United States Department of Agriculture / Forest Service

Rocky Mountain Research Station

General Technical Report RMRS-GTR-194

June 2007

Research Agenda for Integrated 

Landscape Modeling

Samuel A. Cushman

Donald McKenzie

David L. Peterson

Jeremy Littell

Kevin S. McKelvey
Cushman, Samuel A.; McKenzie, Donald; Peterson, David L.; Littell, Jeremy; McKelvey, Kevin 

S. 2007. Research agenda for integrated landscape modeling. Gen. Tech. Rep. RMRSGTR-194. Fort Collins, CO: U.S. Department of Agriculture, Forest Service, Rocky Mountain 

Research Station. 50 p.

Abstract

Reliable predictions of how changing climate and disturbance regimes will affect forest 

ecosystems are crucial for effective forest management. Current fire and climate research 

in forest ecosystem and community ecology offers data and methods that can inform such 

predictions. However, research in these fields occurs at different scales, with disparate goals, 

methods, and context. Often results are not readily comparable among studies and defy 

integration. We discuss the strengths and weaknesses of three modeling paradigms: empirical 

gradient models, mechanistic ecosystem models, and stochastic landscape disturbance 

models. We then propose a synthetic approach to multi-scale analysis of the effects of climatic 

change and disturbance on forest ecosystems. Empirical gradient models provide an anchor 

and spatial template for stand-level forest ecosystem models by quantifying key parameters 

for individual species and accounting for broad-scale geographic variation among them. 

Gradient imputation transfers predictions of fine-scale forest composition and structure across 

geographic space. Mechanistic ecosystem dynamic models predict the responses of biological 

variables to specific environmental drivers and facilitate understanding of temporal dynamics 

and disequilibrium. Stochastic landscape dynamics models predict frequency, extent, and 

severity of broad-scale disturbance. A robust linkage of these three modeling paradigms 

will facilitate prediction of the effects of altered fire and other disturbance regimes on forest 

ecosystems at multiple scales and in the context of climatic variability and change.

Keywords: climate change, climate regime, disturbance regime, modeling paradigms, empirical gradient model, mechanistic ecosystem model, stochastic landscape disturbance 

model

Authors

Samuel A. Cushman is a Research Landscape Ecologist working for the USDA Forest 

Service Rocky Mountain Research Station in Missoula, Montana. His research is centered on 

the influences of spatial and temporal variability on ecosystem structure and function.

Donald McKenzie is a Research Ecologist at the USDA Forest Service Fire and Environment 

Research Applications Team in the Pacific Northwest Research Station. His research is centered 

on a broad range of issues involving climate, fire regimes, and responses of vegetation to 

biophysical drivers.

David L. Peterson is Research Biologist and Team Leader for the USDA Forest Service 

Pacific Northwest Research Station’s Pacific Wildland Fire Sciences Laboratory Fire and 

Environmental Research Applications Team.

Jeremy Littell is a Research Scientist at the University of Washington, Climate Impacts Group. 

His research focuses on relationships between climatic drivers, vegetation distribution and 

productivity, and fire regimes at landscape to regional scales.

Kevin S. McKelvey is a Research Ecologist for the USDA Forest Service, Rocky Mountain 

Research Station in Missoula, Montana.

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Executive Summary

The overall goal of the integrated modeling program described in this document is to obtain 

fine-scale predictions of ecosystem attributes across large geographical areas and project 

them over time under changing climate and disturbance regimes.

Reliable prediction requires focus on mechanisms and responses and attention to spatial 

heterogeneity and temporal disequilibria.

The fundamental unit of ecological analysis is the organism, and fundamental scales are those 

at which the organism strongly interacts with critical or limiting resources.

A multi-scale approach is thus required, incorporating ecological conditions at the scale of 

treefall gaps, slope facets, catchments, and watersheds.

Gradient analysis of environmental tolerances, ecosystem dynamics modeling, and landscape 

dynamics simulation modeling all contribute components required to predict the ecological 

responses of forests to changing climate and disturbance

Many of the sources of uncertainty in gradient modeling can be mitigated by addressing biotic 

interactions, spatial dependence, and scaling relationships with multi-scale modeling and hierarchical variance partitioning within the driver-response paradigm.

Predictive vegetation mapping predicts vegetation composition and structure across complex 

landscapes using gradient models describing relationships between existing vegetation and 

synoptically measured predictor variables to infer vegetation composition and structure at fine 

spatial scales across broad landscapes.

Integration of multi-scale gradient modeling with process-based ecosystem dynamics modeling is needed to robustly predict future vegetation conditions at fine spatial scales.

A major limitation of gradient and ecosystem models is the difficulty of incorporating large-scale 

disturbance processes.

We suggest linking stochastic landscape dynamics models with ecosystem and gradient modeling to address large-scale disturbance, such as wildfire, within the context of individualistic 

species responses to biophysical drivers across space and through time.

We outline four major steps to accomplish this integration.

The first step is multi-scale gradient modeling of vegetation responses to limiting resources 

and conditions.

The second step is gradient imputation to apply gradient models to produce predictive maps 

of current vegetation.

The third step is to link ecosystem dynamics models to gradient modeling and imputation.

The final step is to link landscape dynamics simulation to ecosystem dynamics and gradient 

models.

There are a number of gaps in current understanding of ecological processes that must be 

overcome to complete this integration.

This document identifies these gaps and proposes a research agenda to provide the required 

knowledge and lead to the integration of gradient, ecosystem, and landscape models to predict vegetation dynamics over broad landscapes under changing climatic and disturbance 

regimes.

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Contents

Executive Summary................................................................................. i

Introduction........................................................................................... 1

Key Issues.............................................................................................. 2

Species Niche Relations Along Biophysical Gradients .............................................................2

Scale and Spatial Complexity ...................................................................................................3

Non-Equilibrium Dynamics and Disturbance ............................................................................6

Integrating Biophysical Niche Relationships With Disturbance Regimes .................................7

Review of Research Approaches............................................................ 8

The Biophysical Niche and Gradient Modeling.........................................................................8

Pattern Matching Paradigm (PMP)...........................................................................................8

The Driver-Response Paradigm (DRP) ..................................................................................10

Univariate and Multivariate Approaches to Gradient Modeling...............................................12

Uncertainties in Gradient Modeling.........................................................................................13

Biotic Interactions, Hierarchical Variance Partitioning, Multi-Scale Modeling, 

 and Spatial Dependence .................................................................................................17

Predictive Vegetation Mapping: Univariate Prediction and Multivariate 

 Gradient Imputation .........................................................................................................21

Ecosystem Dynamics Modeling..............................................................................................24

Landscape-Level Disturbance Modeling.................................................................................26

The Challenge of Integration............................................................... 29

The Empirical Anchor..............................................................................................................29

Gradient Modeling and Ecosystem Modeling on Grids...........................................................30

Linking Gradient, Ecosystem, and Landscape Models...........................................................30

An Integrated Research Agenda.......................................................... 34

Step 1—Multi-scale Gradient Modeling ..................................................................................34

Step 2—Gradient Imputation ..................................................................................................36

Step 3—Linking ecosystem dynamics to gradient imputation.................................................38

Step 4—Linking landscape dynamics simulation to ecosystem and gradient models............40

Conclusion........................................................................................... 44

References............................................................................................ 45

ii
USDA Forest Service RMRS GTR-194. 2007 1

Global climate is expected to change rapidly over the 

next century (Thompson and others 1998, Houghton and 

others 2001), affecting forest ecosystems both directly 

by altering biophysical conditions (Neilson 1995, 

Neilson and Drapek 1998, Bachelet and others 2001b) 

and indirectly through changing disturbance regimes 

(Baker 1995, McKenzie and others 1996, Keane and 

others 1999, Dale and others 2001, He and others 2002). 

Changes in biophysical conditions could lead to species 

replacement in communities and latitudinal and altitudinal migrations. Expected increases in the size, severity, 

and frequency of wildfires (Mearns and others 1984, 

Overpeck and others 1990, Solomon and Leemans 1997, 

IPCC 2001) will lead to changes in vegetation structure, 

species composition, and diversity (Christensen 1988, 

McKenzie and others 2004). The changes in distributions of plant species caused by changing climate, and 

associated changes in disturbance regimes, may have 

large impacts on many aspects of ecological diversity 

and function (Peters and Lovejoy 1992, Miller 2003).

Natural resource managers need reliable predictions 

of how changing climate and disturbance regimes will 

affect forest ecosystems at scales from stands to regions. 

To that end, a synthesis of modeling efforts and empirical approaches is needed to unify understanding of 

forest-climate-fire relationships across a range of spatial 

and temporal scales. Such a synthesis must simultaneously address several challenges. First, robust prediction 

of forest response requires researchers to focus on 

mechanistic relationships among organisms, processes, 

and drivers at appropriate scales in space and time. 

Second, spatial heterogeneity and temporal disequilibrium are fundamental attributes of forest systems (Davis 

1986); thus, research must adopt flexible multi-scale 

approaches that address transient dynamics, time lags, 

and site history in the context of spatially complex landscapes. Third, spatially contagious disturbance processes 

(e. g., fire and insect outbreaks) introduce discontinuities 

and spatial dependence into the temporal dynamics of 

ecosystems. Furthermore, the partially stochastic nature 

of individual disturbances often precludes mechanistic 

(deterministic) modeling, thereby introducing incongruities between model paradigms that are difficult to 

resolve.

To understand how climatic change influences vegetation, we need to predict the effects of these changes 

on disturbance regimes; likewise, to predict effects of 

climate change on disturbance regimes, we need to 

understand vegetation response (Clark 1993). Only by 

combining multi-scale studies of disturbance regimes 

with analysis of vegetation responses to biophysical 

gradients across time and space will it be possible to 

understand the interactions between climate change, 

forest vegetation, and disturbance regimes.

