Sampling and Estimation 

Procedures for the 

Vegetation Diversity and 

Structure Indicator

Bethany K. Schulz, William A. Bechtold, and Stanley J. 

Zarnoch

United States 

Department of 

Agriculture

Forest Service

Pacific Northwest 

Research Station

General Technical Report

PNW-GTR-781

January 2009

DEPAR TMENT OF AGRICULT URE
Authors

Bethany K. Schulz is a research ecologist, Pacific Northwest Research Station, 

Forestry Sciences Laboratory, 3301 C Street, Suite 200, Anchorage, AK 99503-

3954; William A. Bechtold is a research forester, and Stanley J. Zarnoch is a 

mathematical statistician, Southern Research Station, 200 Weaver Blvd., Asheville, 

NC 28804.

Cover

Western hemlock forest near Hawk Mine, Alaska (photo by Jonathan Williams).

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.

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Abstract

Schulz, Bethany K.; Bechtold, William A.; Zarnoch, Stanley J. 2009.

Sampling and estimation procedures for the vegetation diversity and structure 

indicator. Gen. Tech. Rep. PNW-GTR-781. Portland, OR: U.S. Department of 

Agriculture, Forest Service, Pacific Northwest Research Station. 53 p.

The Vegetation Diversity and Structure Indicator (VEG) is an extensive inventory of vascular plants in the forests of the United States. The VEG indicator 

provides baseline data to assess trends in forest vascular plant species richness and 

composition, and the relative abundance and spatial distribution of those species, 

including invasive and introduced species. The VEG indicator is one of several 

sets of measures collected by the Forest Inventory and Analysis (FIA) Program 

of the USDA Forest Service to assess forest health. This document describes the 

sampling design, field data collection methods, primary output objectives, and 

estimation procedures for summarizing FIA VEG data.

Keywords: FIA, forest health monitoring, forest structure, forest vegetation, 

plot-based sampling, species composition, species distribution, species richness.

This paper was subjected to an anonymous peer-review process coordinated 

by an independent editor, and the manuscript has been modified accordingly.
Contents

1 Introduction

1 Forest Inventory and Analysis and Forest Health Indicators

1 Vegetation as an Indicator of Forest Health

3 Sample Design

3 Forest Inventory and Analysis Phases Defined

3 P3 Vegetation Indicator Method Basics

8 Vegetation Inventory and Monitoring Issues

12 Plant Community Data Analysis

14 The Nature of Plant Community Data

15 Attributes to Assess as Indicators

23 Plant Community Analysis

26 Estimation

26 Ratios of Means

28 Populations and Domains

29 Partial Plots and Subplots

30 Species-Based Estimator Details

36 Community-Based Estimator Details

43 Change Estimation

44 Notation for Equations

46 Acknowledgments

46 Metric Equivalents

46 Literature Cited
Sampling and Estimation Procedures for the Vegetation Diversity and Structure Indicator

Introduction 

Forest Inventory and Analysis and Forest Health Indicators 

The USDA Forest Service Forest Inventory and Analysis (FIA) Program has 

traditionally conducted timber inventories of the Nation’s forests. Although the 

focus has historically been commodity driven, many researchers have recognized 

the utility of using FIA data to analyze wildlife habitat, range, recreation, hydrology, and more (Rudis 1991, 2003). Recently, a new enhanced FIA Program has been 

implemented to formally respond to customers’ interest in nontimber attributes of 

forests (Bechtold and Patterson 2005). Integration with the Forest Health Monitoring (FHM) Program is the new component of FIA, providing a three-phase nationwide systematic sample of a wide array of forest ecosystem parameters.

The FHM Program, originally established in 1990 as a cooperative effort 

between the U.S. Environmental Protection Agency and the U.S. Forest Service, 

set about to establish measurable indicators of forest conditions (Riitters and Tkacz 

2004). Forest health indicators include a broad suite of attributes that describe forests in terms of ownership, tree crown conditions, lichen community composition, 

down woody material, soil physical and chemical attributes, and vegetation diversity and structure. By measuring forest attributes consistently across the Nation, 

baseline estimates of each indicator can be established. The status and trends of 

those estimates can be monitored over time as they relate to changes in ecological 

conditions of the Nation’s forests (Smith and Conkling 2004, Stapanian et al. 1997).

Vegetation as an Indicator of Forest Health 

Vegetation is the source of primary production—the conversion of sunlight energy 

into energy stored as organic matter—and a fundamental determinant of habitat 

and wildfire fuel profile characterization. All plant communities are in flux; 

vegetation structural stages are often assessed to determine current potential for 

productivity and wildlife habitat. Disturbance of vegetation can have cascading 

effects through an ecosystem whether the changes are brought about gradually 

through natural succession or by sudden destructive events. Changes in species 

diversity and composition, structural diversity (Willis and Whittaker 2002), and the 

abundance of nonnative species are common national concerns, as reflected in the 

international criteria for assessing sustainability of forestry practices (USDA FS 

1995).

The Vegetation Diversity and Structure (VEG) indicator embodies a set of 

measurements based on an inventory of vascular plants on an extensive systematic 

network of forest plots across the United States. The VEG indicator provides data to 

assess trends in forest vascular plant species richness and composition, the relative 

Vegetation is the 

source of primary 

production—the 

conversion of sunlight 

energy into energy 

stored as organic 

matter.
GENERAL TECHNICAL REPORT PNW-GTR-781

abundance and spatial distribution of those species, and overall physical structure 

created by the plant species present (Stolte et al. 2002). Data are also collected to 

describe vegetation community vertical structure and ground cover (i.e., soil/air 

interface). 

Vegetation species composition data allow for species-based and communitybased estimates at both the stand and population levels. Species-based estimates 

include individual species abundance (measured as the canopy cover of a species) 

and frequency (the distribution of a species across a specified area). Communitybased estimates include the combination of species occurring within or across an 

area (i.e., species richness, composition, and stand structure). In addition, the site 

factor variables, other forest health indicator data, and other plot measurements 

can be used to assess species composition in relation to various environmental 

factors with multivariate analyses. Possible analyses include the examination of the 

distribution patterns of any species of interest (e.g., noxious, invasive, or introduced 

species), functional group (e.g., nitrogen fixers, wildfire accelerants or inhibitors), 

life form, or understory structure as it pertains to wildlife habitat, productivity, fuel 

profiles, or disturbance histories. With repeated measures on the same plots, VEG 

indicator data allow estimates of change from paired observations.

Long-term, large-scale vegetation inventory and monitoring programs are rare 

(Stohlgren 1994) but valuable for regional and national condition assessments. Such 

large-scale assessments provide broad overviews to help strategic policy development (Heinz Center 2006, Ingerson and Loya 2008) and allow land managers to 

place local assessments into regional or national perspectives, which facilitates the 

prioritization of limited resources available to managers. Reporting at local levels 

should be within the context of a larger region to clarify the status of a particular 

indicator within the smaller area because local levels may only be represented by 

a few plots that differ from the larger region. When trends or changes that warrant 

further investigation are detected, evaluation monitoring projects are initiated, 

often with intensified sampling effort at local levels, as the next step in forest health 

monitoring (Riitters and Tkacz 2004). 

This document describes the sample design, primary output objectives, and 

estimation procedures for summarizing the VEG data. At the onset of this project, 

the intended audience was primarily FIA statisticians, analysts, and programmers. 

However, as more data become available, researchers and managers from other 

branches of the Forest Service, other agencies, nongovernment organizations, and 

universities should find this documentation useful. 

The technical material in this document is divided into three main sections. The 

“Sample Design” section includes an overview of the FIA Program, a summary 

Vegetation species 

composition 

data allow for 

species-based and 

community-based 

estimates at both the 

stand and population 

levels.
Sampling and Estimation Procedures for the Vegetation Diversity and Structure Indicator

of the current field data collection methods, and specific issues related to collecting vegetation data on FIA plots. The “Plant Community Data Analysis” section 

provides background information on plant community analysis for analysts who are 

new to the subject, and the “Estimation” section defines plot- and population-level 

estimators and variances in equation form for statisticians and programmers. 

Sample Design

Forest Inventory and Analysis Phases Defined

The three phases of the enhanced FIA Program are described in detail by Bechtold 

and Patterson (2005). The primary objective of phase 1 (P1) is to stratify land area 

in the population of interest for the purpose of reducing the variances of estimates. 

Phase 1 entails the use of ancillary data, including remotely sensed imagery in 

the form of aerial photography or satellite imagery, to stratify the land area in the 

population of interest and to assign plots to strata (two at minimum: forest and 

nonforest). Phase 2 (P2) entails visits by field crews to the physical locations of 

permanent ground plots to measure the traditional set of FIA variables such as 

forest type, site attributes, tree species, and tree size. The P2 sample is based on a 

nationwide hexagonal grid array of approximately 6,000-acre hexagons containing 

one permanent ground plot each. The primary objective of phase 3 (P3) is to measure additional variables related to the health of forest ecosystems. The P3 sample is 

a 1/16 subset of the P2 plot network, resulting in a sampling intensity of one plot per 

approximately 96,000 acres (38 400 hectares). Because P3 plots are also P2 plots, 

P3 measurements include all measurements made on P2 plots, plus measurement 

of the biotic and abiotic features associated with forest and ecosystem health. The 

VEG indicator set of measurements is collected on P3 plots. 

Each permanent FIA ground plot consists of four 24-ft-radius (7.3-m) circular 

subplots arranged in a clustered formation (fig. 1). Additional areas within the 

subplots are used for various measurements. For the VEG indicator, three 3.28- by 

3.28-ft (1 m2) quadrats are established per subplot at 15 ft (4.56 m) from subplot 

center along transects at 30°, 150°, and 270°.

P3 Vegetation Indicator Method Basics

Sampling rules—

Permanent plots are established when at least one subplot in the plot configuration 

contains at least some accessible forest. Forested plots (or portions of plots) are 

considered inaccessible and not sampled if they are outside the U.S. boundary, 

access is denied by landowner, hazardous situations exist, or the area falls in census 

water (Bechtold and Patterson 2005).

The primary objective 

of phase 3 is to 

measure additional 

variables related to 

the health of forest 

ecosystems. 
GENERAL TECHNICAL REPORT PNW-GTR-781

Vegetation is sampled only on land classified as accessible forest. Besides 

recording subplot area by land use, no measurements are taken on nonforested or 

inaccessible portions of a plot. No trees or other vegetation are measured in nonforest for two key reasons: (1) the FIA Program focuses on monitoring forest land 

and (2) data collection time is limited. Although extending P3 data to nonforest 

conditions has been considered, without P2 data collection, the augmenting environmental and mensuration variables would not be available. Although data from 

adjacent nonforested areas would be of interest to many users, sending the vegetation specialists into nonforested plant communities would increase their workload 

and time required on plot. In the future, some inventory units may opt to collect 

P2 data on nonforested lands, at which time it may be more practical to include P3 

VEG data collection on nonforested lands.

Each plot is described by one or more “condition classes,” which are delineated 

by variables that include land use, forest type, stand size, regeneration status, tree 

density, stand origin, ownership group, and disturbance history. When more than 

Figure 1—Arrangement of the Forest Inventory and Analysis plot design of four clustered subplots.

Q1

Q2

Q3

120 ft between

subplot centers

1

2

3 4

1 m2

quadrats

24-ft radius

subplot

Azimuth 1–2 = 360°

Azimuth 1–3 = 120°

Azimuth 1–4 = 240°


Sampling and Estimation Procedures for the Vegetation Diversity and Structure Indicator

one distinct condition class is present on a plot, boundaries between them are 

mapped by the field crew collecting mensuration data (P2) for the plot. Mensuration 

data are stored by plot, subplot, and condition class to allow flexibility in summarizing population estimates by condition-class variables.

Although boundaries between forest and nonforest conditions are recognized 

by VEG field crews, boundaries between accessible forest conditions are ignored, 

and only one list of species is maintained for each quadrat and subplot. Assessing vegetation for each unique condition class would again require extra time and 

added complication. Still, subplots with multiple conditions often require special 

handling, as described in the “Estimation” section, and condition-class data from 

the P2 sample are required for compiling population estimates from the P3 VEG 

data. This is necessary to identify partially forested plots, and to permit analysis of 

subsets of forest (i.e., domains of interest), such as a particular forest type.

