥ 2.

A fractal dimension greater than 1 for a 2-dimensional landscape mosaic indicates

a departure from a euclidean geometry (that is, an increase in patch shape complexity). DLFD approaches 1 for shapes with very simple perimeters such as circles

or squares, and approaches 2 for shapes with highly convoluted, plane-filling perimeters. DLFD employs regression techniques and is subject to small sample

problems. Specifically, DLFD may greatly exceed the theoretical range in values

when the number of patches is small (<10), and its use should be avoided in such

cases. In addition, DLFD requires patches to differ in size. Thus, DLFD is undefined and reported as “NA” in the “basename”.full file and as a dot “.” in the

“basename”.land file if all patches are the same size or there is only 1 patch.

Description: DLFD equals 2 divided by the slope of the regression line obtained

by regressing the logarithm of patch area (m2

) against the logarithm of patch

perimeter (m).

110
(L19) Mean Patch Fractal Dimension

Vector Rastor

MPFD =

∑

i=1

m

∑

j=1

n







2lnpij

lnaij







N MPFD =

∑

i=j

m

∑

j=1

n







2ln(0.25pij)

ln aij







N

Units: None.

Range: 1 ≤ MPFD ≤ 2.

A fractal dimension greater than 1 for a 2-dimensional landscape mosaic indicates a

departure from a euclidean geometry (an increase in patch shape complexity). MPFD

approaches 1 for shapes with very simple perimeters, such as circles or squares, and

approaches 2 for shapes with highly convoluted, plane-filling perimeters.

Description: MPFD equals the sum of 2 times the logarithm of patch perimeter (m)

divided by the logarithm of patch area (m2

) for each patch in the landscape, divided

by the number of patches; the raster formula is adjusted to correct for the bias in

perimeter (Li 1990).

(L20) Area-Weighted Mean Patch Fractal Dimension

Vector Raster

AWMPFD = ∑

i=1

m

∑

j=1

n













2lnpij

lnaij













aij

A













AWMPFD = ∑

i=1

m

∑

j=1

n













2ln(0.25pij)

lnaij













aij

A













Units: None.

Range: 1 ≤ AWMPFD ≤ 2.

A fractal dimension greater than 1 for a 2-dimensional landscape mosaic indicates

a departure from a euclidean geometry (an increase in patch shape complexity).

AWMPFD approaches 1 for shapes with very simple perimeters, such as circles or

squares, and approaches 2 for shapes with highly convoluted, plane-filling perimeters.

Description: AWMPFD equals the sum, across all patches, of 2 times the logarithm

of patch perimeter (m) divided by the logarithm of patch area (m2

), multiplied by the

patch area (m2

) divided by total landscape area; the raster formula is adjusted to

correct for the bias in perimeter (Li 1990). In other words, AWMPFD equals the

average patch fractal dimension (FRACT) of patches in the landscape, weighted by

patch area.

(L21) Total Core Area

Vector/Raster

TCA = ∑

i=1

m

∑

j=1

n

aij

c 





1

10,000







Units: Hectares.

Range: TCA ≥ 0, without limit.

111
TCA = 0 when every location within every patch is within the specified edge distance

from the patch perimeters. TCA approaches total landscape area as the specified

edge distance decreases and as patch shapes are simplified.

Description: TCA equals the sum of the core areas of each patch (m2

), divided by

10,000 (to convert to hectares).

(L22) Number of Core Areas

Vector/Raster

NCA = ∑

i=1

m

∑

j=1

n

nij

c

Units: None.

Range: NCA ≥ 0, without limit.

NCA = 0 when TCA = 0 (every location within every patch is within the specified

edge distance from the patch perimeters).

Description: NCA equals the sum of the number of disjunct core areas contained

within each patch in the landscape; that is, the number of disjunct core areas

contained within the landscape.

(L23) Core Area Density

Vector/Raster

CAD =

∑

i=1

m

∑

j=1

n

nij

c

A (10,000)(100)

Units: Number per 100 hectares.

Range: CAD ≥ 0, without limit.

CAD = 0 when TCA = 0 (every location within every patch is within the specified

edge distance from the patch perimeters); in other words, when there are no core

areas.

Description: CAD equals the sum of number of disjunct core areas contained within

each patch, divided by total landscape area, multiplied by 10,000 and 100 (to convert

to 100 hectares).

(L24) Mean Core Area Per Patch

Vector/Raster

MCA1 =

∑

i=1

m

∑

j=1

n

aij

c

N







1

10,000







Units: Hectares.

Range: MCA1 ≥ 0, without limit.