Here we focus on integrating stand- and landscape-level patterns of fire with site-level responses of 

vegetation to biophysical gradients. The major theme of 

this work is the primacy of associating mechanisms with 

responses at appropriate scales in spatially complex and 

temporally varying environments (Turner 1989, Levin 

1992, Schneider 1994). In this paper, we identify key 

issues whose resolution will facilitate analysis of 

forest-climate-fire relationships. We then review three 

components of integrated modeling: gradient modeling 

of individual species responses, ecosystem dynamics 

simulation, and landscape disturbance simulation. We 

discuss the strengths and limits of each type of analysis and propose a synthetic approach to multi-scale 

analysis of forest ecosystem response to disturbance 

mediated climatic change. We focus on forest ecosystems and plant species in this paper; however, the issues 

and approaches discussed will be transferable to other 

ecological research efforts, such as wildlife species 

distributions and population performance.

Introduction
2 USDA Forest Service RMRS GTR-194. 2007

There are several key issues that must be addressed to 

reliably predict future vegetation composition and structure under altered climatic and disturbance regimes. 

For example, past changes in climate often triggered 

disassembly of communities. Subsequently, communities reassembled unpredictably, producing mixtures 

of species that are rare or absent at present (Barnosky 

and others 1987, Bartlein and others 1997). Typically, 

displacement of entire vegetation zones or communities 

did not occur. Instead, species responded individualistically to climate change according to environmental 

tolerance, dispersal ability, and biotic interactions (Davis 

1986, McLachlan and Brubaker 1995). Because species 

do not respond en masse, predicting changes in forest 

composition requires species-level resolution; all hierarchal levels above the species are transient.

Accordingly, we advocate addressing issues of vegetation response to climate and disturbance regime at the 

level of individual species and their interactions with 

key resources and limiting factors. Multivariate models 

characterizing the responses of individual species to 

gradients of ecological conditions are a primary tool 

in this effort. These multivariate models predict the 

response of individual plant species and the composition 

of plant communities. Importantly, they avoid questionable assumptions about the reality and stability of 

categorical vegetation types (Gleason 1926, Whittaker 

1967).

Traditional gradient modeling predicts vegetation 

community composition and structure in an environment composed of multiple, but stable, gradients of 

biophysical conditions and resources. Static speciesenvironment models, however, do not account for the 

influences of temporal dynamics and spatial complexity. 

Thus they often leave a considerable portion of the 

variance in vegetation structure and composition unexplained (Franklin 1995, Guisan and Zimmerman 2000, 

McKenzie and others 2003). Altered disturbance regimes 

compound the challenge. Disturbance regimes have 

been sensitive to past climate change (Clark 1990a). 

Due to feedbacks among species responses to biophysical conditions, spatial heterogeneity in the physical 

environment, vegetation succession, and fluctuating 

climatic and disturbance regimes, forest-climate-fire 

relationships lack stable point equilibria (Pickett and 

others 1994) and are highly sensitive to contingencies 

of history, landscape structure (Baker 2003), and the 

autecologies of individual species. Thus, predicting 

individualistic species responses to changing climate 

and disturbance regimes requires quantification of their 

responses to non-equilibrium and spatially complex 

environmental conditions. Below we identify several of 

these key issues and discuss how they relate to the task 

of integrated landscape modeling of vegetation response 

to changing climatic and disturbance regimes.

Species Niche Relations Along 

Biophysical Gradients

Ecological theory suggests that species exhibit a 

unimodal response to limiting resources in n-dimensional ecological space (Whittaker 1967, Austin 1985, 

ter Braak 1986). The volume of ecological space in 

which the organism can survive and reproduce defines 

its “environmental niche” (Hutchinson 1957, ter Braak 

1986, ter Braak and Prentice 1988, Ohmann and Spies 

1998, Guisan and Zimmerman 2000). Quantification 

of niche space at the species level is a first step toward 

predicting the effects of climatic change and altered 

disturbance regimes on forest communities.

There are three levels of niche characterization important for linking forest vegetation response to climate 

and disturbance regime. The occurrence niche, which 

describes the combination of biophysical conditions 

that are occupied by each species, gives the broadest 

measure of species-environment relationships. Species 

occurrence may not perfectly reflect environmental 

suitability, however. Ecological conditions suitable for 

survival are typically broader than conditions necessary 

for reproduction and optimal growth. Thus, two additional niche characterizations are important. The second 

is the growth niche. A direct measure of current biological 

response of a species to the environment is the association of recent “performance” (for which growth rate is 

a useful proxy) with biophysical gradients. This growth 

niche describes rate of growth as a function of biophysical gradients, adjusted for factors such as stand age, tree 

age, and competitive position. Mature trees, for example, 

may persist for centuries and continue to accrue biomass 

in locations that are no longer optimal due to changing 

climate or biological interactions. These first two niches 

both describe behavior and distribution of mature organisms and can be combined into a “mature” niche. A third 

is the regeneration niche. Regeneration often is limited 

to a restricted subset of conditions (Figure 1). Modeling 

the biophysical conditions conducive to regeneration of 

Key Issues
USDA Forest Service RMRS GTR-194. 2007 3

each species is essential for projecting changes in species 

composition over time in response to changing climate 

and disturbance regimes.

These three environmental niches are described by 

an optimum and isoclines of tolerance in an n-dimensional environmental space. Often, the large number of 

factors that compose the niche can be reduced to a relative few that explain much of the variance in species 

responses. Multivariate gradient analysis (ter Braak and 

Prentice 1988) collapses environmental niche space into 

the few dimensions that maximize explanation of vegetation structure based on patterns of correlation between 

species and environmental conditions. This technique is 

heuristically powerful, but it can often obscure relationships between mechanism and response. Importantly, 

without clear linkages between cause and effect, reliable 

extrapolation to new conditions (e.g., warmer climate) 

is problematic. Therefore, it is preferable to identify 

limiting factors, which are key variables associated with 

species tolerance that explain substantial proportions 

of variance and make sense in terms of well-understood mechanisms. Gradient modeling based on limiting 

factors is likely to produce more interpretable predictions 

of species niche relationships and, most importantly, 

provide a robust means of predicting future responses in 

altered climatic and disturbance regimes.

Scale and Spatial Complexity

Biophysical gradients are clines in n-dimensional 

ecological space. In geographical space these gradients 

often form complex patterns across a range of scales. 

The fundamental challenge to integrating landscape 

and community ecology is linking non-spatial niche 

relationships with the complex patterns of how environmental gradients overlay heterogeneous landscapes 

(Austin 1985, ter Braak and Prentice 1988, Littell and 

others, submitted). By establishing species optima and 

tolerances along environmental gradients, researchers 

can quantify the characteristics of each species’ environmental niche. The resulting statistical model can be 

used to predict the biophysical suitability of each location on a landscape for each species (Figures 2, 3). This 

mapping of niche suitability onto complex landscapes is 

the fundamental task required to predict individualistic 

species responses, and it is fundamentally important as 

a foundation for predicting effects of altered climate and 

disturbance regimes.

Spatial and temporal complexity

High levels of spatial and temporal variability are typically found in forest ecosystems systems. For example, 

site-level variation in air and ground temperatures, moisture, and nutrients are often high (Swanson and others 

1988). This variability in environmental conditions 

strongly affects the distributions and abundances of plant 

species and the structure of plant communities across the 

landscape (Whittaker 1956, Swanson and others 1988, 

Bunn and others 2005a). Landform explains a large 

proportion of variability in successional pathways, even 

in areas having relatively little topographic relief (Host 

and others 1987) or biomass (Host and others 1988). 

The spatial structure of landscapes also has a major 

influence on the type, extent, severity, and frequency 

of disturbance events. Landforms and landscape structure affect the frequency and spatial pattern of natural 

Figure 1. Hypothetical comparison 

of the “mature niche” (occurrence 

and growth) of three species with 

the “regeneration niche.” These 

three species overlap in the space 

of tolerable conditions once established, but not with respect to 

where they can initially establish.
4 USDA Forest Service RMRS GTR-194. 2007

Figure 2. Organisms are influenced 

by multiple factors simultaneously. In this example, the 

tolerances of three species are 

mapped (top) in a 3D environmental space. The lower map 

shows the suitability of each 

cell in 2D geographic space for 

one of the species as a function 

of the three factors. Rigorously 

quantifying organism niches in 

ecological space is essential 

for predicting their distribution 

across landscapes. This linkage 

allows mapping of suitable conditions for each species.
USDA Forest Service RMRS GTR-194. 2007 5

Figure 3. Predictor variables for gradient modeling are measured in the field or extracted from topographical, climatological, 

and remotely sensed data. For gradient models that are robust to climatic change, we eschew surrogate variables that are 

unchanging in ecological time in favor of those that reflect responses of the landscape to climatic variability. Examples of 

the latter are the 1-km DAYMET data (lower left) and modeled output such as soil moisture, evapotranspiration, and water 

balances (Thornton and others 1998, Wigmosta and others 1998, McKenzie and others 2003).
6 USDA Forest Service RMRS GTR-194. 2007

disturbances such as fire, wind, or bark beetle outbreaks. 

For example, in Labrador, fire and topography jointly 

influenced vegetation patterns (Foster and King 1986). 

Similarly, both topographic position and fire history 

contribute to susceptibility to wind damage (Foster 

and Boose 1992, Boose and others 1994, Kulakowski 

and Veblen 2002). Landscape context, i.e., patterns of 

local landforms, geomorphic processes, and existing 

biotic communities, influences both dispersal and biotic 

interactions (Host and others 1988, Swanson and others 

1988, Bunn and others 2005b). Details of the spatial and 

temporal structure of forest ecosystems are important at 

a range of scales, but especially those that constitute the 

organisms’ “operational environment” (Spomer 1973) 

where individual organisms directly interact with local 

topography and microclimate (Bunn and others 2003, 

2005b), respond to successional dynamics, and experience disturbance (Whittaker 1967, Tilman 1982, Levin 

1992, Schneider 1994.