Sampling rules result in a mixture of plot configurations in the database:

1. Four complete subplots within 100-percent accessible forested conditions:

a. In a single condition class

b. More than one condition class

i. Each subplot a single condition

ii. One or more subplots with multiple conditions

2. Fewer than four subplots in accessible forested condition:

a. In a single condition class

b. More than one condition 

i. Each subplot a single condition

ii. One or more subplots with multiple conditions

iii. One or more subplots with less than 100-percent accessible forest land

Other permutations also exist; but the list above captures the general categories. 

This mixture of plot types presents a number of challenges for summarizing data 

at both plot and population levels. Ideally, every plot would be represented by four 

subplots in a single accessible forested condition. However, statistically based 

inventories capture conditions as they occur across the landscape. 

Species data—

Each vascular plant species (including trees) with live stems within or foliage hanging over the forested portion of subplots is recorded. Plants identified to species 

are recorded with the accepted Natural Resources Conservation Service PLANTS 

database code (USDA NRCS January 2000 version). Plants not readily identified 

to species are assigned a genus or standard unknown code and are collected for 

identification if not locally sparse (five or fewer individual plants are present on the 

entire plot or immediate surrounding area).
GENERAL TECHNICAL REPORT PNW-GTR-781

For each species, the following data are recorded:

• Presence/absence on each quadrat

• Total aerial percentage canopy cover by species in 1-percent increments, 

based on the standard subplot area 

• Percentage species canopy cover recorded by height layers, in the same 

increments and tolerances as described above

o Combined layers one and two (zero to 6 ft [0 to 1.83 m] from ground)

o Layer three (>6 to 16 ft [>1.83 to 4.88 m] from ground)

o Layer four (>16 ft [>4.88 m] from ground)

Crews begin by assessing species on quadrats for several reasons. Assessing 

the smaller quadrat areas as soon as possible before the vegetation is damaged or 

inadvertently trampled by other field crew members avoids sampling errors. Also, 

by focusing their eyes on smaller areas first, the vegetation specialists will notice 

small plant species or those that may become inconspicuous when assessing the 

much larger subplot area. Canopy cover is not recorded on quadrats, but each species recorded on a quadrat requires a cover measurement on the subplot. Quadrat 

species presence/absence data are used to describe the distribution of a species on a 

subplot, complementing the record of cover to describe its abundance.

On partially forested subplots where only the forested portions are assessed, 

all cover measurements are estimated based on the full subplot area. That is, if the 

cover of a species on the forested portion of the subplot is about equal to a circle

with a radius of about 5.3 ft, cover is recorded as 5 percent ( 100

(24)

(5.3)

2

2

× 















P

P ) as 

it would be on a totally forested subplot.

Species abundance on partially forested subplots is collected this way primarily to accommodate measurement repeatability. Crews are trained to calibrate 

ocular estimates based on total subplot area, e.g., what 5-percent cover looks like 

on a regular, fully forested subplot. Subplots that are less than fully forested have 

variable proportions of forest. Estimating canopy cover over a consistent shape and 

area is less mentally taxing than having to adjust to smaller areas of variable shapes 

especially given that numerous estimates are made per subplot, and many plots 

are visited over the course of a season. Cover measurements on plots that are less 

than 100-percent forested are adjusted to relate only to the forested portion when 

estimates are computed.

To help standardize the sampling effort in the many different forest types 

across the country, a time limit is imposed for subplot species searches (time spent 

searching for additional species). This discourages the over-zealous crew member 

from searching for every last sprout and fosters the ability to fully sample as many 

subplots (and quadrats) as possible on very diverse or densely vegetated plots.
Sampling and Estimation Procedures for the Vegetation Diversity and Structure Indicator

Vegetation structure and condition of soil/atmosphere interface—

On each subplot, several general assessments are made:

• Percentage of subplot area in accessible forest land is estimated because 

it affects data edit checks related to all ocular estimates. For example, the 

first two measures listed below are based on the percentage of the subplot 

area that is accessible forest; if the accessible forest is only 75 percent, the 

absolute canopy cover recorded by field crews cannot exceed 75 percent, 

and the sum of all ground variables must equal 75 percent.

• Absolute canopy cover, the canopy cover created by all plants present on a 

subplot, in 1-percent increments in each of four height layers 

o Layer one (0 to 2 ft [0 to 0.61 m] from ground)

o Layer two (>2 to 6 ft [> 0.61 to 1.83 m] from ground)

o Layer three (>6 to 16 ft [> 1.83 to 4.88 m] from ground)

o Layer four (above 16 ft [> 4.88 m] from ground)

This cannot be derived from species canopy cover because species cover may 

or may not overlap. 

• Ground variables describe the soil/atmosphere interface in percentage 

cover of cryptobiotic crust, lichen, litter/duff, mineral soil, moss, road/trail, 

rock, standing water, permanent water, trash, and wood in 1-percent increments.

• Nonforest land use is recorded for any portion of the subplot not in the 

forested condition. Broad categories include agricultural uses, rangeland, 

development, and natural nonforest lands. 

• Condition class information, such as forest type and stand size class is 

essential for compiling population estimates from VEG data and is collected by foresters as part of the P2 inventory. 

On each quadrat, assessments include:

• The condition class the quadrat belongs to

• Level of trampling damage

Emphasis is made on completing the entire set of variables for a subplot when 

time limits restrict a crew from completing the entire plot, although this is rare. 

Subplots with complete measurements are more valuable for estimations and analysis than some data from all 12 quadrats with only one or two subplots complete, for 

example. 

The complete P3 VEG field guide is posted on the FIA homepage http://www.

fia.fs.fed.us/library/field-guides-methods-proc/ (USDA FS 2005).

Emphasis is made on 

completing the entire 

set of variables for 

a subplot when time 

limits restrict a crew 

from completing the 

entire plot.
GENERAL TECHNICAL REPORT PNW-GTR-781

Vegetation Inventory and Monitoring Issues

There are many ways to sample vegetation. When planning for vegetation sampling, 

investigators must consider the questions to address, the precision and accuracy 

required to answer those questions, and the ability to collect the needed data in the 

time allotted (Stohlgren 1994). Potential sources of error and measures to control 

or minimize this error should be documented. This section presents factors of the 

sampling design that have influenced the methods used for field data collection, 

given the logistical constraints of FIA inventories. It also addresses known sources 

of error and how they are addressed, including levels of species identification. Other 

investigators are welcome to use the P3 vegetation methods, but they are reminded 

that no one sampling method will meet all needs and are cautioned to carefully consider their own objectives before adopting the methods outlined in this document. 

Sample design issues—

Geographic extent and spatial scale—The P3 grid is extensive; there is one plot 

per 96,000 acres. The FIA plot design is a cluster of four subplots; FIA’s default 

estimation method for processing standard inventory (P2) data (Bechtold and 

Patterson 2005) combines subplot data to the plot level, ignoring the variance 

among subplots. Phase 3 VEG data do not necessarily need to be processed in this 

manner. Two considerations must be highlighted:

1. Plant species composition can be highly variable across much shorter distances than captured by the P3 sample. One objective of plant community 

analysis is to describe and explain the variable nature of species composition. Species composition in plots that straddle multiple forest types may be 

highly variable from subplot to subplot, but the between-subplot variability may be either greater or less than the variability among subplots of the 

same forest types on different plots. For example, consider two plots that 

both have some subplots in a Douglas-fir forest type and some subplots in 

aspen forest type. Even if the plots are a great distance from each other, the 

subplots in the Douglas-fir type often have species compositions that are 

more similar to Douglas-fir type in another plot than to the subplots in the 

aspen forest type on the same plot. 

2. The VEG data are recorded only on the portions of a plot that are accessible and defined as forest. Where fewer than four subplots are forested, the 

measured subplots can still be combined for most plot and population estimates. Plots and subplots that are less than 100-percent forested should not 

be included in some VEG estimators because they need to be derived from 

sampling units of standard size. This is because the relationship between 

number of species and area sampled is not linear (Crawley and Harral 
Sampling and Estimation Procedures for the Vegetation Diversity and Structure Indicator

2001). Analysts may choose to include data from plots less than 100-

pecent forested but should compare variances and note the types of plot 

configurations included in reported estimates. Details about the appropriateness of including partially forested samples are provided in the 

“Estimation” section.

Number and size of plots—Most vegetation inventory and monitoring projects 

determine the number and size of plots based on specific objectives of the project, 

and pilot studies are often used to optimize the plot configuration and sample size 

(Kenkel and Podani 1991). According to McCune and Grace (2002), the “many and 

small” scheme will yield accurate estimates of abundance for the most common 

species, but incomplete species lists. The “few and large” scheme results in a more 

complete species list but overestimates the abundance of rarer species. The FIA 

sample design—plots composed of a cluster of subplots—is a tradeoff between the 

two approaches.

For any subset of data subjected to analysis and summary, the population 

should be described in terms of numbers of full and partial plots and homogeneity 

of conditions found on those plots. Mixed-condition and partially forested plots 

should receive special consideration in plot summaries and population estimates, as 

described in the “Estimation” section. 

Duration and remeasurement of site visits—Plots are usually visited on a single 

day every 5 to 10 years. Limited time on the plot and the phenological state of the 

vegetation will affect the thoroughness of the species list and the measures of species total cover. Limiting search times helps standardize the “sampling effort” for 

species lists. We acknowledge that percentage canopy cover for many species can 

change dramatically over very short periods during the growing season. 

Ocular estimation issues—

Ocular canopy cover measures of abundance are commonly used in plant community analysis (Daubenmire 1959, Elzinga et al. 1998, McCune and Grace 2002, 

Mueller-Dombois and Ellenberg 1974). Although cover is a percentage of a standard 

area and therefore “absolute,” it is not a precise measurement. Many studies have 

been conducted to evaluate the repeatability of canopy cover measures (Hatton et 

al. 1986, Helm and Mead 2004, Kennedy and Addison 1987, Sykes et al. 1983, van 

Hees and Mead 2000). These studies show that cover estimates are most variable at 

the moderate level (30 to 70 percent). Even though some may question the repeatability of canopy cover as an abundance measure, it has been shown to be reliable 

for species abundance in broad-scale studies encompassing a variety of plant 

communities (Mueller-Dombois and Ellenberg 1974). Most plant ecology studies 

Limited time on the plot 

and the phenological 

state of the vegetation 

will affect the 

thoroughness of the 

species list and the 

measures of species 

total cover.
10

GENERAL TECHNICAL REPORT PNW-GTR-781

employ cover classes when evaluating canopy cover with ocular estimates. Many 

cover class schemes that have been developed have smaller increments at either 

end of the scale and wide margins in the middle (McCune and Grace 2002). It is 

accepted that such schemes reduce variability issues among observers (MuellerDombois and Ellenberg 1974). Although species abundance in P3 VEG are recorded 

as percentage canopy cover “to the nearest 1 percent,” measurement quality objectives tolerances for precision of field-collected data mimic cover classes described 

above. Analysts are cautioned that the raw data should be transformed to cover 

classes when applying multivariate methods. Use of raw data, or even midranges of 

cover classes, tend to overemphasize dominant species over those in the mid to low 

abundance classes (McCune and Grace 2002). Note that usually more than half of 

all species canopy cover measures in the VEG database are 1 percent.

Some researchers have suggested stem counts instead of canopy cover estimates. Although counts of individuals belonging to a single species are well-suited 

to specific monitoring efforts concerning rare species or treatment effects, they are 

very time-consuming and are generally limited to studies concerning a single or 

a few species on any given site (Elzinga et al. 1998). Counting individual plants is 

impractical and unnecessary for the objectives of the P3 VEG indicator. To further 

address this point, advantages and disadvantages of each method are tabulated 

below. When assessing species’ distribution over space and time, a combination of 

cover and frequency gives a broader evaluation (Daubenmire 1959). The P3 VEG 

indicator measures generate both cover and frequency data.