112
Ultimately, the range in MCA1 is limited by the grain and extent of the image and the

minimum patch size in the same manner as mean patch size (MPS), but MCA1 is

also affected by the specified edge width. MCA1 = 0 when TCA = 0 (every location

within every patch is within the specified edge distance from the patch perimeters); in

other words, when there are no core areas. MCA1 approaches MPS as the specified

edge width decreases and as patch shapes are simplified.

Description: MCA1 equals the sum of the core areas of each patch (m2

), divided by

the number of patches, divided by 10,000 (to convert to hectares). Note that MCA1

equals the average core area per patch, not the average size of disjunct core areas,

as in MCA2.

(L25) Patch Core Area Standard Deviation

Vector/Raster

Units: Hectares.

Range: CASD1 ≥ 0, without limit.

CASD1 = 0 when all patches in the landscape have the same core area or when

there is only 1 patch (no variability in core area).

Description: CASD1 equals the square root of the sum of the squared deviations of

each patch core area (m2

) from the mean core area per patch (MCA1), divided by

the number of patches, divided by 10,000 (to convert to hectares); that is, the root

mean squared error (deviation from the mean) in patch core area. This is the population standard deviation, not the sample standard deviation, and CASD1 represents

the variation in core area among patches, not among disjunct core areas as in

CASD2.

(L26) Patch Core Area Coefficient of Variation

Vector/Raster

CACV1 = CASD1

MCA1 (100)

Units: Percent.

Range: CACV1 ≥ 0, without limit.

CACV1 = 0 when all patches in the landscape have the same core area or when

there is only 1 patch (no variability in core area).

Description: CACV1 equals the standard deviation in core area (CASD1) divided by

the mean core area per patch (MCA1), multiplied by 100 (to convert to percent); that

is, the variability in core area relative to the mean core area. This is the population

coefficient of variation, not the sample coefficient of variation, and CACV1 represents

the variation in core area among patches, not among disjunct core areas as in

CACV2.

CASD1

a

a

N

N

1

10,000

ij

c

ij

c

j 1

n

i 1

m

j 1

n

i 1

m

2

=

−

F

H

G

G

G

G

G

I

K

J

J

J

J

J

L

N

M

M

M

M

M

M

O

Q

P

P

P

P

P

P F

H

G I

K

J

= =

= =

∑∑

∑∑

113

(L29) Disjunct Core Area Coefficient of Variation

Vector/Raster

CACV2 = CASD2

MCA2 (100)

Units: Percent.

Range: CACV2 ≥ 0, without limit.

CACV2 = 0 when all disjunct core areas are the same size or when there is only

1 core area (no variability in core area).

Description: CACV2 equals the standard deviation in the size of disjunct core areas

(CASD2) divided by the mean size of disjunct core areas (MCA2), multiplied by 100

(to convert to percent); that is, the variability in core area relative to the mean core

area. This is the population coefficient of variation, not the sample coefficient of

variation, and CACV2 represents the variation in size of disjunct core areas, not

patch core areas as in CACV1.

(L30) Total Core Area Index

Vector/Raster

TCAI =

∑

i=1

m

∑

j=1

n

aij

c

A (100)

Units: Percent.

Range: 0 ≤ TCAI < 100.

TCAI = 0 when none of the patches in the landscape contain any core area

(CORE = 0 for every patch); that is, when the landscape contains no core area.

TCAI approaches 100 when the patches, because of size, shape, and edge width,

contain mostly core area.

Description: TCAI equals the sum of the core areas of each patch (m2

), divided by

the total landscape area (m2

), multiplied by 100 (to convert to a percentage); that

is, TCAI equals the percentage of the landscape that is core area.

(L31) Mean Core Area Index

Vector/Raster

MCAI =

∑

i=1

m

∑

j=1

n 





aij

c

aij







N (100)

Units: Percent.

Range: 0 ≤ MCAI < 100.

MCAI = 0 when none of the patches in the landscape contain any core area

(CORE = 0 for every patch); that is, when the landscape contains no core area.

MCAI approaches 100 when the patches, because of size, shape, and edge width,

contain mostly core area.

115
Description: MCAI equals the sum of the proportion of each patch that is core area

(that is, core area of each patch [m2

] divided by the area of each patch [m2]), divided

by the number of patches, multiplied by 100 (to convert to a percentage); in other

words, MCAI equals the average percentage of a patch in the landscape that is core

area.

(L32) Mean Nearest Neighbor Distance

Raster

MNN =

∑

i=1

m

∑

j=1

n′

hij

N′

Units: Meters.