Scale

There is no single correct scale of analysis for forest 

ecology. The fundamental unit of ecological analysis is 

the organism (Schneider 1994) and fundamental scales 

are those at which the organism strongly interacts with 

critical or limiting resources in its environment. Each 

species will respond to factors across a range of scales 

in space and time based on its life history strategy and 

ecological adaptations (Ball and Gimblett 1992, Ettl and 

Peterson 1995, Peterson and Peterson 2001). Ecological 

responses to biophysical gradients must be quantified at 

scales that match the biological interactions of individual 

organisms. Analyses at inappropriate scales risk missing 

or misconstruing relationships between mechanisms 

and responses (Wiens 1989, Cushman and McGarigal 

2003). Biophysical conditions directly experienced 

by individual trees, for example, occur at the scale of 

treefall gaps, slope facets, or stands. Site-level conditions are necessary, but not sufficient, to explain current 

vegetation or predict future changes due to disturbances, 

species movements, and succession. While the scale of 

direct species-environment interactions is fundamental 

to understanding and prediction, one must also address 

the influences of landscape context, including landform, vegetation, and climate on ecosystem patterns and 

processes. Accounting for multiple interactions across 

ranges of spatial and temporal scales is the fundamental 

challenge to understanding relationships between forests, 

climate, and disturbance regimes (Levin 1992, Turner 

and others 2003). Thus, studies of relationships between 

forest communities, climate, and disturbance regimes 

should use multi-scale approaches that are directly tied 

to the dominant scales of organism interaction with the 

environment. Where data allow, it is advantageous to 

quantitatively measure the relationships among driving 

factors across a range of scales simultaneously to identify these dominant scales and quantify interaction 

of factors across scale (e.g., Cushman and McGarigal 

2003). Ideally, ecological analysis will therefore not 

be between hierarchical “levels,” such as populations,

communities, or ecosystems, but instead will focus on 

relationships among organisms and driving processes 

across continuous ranges of scale (Levin 1992, Littell 

and others, submitted).

Non-Equilibrium Dynamics 

and Disturbance

Disturbance is central to forest landscape dynamics 

(Cooper 1913, Leopold 1933, Watt 1947, Reiners and 

Lang 1979, Turner and others 2003). Many ecosystems 

are inherently non-equilibrial or depend on disturbances 

to maintain community structure and ecosystem function (White 1979, Mooney and Godron 1983, Sousa 

1984, Glenn and Collins 1992, Collins and others 

1998). Linking niche relationships of forest trees to 

current and future vegetation at the local and landscape 

levels is complicated by changing biophysical conditions through time, species invasion and succession, 

and the legacy of past disturbances (Peet and Loucks 

1977, Pickett 1980). Older stand elements originated in 

a possibly quite different environment, creating a legacy 

of species composition and forest structure that may not 

be in equilibrium with current biophysical conditions or 

disturbance regimes (Baker 2003). In a changing climate, 

the plant communities established after disturbance may 

differ from those present at the time of disturbance. 

Mature trees usually tolerate short-term climatic fluctuations, and species best adapted to current climate may 

colonize only following disturbance (Dunwiddie 1986). 

Thus, adjustment of forest composition to climatic 

change may take centuries (Campbell and McAndrews 

1993). Therefore, community composition and structure in older forests likely reflect a long sequence of 

climatic conditions and disturbances no longer present 

in the landscape (Baker 2003). If so, current biophysical 

conditions and disturbance regime will not fully explain 

existing forest structure (Clark 1990b).

Recovery following disturbance is sensitive to spatial 

patterns created by the disturbance and is influenced 

by biological legacies. The ecological characteristics 

of individual species play a key role in determining the 

biological effects of a disturbance and the nature of the 

following recovery (Connell and Slatyer 1977, Noble 

and Slatyer 1980, Peet and Christensen 1980, Pickett 

and others 1987, Halpern 1988). Species responses vary 
USDA Forest Service RMRS GTR-194. 2007 7

depending on the kind and severity of a disturbance and 

its broader spatial and temporal context (Finegan 1984, 

Glenn and Collins 1992). Species life-history characteristics determine what the effects of disturbance 

size, heterogeneity, and distance from undisturbed sites 

may have on recolonization and subsequent succession (Denslow 1980, Hartshorn 1980, Miller 1982, 

Malanson 1984, Turner 1989, Peterson and Carson 

1996). Ultimately, successional patterns of vegetation are constrained by the availability of seeds, which 

depends on species traits, plant health, long- and shortterm weather, distance to seed source, and predation (Eis 

and Craigdallie 1983, Nepstad and others 1990, Johnson 

1992, Aide and Cavelier 1994, da Silva and others 1996, 

He and Mladenoff 1999b).

Vegetation communities do not adjust immediately to 

altered disturbance regimes (Baker 1995). For example, 

the extent to which landscape heterogeneity controls 

fire spread determines the time required to fully burn 

through a landscape and reset both disturbance regime 

and succession (Givnish 1981, Foster 1983, Foster and 

King 1986, Baker 2003). Baker (1995) argued that 

the time required for fire regimes to adjust to climatic 

change may often exceed the time that climate is stable, 

creating a perpetual temporal disequilibrium between 

climate, fire regimes, fuel loads, and forest structure. 

If climate changes gradually in a directional way, then 

the fire regime will be perpetually adjusting to the new 

climate, constrained by the legacy of fuel loads and 

forest structures (Baker 1995, 2003).

Integrating Biophysical Niche 

Relationships With Disturbance Regimes

Biophysical niche relationships are inextricably 

linked to landscape disturbance. For example, although 

the ultimate cause of post-glacial vegetation change in 

the Pacific Northwest was climate, the proximate cause 

was altered fire regime (Cwynar 1987, Prichard 2003). 

A small change to a drier climate probably triggered a 

significant increase in fire frequency, allowing colonization by fire-adapted species (Cwynar 1987).

Existing vegetation and underlying biophysical 

gradients influence ecological processes across a 

broad range of scales, from interactions of individual 

organisms with their operational environment to 

dynamics of landscape structure associated with climate, 

fire regime, and subsequent succession. The key to 

understanding and predicting these multi-scale dynamics 

across space and time lies in the responses of individual 

organisms to climate, other species, and disturbance 

across a range of spatial and temporal scales (Rowe 1981, 

Woodward 1987, 1988, Woodward and others 2004). 

We submit that the analysis of these dynamics has three 

parts. First, we require mechanistic understanding of the 

key drivers that limit occurrence, growth, and regeneration. Second, we need to explain current spatial patterns 

of distribution, growth, and regeneration across complex 

landscapes. Third, we need to understand how landscape 

spatial processes, i.e., disturbance and dispersal, condition these drivers, thereby modifying said patterns.

Recent research has provided substantial insight 

into this challenging task. In the following sections we 

review several major research approaches in the context 

of integrated vegetation modeling. Gradient analysis of 

niche relationships, ecosystems dynamics modeling, 

fire behavior and effects modeling, fire history research, 

landscape dynamics modeling, and global circulation 

modeling of climate have all contributed greatly. None 

of these approaches in itself is sufficient, however, to 

provide rigorous understanding or robust prediction of 

forest-climate-fire interactions. Below we suggest how 

progress might be made by integrating methods associated with several of these lines of research. Incorporating 

site history and environmental gradients into models 

of occurrence, growth, and regeneration provides 

a means to mechanistically understand and predict 

forest community dynamics at scales from stands to 

landscapes. The data-rich models arising from this integration can populate key parameters in process-based, 

ecosystem dynamics models. Finally, linking both types 

of models to spatially explicit simulations of alternative 

disturbance regimes provides a means to incorporate 

the influence of non-equilibrium conditions. This suite 

of models, properly integrated, can provide a coherent 

and practical approach for estimating the likely effects 

of climate change on forest ecosystems.
8 USDA Forest Service RMRS GTR-194. 2007

The Biophysical Niche and 

Gradient Modeling

All species occur in a characteristic, limited range of 

biophysical conditions. Within that range, a species will 

tend to be most abundant and have the highest growth 

and reproductive rates towards the center. A species not 

only requires a certain minimum amount of each resource 

but also cannot tolerate more than a certain maximum 

amount (Shelford 1931, Schwerdtfeger 1977). Therefore, 

each species performs best near an optimum (modal) 

value of a necessary environmental variable and cannot 

survive when the value diverges beyond its tolerance 

(Shelford 1931, Schwerdtfeger 1977). The relationships 

between a species performance and gradients of critical 

resources and conditions describe its fundamental niche 

(Hutchinson 1957). The composition of biotic communities changes along biophysical gradients because of 

how the niche relationships of the constituent species 

interact with the spatial structure of the environment and 

competing species (Hutchinson 1957, Whittaker 1967, 

Tilman 1982, Austin 1985). Species replacements occur 

as a function of variation in the environment (ter Braak 

and Prentice 1988) or with successional time (Pickett 

1980, Peet and Loucks 1977).

When data are collected over a sufficient range of environmental conditions, species occurrence, abundance, 

and regeneration success will change nonlinearly along 

environmental gradients (Whittaker 1967, ter Braak 

1986). It is therefore inappropriate to evaluate niche 

space using standard statistical methods that assume 

linear responses. The Gaussian response distribution has 

received most attention as a model for species responses to 

environmental gradients (ter Braak 1986). When species 

are measured along gradients of environmental variables 

that are critical and limiting, unimodal responses should 

be seen that are approximated by the Gaussian distribution (Guisan and Zimmerman 2000, Austin 2002). 

Many studies have reported non-Gaussian responses of 

vegetation to environmental gradients (MuellerDombois and Ellenberg 1974, Austin and Cunningham 

1981, Austin 1987). In many cases the measured environmental variables are not critical or limiting factors. 

In other cases, critical factors may be measured, but at 

incorrect scales that distort their relationship with species 

response. In such cases, species responses may appear 

to follow complex, multimodal patterns that cannot be 

modeled with the Gaussian distribution.