 The following tabulation shows the advantages and disadvantages of counts as 

a measure of vascular plant species abundance:

Advantages Disadvantages

1. When used within a given area, 1. Difficult to use with clonal species

quantifying the number of individual (hard to distinguish individuals,

plants of a given species can give a e.g., rhizomatous grasses, aspen clones). 

complete census, and therefore, is 2. Accuracy can be poor owing to

not an estimate. missed individuals (small individuals,

2. Preferred method for monitoring a individuals at different life stages).

single species, or a small group of 3. Insensitive as a vigor-related measure in

species (i.e.,. trees on plot). long-lived species, such as trees or 

3. Can be reported as numbers of indi- shrubs.

viduals per unit area, so sample areas 4. Very time consuming, especially

do not need to be equal to compare when each species must be assessed

results from multiple sources. over a fairly large area (subplot)

and vegetation is dense. (This alone

makes the method prohibitive on P3

plots, visited 1 day (4 to 6 hours) every

5, 7, or 10 years).
11

Sampling and Estimation Procedures for the Vegetation Diversity and Structure Indicator

The following tabulation lists the advantages and disadvantages of canopy 

cover as a measure of vascular plant species abundance:

Advantages Disadvantages

1. Expresses a species’ “influence” 1. Can change dramatically over the

on the area of interest. course of a growing season for most

2. Does not require individual plants species other than dwarf shrubs

to be identified. and other low woody plants.

3. Quantitative method that can be 2. Visual estimates can differ

applied to just about all life forms; among observers.

therefore, they can be evaluated 3. Difficult to assess plants above 1 m

with the same parameter. (Equal- in height (or waist height of observer).

izes the contribution of small but

abundant species with those that

are larger but few.)

4. Rapid visual evaluation of many

species is possible.

5. Widely used in ecological studies.

6. Meets criteria for structural classification (spacing and height).

(Summarized from Daubenmire 1959, Elzinga et al. 1998, Jukola-Sulonen and Salemaa 

1985, McCune and Grace 2002, and Mueller-Dombois and Ellenberg 1974.)

Species identification issues— 

Data are collected on all vascular plants rooted in or overhanging the forested 

subplot space. In addition to species that are overlooked because of low abundance 

or absence at the time of the plot visit (ephemerals), there may be species that cannot 

be identified because of phenological stage of development, sparse numbers of 

individuals for collection, or damaged condition. These factors are inherent in all 

plant surveys, and contribute to the uncertainty of species composition and richness 

estimates. There are accepted methods that account for undiscovered species in 

population estimation of gamma, as explained in the “Estimation” section. However, although it is rare for plant inventory and monitoring studies to report unidentified species as a source of error (Scott and Hallam 2002), FIA acknowledges and 

reports the percentage of species distinguished but not identified. 

Steps are taken to maximize the quality of the data collected. Data are collected 

by specialists with prior botanical experience who are certified in the P3 VEG 

sampling methods. Repeatability studies on vegetation data collected by FIA have 

shown that crews on average identify 75 percent of plants to species, and 89 percent 

to genus. They agree on 71 percent of the species identifications, with most differences attributed to closely related species and plants overlooked because of low 

abundance (Gray and Azuma 2005). These results are similar to other vegetation 

inventory repeatability studies, but the expected repeatability in identification does 

affect the ability to track all species over time with the same reliability. Species that 
12

GENERAL TECHNICAL REPORT PNW-GTR-781

are frequently encountered or are abundant are likely to be identified correctly more 

often than those species that are very infrequent or present in trace amounts. 

Crews collect specimens of plants they cannot readily identify unless the plant 

is locally sparse or in very poor condition for identification. If a plant species cannot 

be determined, genus or standard unknown codes are accepted. Standard unknown 

codes provide information about the plants’ life form, which enables those records 

to be included in analysis of plant communities by life form and to contribute to 

species counts for any plot. 

The incorporation of standard unknown codes (USDA NRCS 2000) has 

reduced the number of unknown codes that cannot be interpreted by anyone other 

than the person collecting data, and the total number of species per plot is tracked 

with the inclusion of a “unique species number” variable. A species list is maintained for each plot. When an unknown plant is first encountered, an unknown code 

is assigned (e.g., 2FDA, representing an annual dicot forb [all standard unknown 

codes begin with ”2”]). A unique species number of “1” is assigned to the record. 

The next time the code 2FDA is entered on that plot, the field crew must consider 

“is this the same 2FDA as recorded earlier?” If yes, the same unique species 

number is assigned (1). If no (it is another unique species), a unique species number 

of “2” is assigned. The two species are distinguished by the unique species number 

maintained in the database, and the number of species observed on each plot is 

accurately recorded in the database, even if they are not all identified. This maintains the ability to count the number of distinguishable species per quadrat, subplot, 

and plot.

Use of general codes may cause underestimation of gamma diversity (number 

of unique species) because all the collective 2FDAs that remain in the database 

after all possible identifications are made do not represent the same species on 

different plots nor are they all unique species. However, they reduce the number of 

unknown codes that do not supply any information about the plant in question and 

that would inflate values of gamma. Prior to implementation of this scheme, gamma 

from data collected between 2001 and 2003 included 2,018 “free-form” distinct 

unknown codes. Many of these could have referred to the same species. That number was reduced to 27 when codes were converted to standardized unknown codes, 

resulting in reduction of population gamma while maintaining observed plot-level 

species richness (alpha)

Plant Community Data Analysis

The fundamental analysis goal of the VEG indicator is to assess vascular plant 

species assemblages in the Nation’s forests. Data are compiled to describe the 
13

Sampling and Estimation Procedures for the Vegetation Diversity and Structure Indicator

species encountered and the plant communities of the sampled area. Assessment 

objectives include estimation of plot-level and population-level attributes that serve 

as indicators of forest condition (e.g., individual species distribution and abundance, 

species diversity, stand physical structure) and pattern recognition (e.g., presence 

and abundance of introduced species, community type descriptions, and indicator 

species analysis). 

The FIA plot design (fig. 1) spreads four subplots over an area larger than 

would be sampled by a single plot of equivalent size. As a result, plots are “homogenized” and the between-plot variance of P2 timber volume estimates is reduced, 

thus reducing the number of plots needed to achieve a given accuracy standard 

(Bechtold and Patterson 2005). Somewhat in contrast, the aim of plant community 

analyses is to capture and explain the variability observed, and thereby increase 

the ability to predict where similar patterns in species composition may occur. The 

four-subplot plot design can blur the lines between distinct plant communities that 

may occur on a plot and decrease the resolution of the sample for plant community 

analysis. These differences, the different intensities of the sampling grids, and 

logistic constraints, all influence the type of estimations possible from each phase 

of the forest inventory. 

The sparse nature of the P3 sample makes it most appropriate for national or 

regional population reporting. When data are stratified by forest type after collection and reported at the scale of an ecological region, variances may be reduced. 

Ecological provinces, as described by Bailey (1995) and Cleland et al. (2005), define 

areas with similar physical and biological features that influence vegetation and are 

also appropriate for defining populations for which reliable estimates can be made. 

However, because permanent plots are installed and revisited over time, stand-level 

changes can be assessed and reported at a local level and compared to changes over 

a larger region. 

Differences in the distribution and abundance of individual species, and differences in composition and structure between and within plots can be examined. 

Indicator species analysis can be applied to determine if a species of interest has 

an affinity for unique environmental conditions (Klinka et al. 1989, McCune and 

Grace 2002). Trend and pattern analyses across time and space are possible by 

calculating similarity between plots based on species composition and site environmental data.

This section describes the nature of plant community data, concepts of the 

individual attributes assessed, and the utility of species composition data. Detailed 

equations for the estimators and their variances are provided in the next section. 

The various basic estimators for the VEG indicator are listed in table 1.
14

GENERAL TECHNICAL REPORT PNW-GTR-781

The Nature of Plant Community Data

A species inventory indicates how many species are contained within an ecological 

unit or population of interest, and the species lists for individual plots allow analysts 

to assess how those species are grouped or distributed over the area of interest. A 

species matrix—a table of species recorded by sample unit (plot, subplot, or quadrat)—is the basic data building block used to describe both the individual plots and 

species’ distributions over a population area of interest (table 2). However, multiple 

species create highly multivariate data. Whereas some groups of plots will have 

species composition that is very similar, other such groups will have no species in 

Table 2—Sample species matrix with presenceabsence data

Species Plot 1 Plot 2 Plot 3 Plot 4 ... Plot n

Sp1 0 1 1 0 ... 1

Sp2 1 1 0 1 ... 1

Sp3 1 0 1 0 ... 1

... ... ... ... ... ... ...

Sps 0 1 0 1 ... 0

Table 1—Summary of vegetation indicator estimators and appropriate sampling 

units 

Plot level Population level

Describing individual species observed

Species distribution Frequency Frequency

Quadrat Quadrat

Subplot Subplot

 Plot

Species abundance Average % cover Average % cover

Average % cover by layer Average % cover by layer

Describing plant communities 

Diversity

 Species richnessa Average quadrat alpha Average quadrat alpha

Average subplot alpha Average subplot alpha

Plot alpha Average plot alpha

 Total number of species Plot gamma Gamma

Jackknife estimates 

 Differential Plot beta Population beta

Structure

 Absolute coverb Average % cover 0-2 ft Average % cover 0-2 ft

Average % cover 2-6 ft Average % cover 2-6 ft 

Average % cover 6-16 ft Average % cover 6-16 ft

Average % cover 16+ ft Average % cover 16+ ft

 Ground coverc Average % cover Average % cover

a Number of species per standard area.

b All species over subplot area.

c Various descriptors over subplot area.

Some variation in 

species composition is 

due to environmental 

factors; other 

sources of variation 

include chance, local 

disturbances, and the 

statistical limitations of 

sampling.
15

Sampling and Estimation Procedures for the Vegetation Diversity and Structure Indicator

common. Some variation in species composition is due to environmental factors; 

other sources of variation include chance, local disturbances, and the statistical 

limitations of sampling. As the species matrix grows to include more plots over 

larger areas and more variable conditions, it becomes increasingly “sparse,” with 

many zeros, because most species occur on only a small portion of plots. This leads 

to high coefficients of variation and lack of normality, limiting the applicability of 

normal-theory multivariate methods. Despite this, there are many ways to summarize and analyze data to provide useful information. 

Attributes to Assess as Indicators

Individual species distribution—

The full inventory of vascular plants on forested plots provides, at a most basic 

level, information on where a species occurs and where it is absent. Presence/

absence (P/A) information is used to describe how the observed species are dispersed over an area of interest. It is useful in large-scale projects where vegetation 

composition changes dramatically across the area of interest (McCune and Grace 

2002). Although P/A data are very simplistic, they cannot be extracted from surveys 

that only record a limited subset of the actual species present (e.g., surveys that 

record only the most abundant species or species on a list). The P/A data can be 

expressed as relative frequency; the ratio of the number of sample or subsample 

units where a species was recorded to the number of total sample or subsample 

units visited (table 3). Relative frequency will be referred to as simply “frequency” 

throughout this document. 

Frequency—Frequency describes the distribution patterns of a species on a plot 

or within a stand, i.e., clumped vs. dispersed (Elzinga et al. 1998). Frequency is 

often calculated from data collected at multiple scales and is most informative when 

reported at multiple scales (table 3). Frequency is used for change detection in species’ spatial distribution over time; this is especially useful for monitoring invasive 

species (fig. 2). For the VEG indicator, frequency measures are more reliable than 

cover measures for detecting change. Species cover can vary greatly owing to 

phenological changes throughout a growing season (Smith et al. 1986) and climatic 

variations from year to year, whereas frequency reflects where a species is rooted 

on a set of permanent (revisited) plots.