Range: MNN > 0, without limit.

MNN is reported as “None” in the “basename”.full file and as a dot “.” in the

“basename”.land file if none of the patches have a nearest neighbor (every patch

type consists of only 1 patch). MNN is reported as “NA” in the “basename”.full file

and as a dot “.” in the “basename”.land file if the user chooses not to calculate

nearest neighbor distance.

Description: MNN equals the sum of the distance (m) to the nearest patch of the

same type, based on nearest edge-to-edge distance, for each patch in the landscape with a neighbor, divided by the number of patches with a neighbor.

(L33) Nearest Neighbor Standard Deviation

Raster

Units: Meters.

Range: NNSD ≥ 0, without limit.

NNSD = 0 when all patches have the same nearest neighbor distance (no variability

in nearest neighbor distance). NNSD is reported as “NA” in the “basename”.full file

and as a dot “.” in the “basename”.class file if none of the patches have a nearest

neighbor. Similarly, NNSD is reported as “NA” in the “basename”.full file and as a dot

“.” in the “basename”.land file if the user chooses not to calculate nearest neighbor

distance.

Description: NNSD equals the square root of the sum of the squared deviations

of each patches’ nearest neighbor distance (m) from the mean nearest neighbor

distance (MNN), divided by the number of patches; that is, the root mean squared

error (deviation from the mean) in patch nearest neighbor distance. This is the

population standard deviation, not the sample standard deviation.

NNSD

h

h

N

N

ij

ij

j 1

n

i 1

m

j 1

n

i 1

m

2

=

− ′

F

H

G

G

G

G

G

I

K

J

J

J

J

J

L

N

M

M

M

M

M

M

O

Q

P

P

P

P

P

P ′

=

′

=

=

′

=

∑∑

∑∑

116
(L34) Nearest Neighbor Coefficient of Variation

Raster

NNCV = NNSD

MNN (100)

Units: Percent.

Range: NNCV ≥ 0, without limit.

NNCV = 0 when all patches have the same nearest neighbor distance (no variability in nearest neighbor distance; NNSD = 0). NNCV is reported as “NA” in the

“basename”.full file and as a dot “.” in the “basename”.class file if none of the

patches have a nearest neighbor. Similarly, NNCV is reported as “NA” in the

“basename”.full file and as a dot “.” in the “basename”.land file if the user chooses

not to calculate nearest neighbor distance.

Description: NNCV equals the standard deviation in nearest neighbor distances

(NNSD) divided by the mean nearest neighbor distance (MNN), multiplied by 100

(to convert to percent); that is, the variability in nearest neighbor distance relative to

the mean nearest neighbor distance. This is the population coefficient of variation,

not the sample coefficient of variation.

(L35) Mean Proximity Index

Raster

MPI =

∑

i=1

m

∑

j=1

n

∑

s=1

n

aijs

hijs

2

N

Units: None.

Range: MPI ≥ 0.

MPI = 0 if no patch has a neighbor of the same type within the specified search

radius. MPI increases as patches become less isolated from patches of the same

type and the patch types become less fragmented in distribution. The upper limit

of MPI is determined by the search radius and minimum distance between patches.

MPI is reported as “NA” in the “basename”.full file and as a dot “.” in the “basename”.

land file if the user chooses not to calculate nearest neighbor distance.

Description: MPI equals the sum of patch area (m2

) divided by the squared nearest

edge-to-edge distance (m) between the patch and the focal patch of all patches of

the corresponding patch type whose edges are within a specified distance (m) of the

focal patch, summed across all patches in the landscape and divided by the total

number of patches. In other words, MPI equals the average proximity index for

patches in the landscape. When the search buffer extends beyond the landscape

boundary for focal patches near the boundary, only patches contained within the

landscape are considered in the computations.

117
(L36) Shannon’s Diversity Index

Vector/Raster

SHDI = − ∑

i=1

m

(Pi o lnPi)

Units: None.

Range: SHDI ≥ 0, without limit.

SHDI = 0 when the landscape contains only 1 patch (no diversity). SHDI increases

as the number of different patch types (patch richness, PR) increases or the proportional distribution of area among patch types becomes more equitable, or both.

Description: SHDI equals minus the sum, across all patch types, of the proportional

abundance of each patch type multiplied by that proportion.

(L37) Simpson’s Diversity Index

Vector/Raster

SIDI = 1 − ∑

i=1

m

Pi

2

Units: None.

Range: 0 ≤ SIDI < 1.