There are two general kinds of models used to evaluate 

species-environment relationships along environmental 

gradients (Table 1). In the first, the Pattern Matching 

Paradigm (PMP), the focus is on developing the most 

successful predictions of current patterns, rather than 

providing explanations for observed responses or means 

to predict future changes (e.g., Moisen and Frescino 

2002). In the second, the Driver Response Paradigm 

(DRP), prior knowledge or preliminary modeling is 

used to identify critical and limiting environmental 

gradients and proper spatial and temporal scales for 

the modeling effort (e.g., McKenzie and others 2003). 

This second approach directly links species responses to 

driving mechanisms at appropriate scales, providing the 

strongest explanations of current conditions and predictions of expected future changes. There are advantages 

and disadvantages of both kinds of modeling, discussed 

below (Figure 4).

Pattern Matching Paradigm (PMP)

In PMP, the goal is to describe the strongest empirical 

correlations between measured vegetation conditions 

and a suite of independent variables describing aspects 

of the environment thought to be related to species occurrence or performance. A common objective is to produce 

maps of current vegetation composition and structure 

across broad geographical areas, rather than to explain 

Review of Research Approaches

Table 1. Classification of biophysical modeling approaches. Machine-learning methods 

often have superior explanatory power or classification accuracy for pattern matching, 

whereas parametric models are more robust and appropriate for driver-response 

relationships.

Predictor variables

Statistical method Pattern matching (Elevation, Driver-response (climate &

geographic coordinates, climate-derived variables,

satellite spectra) biotic factors)
USDA Forest Service RMRS GTR-194. 2007 9

Figure 4. Whatever statistical modeling method is employed, there are three general steps in conducting biophysical gradient 

modeling. First, a large and representative sample of plots must be sampled for both vegetation response variables and 

biophysical driver variables. Second, these samples are compiled into matrices recording patterns of vegetation among plots 

and biophysical variables among plots. Third, these matrices, or selected vectors within them, are analyzed with canonical 

ordination or regression approaches to predict the realized niche structure and functional response of the vegetation variables 

to biophysical variables at multiple spatial scales. These models produce functions describing the quantitative relationships 

between response variables and biophysical variables, and provide parameters for modeling ecosystem dynamics and landscape disturbance. They also provide the relationship space for imputation.

observed patterns on the basis of relationships between 

environmental drivers and species responses.

A variety of methods have been used in this kind of 

modeling, including gradient modeling and machinelearning or expert-system methods (Frescino and others 

2001, Moisen and Frescino 2002, Ohmann and Gregory 

2002, Olden and Jackson 2002). Generalized additive 

models (GAMs—Hastie and Tibshirani 1986), that 

include non-parametric terms to extend the generalized linear model, have often proven quite effective in 

predicting current vegetation (Moisen and Edwards 1999, 

Frescino and others 2001, Moisen and Frescino 2002). 

Classification and regression trees (CART) use binary 

recursive partitioning to divide the data into branches 

that maximize the relationship between predictor and 

response variables (Morgan and Sonquist 1963, Breiman 

and others1984). CART was one of the least successful 

of the five modeling techniques compared by Moisen 

and Frescino (2002) for predicting forest composition 

and structure. This may be because CART imposes 

a categorical model structure on continuous gradient 

responses. Predicted responses for new observations in 

CART are limited by its hierarchical structure to those 

already estimated by the original model (Clark and 

Pregibon 1992). Multivariate adaptive regression splines 

(MARS; Friedman 1991) generalize the piecewise categorical functions of CART into continuous functions by 

fitting multivariate splines and matching the values at 

the boundaries of the regions. MARS and GAM were the 

most successful methods tested by Moisen and Frescino 

(2002).

A recent implementation of a genetic algorithm—the 

Genetic Algorithm for Rule-set Prediction (GARP—

Stockwell and Peters 1999)—has proven successful in 

modeling the ecological niches of both plant and animal 

species across a wide range of ecosystems (Peterson 
10 USDA Forest Service RMRS GTR-194. 2007

and others 1999, Anderson and others 2003, Oberhauser 

and Peterson, 2003). GARP generates a set of rules for 

predicting presence or absence, each of which applies 

to a portion of the data. Some of these rules (“logit” 

rules) are rule-based analogues to logistic regression, 

whereas others determine presence or absence of a 

species based on ranges of predictors or on whether one 

or more predictors takes on a unique value or values. In 

contrast to classical models, not all rules apply to every 

data point. For a full description of the GARP algorithm, 

see Stockwell and Noble (1992) or Stockwell and Peters 

(1999).

Such flexible non-parametric or machine-learning 

statistical methods can optimize the fit of one pattern 

to another, providing a means of producing predictions 

across broad spatial extents, but they have limited ability 

to distinguish drivers and responses and are vulnerable to 

overfitting (Venables and Ripley 2002). Such fine-scale 

model fitting may offer high performance for predicting 

within a single data set but is less successful in 1) identifying the form of underlying mechanistic relationships, 

2) extrapolating or interpolating beyond the samples, or 

3) making predictions for the future under altered conditions. Thus, while pattern-fitting approaches equal or 

exceed parametric models in prediction accuracy, they 

are more difficult to interpret with respect to limiting 

factors, are less parsimonious in variable selection, and 

often are computationally expensive (Stockwell and 

Peters 1999, McKenzie unpubl. data1). Further, they 

often perform better in simulation studies than with real 

data, giving a false sense of accuracy and robustness to 

extrapolation (Moisen and Frescino 2002). The strengths 

of PMP are for prediction within a given time and space; 

the lack of mechanistic underpinnings is far less critical 

for interpolation than for extrapolation, and the flexibility of the algorithms allows precise fit to specific data 

sets. However, evaluating the effects of future climates 

on a forested landscape or applying models developed 

in one area to produce predictions in another are clearly 

extrapolative in nature, and PMP is likely to produce 

erratic results when used in this context.

The Driver-Response Paradigm (DRP)

DRP seeks to identify limiting factors and the functional relationships between these limiting factors and 

vegetation responses using gradient modeling (Figure 5). 

By focusing on limiting factors it is possible to interpret 

1 Unpublished manuscript on file at Pacific Wildland Fire 

Sciences Lab, Seattle, WA.

species-environment relationships with more confidence than is possible using PMP. Importantly, gradient 

modeling is better grounded in ecological theory than 

more complex approaches using machine-learning 

techniques (ter Braak and Prentice 1988). Parametric 

gradient models also provide better discrimination 

among the niches of closely related species (Doebell and 

Dieckmann 2003) and are more amenable to multi-scale 

and hierarchical analysis (Cushman and McGarigal 2003) 

than non-parametric or machine learning approaches. 

Finally, in the integrated modeling environment we 

propose below, clearly defined species responses to 

biophysical gradients are essential because they are 

used to specify parameters in ecosystem models. We 

therefore propose a combined approach that nests mechanistic biophysical modeling of limiting factors within a 

more general gradient modeling framework (Figure 3). 

Multi-scale, hierarchical gradient modeling facilitates 

both mechanistic understanding and robust extrapolation for landscape mapping.

DRP gradient modeling and limiting resources

There are three major challenges to obtaining suitable predictor variables for parametric DRP gradient 

modeling. First, one must identify the key factors that 

govern the responses of each species across space, time, 

and biophysical conditions. Second, one must be able 

to obtain accurate measurements of these factors, or 

appropriate surrogates, for a large number of sample 

locations distributed across a representative combination 

of biophysical conditions in broad landscapes. Third, 

these measurements must be made at the scales at which 

the species is most strongly responding to the limiting 

factor; measurements at other scales may not produce 

clear or consistent predictions (Wiens 1989).

Examples of key limiting resources are energy and 

water. Energy and water limitations interact to affect 

water balance at the level of sites and individual organisms (Stephenson 1990, 1998). Indeed, water balance 

is a key variable in both ecosystem simulation models 

(Neilson 1995) and empirical gradient models, though 

indirectly in the latter via energy and water variables. 

Hawkins and others (2003) suggest that energy and water 

balances and their interactions globally affect species 

distributions and patterns of species richness. Milne 

and others (2002) used terrain modeling to quantify a 

threshold between energy-limited and water-limited 

ecosystems in the Interior Columbia River Basin. Much 

of the biophysical gradient modeling heretofore accomplished, including that of Milne and others (2002), was 

either in clearly water-limited systems—e.g., arid mountains or shrublands—or in extreme environments in 

which biotic interactions are less important than abiotic 
USDA Forest Service RMRS GTR-194. 2007 11

Figure 5. The strongest inferences about causality and the most robust predictions to new locations or future conditions are 

obtained from modeling the occurrence or performance of each species along gradients of limiting biophysical variables. 

In this example, the limiting biophysical variables are water, temperature, and energy and the response variable is annual 

growth. Each species will have unique response curves along each of these critical resource gradients. Response curves for 

a hypothetical species are shown at the top. The bivariate response surfaces for each pair of these resources are shown in 

the middle, and the trivariate response volume is shown at the bottom. In the response volume, the outer blue shell represents 

a 25% of maximum growth isocline, the purple shell a 50% of maximum, and the inner lavender shell 75% of maximum growth 

rate. By modeling species responses directly on limiting biophysical variables, one can link mechanistic relationships between 

driving variables and biotic responses directly.
12 USDA Forest Service RMRS GTR-194. 2007

limiting factors (Austin and others 1994, Franklin 1998, 

Bolliger and others 2000a, McKenzie and others 2003). 

Correlations between individual species responses and 

moisture may, in many other systems, be more difficult 

to identify due to the confounding effects of biotic interactions (i.e., competition—McKenzie and others 2003), 

or may be correlated with other controlling factors. For 

example, Peterson and Peterson (2001) found that spring 

snowpack clearly limited growth of mountain hemlock 

(Tsuga mertensiana) in the upper elevations of its range 

in the Pacific Northwest, but at drier lower elevations 

growth was limited by moisture deficits. At high elevations, abundant moisture in the form of snow was 

correlated with reduced light and temperature leading to 

differential responses to moisture with changing elevation. Biotic interactions and correlations with other 

limiting factors can cause the effects of any limiting 

factors to be increased or decreased under climatic 

change, and within a specific species may differ across 

its range. In general, however, unimodal response functions identify limiting factors at both ends of a species’ 

range, if sampled gradients are broad enough to span all 

or most of that range.