Frequency is dependent on the size of the area sampled (McCune and Grace 

2002) and, thus, frequency estimates should be based on fixed-area samples. For 

the VEG indicator, this is problematic because partially forested plots cause variations in the area from which vegetation is sampled. Estimations can be made by 
16

GENERAL TECHNICAL REPORT PNW-GTR-781 Table 3—Distribution of selected native (N) and introduced (I) species over 915 plots Constancyb Plots where present Number Growth over all Average Subplot Quadrat of plots habit Scientific namea Common name Origin 915 plots cover frequency frequency

Percent

376 Vine Parthenocissus quinquefolia L. Virginia creeper

N 41.09 6.53 0.79 0.36

324 Tree Acer rubrum L. red maple

N 35.41 15.10 0.77 0.33

297 Shrub, vine Toxicodendron radicans (L.) Kuntz eastern poison ivy

N 32.46 7.90 0.63 0.21

274 Tree Quercus rubra L. northern red oak

N 29.95 10.40 0.59 0.09

215 Vine, shrub Rosa multiflora Thunb. ex Murr. multiflora rose I 23.50 7.83 0.62 0.16

159 Tree, shrub Sassafras albidum (Nutt.) Nees sassafras

N 17.38 8.90 0.72 0.21

77 Graminoid Achnatherum hymenoides (Roemer &

 J.A. Schultes) Barkworth Indian ricegrass

N 8.42 1.51 0.64 0.11

77 Graminoid Bromus tectorum L. cheatgrass I 8.42 4.46 0.72 0.33

75 Shrub Lonicera canadensis Bartr. ex Marsh American fly honeysuckle

N 8.20 2.63 0.60 0.11

52 Subshrub Mahonia repens (Lindl.) G. Don creeping barberry

N 5.68 2.79 0.62 0.25

51 Vine Lonicera japonica Thunb. Japanese honeysuckle I 5.57 16.90 0.64 0.34

49 Forb/herb Daucus carota L. Queen Anne’s lace I 5.36 3.86 0.50 0.1849 Forb/herb Phytolacca americana L. American pokeweed

N 5.36 3.57 0.46 0.07

41 Forb/herb Alliaria petiolata (Bieb.) Cavara & Grande garlic mustard I 4.48 8.85 0.67 0.33

41 Forb/herb Apocynum androsaemifolium L. spreading dogbane

N 4.48 1.70 0.50 0.16

41 Forb/herb Circaea lutetiana L. enchanter’s nightshade

N 4.48 2.36 0.62 0.22

41 Forb/herb Leucanthemum vulgare Lam. oxeye daisy I 4.48 2.10 0.47 0.1141 Forb/herb Sanguinaria canadensis L. bloodroot

N 4.48 2.20 0.49 0.10

a USDA NRCS 2000. b Constancy is the percentage of plots where recorded (plot frequency x 100).
17

Sampling and Estimation Procedures for the Vegetation Diversity and Structure Indicator

Figure 2—Frequency tracks change in species distribution over time. For purposes of 

the P3 VEG indicator, frequency is defined as the ratio of the number of plots, subplots, 

or quadrats where a species was recorded to the number of plots, subplots, or quadrats 

visited.

Time 2

Time 1

 Species X

Plot frequency = 1

Subplot frequency = 0.5

Quadrat frequency = 0.083

 Species X

Plot frequency = 1

Subplot frequency = 0.75

Quadrat frequency = 0.33
18

GENERAL TECHNICAL REPORT PNW-GTR-781

using only 100-percent accessible forested subplots or plots (to adhere to standard 

size area), or by using all plots visited, including those that are not fully forested. 

Additional information provided by data collected on sample units that are less 

than 100-percent accessible forest is captured when estimates are computed from 

all plots and subplots visited. To illustrate the difference between estimates using 

“full” and “all” plots, consider multiflora rose, (Rosa multiflora Thunb. ex Murr.), 

an important invasive species in the Eastern United States: results from data 

collected between 2001 and 2004 show this species has a plot frequency of 0.176, 

based on plots composed of four fully forested subplots, whereas its plot frequency 

based on all plots, regardless of percentage of accessible forest, is 0.249, indicating 

it is often found on forest edges. Analysts would miss this indication of a species 

invasion pattern if limited to observing frequencies based on 100-percent forested 

plots, especially when summarizing results over large geographic regions. 

For purposes of the P3 VEG indicator, frequency is defined as the proportion 

of plots, subplots, or quadrats where a species was recorded (fig. 2 and table 3). 

Constancy is another way to express frequency, where the proportion is simply multiplied by 100 and expressed as the percentage of sample units where the species 

was recorded. Constancy is used along with cover measures when describing plant 

community composition (i.e., DeVelice et al. 1999, Johnson and Swanson 2005, 

Tart et al. 2005) and is also useful for reporting a species distribution on very broad 

scales. When reporting results, analysts must distinguish if all plots or only full 

plots are included.

Individual species abundance—

Species abundance is recorded as aerial canopy cover (two-dimensional view from 

directly above) for total cover. Vertical arrangement is obtained by estimating 

canopy cover by individual height layers. These abundance measures are used to 

assess species’ relative abundance to each other, classify plots into community 

types (Tart et al. 2005), and describe plant community structure in terms of species distribution both horizontally and vertically. This information can be used to 

characterize wildlife habitat (Cooperrider et al. 1986, MacArthur and MacArthur 

1961), wildland fuel profiles (Greenough 2001, Lutes et al. 2003), and impacts of 

disturbance, including invasive species. Ocular estimation of percentage canopy 

cover is the most common approach among ecologists to measuring species abundance (McCune and Grace 2002). Ocular estimates are quick and nondestructive, 

providing efficient assessments of abundance. Note, however, that although canopy 

cover measures are absolute in terms of percentage of a given area, they should not 

be considered to be precise. 

Ocular estimates 

are quick and 

nondestructive, 

providing efficient 

assessments of 

abundance.
19

Sampling and Estimation Procedures for the Vegetation Diversity and Structure Indicator

Species average cover—The average cover of an individual species is compiled 

from raw subplot data. Cover values are summed and then divided by the number of 

subplots in the sample, both for plot-level and population-level estimates. 

Users must be cautioned that population estimates over large regions are likely 

to have high variances, given the extensive nature of the P3 grid. This is also a 

reflection of nonrandom spatial distribution of plant species. Species may occur in 

high abundance in a few places and in low abundance (or absent) in most others, so 

that there are many plots where a species was not recorded. Although it is possible 

to compile average cover on national or regional scales, it is generally more informative to define a population in more specific terms, such as in a particular forest 

type within a particular EcoProvince.

For some purposes, a more informative description of species abundance 

within a population of interest is compiled from only the plots where the species 

was observed (no zero values are included). This convention is sometimes used to 

summarize and describe floristic composition in plant-community type classifications, and is usually compiled after a community classification exercise. Constancy 

can be reported along with species average cover to reflect how often that species 

was recorded within the plots of a community type (defined in the classification 

exercise). Another example of this application is for reporting species distribution 

summaries over broad scales, as shown in table 3. 

Species average cover by layer—To describe a species’ vertical distribution, cover 

is reported for each of three general height layers (0 to 6 ft, 6 to 16 ft, and above 16 

ft). The objective is to describe how that species is distributed throughout the height 

layers when the species is recorded (fig. 3). This provides information useful for 

fuels or wildlife habitat characterization.

Diversity of plant communities—

Species diversity can be assessed in a number of ways, based on the scope and scale 

of an inventory project or plant community study (Conkling et al. 2005, Ludwig 

and Reynolds 1988, McCune and Grace 2002, Pitkanen 1998, Whittaker 1975). 

Traditionally, diversity is composed of two distinct components: species richness 

(the total number of species) and evenness (how abundant each species is relative 

to other species). Diversity indices attempt to combine these two components, but 

are difficult to interpret because they combine, and therefore confound, a number of 

variables (Ludwig and Reynolds 1988). Diversity indices such as Simpson’s index, 

Shannon-Wiener index, and Hill numbers may be of interest when the plot grid is 

intensified, as in special projects. These indices lose meaning at the extensive scale 
20

GENERAL TECHNICAL REPORT PNW-GTR-781

of the P3 grid, and the concepts are difficult to explain (McCune and Grace 2002). 

However, the VEG indicator species composition data do provide data on both 

species richness and abundance, and users have the option to explore the use of 

diversity indices for specific applications, if desired. 

Standard estimators of diversity for P3 VEG data concentrate instead on basic 

species richness and differential diversity, the differences in species composition 

between sampling units or populations. These can be expressed at a number of 

scales as will be described.

Species richness—The total number of species in a population of interest is the 

most fundamental and easily interpretable measure of diversity. It is most meaningful when the sample units are equivalent in terms of sample area as well as time 

Figure 3—Species cover by height layers provides information on each species contribution to 

stand structure. Although figure shows individual plants, a single cover estimate is recorded to 

include all plants of a given species. 

20% cover

6

0

16

20% cover

Height above ground (feet)

Total cover

Cover 0–6 feet

Cover 6 –16 feet

Cover >16 feet

20%

20%

15%

10%

20%

0%

15%

20%

The total number of 

species in a population 

of interest is the most 

fundamental and easily 

interpretable measure 

of diversity.
21

Sampling and Estimation Procedures for the Vegetation Diversity and Structure Indicator

spent searching. There are two common measures of species richness; alpha and 

gamma diversity.

Alpha diversity is traditionally defined as species richness, the number of 

species per unit area. For the VEG indicator, alpha can be reported at multiple 

scales: quadrat (10.76 ft2 or 1 m2), subplot area (242 �ft2), or plot area (4 x 242 �ft2). 

Because unit area must be held constant, only whole subplots and plots should be 

used for plot- or population-level estimates. Alphas based on each of these sizes 

are used to describe and compare species richness at multiple scales in different 

ecological regions or forest types (fig. 4). 

Gamma diversity is the total number of unique species recorded in the population of interest.

Both alpha and gamma diversity can be summarized by proportion of native 

and introduced species, and plants not identified to species. Table 4 shows how 

gamma can be reported in terms of native, introduced, and species of unknown 

origin for various community types. 

Figure 4—Average plot, subplot, and quadrat alphas for 12 populations defined by forest types 

within ecological provinces. Error bars show plus and minus one standard error. See table 4 for 

explanation of codes. 
22

GENERAL TECHNICAL REPORT PNW-GTR-781

Unobserved species are a factor in any inventory (Chao et al. 2000, Colwell 

et al. 2004, Heltshe and Forrester 1983). This is especially true when assessing all 

forest vascular plant species at the geographical extent and spatial scale of the FIA 

P3 sample; it is not expected that this inventory will encounter all possible species. 

There are methods to estimate the “true” number of species in a given population, 

such as extrapolating from species-area curves, parametric methods that are dependent on counts of individuals, and nonparametric estimators (McCune and Grace 

2002, Scheiner 2003). Comparing species richness of two or more populations must 

address the differences in the sample sizes representing the populations; rarefaction methods allow for such comparisons (Gotelli and Colwell 2001, Koellner et al. 

2004). This is discussed in more detail in the “Estimation” section. 

Beta diversity—Beta diversity can be calculated a number of ways; in any of its 

forms, it describes differential diversity, the extent to which species composition 

and abundance differ from one place to another (Scheiner 2003, Whittaker et al. 

Table 4—Species richness and nativity of identified species for 12 ecological province/forest 

type pairs represented by fully forested plots

Plants identified

Ecological province (code)a Plots Mean plot Gammab to species Unknown

and forest type (n) alpha ( ) (γ) Native Introduced originc

 Number of species

Laurentian mixed forest (212):

Northern white-cedar 13 50.0 270 221 10 39

Sugar maple/beech/birch 28 42.8 335 256 25 54

Hard maple/basswood 14 44.9 271 203 13 55

Aspen 33 48.8 438 325 39 74

Eastern broadleaf forest (221):

White oak/red oak/hickory 10 62.6 250 178 23 49

Sugar maple/beech/birch 11 43.5 201 135 14 52

Midwest broadleaf forest (222):

White oak/red oak/hickory 10 41.8 218 161 20 37

Central interior broadleaf forest (223):

White oak/red oak/hickory 42 53.3 470 352 24 94

White oak 10 59.6 262 199 11 52

Colorado plateau semidesert (313):

Pinyon/juniper woodland 12 17.9 98 76 5 17

Interior semidesert and desert (341):

Pinyon/juniper woodland 34 20.5 248 194 9 45

Nevada-Utah mountain semidesert coniferous forest (M341):

Pinyon/juniper woodland 13 18.5 100 78 1 21

a Ecoolgical province codes are used in figure 4 to simplify labels.

b Gamma represents the total number of unique plant codes recorded in a community, including codes for plants identified to 

species or genus, and symbols for plants that cannot be identified to genus.

c Unknown origin includes plants not identified to species.