SIDI = 0 when the landscape contains only 1 patch (no diversity). SIDI approaches

1 as the number of different patch types (patch richness, PR) increases and the

proportional distribution of area among patch types becomes more equitable.

Description: SIDI equals 1 minus the sum, across all patch types, of the proportional

abundance of each patch type squared.

(L38) Modified Simpson’s Diversity Index

Vector/Raster

MSIDI = −ln ∑

i=1

m

Pi

2

Units: None.

Range: MSIDI ≥ 0.

MSIDI = 0 when the landscape contains only 1 patch (no diversity). MSIDI increases

as the number of different patch types (patch richness, PR) increases and the proportional distribution of area among patch types becomes more equitable.

Description: MSIDI equals minus the logarithm of the sum, across all patch types,

of the proportional abundance of each patch type squared.

118
(L39) Patch Richness

Vector/Raster

PR = m

Units: None.

Range: PR ≥ 1, without limit.

Description: PR equals the number of different patch types present within the

landscape boundary.

(L40) Patch Richness Density

Vector/Raster

PRD = m

A (10,000) (100)

Units: Number per 100 hectares.

Range: PRD > 0, without limit.

Description: PR equals the number of different patch types present within the landscape boundary divided by total landscape area (m2

), multiplied by 10,000 and 100

(to convert to 100 hectares).

(L41) Relative Patch Richness

Vector/Raster

RPR = m

mmax (100)

Units: Percent.

Range: 0 < RPR ≤ 100.

RPR approaches 0 when the landscape contains a single patch type, yet the number

of potential patch types is very large. RPR = 100 when all possible patch types are

represented in the landscape. RPR is reported as “NA” in the “basename”.full file

and as a dot “.” in the “basename”.land file if the maximum number of classes is not

specified by the user.

Description: RPR equals the number of different patch types present within the landscape boundary divided by the maximum potential number of patch types based on

the patch type classification scheme, multiplied by 100 (to convert to percent).

(L42) Shannon’s Evenness Index

Vector/Raster

SHEI =

− ∑

i=1

m

(Pi o lnPi)

lnm

Units: None.

Range: 0 ≤ SHEI ≤ 1.

119
SHDI = 0 when the landscape contains only 1 patch (no diversity) and approaches

0 as the distribution of area among the different patch types becomes increasingly

uneven (dominated by 1 type). SHDI = 1 when distribution of area among patch

types is perfectly even (proportional abundances are the same).

Description: SHEI equals minus the sum, across all patch types, of the proportional

abundance of each patch type multiplied by that proportion, divided by the logarithm

of the number of patch types. In other words, the observed Shannon’s Diversity

Index divided by the maximum Shannon’s Diversity Index for that number of patch

types.

(L43) Simpson’s Evenness Index

Vector/Raster

SIEI =

1 − ∑

i=1

m

Pi

2

1 − 





1

m







Units: None.

Range: 0 ≤ SIEI ≤ 1.

SIDI = 0 when the landscape contains only 1 patch (no diversity) and approaches

0 as the distribution of area among the different patch types becomes increasingly

uneven (dominated by 1 type). SIDI = 1 when distribution of area among patch types

is perfectly even (proportional abundances are the same).

Description: SIEI equals 1 minus the sum, across all patch types, of the proportional

abundance of each patch type squared, divided by 1 minus the quantity 1 divided by

the number of patch types. In other words, the observed Simpson’s Diversity Index

divided by the maximum Simpson’s Diversity Index for that number of patch types.

(L44) Modified Simpson’s Evenness Index

Vector/Raster

MSIEI =

−ln ∑

i=1

m

Pi

2

ln m

Units: None.

Range: 0 ≤ MSIEI ≤ 1.

MSIDI = 0 when the landscape contains only 1 patch (no diversity) and approaches

0 as the distribution of area among the different patch types becomes increasingly

uneven (dominated by 1 type). MSIDI = 1 when distribution of area among patch

types is perfectly even (proportional abundances are the same).

Description: MSIEI equals minus the logarithm of the sum, across all patch types, of

the proportional abundance of each patch type squared, divided by the logarithm of

the number of patch types. In other words, the observed modified Simpson’s diversity

index divided by the maximum modified Simpson’s diversity index for that number of

patch types.

120
(L45) Interspersion and Juxtaposition Index

Vector/Raster

IJI =

− ∑

i=1

m′

∑

k=i+1

m′













eik

E







o ln





eik

E













ln(1⁄2[m′(m′ − 1)]) (100)

Units: Percent.

Range: 0 < IJI ≤ 100.