Once the key limiting factors are identified it is essential to obtain accurate measurements or predictions of 

these factors for each sample plot. This usually will 

require measurements or estimates of each driving variable at hundreds to thousands of individual locations 

across complex landscapes for which existing vegetation 

and disturbance history are also quantified. The challenge 

is obtaining direct measurements of climatic and edaphic 

variables for such large and dispersed grids of sample 

plots. A combination of approaches, including networks 

of sensor stations placed on the sample grid and spatial 

modeling relationships between terrain and climatic 

conditions, will provide the most reliable inferences. In 

the research agenda section at the end of this document we 

identify several alternative approaches for obtaining these 

key independent variables for large and dispersed sample 

grids across complex landscapes. Once these driving 

variables have been obtained for all sample plots, the next 

main consideration is what approach to use for gradient 

modeling. In this regard there are two major alternatives, 

univariate and multivariate gradient modeling.

Univariate and Multivariate Approaches to 

Gradient Modeling

Parametric gradient models of species-environment 

relationships can be fit in both univariate and multivariate frameworks. Individual species responses to 

environmental gradients can be quantified using generalized linear models by specifying polynomial or other 

nonlinear terms in the linear predictor (Forsythe and 

Loucks 1972, McCullagh and Nelder 1989, Guisan 

and others 2002). Lenihan (1993) fit two- and threedimensional response surfaces to boreal tree species 

distributions using logistic regression and biophysical variables (snowfall, degree days, minimum 

temperature, soil moisture deficit, and evapotranspiration). Austin and others (1994) successfully modeled 

Australian vegetation by modeling unimodal response 

with a right-skewed beta function. Bolliger and others 

(2000b), modeling subalpine species in Switzerland, and 

McKenzie and others (2003), modeling conifer species 

in the Pacific Northwest, USA, identified proxy sets of 

predictor variables (Booth and others 1994), grouping 

variables associated with expected limiting factors of 

energy (mean temperature, growing degree days, soil 

temperature, etc.) and moisture (precipitation, snowfall, soil moisture, etc.). Only one variable from each 

set was allowed as a predictor, reducing collinearity 

and clarifying potential limits to growth or distribution. 

McKenzie and others (2003) also fit unimodal response 

curves successfully for the majority of species tested.

When the number of species is large, it may be 

impractical to conduct separate analyses for each. It 

is also challenging to combine separate analyses to 

quantify species interactions and niche separation, 

particularly when there are more than 2-3 environmental 

variables. Additionally, regression is often limited in 

studying vegetation responses to biophysical gradients 

because vegetation data contain many zeros, violating 

the assumption of normal error distribution implicit in 

many regression techniques. In addition, environmental 

variables are often highly correlated, violating assumptions of independent predictor variables implicit in most 

regression approaches. These challenges can be most 

readily addressed in a multivariate context.

In a multivariate context, canonical ordination 

(ter Braak 1986, ter Braak and Prentice 1988, Palmer 

1993) uses a heuristic mathematical approximation to 

a Gaussian response curve, applied simultaneously to 

each species. Canonical ordination is unaffected by zero 

values in the species data and is quite robust to intercorrelation among predictors (Palmer 1993). Thus, if 

species react to the same linear combinations of environmental variables according to a common response 

model, canonical ordination is an attractive alternative 

to individual regression models (ter Braak and Prentice 

1988).

The decision whether to use constrained ordination 

or a series of separate regressions depends on if there 

is an advantage to analyzing all species simultaneously 

(ter Braak and Prentice 1988). Constrained ordination 
USDA Forest Service RMRS GTR-194. 2007 13

assumes that species react to the same biophysical gradients, while, in regression, a separate composite gradient 

is constructed for each species. Regression, therefore, 

allows more detailed and accurate prediction and calibration. Single-species models often yield better predictions 

than a multi-species model for the same species (Guisan 

and others 1999). However, single-species regressions 

lose information about the co-occurrence of multiple 

species within samples (Gottfried and others 1998), 

whereas constrained ordination makes use of this information in the weighted averaging algorithm (Ohmann 

and Gregory 2002). Also, multi-species constrained 

ordination ensures that predicted plant communities are 

realistic assemblages of species and structures. If all 

species distributions were modeled independently and 

then assembled into communities, it is likely that unrealistic collections of species would be predicted (Moeur 

and Stage 1995).

Uncertainties in Gradient Modeling

Despite their theoretical and practical advantages, 

past applications of gradient modeling have usually left 

a substantial proportion of the variance in species abundance or occurrence unexplained (e.g., Ohmann and 

Gregory 2002, McKenzie and others 2003). We identify 

three types of error associated with gradient models. The 

first two are partially avoidable within the paradigm, 

whereas the third is intrinsic to the paradigm and necessitates integration with other paradigms:

 Technical issues requiring better quality control and 

minimization of error.

Model assumptions are inappropriate for the 

covariance structure within the data. Lack of fit 

appears in strongly patterned residuals or unequal 

variances, particularly at the ends of ranges (Littell 

and others, submitted).

Response or predictors or both not accurately 

measured. This is likely, for example, when 

data-poor extrapolations are made to unsampled 

sites, when predictor variables are assumed to be 

homogeneous across complex terrain, or when 

questionable allometry is used to calculate response 

variables.

Limitations partially resolvable within the paradigm. 

Addressing the first two of these requires coupled 

models within the paradigm. Addressing the second 

two requires some additional creative thinking about 

driver-response vs. pattern matching methods. We 

take up these topics up later in this section.

Biotic interactions are not considered. For example, 

in energy-limited systems with high biomass and 

1.

a)

b)

2.

a)

productivity, such as mesic low-elevation forests, 

the majority of trees are buffered from the “true” 

biophysical environment but limited by competition 

for scarce resources (energy, e.g., light) by more 

dominant individuals.

Spatial dependence is not considered. This is not 

a problem in the mechanism-response relation 

per se, but a question of adding another statistical 

coupling to take advantage of knowing true 

degrees of freedom and weighting observations 

accordingly.

The use of surrogate variables leads to imperfect 

coupling of driver and response (Figure 6). 

Much past gradient modeling has been based on 

correlating patterns of species in the environment 

to spectral, topographic, or other spatial variables. 

These predictor variables are not themselves actors 

on the organisms. Organisms respond to limiting 

resources that may vary in correlation with these 

surrogates, but not to these surrogates themselves. 

In complex environments, it is common that the 

surrogate relationship between organism responses 

and these proxy variables is non-stationary 

across space, time, and biophysical context. This 

increases model imprecision and can lead to spatial 

bias. It also prevents mechanistic understanding 

of relationships between species and the limiting 

resources that actually drive their responses. 

Reliable understanding and prediction requires that 

the variables that govern species response must be 

directly measured and associated with organism 

performance.

A scale mismatch between the action of the driving 

variable, the response of the organism and the 

scales at which the variable and the organism 

are measured obscures or distorts the nature of 

the species-environment relationship (Figure 7). 

The response of organisms to driving variables 

will be expressed over a limited range of scales. 

Incorrect scale of measurement of the driving 

variable or the organism responses may lead to 

incorrect conclusions about the importance and 

nature of the relationship between that factor and 

that organism (Wiens 1989). Scaling issues pertain 

to both response and predictor variables. Often, the 

response variable is predicted at a different scale 

than it was measured, requiring data aggregation 

that is a source of substantial error (Rastetter and 

others 1992). Increasing spatial scale in prediction 

can be achieved through spatial imputation of 

results at the native grain (see Imputation section 

below), which maintains the scaling relationships 

b)

c)

d)
14 USDA Forest Service RMRS GTR-194. 2007

Figure 6. A. Relationships between biological responses and limiting biophysical variables usually have high predictive power 

and low residual deviance. B. In contrast, relationships between limiting biophysical variables and spatial surrogates, such 

as elevation for temperature, usually have somewhat weaker relationships and higher residual deviance. C. Relationships 

between the surrogate and the biological response compounds the imprecision in both A and B, resulting in weaker 

relationships with high residual deviance. There are many factors that influence temperature regimes across complex 

landscapes in addition to elevation. D. For example, elevation and aspect interact to influence local temperature regime. 

The interaction of several factors results in low predictive power for any particular surrogate variable.

Figure 7. The strength and nature of relationship observed between a response variable and a predictor variable will 

change as functions of the scale of each (A). Scaling response variables is problematic and requires either upscaling 

(e.g., plot-level vegetation response to predicted landscape-level aggregate properties) (B), or downscaling (e.g., 

1-km scale measured response data to plot-level predicted response) (C). These extrapolations require information 

at multiple scales. Forest plots are rarely nested across a broad range of scales, for example. The errors associated 

with scaling response variables are avoided by making predictions at the same grain at which response variables were 

measured. Spatial scope can then be achieved by imputing model predictions across large spatial extents at the native 

grain of the response variable (see Imputation section). Scaling predictor variables, in contrast, is an essential task in 

modeling species-environment relationships. The grain at which environmental data are most strongly related to the 

response of the dependent variable may be finer (D) or coarser (E) than the grain of the response variable. Haphazard 

selection of scales of variables leads to equivocal conclusions. Ideally, the grain of the response variable should be 

fixed at an appropriate level and modeled across spatial and temporal extents (F). The predictor variables ideally 

would be measured at the finest possible grain over the largest possible extent. Partial bivariate scaling (Figure 7F and 

Figure 9) could then be used to identify the neighborhood extent around sampling units at which the predictor variable 

has the strongest relationship with the response variable.
USDA Forest Service RMRS GTR-194. 2007 15
16 USDA Forest Service RMRS GTR-194. 2007

between patterns and processes while extending 

predictions across broad spatial extents. Scaling 

predictor variables is an equally important issue. 