Â′′
23

Sampling and Estimation Procedures for the Vegetation Diversity and Structure Indicator

2001). For the VEG indicator, it describes the degree of change in species composition between or within sample units or populations (Whittaker et al. 2001) and is 

calculated as the ratio of species richness of the total area sampled to the average 

number of species in the smaller individual samples. It is a measure of species 

heterogeneity across a population, and an index of the number of distinct communities present in the sample (Conkling et al. 2005, McCune and Grace 2002, Wilson 

and Shmida 1984). 

Structure and condition of soil-atmosphere interface—

In addition to species data, the VEG indicator collects data on overall structure 

and conditions of the soil-atmosphere interface on each subplot. These data, along 

with variables collected on plots by P2 mensuration crews and other P3 indicators, 

describe environmental conditions on the plot and can be used as explanatory 

variables for multivariate analysis. 

Absolute canopy cover by layer—These ocular estimates across the subplot area by 

four height layers (0 to 6 ft, 2 to 6 ft, 6 to 16 ft, and above 16 ft) assess the canopy 

cover of all vascular plants, regardless of species present or the amount of overlapping vegetation within a given layer. This cannot be derived directly from species 

canopy cover because species’ cover may or may not overlap. Results are summarized either for the plot or population of interest. This basic assessment is useful for 

evaluating wildfire fuel characteristics and wildlife habitat.

Ground cover—Ground (soil-air interface) conditions are recorded as percentage cover of cryptobiotic crust, lichen, litter/duff, mineral soil, moss, road/trail, 

rock, standing water, permanent water, trash, and wood at the subplot level. These 

measurements are used to describe the physical conditions of the plot in terms of 

space available for vascular plant establishment. These data are used to populate 

an environmental matrix that describes physical features that potentially control or 

predict the plant species occurring on the plot (McCune and Grace 2002). 

Plant Community Analysis 

Species’ distributions and abundance are fundamental to understanding patterns of 

communities and their relations to environmental conditions (Ludwig and Reynolds 

1988, McCune and Grace 2002). One of the most basic steps in vegetation analyses 

is classification of community types. Classification is the process of grouping similar entities together into classes based on selected shared characteristics (Tart et al. 

2005). In the case of plant communities, vegetation and environmental features are 

used to describe units that are useful for management applications (Boggs 2000). 

Species’ distributions 

and abundance 

are fundamental to 

understanding patterns 

of communities 

and their relations 

to environmental 

conditions.
24

GENERAL TECHNICAL REPORT PNW-GTR-781

Management applications that use classification information include describing the 

variety of vegetation communities occupying an area, characterizing the effect of 

disturbance or management on plant species, assessing resource conditions and 

risks, reporting presence and relative abundance of introduced species, developing 

wildfire-fuels-related analysis products, and enhancing effective communication 

between land managers (Tart et al. 2005).

Species composition data from FIA P2 plots only include tree species. These 

data are amenable to community classification, but typically can only be used 

to help define relatively broad types, e.g., at the group level of the revised U.S. 

National Vegetation Classification (USNVC) (FGDC 2007). Tree data can often 

be used to assign plots to alliances with existing USNVC keys (Faber-Langendoen 

and Menard 2006). However, additional data at the P3 level would provide a much 

stronger basis for developing types and assigning plots to existing types. In fact, the 

P3 plots could help validate P2-based decisions. The P3 VEG data can be used to 

further refine pre-assigned community types (e.g., forest types within a particular 

ecological province) and new classifications can be formulated by assessing similarities of sample unit species composition by using multivariate clustering techniques. 

Vegetation indicator data meet the requirements for the USNVC standards (FGDC 

2007, Jennings et al. 2006). Clients and cooperators are interested in data generated 

by the VEG indicator for its use in classification.

The first step in classification, as with most multivariate analysis methods, is 

to compute similarities or “distances” between sample units. Similarity or distance 

measures are used to compare the species assemblages or site environmental data 

of two or more communities of interest. Classic methods for computing similarities 

include Jaccard (1901) and Sørenson (1948), among others. New approaches for 

assessing similarity of species compositions are being developed (Chao et al. 2005). 

Many are applicable to VEG indicator data. Clustering techniques can then be used 

to assign sample units into groups or classes. 

Explanatory variables for species compositional differences must be considered 

at the scale of comparisons: regional or continental scales may be well explained by 

climatic variability, but landscape and local differentiation may be better explained 

by recent disturbances, local soil gradients, or other local geographic variants 

(Whittaker et al. 2001). The species and environmental data from the P3 VEG Indicator and other corresponding data for P3 plots generate complex data matrices that 

can be analyzed by multivariate techniques to discover and explore these trends. 

Methods of analysis have rapidly evolved in recent years for relating species 

composition, abundance, and environmental data through the use of cluster analyses, 
25

Sampling and Estimation Procedures for the Vegetation Diversity and Structure Indicator

ordination, and other multivariate methods (Frelich et al. 2003, McCune and 

Grace 2002, Nygaard and Ødegaard 1999, Pausas and Austin 2001, Pitkanen 1997, 

Scheller and Mladenoff 2002). Multivariate methods reduce complex data sets 

involving a large number of variables over many sample units into fewer synthesized or derived variables over groups of observations so that relationships may be 

revealed. Reducing complex data sets into fewer dimensions is useful for revealing 

patterns and trends (Ludwig and Reynolds 1988). Differences in the performance 

of individual species, and differences in composition and structure between sample 

units can be examined. Indicator species analysis can be applied to determine if a 

species of interest has an affinity for unique environmental conditions (Klinka et al. 

1989, McCune and Grace 2002).

Change over time in multiple variables or estimators can also be explored by 

using multivariate methods that integrate the responses of the individual variables 

(McCune and Grace 2002). Species matrices at time t and time t+1 are tested 

for distances (dissimilarity) by using the Mantel test (McCune and Grace 2002, 

McCune and Mefford 1999). Differences in species composition can be compared 

with differences in environmental measures (ground cover, total foliar cover by 

layer, and applicable P2 attributes, for example) to examine the relations between 

changing plant communities and other measured variables (i.e., what controls 

overall species diversity, what physical features predict where changes will occur in 

the future?). 

The process of multivariate analysis is usually iterative. For some analyses, data 

are transformed (e.g., converting cover measures to cover classes), relativized, or 

normalized; species lists are reduced; different approaches to determining similarities and clustering can be applied; and various ordination techniques can be tested. 

True patterns and trends will usually be revealed by using various techniques but 

may be best conveyed with one or two approaches. It is essential for analysts to 

keep track of the steps they use so they can be repeated as necessary and reported 

with results. Analysts should seek formal training in multivariate techniques if they 

are not familiar with them. There are numerous multivariate software packages 

available, but user-friendly software does not guarantee appropriate application of 

techniques. 

Although multivariate methods can be useful for discovering patterns, they are 

difficult to apply to hypothesis testing in a direct manner. Emerging methodologies 

may provide univariate estimates for diversity patterns (Scheiner 1992), and analysts are encouraged to explore these methods as they become available.

Although multivariate 

methods can be 

useful for discovering 

patterns, they are 

difficult to apply to 

hypothesis testing in a 

direct manner.
26

GENERAL TECHNICAL REPORT PNW-GTR-781

Estimation

The estimators presented here are separated into two major types: (1) those that 

describe the distribution and abundance of individual plant species (i.e., speciesbased estimators) and (2) those that describe the plant community within the area 

sampled in terms of diversity and structure (i.e., community-based estimators). 

Estimators produced from VEG data yield output for mapped products (figs. 5 and 

6), as well as standard tables for state, regional, and national reports (tables 3 and 

4). Plot-level estimators are generally most useful for mapped products; populationlevel estimators are generally most useful for tabular output. This section proceeds 

with a discussion of species-based and community-based estimators, at the plot and 

population levels.

The VEG species data recorded for each plot are stored at the level at which 

they were collected: plots, subplots, and quadrats. General descriptions of the 

sampled area such as condition-class data are obtainable from ancillary P2 data sets 

so that data can be identified, selected, and compiled to create estimates for various 

populations and domains of interest. Ecoregion designations to subsection are available at the plot level, providing additional ancillary data at regional and landscape 

scales. Additional ancillary information from other P3 indicators and geographic 

information systems (GIS) can also be used, but exact plot locations are usually 

required for use of ancillary GIS data.

Ratios of Means

All of the estimators described here are based on ratio-of-means (ROM) estimators 

(Cochran 1977: section 6.2). These estimators are very similar to those used by FIA 

to process P2 inventory data (Bechtold and Patterson 2005), but simpler because 

they do not require stratified estimation, and they avoid a complicated adjustment (involving per-unit-area estimators and partial plots that straddle population 

boundaries), which is not necessary for any of the VEG estimators. This simplified 

approach is advantageous in that it does not require any data from FIA’s phase 1

sample and can use software available in existing statistical packages such as SAS 

PROC SURVEYMEANS (SAS Institute Inc. 2004). The main disadvantage is that 

the double sampling for stratification technique used by FIA reduces the variance 

associated with many P2 estimators and would likely yield similar results for at 

least some of the VEG estimators. If P1 data are available and variance reduction 

through stratified sampling is of major concern to the analyst, the stratified estimation process described in Bechtold and Patterson (2005) may be applied to the VEG 

data. SAS PROC SURVEYMEANS also has the capability to incorporate stratification, which may be a simpler alternative to those who prefer to use stratified 

sampling. 

Plot-level estimators 

are generally most 

useful for mapped 

products; populationlevel estimators are 

generally most useful 

for tabular output.
27

Sampling and Estimation Procedures for the Vegetation Diversity and Structure Indicator

Figure 5—Plot average of subplot species richness. Plot locations are approximate.

0 20 00 Miles

Species per 1/24-acre subplot (plot average)

1.67 - 14

14 - 21.7

21.76 - 29.33

29.34 - 38.

38.1 - 72

3

Figure 6—Distribution and average subplot cover of selected shrub species on plots where present, Northeastern United States. Plot locations are approximate. 

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0 20 00 Miles

Average subplot canopy cover (percent)

Multiflora rose

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Buckthorn

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!( 25 - 50

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Japanese honeysuckle

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!( 50 - 61

3
28

GENERAL TECHNICAL REPORT PNW-GTR-781

The basic ROM estimator is specified as

 

∑

∑

=

= = = n

c

c

n

c

c

x

y

x

y R

1

ˆ 1

 

(1)

with estimated variance

 



 





+ −

−

= ∑ ∑ ∑

∑ = = =

=

n

c

n

c

n

c

n c c c c

c

c

y R x R y x

x n

V R

1 1 1

2 2 2

2

1

ˆ 2 ˆ

n(n 1) ( / )

1 )ˆ (ˆ (2)

where

yc = the variable of interest observed on cluster c, 

xc = an auxiliary variable observed on cluster c that is correlated with c y , 

n = the number of clusters associated with the estimator of interest in the population of interest.

The estimators produced from equations (1) and (2) are either plot-level or 

population-level means. Plot-level means are averaged across the observations 

obtained from each of the four subplots, so the number of clusters (n) equals four. 

Population-level means are averaged from observations obtained from plots, so for 

population-level means the number of clusters (n) equals the number of plots in the 

population of interest. Note that n defined in this manner accounts for the first-stage 

clustering of observations resulting from the nested sampling design, where subplots are clustered on plots and quadrats are clustered on subplots. When n relates 

to subplots, observations are either observed directly from each subplot, or summarized across the quadrats on each subplot. When n relates to plots, observations are 

either observed directly from the plot, or summarized across the four subplots on 

that plot (or in some cases summarized across the 12 quadrats on that plot). Clustering beyond the first stage is ignored because the added complication rarely changes 

variance estimates significantly (Cochran 1977: 279). 

Populations and Domains

The distinction between population variables (which are also referred to as design 

variables) and domain variables is also important with respect to n. Population 

variables are used to define the population of interest. They are known before the 

sampling occurs, and include such variables as state, county, ecological province, 

inventory panel, and year. For FIA P2 estimation, populations are typically defined 

as counties (Bechtold and Patterson 2005). For P3 estimates, ecological provinces 

(Bailey 1995, Cleland et al. 2005) are often more appropriate. Ecological provinces 
29

Sampling and Estimation Procedures for the Vegetation Diversity and Structure Indicator

have similar physical and biological features that influence vegetation, and are often 

more meaningful than political boundaries when reporting results of VEG analyses. 