IJI approaches 0 when the distribution of adjacencies among unique patch types

becomes increasingly uneven. IJI = 100 when all patch types are equally adjacent to

all other patch types (that is, maximum interspersion and juxtaposition). IJI is

undefined and reported as “NA” in the “basename”.full file and as a dot “.” in the

“basename”.land file if the number of patch types is less than 3.

Description: IJI equals minus the sum of the length (m) of each unique edge type

divided by the total landscape edge (m), multiplied by the logarithm of the same

quantity, summed over each unique edge type; divided by the logarithm of the

number of patch types times the number of patch types minus 1 divided by 2;

multiplied by 100 (to convert to a percentage). In other words, the observed

interspersion over the maximum possible interspersion for the given number of patch

types. IJI considers all patch types present on an image, including any present in the

landscape border, if a border was included. All background edge segments are

ignored, as are landscape boundary segments if a border is not provided, because

adjacency information for these edge segments is not available.

(L46) Contagion Index

Raster

CONTAG =

















1 +

∑

i=1

m

∑

k=1

m















(Pi)















gik

∑

k=1

m

gik





























o















ln(Pi)















gik

∑

k=1

m

gik





























2ln(m)

















 (100)

Units: Percent.

Range: 0 < CONTAG ≤ 100.

CONTAG approaches 0 when the distribution of adjacencies (at the level of

individual cells) among unique patch types becomes increasingly uneven. CONTAG

= 100 when all patch types are equally adjacent to all other patch types (that is,

maximum interspersion and juxtaposition). CONTAG is undefined and reported as

“NA” in the “basename”.full file and as a dot “.” in the “basename”.land file if the

number of patch types is less than 2.

121
Description: CONTAG equals 1 plus the sum of the proportional abundance of each

patch type multiplied by number of adjacencies between cells of that patch type and

all other patch types, multiplied by the logarithm of the same quantity, summed over

each patch type; divided by 2 times the logarithm of the number of patch types;

multiplied by 100 (to convert to a percentage). In other words, the observed contagion over the maximum possible contagion for the given number of patch types.

CONTAG considers all patch types present on an image, including any present in

the landscape border, and considers like adjacencies (cells of a patch type adjacent

to cells of the same type). All background edge segments are ignored, as are landscape boundary segments if a border is not provided, because adjacency information

for these edge segments is not available.

122
This page has been left blank intentionally.

Document continues on next page.
This page has been left blank intentionally.

Document continues on next page.
McGarigal, Kevin; Marks, Barbara J. 1995. FRAGSTATS: spatial pattern analysis

program for quantifying landscape structure. Gen. Tech. Rep. PNW-GTR-351.

Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest

Research Station. 122 p.

This report describes a program, FRAGSTATS, developed to quantify landscape

structure. FRAGSTATS offers a comprehensive choice of landscape metrics and

was designed to be as versatile as possible. The program is almost completely

automated and thus requires little technical training. Two separate versions of

FRAGSTATS exist: one for vector images and one for raster images. The vector

version is an Arc/Info AML that accepts Arc/Info polygon coverages. The raster

version is a C program that accepts ASCII image files, 8- or 16-bit binary image

files, Arc/Info SVF files, Erdas image files, and IDRISI image files. Both versions

of FRAGSTATS generate the same array of metrics, including a variety of area

metrics, patch density, size and variability metrics, edge metrics, shape metrics,

core area metrics, diversity metrics, and contagion and interspersion metrics. The

raster version also computes several nearest neighbor metrics.

Keywords: Landscape ecology, landscape structure, landscape pattern, landscape

analysis, landscape metrics, spatial statistics.

The Forest Service of the U.S. Department of

Agriculture is dedicated to the principle of multiple

use management of the Nation’s forest resources for

sustained yields of wood, water, forage, wildlife, and

recreation. Through forestry research, cooperation with

the States and private forest owners, and management

of the National Forests and National Grasslands, it

strives—as directed by Congress—to provide

increasingly greater service to a growing Nation.

The United States Department of Agriculture (USDA)

Forest Service is a diverse organization committed to

equal opportunity to employment and program delivery.

USDA prohibits discrimination on the basis of race,

color, national origin, sex, religion, age, disability,

political affiliation, and familial status. Persons believing

that they have been discribminated against should

contact the Secretary of Agriculture, U.S. Department

of Agriculture, Washington, DC 20250, or call

202-720-7327 (voice), or 202-720-1127 (TDD).

Pacific Northwest Research Station

333 S.W. First Avenue

P.O. Box 3890

Portland, Oregon 97208-3890
This page has been left blank intentionally.