The relationship between a predictor and a response 

variable will change as a function of the extent 

over which the predictor variable is measured. 

It is important to identify the scale(s) at which 

this relationship is strongest. Bivariate scaling 

(Figure 9) is a formal approach to determine the 

scales at which environmental variables are most 

strongly influencing the response of vegetation at 

the scale at which the vegetation is sampled.

Figure 8. Biophysical conditions at each location in a landscape fluctuate over time on seasonal, annual, and decadal 

time scales. Thus the biophysical character of a location cannot be adequately represented by measurements taken 

at a single time. The current vegetation at the site reflects the results of a variety of nonequilibrium processes over 

various temporal scales, so it is essential to address temporal variability. In this figure the axes represent the limiting 

resources of water, temperature, and solar energy. The surfaces reflect the concentric 25th, 50th, and 75th percentile 

of maximum annual growth for a hypothetical species along those three limiting resources. The black dots represent 

sequential measurements of biophysical conditions at a single plot. The trajectory illustrates variable biophysical 

conditions over time. The pathway of the trajectory through the growth isoclines indicates temporal changes in the 

suitability of this single plot location for growth of the species.

 Limitations requiring integrating gradient modeling 

with other paradigms

Lag effects and non-equilibrium dynamics

compromise the interpretation and power of 

equilibrium models. Lag effects incorporate the 

entire history of the site prior to the point at which 

vegetation and biophysical limiting factors were 

measured. These effects persist across a vast range 

of temporal scales. Species occurrence on a site 

will be related not only to current moisture and 

temperature gradients, but also to the separation 

of the North American continent from Europe 

3.

e)
USDA Forest Service RMRS GTR-194. 2007 17

Figure 9. Partial bivariate scaling to identify the appropriate scales for each explanatory variable. This example illustrates the 

process for a single hypothetical explanatory variable measured over five spatial scales. In the image in the upper left, the 

square represents the footprint of the sample plot, and the concentric rings each of four radii around the plot. The variable is 

extracted from each of these five spatial scales. Across plots, we derive a matrix of plots by variable-by-scale combinations 

(lower left), and a matrix of plots by species (upper right). Bivariate scaling associates the patterns in the species among 

plots with the values of the variable-by-scale among plots. The first step is to model the species response as a function of all 

scales of the variable 1). In this example, scale 1, 2, and 5 have statistically significant explanatory power, and scale 1 has 

the largest marginal explanatory power. Scale 1 is selected. In step 2, the model is rebuilt using scales 2-5 as explanatory 

variables and scale 1 as a covariable. In this step, scale 5 is found to be the only significant scale and is selected. In step 3 

no additional significant scales are selected. Scales 1 and 5 are selected for inclusion in the model building and the process 

is repeated for the next explanatory variable.

(millions of years), presence of ice-age refugia 

(thousands of years), fire history (hundreds of 

years), and more immediate influences such as the 

seasonal, annual, and decadal climatic variability. 

Any particular plot will follow a trajectory through 

biophysical conditions, and thus species tolerance, 

space (Figure 8), and composition and growth will 

be strongly influenced by past events.

Limiting factors are not stationary. Even if one 

could solve the problem of lag effects within an 

equilibrium model, the parameters of gradient 

models would be expected to change over time. For 

example, if limiting factors change, so will the key 

f)

predictor variables (Peterson and Peterson 2001). 

For dynamic modeling, then, gradient models are 

best utilized for establishing initial conditions and 

for building transfer functions to take landscape 

outputs in future time-steps back to fine-scale 

ecosystem attributes (see below).

Biotic Interactions, Hierarchical Variance 

Partitioning, Multi-Scale Modeling, 

and Spatial Dependence

Many of the sources of error and imprecision detailed 

above can be mitigated within the gradient modeling 
18 USDA Forest Service RMRS GTR-194. 2007

approach by addressing biotic interactions, spatial 

dependence, and scaling relationships with multiscale modeling (Thompson and McGarigal 2002), 

and hierarchical variance partitioning (Cushman and 

McGarigal 2003, Cushman and Wallin 2002, Cushman 

and McGarigal 2004). The relationships between a 

species and an important environmental variable will 

appear only when measurements are made at appropriate spatial scales (Wiens 1989). Thus it is essential 

to optimally match the scale of environmental pattern 

in each predictor variable to vegetation response. In the 

past, most efforts have been restricted to single scales of 

analysis, often arbitrarily imposed by the scale of available data (e.g., TM or AVHRR imagery). Much effort 

has recently been committed to determining which 

methods are most effective at identifying the correct 

scale for associating environmental variation to species 

responses; partial bivariate scaling (Thompson and 

McGarigal 2002, Grand and others 2004) is among the 

most effective.

Partial bivariate scaling

In partial bivariate scaling, the patterns of the response 

variables (vegetation composition and structure) are 

associated with multiple environmental variables, each 

measured across a range of spatial scales. A priori, we 

have no basis to assume which spatial extent surrounding 

the sampled plot is the scale at which the environmental 

variable is most strongly related to vegetation response. 

Accordingly, it is best to measure each environmental 

variable across a broad range of radii surrounding the 

plot. Partial CCA or partial regression is then used to 

determine the scale(s) at which each predictor variable is most related to vegetation response (Figure 9). 

Separate models are constructed for each predictor variable, with each model including variables at each spatial 

scale. Canonical ordination or regression then identifies 

the spatial scale with the largest marginal relationship 

between the response and any predictor variable. If there 

is no scale at which a variable is significant then that 

variable is dropped. If the most influential scale is a 

significant predictor, the process is repeated, treating the 

previously identified scale as a covariate. If additional 

scales are found to be significant predictors then they 

too are selected and partialled out, and the process is 

continued until no more scales contribute significantly 

to prediction. In practice, one or at most two significant 

scales are usually associated with each variable, and 

many variables have no significant explanatory power 

and are dropped (Grand and others 2004).

Hierarchical gradient modeling

Once the appropriate scales have been identified for 

each variable, gradient models are then built using stepwise approaches incorporating significant variables at the 

identified scales. In this model building, it is often useful 

to use hierarchical variance partitioning (Cushman and 

McGarigal 2003, Cushman and Wallin 2002, Cushman 

and McGarigal 2004). Hierarchical variance partitioning 

is a statistical method that breaks down the explanatory 

power among multiple sets of explanatory variables into 

their individual components (Figure 10). The method 

translates a hierarchical or multi-scale conceptual model 

into a statistical decomposition of variance. The decomposed model allows one to assess the relative importance, 

confounding, and interaction among variables. This 

facilitates ecological understanding of the relationships 

between mechanisms and responses across scale and 

organizational levels. Hierarchical model partitioning 

is particularly useful for the specific challenges facing 

research on relationships among forest vegetation, fire, and 

climate. It allows quantitative assessment of the relative 

predictive abilities and interactions of 1) local “fine-filter” 

measurements of environmental conditions in the field 

and “coarse-filter” environmental conditions extracted 

from synoptic GIS, 2) mechanistic limiting factors and 

the potpourri of other available surrogate variables, 

3) abiotic environmental conditions and biotic interactions, 4) spatial dependence, and 5) time lag effects.

Biotic-interactions and time lag effects—Hierarchical, 

multi-scale gradient models can also incorporate biotic 

interactions, succession, disturbance history, and 

temporal disequilibria between current vegetation and 

the environment (Figure 10). Both temporal and environmental variables are included as separate predictor 

sets and partitioned to quantify the relative effects and 

interaction of time since disturbance, disturbance type, 

and environmental gradients. For example, the effect 

of competition upon a target species can be seen as a 

local modification of environmental conditions by other 

species (Tilman 1990). Biotic interactions can be modeled 

directly, where vectors of proportional composition are 

a multivariate response (Aitchison 1986, Billheimer 

and others 2001, Cumming 2001). Although this technique is of theoretical interest, it may prove difficult to 

apply to any but the simplest compositional patterns (but 

see Cumming 2001). For example, McKenzie (unpublished) was able to explain negligible variance with this 

approach using the same data (McKenzie and others 

2003) that produced robust gradient models for individual species.
USDA Forest Service RMRS GTR-194. 2007 19

An analogous indirect method is to estimate proportional composition of individual species via a GLM of 

the binomial family, as is used to predict probability of 

presence/absence. Like the methods of Aitchison (1986) 

and others, this approach requires a non-zero value for 

every species in every observation or plot so it is difficult 

to apply in real ecosystems. A more practical approach 

may be a canonical ordination method such as canonical correspondence analysis, where individual species’ 

optima and tolerances in multidimensional gradient space 

are constrained both by predictor variables (linearly) 

and by changes in species composition itself (via 

unimodal functions), thereby implicitly incorporating 

biotic interactions among species. Hierarchical variance 

partitioning of canonical ordination models provides a 

means of addressing species interactions by including 

appropriate biotic variables among the environmental 

predictor sets. It is then possible to separate the effects of 

abiotic environmental control from the effects of species 

interactions (Figure 10).