Domain variables are not part of the sampling design, and their values are not 

known before sampling occurs. The condition-class variables collected by FIA (i.e., 

land use, forest type, stand size, regeneration status, tree density, stand origin, ownership group, and disturbance history) qualify as domain variables. Domains can 

also include other attributes that are measured (e.g., percentage slope) or computed 

from tree data (e.g., percentage stocking) or VEG data (e.g., plant community type 

as defined by classification exercises).

By definition, all domains of interest must be contained within the population 

of interest. However, some domains in the population of interest are not domains of 

interest. Note that all observations within the population of interest contribute to n, 

even those observations that are not in the domain of interest (e.g., nonforest). Also 

note that for plot-level estimators, the plot is defined as the population of interest.

Partial Plots and Subplots

Analyses can become complicated when plots or subplots are partially forested or 

otherwise fall into multiple condition classes (i.e., domains). Some of these estimators require that 100 percent of a subplot or 100 percent of a plot must be within 

the domain of interest because it is important to restrict observations to areas of 

uniform size. Partially forested observations are thus excluded from certain estimations because no VEG data are recorded in nonforest conditions. For those analyses 

where partial observations are mixed with complete observations, results from 

full subplots (or plots) can be reported as “interior” or “intact” forested conditions 

and partial observations can be reported as “edge” conditions, although additional 

information regarding plot proximity to roads or other human disturbance might be 

used to verify the degree of fragmentation that may influence plant composition. 

Comparisons among observations of mixed sizes must be qualified with the number 

of subplots and quadrats sampled, and the presence or absence of any nonforested 

areas on the plot.

Also, as previously noted, the VEG indicator ignores boundaries between different forested conditions when such boundaries bisect a subplot. However, depending on how a domain of interest is defined, a plot with multiple condition classes 

may be within a single domain of interest. On the other hand, restricting analyses to 

a specific domain (e.g., a particular forest type) may reduce a complete observation 

to a partial observation. Options for handling subplots or plots that are not fully 

within the domain of interest include:
30

GENERAL TECHNICAL REPORT PNW-GTR-781

1. Assigning the subplot (or plot) to the condition at subplot center and assuming that species are distributed evenly across all forested conditions located 

there. 

2. Identifying subplots (or plots) with mixed forest conditions by labeling 

them as such.

3. Excluding mixed observations from the analysis.

Analysts may consider calculating all approaches and comparing results. When 

reporting, results should be qualified with the approach used.

For those estimators where it is acceptable to use partial plots or partial 

subplots, it may occasionally happen that a plot or subplot straddles a population 

boundary. When this occurs, n is incremented by 1 if any portion of that plot or 

subplot cluster is in the population of interest. Note that n is incremented by 1 even 

if no portion of a cluster is in the domain of interest, as long as the cluster is in the 

population of interest.

Species-Based Estimator Details

Frequency—

Frequency is the proportion of sample units where a species was found compared 

to the number of sample units measured. Frequency can be reported on a quadrat, 

subplot, or plot basis, but requires a standard sample area at each level. When 

comparing the distribution of several species, frequencies are most informative 

when all three levels are reported from the same plot or population. The frequency 

estimators presented below may also be expressed as estimates of constancy, where 

the proportions are multiplied by 100 to convert them to percentages. 

Plot-level frequency on a quadrat basis—Frequency at the quadrat level provides 

the finest detail about the distribution of a species across a plot. For example, a 

physically small species may have minimal canopy cover, but individuals may be 

spread widely over the plot. The ROM estimator for plot-level quadrat frequency is 

 

∑

∑

=

= = n

j

ij

n

j

ij

is

x

y

f

1

1 ˆ

 

(3)

where

fis = ˆ the proportion of quadrats where species s is observed in the domain of interest on plot i,

When comparing the 

distribution of several 

species, frequencies 

are most informative 

when all three levels 

(quadrat, subplot, 

plot) are reported 

from the same plot or 

population.
31

Sampling and Estimation Procedures for the Vegetation Diversity and Structure Indicator

∑=

= Ι

3

q 1

ij ijq ijqs y D = the number of quadrats where species s is present in the domain

 of interest on subplot j of plot i,

∑=

=

3

q 1

ij ijq x D = the number of quadrats in the domain of interest on subplot j of

plot i,

δijq = a zero-one domain indicator function, that is 1 if quadrat q of subplot j of 

plot i is within the domain of interest, 0 otherwise. Because only accessible forest 

is sampled, the domain of interest must be accessible forest, or some subset thereof 

(such as a particular forest type),

Ιijqs = a zero-one species indicator function that is 1 if species s is present on 

quadrat q of subplot j of plot i, 0 otherwise, and 

n = the number of subplots on plot i in the population of interest, which is usually 

four unless the plot straddles a population boundary.

The variance of equation (3) is estimated by replacing the c subscripts in 

equation (2) with ij subscripts and the index of summation with j (to specify that the 

clusters being summed are subplots on plot i), and supplying the appropriate values 

for yij, xij, and n.

Population-level frequency on a quadrat basis—At the population level, quadrat 

frequency is calculated as:

 

∑

∑

=

= = n

i

i

n

i

i

s

x

y

F

1

ˆ 1

 

(4)

where

Fˆ

s = the proportion of quadrats where species s is observed in the domain of interest in the population of interest,

∑ ∑= =

= Ι

3

1

4

1 q

ijq ijqs

j

i y δ = the number of quadrats where species s is present in the 

domain of interest on plot i, 

∑ ∑= =

=

3

1

4

1 q

ijq

j

i x D = the number of quadrats in the domain of interest on plot i, 

the indicator functions δijq and Iijqs remain as defined in equation (3), and 

n = the number of plots in the population of interest.

The variance of equation (4) is estimated by replacing the c subscripts in 

equation (2) with i subscripts (to specify that the clusters being summed are plots), 

and supplying the appropriate values for yi, xi, and n. Unless otherwise noted, the 

variances of the remaining estimators are calculated similarly—by replacing the c
32

GENERAL TECHNICAL REPORT PNW-GTR-781

subscripts in equation (2) with ij or i and index of summation with j or i to specify 

whether subplots or plots are being summed, respectively.

Plot-level frequency on a full subplot basis—Although quadrat frequency has the 

potential to provide the most detail about the spatial distribution of a species, if a 

distribution is clumped, the species may occur less frequently on quadrats than it 

would if evenly dispersed. Subplot frequency can provide more information for 

these species. Only subplots that are 100-percent within the domain of interest are 

included for this estimator because it is important for observational units to be of 

uniform area. Note that the 100-percent specification is not necessary for quadrats 

because quadrats are too small to map, and are therefore measured as all in or all 

out of any given domain or population. Subplot frequency is calculated as

 

∑

∑

=

= ′ = n

j

ij

n

j

ij

is

x

y

f

1

1 ˆ

 

(5)

where

fis′ = ˆ the proportion of full subplots where species s is observed in the domain of 

interest on plot i, 

ij ij ijs y = D Ι ,

ij ij x = D ,

Ιijs = a zero-one species indicator function that is 1 if species s is present on 

subplot j of plot i, 0 otherwise,

δij = a zero-one domain indicator function that is 1 if subplot j of plot i is 100 

percent within the domain of interest, 0 otherwise. Because only accessible forest 

is sampled, the domain of interest must be accessible forest, or some subset thereof. 

If a subset (such as a particular forest type) is specified, the subplot must be 100 

percent within the specified subset, and 

n = the number of subplots on plot i, which is usually four unless the plot straddles 

a population boundary. 

Population-level frequency on a full subplot basis—At the population level, subplot frequency is calculated as:

∑

∑

=

= ′ = n

i

i

n

i

i

s

x

y

F

1

ˆ 1

(6)

where

Fˆ

s

′ = the proportion of subplots where species s is observed in the domain of interest in the population of interest, 
33

Sampling and Estimation Procedures for the Vegetation Diversity and Structure Indicator

∑=

= Ι

4

j 1

i ij ijs y D = the number of subplots where species s is present in the domain of

 interest on plot i,

∑=

=

4

j 1

i ij x D = the number of subplots in the domain of interest on plot i, 

the indicator functions δij and Iijs remain as defined for equation (5), and

n = the number of plots in the population of interest.

Population-level frequency on a full plot basis—This estimator is limited to plots 

where all four subplots are completely within the domain of interest:

∑

∑

=

= ′′= n

i

i

n

i

i

s

x

y

F

1

ˆ 1 (7)

where

Fˆ

s

′′= the proportion of plots where species s is observed in the domain of interest 

in the population of interest,

yi = δiIis ,

xi = δi ,

Iis = a zero-one species indicator function that is 1 if species s is present on plot i, 0 

otherwise,

δi = a zero-one species indicator function that is 1 if plot i is 100 percent within 

the domain of interest, 0 otherwise. Because only accessible forest is sampled, the 

domain of interest must be accessible forest or some subset thereof. If a subset (such 

as a particular forest type) is specified, the plot must be 100 percent within the 

specified subset, and

n = the number of plots in the population of interest. 

Frequency on all-subplots basis or all-plot basis—For some applications, it is 

useful to relax the 100-percent restriction on the domain of interest for the frequency estimators specified in equations (5), (6), and (7). The equations remain the 

same, but the domain indicators δij or δi are 1 on all subplots or plots that are fully 

or partially in the domain of interest, and 0 otherwise. This allows the use of data 

from partial subplots, which may reveal information about species that are found 

more often on the edges of the forest. However, these revised estimators violate the 

rule of uniform areas, and should therefore be used with caution; for most analyses 

involving frequency only full sample units are included. Some estimators described 

later in this section do not require the 100-percent restriction. Primes are added to 

the domain indicators that do not require the 100-percent restriction (e.g., ij D ′ ).
34

GENERAL TECHNICAL REPORT PNW-GTR-781

Species abundance—

Species canopy cover for any species, as a measure of species abundance, is 

recorded directly in the field, within a range of trace (0.1 percent) up to 100 percent, 

in increments of 1 percent. Canopy cover is recorded at the subplot level as both 

total cover and cover by layer.

Vegetation information is not collected on nonforest plots or the nonforested 

portions of partially forested plots. Boundaries between forested conditions (which 

differ by some factor such as structural stage or community type) are ignored at 

the subplot level. Any of the options described thus far for handling subplots that 

are not fully within the domain of interest also apply to the abundance estimators 

discussed here.

For partial subplots, the percentage of cover recorded in the field relates to the 

standard subplot area. For example, a species with cover over a 4- by 4-ft square is 

about 1 percent cover for a full subplot. If the subplot is only 50-percent forested, 

the field crew would still enter 1 percent for the species. Because no observations 

are recorded in nonforest or inaccessible conditions, the cover estimates must be 

adjusted to correctly represent the portion of a subplot in accessible forest. So for 

the above example where 1 percent cover is recorded for a subplot that is 50 percent 

forest, the adjustment to 2 percent cover (2 percent of the forested portion) is made 

in the equations below by placing adjij in the denominator of yij. 

Average aerial species cover—Aerial cover refers to the two-dimensional cover of 

a species as seen from above.

Plot-level species cover—Plot-level estimates of average subplot cover by species 

s, which are especially useful for display in mapped products, are calculated as 

follows:

 

∑

∑

=

= = n

j

ij

n

j

ij

is

x

y

c

1

1 ˆ (8)

where

ĉis = the mean percentage cover of species s in the domain of interest on plot i,

ij

ijs ij

ij adj

c

y

D ′ = = the percentage cover of species s in the domain of interest of

subplot j of plot i, adjusted to represent cover on the portion of the subplot in accessible forest,

cijs = the percentage cover of species s in the accessible forest portion of subplot j of 

plot i, based on the standard subplot area,

Canopy cover is recorded at the subplot 

level as both total 

cover and cover by 

layer.
35

Sampling and Estimation Procedures for the Vegetation Diversity and Structure Indicator

adjij = the proportion of subplot j of plot i, in accessible forest,

′

ij D = a zero-one domain indicator function that is 1 if subplot j of plot i contains 

a domain of interest, 0 otherwise. Note that the cover estimate is assumed to be 

evenly distributed across all forested domains on subplot j of plot i.

xij = ′

ij D , and

n = the number of subplots on plot i in the population of interest, which is usually 

four unless the plot straddles a population boundary.