Success in this effort will depend on samples from 

combinations of all pertinent biophysical contexts with 

and without past disturbance types of interest. The 

database of sample plots must contain the full combination of species occurrences along environmental 

gradients. Quantifying competition and species interactions requires measurement of performance of each 

species in each biophysical context both in the presence 

Figure 10. Hierarchical model building and decomposition. In regression and canonical ordination, subsets of variables are partitioned to quantify their independent and interactive influences. In this example, we hierarchically 

build a model to explain vegetation composition and structure based on spatial, temporal, and environmental 

factors. Each of these data sets in turn contains nested subsets. By decomposing the relationships among 

these components we can quantify the relative importance, interaction, and confounding among multiple 

explanatory variables derived at different spatial scales and different organizational levels. This provides a 

means to both build the most powerful predictive models, but also to gain the most complete insight into the 

importance and shape of the relationship between each driving factor and vegetation response.
20 USDA Forest Service RMRS GTR-194. 2007

and the absence of the putative competitors. For example, 

vegetation responses are highly sensitive to the details 

of site level resources and disturbance history (Bunn and 

others 2003). Seed dispersal depends on release height, 

topography, wind speed and direction, tree density, and 

seed morphology (Johnson and others 1981, Van der 

Pijl 1982, Green and Johnson 1996). Cycling of organic 

matter and nutrients depends on litterfall, atmospheric 

deposition, and decomposition (Waring and Schlesinger 

1985), which are highly influenced by local stand conditions, history, and biophysical context. In a hierarchical 

gradient model, these local influences can be separated 

from coarse-scale influences, rather than just combined 

with them in interaction terms, and the variance attributable to each can be precisely quantified (Cushman 

and McGarigal 2004). Such an approach partially overcomes errors associated with spatial scale mismatches 

and temporal lag effects.

Spatial Dependence and Autocorrelation—Biotic 

response along environmental gradients has two components of spatial dependence: spatial biotic processes 

within the community and the spatial structure of environmental factors (Legendre 1993). Spatial dependence 

among observations reduces degrees of freedom in a 

model and can drastically change significance levels. 

Because many ecological processes exhibit spatial autocorrelation to some degree, ignoring spatial dependence 

where non-negligible can distort ecological inference. 

The core statistical techniques in gradient modeling 

(multiple regression, GLMs, canonical ordination in 

its regression phase) carry assumptions of independence. Violation of these assumptions does not bias 

estimation per se, but it does render significance tests 

unreliable. Explicit consideration of spatial dependence 

can improve model estimation and in some cases predictive power. For example, Miller and Franklin (2002) 

improved predictive models for shrub species in the 

American Southwest by combining GLMs (including 

a preponderance of unimodal functions) with indicator 

Kriging (Isaaks and Srivastava 1989).

Hierarchical gradient modeling with direct ordination can account for spatial dependence in several ways. 

First, one can include spatial variables, such as the terms 

of a trend surface analysis, as predictor variables. By 

partitioning the models one can determine the amount 

of variance attributable to independent environmental 

control, spatially structured environmental control, and 

biotic spatial autocorrelation (Borcard and Legendre 

1994). Alternatively, Wagner (2004) integrated geostatistical spatial modeling with direct canonical ordination 

to address spatial autocorrelation in community patterns. 

This allows the ordination results to be portioned by 

distance and integrated with geostatistics. The diagnostic tools provided by direct multi-scale ordination 

(sensu Wagner 2004) allow ecologists to distinguish 

between spatial dependence and spatial autocorrelation and to check assumptions of independent residuals, 

stationarity, and scale-invariant correlation.

Not all biophysical gradient models will benefit from 

incorporating spatial dependence, however. Spatial autocorrelation will be evident in sample data only if its range 

(more precisely, the range of its empirical variogram) 

is much greater than the average geographic distance 

between observations. In complex terrain, observations 

have to be very close in space for this to be true. For 

example, McKenzie and others (2003) tested for spatial 

dependence indirectly by computing empirical variograms of the residuals from their gradient models, finding 

no mean change in covariance from adjacent plots to 

those separated by kilometers. However, in imputation 

(see below), predictions are made for all pixels across 

all lag distances. Accounting for spatial dependence will 

be of great importance in producing the most accurate 

imputed maps of expected vegetation conditions across 

complex landscapes.

Existing FIA sample protocols use a sub-plot design 

that could be utilized to provide a measure of spatial 

autocorrelation by comparing vegetation, climate, disturbance, and biophysical environments between sub-plots. 

FIA plot structures allow autocorrelation to be computed 

at 2 lag-distances (36.6 and 63.4 m). Additional plots 

could be added to provide additional scales at which autocorrelation could be measured. Spatial autocorrelation 

itself can then be modeled as an autoregressive gradient 

function of disturbance and biophysical environment.

Implementing Multi-scale Gradient Modeling with 

Canonical Ordination—Multi-scale and hierarchical 

gradient modeling has been developed using partial 

canonical correspondence analysis (ter Braak 1986, 

Cushman and McGarigal 2003, 2004). Partial CCA is a 

particularly useful tool for analysis of temporal, multiscale, or hierarchical relationships (e.g., Cushman and 

McGarigal 2003). Partial CCA can be used to separate 

the effects of environmental control from the autogenic 

changes in the community related to successional time. 

It is also an ideal tool with which to identify the scales 

at which each biophysical variable is most strongly 

related to the species responses (Figure 4) and to partition the effects of variables from multiple data sources 

and organizational levels (Cushman and McGarigal 

2003, Figure 5). Thus partial CCA provides a rigorous 

framework to quantitatively link vegetation responses to 

the influences of environmental factors across a range 

of spatial scales, temporal dynamics, and succession 
USDA Forest Service RMRS GTR-194. 2007 21

and to partition the effects of factors measured across 

multiple levels of organization. Bivariate scaling and 

hierarchical gradient modeling should be possible using 

alternative approaches such as GAM and nonlinear 

regression. However, more development is required 

before the potential of these other methods is known. 

At this time, multi-scale, hierarchical gradient modeling 

is the only well-developed tool allowing proper linkage 

of the patterns and processes across spatial scales and 

over time essential to the task of predicting relationships 

between climate, fire regimes, and forest ecosystems.

Predictive Vegetation Mapping: 

Univariate Prediction and Multivariate 

Gradient Imputation

Spatially explicit predictions of species composition 

and the structure of forest vegetation are needed at broad 

spatial scales (Moisen and Frescino 2002, Ohmann and 

Gregory 2002). A detailed spatial prediction of current 

vegetation composition and structure is the foundation 

on which predictions of the effects of future climate 

and disturbance regimes are based and evaluated. This 

information is obtained through predictive vegetation mapping (Franklin 1995). Predictive vegetation 

mapping uses relationships between observed patterns 

of species occurrence, obtained from a large, representative sample of field plots, and synoptically measured 

predictor variables.

Most efforts at predictive vegetation mapping 

have been based on classification of satellite imagery. 

Categorical, patch-based classifications are limited 

to general characteristics of upper canopy (Cohen 

and others 2001, Wolter and others 1995, Woodcock 

and others 1994) and cannot reflect the continuously 

varying structure of the plant community. If a minimum 

patch size is imposed, small scale features may vanish. 

Perhaps even more importantly, classification results is 

a necessary compromise between information loss and 

categorical error rates. As the numbers of classification 

types increase, error rates also increase (Hunsaker and 

others 2001, McGarigal and Cushman 2005). Thus classified maps are limited to relatively few, broadly defined 

patch types.

An alternative approach is to predict detailed vegetation conditions at each cell across the landscape based 

on a gradient model (Van Deusen 1997). There are two 

main approaches for predictive vegetation mapping. If 

univariate models are used the model itself can produce 

predictions for each unsampled location based on 

the value of predictor variables at each location. For 

example, Frescino and others (2001) used generalized 

additive models to predict forest presence, lodgepole 

pine (Pinus contorta) presence, basal area, shrub cover, 

and snag density in the Uintah Mountains of Utah. The 

input data was provided by the Interior West Resource 

Inventory, Monitoring and Evaluation Program database, 

and consisted of forest vegetation measurements taken 

from 0.4 ha plots. The explanatory variables included 

downscaled PRISM precipitation data, elevation, aspect 

and slope, geology, geographic location, classified TM 

imagery, unclassified TM imagery, and AVHRR imagery. 

All variables were rescaled within GIS to a cell size of 

0.4 ha. Their results indicate that TM data, elevation, 

and geology are significantly related to the response 

variables, but predictive accuracy was low. Prediction 

accuracy for forest vs. non-forest was 88% and was 80% 

for lodgepole pine. Only 62% of predictions for basal 

area, shrub cover, and snag density fell within 15% of 

measured values.

Moisen and Frescino (2002) compared five modeling 

approaches for predicting forest presence: spruce-fir 

forest, biomass, tree age, quadratic mean diameter, and 

crown cover. Vegetation training data were from FIA 

plots at a spatial resolution of 0.4 ha. The explanatory 

variables included elevation, slope, aspect, geographic 

location, AVHRR data, and TM-classified land cover 

data. All predictions were made to 1-km output pixels. 

The modeling approaches included simple linear models, 

GAM, CART, MARS, and artificial neural networks 

(ANN). Models built on simulated complex nonlinear 

responses indicated that MARS and ANN performed 

best. In contrast, models built using measured data 

appeared to favor GAM and MARS. Predictive success 

was relatively low overall, however. Kappa values for 

predicting forest vs. nonforest ranged between 0.3 and 

0.8. Correlations between observed and predicted values 

for continuous variables were relatively low, with none 

over 0.6. Few models produced maps with more than 

50% of predicted values within 25% of actual.

When a multivariate approach is adopted, in which 

the responses of multiple species are simultaneously 

predicted based on combinations of predictor variables, 

it is not possible to use the model to directly predict 

expected values of each species. When a multivariate 

gradient model is used, gradient imputation (Figure 11—

Ohmann and Spies 1998, Ohmann and Gregory 2002, 

Wimberly and Ohmann 2004) provides an efficient 

means of estimating expected values for dependent variables at unsampled locations based on the complex of 

environmental gradients at those locations. Gradient 

imputation has several technical advantages over alternative methods. First, gradient models utilize patterns 

of covariance among interrelated biological patterns 
22 USDA Forest Service RMRS GTR-194. 2007

Figure 11. Gradient imputation of niche structure with scaled biophysical variables. (A) 

Independent variables at a range of spatial 

scales are used for a nonlinear gradient model 

of niche structure for each species. This 

example uses CCA (ter Braak and Prentice 

1986). Axes are orthogonal dimensions of 

ecological space. Species optima locate the 

center of their environmental niche with respect 

to the measured predictor variables. (B) The 

niche model uses ecological space, but we can 

make inferences about suitability in geographic 

space using gradient imputation (Ohmann and 

Gregory 2002). Each unsampled location (cell) 

is projected iteratively into the environmental 

space defined by the niche model. By imputing 

the value of the species at the nearest sampled 

plot (or a weighted average of nearby plots) we 

estimate the suitability of the new location for 

that species. (C) Gradient imputation allows 

the explicit translation from quantitative models 

in environmental space to suitability maps 

in geographic space. Normalized values for 

multiple species at each location provide equilibrium estimates of relative competitive ability, 

useful for defining parameters in ecosystem 

dynamics (gap) models.
USDA Forest Service RMRS GTR-194. 2007 23

and processes to make their predictions. This yields 

models that are self-calibrating and do not suffer from 

compounding error rates across levels of estimation 

(McKenzie and others 1996). Second, the imputations are 

made at the native scale of the input predictor variables, 

avoiding the very troublesome issues of aggregation and 

extrapolation error (King 1991, Rastetter and others 1992. 