Population-level species cover—Average cover of a species at the population level 

is estimated as the ratio of cover to forest area, as described below. Users are 

cautioned that variances will be high, especially when the population is broadly 

defined (e.g., the total area of a species over a state or region). Most species occur 

in low abundance; there may be many plots where the species was not recorded. 

Variances may be reduced when the population is subdivided into more specific 

domains of interest (e.g., the cover of a species in red pine plantations in Michigan 

within a particular ecological province).

This estimator can also be used to summarize and describe floristic composition in plant community types where the species of interest has been observed. 

To calculate the average species cover where recorded, the domain of interest is 

defined as subplots where the species of interest has been recorded within the 

population under inquiry. 

At the population level, cover is calculated as:

 

∑

∑

=

= = n

i

i

n

i

i

s

x

y

C

1

ˆ 1 (9)

where

Ĉs = the mean percentage cover of species s in the domain of interest in the population of interest,

∑=

′ =

4

j 1 ij

ijs ij

i

adj

c

y

D

 = the sum (across all subplots) of the percentage canopy cover of 

species s in the domain of interest on plot i, adjusted to represent the cover of each 

subplot in accessible forest.

∑=

= ′ 4

j 1

i ij x D = the sum of subplots on plot i that contain a domain of interest, 

cijs and ij D ′ are as defined in equation (8), and

n = the number of plots in the population of interest.
36

GENERAL TECHNICAL REPORT PNW-GTR-781

Average species cover by layer—

Plot-level species cover by layer—The objective of this estimator is to describe how 

a species is distributed throughout the height layers on the subplots. The calculation 

of ĉils (the mean percentage cover of species s in layer l in the domain of interest of 

plot i), is the same as equation (8) except:

ij

ijls ij

ij adj

c

y

D ′ = = the percentage cover of species s in layer l of subplot j of plot i in 

the domain of interest, adjusted to represent cover on the portion of the subplot in 

accessible forest, where 

cijls = the percentage cover of species s in the accessible forest portion of layer l of 

subplot j of plot i, based on the standard plot area.

Population-level species cover by layer—At the population level, the calculation of 

Ĉls (the mean percentage cover of species s in layer l of the domain of interest in the 

population of interest) is the same as equation (9) except :

∑=

′ =

4

j 1 ij

ijls ij

i

adj

c

y

D

 = the sum (across all subplots) of the percentage canopy cover of 

species s in layer l in the domain of interest on plot i, adjusted to represent cover on 

the portion of each subplot in accessible forest.

Community-Based Estimator Details

Diversity and structure estimators describe the area sampled for scales ranging 

from an individual stand to a larger population. Diversity measures are directly 

related to species composition, and so are derived from species matrices. Structure 

is defined as the vertical arrangement of vascular plants as well as information 

collected to describe the soil/air interface. 

Diversity—

Species matrices are summarized to report diversity in terms of species richness 

and differential diversity (compositional change) across a plot or a population. 

Average species richness (alpha) can be estimated at multiple scales: quadrat 

(α), subplot (α') and plot levels (α"). Species richness is reported for standard areas 

of uniform size because numbers of species cannot be assumed to be linearly 

related to area (Whittaker et al. 2001). Therefore, only sampling units that are 100-

percent within the domain of interest are included in order to maintain a standard 

area (3.28 ft2 [1 m2], 1/24 acre, or 1/6 acre).

The total number of species recorded for a plot or population, gamma (γ), is 

reported with the total area sampled. Plot-to-plot comparisons of plot-level gamma 

should be limited to plots of equal forested area. Comparisons of population-level 

Species matrices are 

summarized to report 

diversity in terms of 

species richness and 

differential diversity 

(compositional change) 

across a plot or a 

population.
37

Sampling and Estimation Procedures for the Vegetation Diversity and Structure Indicator

gammas with unequal sample sizes should employ rarefaction methods to achieve 

equal sizes, as described below in the “Gamma” section.

Alpha and gamma are also summarized by species’ origin and level of identification; e.g., number of introduced species, native species, and plants not identified 

to species but recognized as unique from other identified species on a plot (table 4). 

Differential diversity is reported as beta, but the species matrix, containing 

both composition and abundance data, provides information for additional pattern 

and trend analysis beyond standard estimations.

Species richness—

Alpha—The average number of species occupying a fixed-size area (defined by 

quadrats, full subplots, or full plots) is used to display and compare species richness 

from plot to plot or population to population. 

Plot-level alpha on a quadrat basis—The estimator αi ˆ (the mean number of species per quadrat in the domain of interest on plot i) is the same as specified in equation (3) except:

∑=

=

3

q 1

ij ijq ijq y D S = the sum of species totals from all quadrats in the domain of 

interest on subplot j of plot i, where 

Sijq = the total number of species tallied on quadrat q of subplot j of plot i.

Population-level alpha on a quadrat basis—At the population level, quadrat-level 

alpha Â (the mean number of species recorded per quadrat in the domain of interest 

in the population of interest) is calculated as specified in equation (4) except:

∑ ∑= =

=

3

1

4

1 q

ijq ijq

j

i y D S = the sum of species totals from all quadrats in the domain of 

interest on plot i.

Plot-level alpha on a full-subplot basis—As with most previously discussed estimators, this plot-level species-richness metric can only be compared using subplots of 

uniform size (i.e., 100 percent within the domain of interest). At the plot level, Ai ˆ′

(the mean number of species recorded per full subplot in the domain of interest in 

the population of interest) is calculated as specified in equation (5) except:

yij = δijSij = the sum of species totals from all full subplots in the domain of interest 

on plot i, where 

Sij = the total number of species tallied on subplot j of plot i.

Population-level alpha on a full-subplot basis—At the population level, Â' (the 

mean number of species recorded per full subplot in the domain of interest in the 

population of interest) is calculated the same as equation (6) except:
38

GENERAL TECHNICAL REPORT PNW-GTR-781

∑=

=

4

j 1

i ij ij y D S = the sum of species totals from all full subplots in the domain of 

interest on plot i.

Plot-level alpha on a full-plot basis—Plot-level alpha on a full-plot basis is not estimated, but observed directly: 

 α"i = δiSi (10)

where

α"i = plot alpha, the total number of unique species recorded on plot i,

Si = the total number of species tallied on plot i, and

δi = 1 if plot i is 100 percent within the domain of interest, 0 otherwise. Because 

only accessible forest is sampled, the domain of interest must be accessible forest, 

or some subset thereof. If a subset (such as a particular forest type) is specified, the 

subplot must be 100 percent within the specified subset.

Because α"i is measured directly and not estimated, its variance is zero.

Population-level alpha on a full-plot basis—At the population level, the calculation 

of Â" (the mean number of species recorded per full plot in the domain of interest in 

the population of interest) is the same as equation (7) except:

yi = δi Si

where Si = the total number of species tallied on plot i.

Gamma—Gamma (γ) is defined as the total number of unique species codes recorded in a population of interest (or a domain of interest within a population of 

interest). Estimates of gamma can relate to any size area, but comparisons among 

gammas must involve areas of similar size because species richness and area are 

not linearly related. The fixed-size areas of most interest here include plots and 

populations. Plot-level differences can be addressed by restricting the analysis to 

full plots. At the population level, estimates of gamma must be adjusted for differences in the sizes of the areas sampled. 

Rarefaction—When comparing the species richness (alpha or gamma) of two or 

more regions or domains, sample size differences must be addressed. It is expected 

that sample sets (representing regions or domains) with more sample units, and 

therefore a larger total sample area would include more species, so direct comparison of the number of species found in each region is not appropriate. Rarefaction 

methods should be used to equalize the sample sets (Gotelli and Colwell 2001, 

Koellner et al. 2004). The rarefaction method enables comparison of the number 

of species found in two regions when the sampled areas are unequal. Rarefaction 

uses the data from the larger sample to estimate how many species would have been 
39

Sampling and Estimation Procedures for the Vegetation Diversity and Structure Indicator

found in a smaller sample. If n plots are inventoried in the less-sampled region, rarefaction takes a number of hypothetical subsets of n plots from the more-sampled 

region and calculates the average number of species from n plots. This average can 

be compared to the number of species actually found in the less-sampled region. 

See Colwell et al. (2004) for a demonstration of how rarefaction is derived and used 

to equalize population sizes.

Nonparametric adjustment—Aside from adjusting for areas of different size, 

gamma is usually adjusted to correct for unobserved species, which are a factor in 

any inventory. Parametric methods to adjust gamma are lacking, but nonparametric methods can estimate the “true” number of species, shown below as jackknife 

methods. 

Species richness estimates must acknowledge that some species go undetected. 

Indeed, our sampling extent and focus cannot begin to approach the true number 

of species in a population. However, there are many ways to estimate the “true” 

number of species within a community of interest (Colwell and Coddington 1994) 

including extrapolating from species-area curves, parametric methods that are 

dependent on counts of individuals, and nonparametric estimators.

Nonparametric estimators have proven very useful for estimating the true 

number of species in plant inventories (Chazdon et al. 1998, Colwell and Coddington 1994) because they avoid assumptions about species distribution and discovery 

rates (Chao 2005). Several methods require only incident data (presence/absence) 

and are based on the number of rare or infrequent species:

• First-order jackknife methods base this estimate of the “true” number of species on the number of “rare” species; those species that are 

only recorded on a single plot (reduces bias of a biased estimator) (Chao 

2005, Heltshe and Forrester 1983, McCune and Grace 2002, Scheller and 

Mladenoff 2002).

• Second-order jackknife methods incorporate those species found on only 

one or two plots. Although this method can perform poorly with small 

sample sizes that have some “doubletons” and no “singletons,” it has been 

shown to be the least biased for small sample sizes (McCune and Grace 

2002).

• Incidence-based coverage estimator (ICE) incorporates infrequent species 

that have been detected 10 or fewer times over all sample units. Chazdon et 

al. (1998) found ICE to be the best estimator to meet the criteria of (1) independence of sample size (above a minimum threshold), (2) insensitivity to 

patchiness of species distribution, and (3) insensitivity to sample order.

Species richness 

estimates must 

acknowledge that some 

species go undetected. 
40

GENERAL TECHNICAL REPORT PNW-GTR-781

Of the above three methods, first-order jackknife is recommended for its simplicity. Jackknife estimations of the true number of unique species are computed by 

considering the number of unique species across all samples except for one. This is 

calculated n times for a data set containing n samples. See Helthshe and Forrester 

(1983) for a complete derivation. Many software packages include a routine for firstorder jackknife estimates of the true number of species (e.g., Colwell 2005, McCune 

and Mefford 1999, Seaby and Henderson 2006). As more data become available and 

unknown codes are standardized, analysts can test the performance of the secondorder jackknife and ICE estimators. These estimators can be supplemented with 

species-area curves (plots of the number of species vs. the number of sample units) 

as an indicator of how well the sample represents the population of interest. 

Beta diversity—

Plot-level beta—Beta is defined as the ratio of gamma to alpha, which is the ratio 

of species richness of a larger sampled area to the average species richness of the 

smaller individual samples that compose the larger sample. At the plot level, this ratio indicates similarity of species composition among subplots, reflecting influences 

of multiple forest types, for example. A beta value of 1 indicates all subplots have 

the same species. As beta increases there is less similarity between subplots. Using 

the plot-level alphas described above, plot-level beta is defined as

 

i

i

i

α

α β ′

′′ ′′= ˆ

ˆ (11)

where

βi

′′= ˆ the ratio of plot-to-subplot species richness for plot i.

Because beta is dependent on area-sensitive estimations, it can only be compared among plots where the numbers of subplots are the same. In general, this will 

limit the use of plot-level beta to full plots.

Using the notation from equation (11), and assuming there is no covariance 

between the numerator and denominator, Cochran (1977: sec. 6.19, eq. 6.95) estimated the variance of a ratio of two estimators as 

 ( )

( )

( )

( ) 



 





′

′ + ′′′′

 2 2 ˆ

ˆ ˆ ˆ

i

i

i

V i V

A

A

A

A ( )  x



 





















′

′′ =















′

′′ ′′ =

i

i

i

i V i V

A

A

A

A B ˆ ˆ ˆ ˆ ˆ 2

(12)

Because ( ) 0 Vˆ ai

′′ = , equation (12) simplifies to

 ( ) 































′

′′ =















′

′′ ′′ =

2

ˆ ˆ ˆ ˆ ˆ

i

i

i

i V i V

A

A

A

A B ( )

( ) 



 





′

′

 2 ˆ

ˆ ˆ

i

V i

A

A

x (13)
41

Sampling and Estimation Procedures for the Vegetation Diversity and Structure Indicator

Population-level beta—Population-level beta estimates the similarity of species 

composition among plots. The closer to 1, the more similar the species composition; 

the higher the number, the higher the “turnover” in species (or, the more communities included within the population and domain of interest).

Beta diversity is a property of the sample more so than an inherent property of 

the community (Greig-Smith 1983), as is gamma. If the analysis includes a comparison of betas of two or more populations, sample-based rarefaction estimates of 

gamma should be used to ensure equal sample areas are compared.

Using the population-level alpha (Â") described above, population-level beta is 

defined as

 Α′′ Β = ˆ

ˆ ˆ G (14)

where gamma (γˆ) and its variance are usually estimated with one of the nonparametric techniques discussed previously.

The variance of plot-level beta can be estimated by substituting the appropriate 

values into equation (12)

 ( ) 













 



 





Α′′  =



 





Α′′ Β =

2

ˆ

ˆ

ˆ

ˆ ˆ ˆ ˆ G G V V ( ) ( )

( ) 













Α′′

Α′′ + 2 2 ˆ

ˆ ˆ

ˆ

ˆ Vˆ V

G

G x (15)

Structure and condition of soil-atmosphere interface—

Plot structure measurements specific to the VEG indicator include total foliar cover 

by layers and ground cover assessments, both derived from field-recorded ocular 

estimates. Calculated means may have large variances, depending on how the 

populations or domains are defined. Variances can be calculated, but ranges may be 

a more intuitive description of variability of conditions across populations for many 

users.

Absolute canopy cover by layer—This estimator reflects overall canopy cover of 

all vascular plant species, assessed without species differentiation, in each layer. 

This cannot be derived directly from species canopy cover because the various species’ foliage or live twigs may or may not overlap. Cover is recorded in 1-percent 

increments. Similar to the way cover is recorded for species abundance, field crews 

record cover estimates on a full subplot basis, and these estimates are adjusted for 

partially forested subplots when the data are processed.

Plot-level average absolute cover by layer—Plot-level average absolute cover by 

layer (ĉil) is calculated as specified in equation (8) except:

Plot structure 

measurements 

specific to the VEG 

indicator include 

total foliar cover by 

layers and ground 

cover assessments, 

both derived from 

field-recorded ocular 

estimates.
42

GENERAL TECHNICAL REPORT PNW-GTR-781

ij

ijl ij

ij adj

c

y

D′ = = the percentage cover of all vascular plant species in layer l of 

subplot j of plot i in the domain of interest, adjusted to represent cover on the portion of the subplot in accessible forest, where 

cijl = the percentage cover of all vascular plant species in the accessible forest portion of layer l of subplot j of plot i, based on the standard plot area.

Again, the variances of the cover estimators presented here and below are 

calculated by substituting the appropriate variables into equation (2).

Population absolute cover by layer—This estimator measures the mean cover of all 

vascular plants in the population on a subplot basis and is assessed without species 

differentiation in each layer. This cannot be derived from species canopy cover, 

as species may or may not overlap. As with species canopy cover, only accessible 

forested land is assessed, but measures are based on the standard subplot area. 

Population-level absolute cover by layer (Ĉl) is calculated as specified in equation 

(9) except:

∑=

′ =

4

j 1 ij

ijl ij

i

adj

c

y

D

 = the sum (across all subplots) of the percentage canopy cover 

of all vascular plant species in layer l of plot i in the domain of interest, adjusted to 

represent the cover of each subplot in accessible forest.

The domain is always limited to accessible forest land, but could be further 

limited by attributes of interest such as forest type or ecoregion.

Ground cover—Ground cover variables describe the soil surface conditions on 

the subplot. These variables include cryptobiotic crust, lichen, litter/duff, mineral 

soil, moss, rock, standing water (flood), permanent water (streams, lakes), trash, 

and wood, as defined in the field guide. As with species and absolute canopy cover, 

these measures are taken in the field based on the standard subplot area and then 

adjusted for partially forested subplots when the data are processed.

Plot-level ground cover—Plot-level average ground cover (ĉig) is calculated as 

specified in equation (8) except:

ij

ijg ij

ij adj

c

y

D ′ = = the percentage ground cover on subplot j of plot i in the domain 

of interest, adjusted to represent cover on the portion of the subplot in accessible 

forest, where 

cijg = the percentage ground cover on the accessible forest portion of subplot j of 

plot i, based on the standard plot area.
43

Sampling and Estimation Procedures for the Vegetation Diversity and Structure Indicator

Population-level ground cover—Population-level absolute cover by layer (Ĉg) is calculated as specified in equation (9) except

∑=

′ =

4

j 1 ij

ijg ij

i

adj

c

y

D = the sum (across all subplots) of the percentage ground cover on 

plot i in the domain of interest, adjusted to represent ground cover on the portion of 

each subplot in accessible forest.

Change Estimation

The FIA Program’s sample design of measuring permanent plots results in a powerful means of detecting change, even at the extensive scale of the P3 grid. Change 

detection is enhanced with permanent plots that are remeasured over time, much 

more than if randomly selected plots were used (Elzinga et al. 1998). Change can be 

assessed with both plot- and population-level estimators by calculating the differences in the estimators obtained at time t and time t+1. Some estimators will be 

more directly interpretable than others. For example, changes in a species quadrat 

frequency between time t and time t+1 will reveal if a species is becoming more 

or less dispersed over plots. A lack of change in species richness over a domain of 

interest only reveals that the number of species has remained the same, but does not 

provide any information regarding changes in species composition.

Plot- and population-level estimators at time t and time t+1 are compared with 

paired t-tests for any plot visited at both times when sample size allows (Elzinga et 

al. 1998, Sokal and Rohlf 1981) or the equivalent nonparametric Wilcoxon signed 

rank test (Conover 1980, Sokal and Rohlf 1981). If more than two times are available, then this turns into a typical repeated measures analysis where trend over time 

could be tested along with individual comparisons that would use an experment-wise 

alpha with the Bonferroni adjustment.

Changes in species richness can be assessed in a straightforward manner by 

using paired t-tests. Paired t-tests can be used to assess changes in individual 

species’ frequencies at quadrat and subplot levels when the next larger sample level 

is considered to be the sample unit (i.e., quadrat frequency within subplots or plots, 

subplot frequency at plot level). 

For estimators based on cover measures, paired t-tests can be applied to both 

raw measures, or raw measures transformed by appropriate methods for the question at hand (McCune and Grace 2002). Both approaches may be used and results 

compared. Changes in individual species’ cover are likely to be most confounded 

by differences in climatic variation from year to year, and differences in phenological timing of the plot visits. Changes in absolute average percentage canopy cover 

by layer may be less sensitive to influences based on plot visit timings and climatic 

variations than is individual species cover, but should still be treated cautiously. 

The FIA Program’s 

sample design of 

measuring permanent 

plots results in a 

powerful means of 

detecting change, even 

at the extensive scale 

of the phase 3 grid.
44

GENERAL TECHNICAL REPORT PNW-GTR-781

Changes in ground cover are not expected to be as sensitive to timing of plot visits, 

but cover percentages may also be converted to classes to acknowledge the differences in observers. 

Frequency is the recommended estimator for assessing change in an individual 

species’ distribution, with changes in species cover used as a supplemental descriptor of change in abundance.

The McNemar test statistic (T) can also be used for assessing differences in 

proportions (such as frequency) when permanent plots are remeasured. This test 

is most powerful when the observations are highly correlated, as when the same 

sample units are measured at time t and time t+1. With this test, each level of 

frequency (quadrat, subplot, plot) can be treated as the sampling unit (Elzinga et al. 

1998).

 ( )

(b c)

b c T

+

− =

 2

(16)

where 

b = the number of sample (or subsample) units where a species (or group of species) 

was found in year 1 but not year 2, and

c = the number of sample (or subsample) units where the species (or group of species) was not found in year 1 but found in year 2.

The test statistic (equation 16) is then compared to the chi-square distribution 

with 1 degree of freedom. The null hypothesis of no change is rejected if the test 

statistic exceeds the chi-square table value for 1 degree of freedom.

Notation for Equations

Indices

i = plot index, i = 1, . . . ,

j = subplot index, j = 1, . . . , 4

q = quadrat index, q = 1, . . . , 3

s = species index, s = 1, . . . ,

n = total number of plots in the population of interest (or the number of subplots on 

a plot when the population of interest is defined as a plot)

l = layer index, defining vertical layer ranges

g = ground cover variable index

Frequency is the recommended estimator 

for assessing change 

in an individual 

species’ distribution.
45

Sampling and Estimation Procedures for the Vegetation Diversity and Structure Indicator

Species-Based Estimators

fis = ˆ plot-level frequency on a quadrat basis

Fˆ

s = population-level frequency on a quadrat basis

fi

′

s = ˆ plot-level frequency on a subplot basis

Fˆ

s

′ = population-level frequency on a subplot basis

Fˆ

s

′′= population-level frequency on a plot basis

ĉis = cover, percentage of subplot area averaged at the plot level

Ĉs = cover, percentage of subplot area averaged at the population level

Is = zero-one species indicator function that is 1 if species s is present, 0 otherwise 

Community-Based Estimators

δ = zero-one domain indicator function that is 1 if the sample unit (quadrat, subplot, or plot) is 100 percent within the domain of interest, 0 if otherwise

δ' = zero-one domain indicator function that is 1 if the sample unit (quadrant, 

subplot, or plot) contains the domain of interest, 0 if otherwise

pij = the proportion of a subplot in accessible forest condition or within a more 

restricted domain of interest

α = alpha, species richness of a standard area.

Ai ˆ = the plot average of number of species per quadrat

Â = the population average number of species per quadrat

Ai ˆ′ = the plot average of number of species per full subplot

Â' = the population average number of species per full subplot

α"i = the total number of unique species on a full plot

Â" = the population average number of species per full plot

ˆ

β = beta, ratio of gamma to alpha representing similarity (difference) in plant species composition across a plot

Βˆ = beta, ratio of gamma to alpha representing similarity (difference) in plant species composition across a population

S = total number of unique species recorded on a full sample unit (quadrat, subplot, 

or plot)

γ = gamma, the total number of unique species tallied in the population of interest 
46

GENERAL TECHNICAL REPORT PNW-GTR-781

Acknowledgments

The Vegetation Diversity and Structure indicator began as an interagency effort 

within the Forest Health Monitoring Program in the mid-1990s. Significant early 

contributions to the development of this indictor were made by Martin Stapanian, 

Ken Stolte, Tom Stohlgren, Kelly Rimar, Florence Peterson, and Rick Shory. 

In more recent years, Andrew Gray, Katherine Johnson, Cassandra Olson, Sarah 

Butler, Darin Toone, and Cyndi Herbert have been key players in refining methods 

and assuring quality data are collected. Special attention to data management has 

been essential, and the author is in debt to Kevin Dobelbower, Lisa Mahal, Jane 

Reid, and Chuck Veneklase for their clear vision of required detail for quality data 

stewardship.

The author also thanks the many reviewers who have guided the development and documentation of this indicator, including various FIA personnel and 

anonymous reviewers. Special thanks to Tara Barrett and Vicente Monleon of the 

PNW Research Station, Forest Inventory and Analysis Program for their thoughtful review and patient statistical guidance. Thanks also to Dave Allen of Chugach 

National Forest for designing figures 1, 2, and 3. The author also appreciates the 

attention to detail given to this document by Lynn Sullivan, technical editor with 

the PNW research Station’s Communications and Applications Group.

Metric Equivalents

When you know: Multiply by: To find:

Feet (ft) 0.305 Meters (m)

Square feet (ft2) .0929 Square meters (m2)

Acres .405 Hectares

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