Gradient modeling also avoids the subjectivity and information losses associated with discrete classifications of 

inherently continuous and covarying ecological gradients 

(McGarigal and Cushman 2005) and facilitates optimal 

multi-scale analysis of multiple response surfaces.

Ohmann and Gregory (2002) used canonical ordination (CCA) and gradient nearest neighbor (GNN) 

imputation (Figure 11) to produce predictive maps of 

forest composition and structure in coastal Oregon. 

CCA is effective at predicting responses of multiple, 

continuous biotic response variables, is widely used by 

ecologists, and is robust to correlations among environmental variables and sparse data matrices (Palmer 1993, 

Guisan and Zimmerman 2000, Ohmann and Gregory 

2002). Response variables were basal area by species 

and size class. Predictor variables were derived from 

LANDSAT TM bands, PRISM climatic data, geographic 

location, topographical indices, and geologic variables. They argued that the GNN method has several 

advantages over alternatives. First, each imputed pixel 

is attributed with a list of trees by species, size, and 

density (essentially the tree list required by vegetation 

simulators), so vegetation data are not transformed and 

thereby subject to information loss. Second, because 

GNN imputes from a single nearest-neighbor plot the 

covariance among predicted species and structures is 

not under-estimated. Third, the range of variability 

present in the sampled stands is maintained in predictions. Fourth, CCA models are interpretable in terms of 

species responses, connecting regional environmental 

gradients directly to forest vegetation.

Uncertainty in gradient imputation

As with any modeling, the choice of modeling 

approach, predictive variables, and scales of measurement 

have profound influences on imputation performance. 

The uncertainties associated with gradient imputation 

arise from the interplay of several factors.

Spatial variables used to construct the models often 

do not reflect the factors to which the vegetation is 

responding. In the past, most imputation efforts have 

used what spatial data were available, rather than 

seeking out specific variables that represent driving 

mechanisms.

•

The spatial data used to construct the models are 

often at inappropriate scales. Many data layers used 

to predict species responses at the scale of an FIA plot 

(0.4 ha) have a grain that is much larger. This scale 

mismatch greatly reduces the likelihood of observing 

strong relationships. For example, AVHRR data has 

a 1-km cell size. Vegetation structure at a finer spatial scale cannot be accurately resolved from AVHRR 

data regardless of the modeling method used. It will 

be informative to use GNN modeling approaches 

using higher resolution remotely sensed data sets, 

such as hyperspectral imagery, Quickbird, and NAIP 

imagery.

The climate data often used in imputation modeling 

are derived from coarse-scale GIS layers or modeled extrapolations of low elevation, valley bottom 

climate from meteorological stations. Microclimate 

varies over much finer scales and is a strong influence on vegetation patterns. It is essential to obtain 

climatic data at a spatial scale that matches the scale 

of the plot-level response of vegetation. DAYMET 

(1 km) and PRISM (4 km) data are too coarse to meet 

this need. If, for example, gradient models used a grid 

of micro-weather stations placed across the range of 

biophysical conditions, the scales of predictors and 

response would match.

Most models developed to predict vegetation use 

spectral, topographical, and mapped geological data 

at the immediate footprint of each plot. It is likely, 

however, that these predictor variables drive vegetation responses at a variety of spatial extents, and not 

necessarily most strongly at the scale of the plot’s 

immediate footprint. Accordingly, using multi-scale 

ordination and partial bivariate scaling (Figure 9) 

may improve models by identifying the scales at 

which each variable has the strongest influence on 

plot-level vegetation response.

In many cases, models built on fine-scale plot-level 

data make inferences to much larger spatial extents. 

For example, Moisen and Frescino (2002) produced predictions at a 1-km scale from single 0.4 ha 

plots nested within. This assumes that the sampled 

plot is representative of the vegetation condition 

throughout the 1-km cell. Given the high spatial variability of vegetation and biophysical gradients within a 

1-km scale, this is an unsupportable assumption. 

Such unsupported scale extrapolations produce highly equivocal predictions.

Most past gradient imputation has ignored the issues 

of temporal nonequilibrium and time lags. However, 

•

•

•

•

•
24 USDA Forest Service RMRS GTR-194. 2007

by including disturbance history and stand age as 

predictor variables in hierarchical gradient modeling 

we will be able to incorporate temporal dynamics in 

the models by in effect trading space for time.

In the past, gradient imputation has ignored patterns 

of spatial autocorrelation. As these patterns are strong 

at the fine scales to which imputation modeling is defined, their influence can be profound.

Most of the sources of uncertainty listed above are 

directly addressable either through more sophisticated 

modeling, better data collection, or both. The interpretability or gradient models and their utility in making 

predictions at fine scales, in new landscapes, or in 

future conditions will be improved by building gradient 

models with theoretically understood limiting factors. 

Additionally, bivariate scaling and variance partitioning 

address important sources of uncertainty associated with 

imputation modeling. By linking gradient imputation to 

canonical ordination models developed using partial 

bivariate scaling and hierarchical variance partitioning 

of limiting factors we should be able to improve both 

predictions of current conditions and inferences about 

expected changes in occurrence, growth, and regeneration under possible future climate and disturbance 

regimes.

Intrinsic limits to gradient modeling

By linking the limiting factor niche modeling 

(McKenzie and others 2003), hierarchical partitioning 

(Cushman and McGarigal 2003), partial bivariate scaling 

(Thompson and McGarigal 2002), and gradient imputation (e.g., Ohmann and Gregory 2002), we can address 

most key issues of spatial and temporal scale, spatial autocorrelation, and temporal disequilibrium in models of 

species occurrence, growth, and regeneration. However, 

gradient models do not explicitly address a chain of 

causation. Gradient models are rooted in species-environment correlations, which do not always reflect causation. 

Also ecological mechanisms have transient dynamics. 

These temporal dynamics of biophysical conditions are 

difficult to represent in equilibrium gradient models. In 

contrast, process-based modeling with explicit timesteps can more directly relate organism responses to 

the action of specific mechanisms and address temporal 

disequilibria and transient dynamics (Neilson 1995, 

Keane and others 1996, Waring and Running 1998). 

We therefore suggest that understanding the causes and 

effects of pattern-process relationships in forest systems 

will benefit from linking empirical gradient models with 

mechanistic ecosystem models. Also, gradient models 

are limited in their ability to project landscape changes 

from large-scale and temporally punctuated disturbances 

•

such as insects and wildfire, which are disturbances that 

will likely be the direct agents of ecosystem changes in 

response to global climate change (McKenzie and others 

2004). Thus we suggest integrating landscape dynamics 

modeling of broad-scale disturbance with gradient and 

ecosystem dynamics models. The following sections 

review these two additional modeling paradigms in the 

context of integrated landscape modeling.

Ecosystem Dynamics Modeling

Time lags, nonequilibrium dynamics, and mismatch of 

temporal scale between responses and drivers reduce the 

effectiveness of equilibrium models. Gradient models can 

address time lags and non-equilibrium dynamics implicitly by incorporating dynamic climates, disturbance 

history, and species interactions within the hierarchical 

gradient modeling framework. In contrast, ecosystem 

dynamics models bring an explicit temporal dimension by simulating responses of vegetation to specific 

combinations of mechanisms across formal time-steps. 

Whereas gradient models in effect trade space for time 

(McGarigal and Cushman 2002), ecosystem dynamics 

models make predictions at successive time-steps, with 

each state depending on the previous one. This greatly 

improves the realism and flexibility with which time 

lags and temporal dynamics can be addressed.

Comprehensive reviews of ecosystem dynamics 

models are found in Waring and Running (1998) and 

Keane and Finney (2003). We focus on the characteristics of ecosystem dynamics models that would mesh with 

gradient and landscape dynamics modeling to synthesize 

analyses of forest vegetation responses to climate and 

disturbance regimes across spatial and temporal scale. 

Vegetation dynamics models use mechanistic approaches 

to simulate plant growth, regeneration, mortality, decomposition, and nutrient cycling (Landsberg and Gower 

1997). Waring and Running (1998) distinguish between 

biogeochemical (BGC) models and “gap-phase” (gap) 

models. BGC-type models emphasize physiology and 

biogeochemistry, whereas gap models emphasize lifecycle dynamics.

Gap-phase models simulate relationships between 

species occurrence, growth, and regeneration and 

biophysical drivers over time. They are readily linked 

to multi-scale gradient models because both predict the 

same response variables (vegetation composition and 

structure) based on the same predictor variables (biophysical drivers at the level of each plot). Gap models track 

individual trees and distinguish vegetation responses at 

the species level, thereby factoring in competitive interactions via reciprocal influences of individual trees on 

each other’s microenvironment. Comprehensive reviews 
USDA Forest Service RMRS GTR-194. 2007 25

of gap models are provided by Botkin and Schenk (1996) 

and Urban and Shugart (1992).

The FM model (Miller and Urban 2000, Miller 2003), 

an extension of ZELIG (Urban and others 1991), exemplifies how ecosystem modeling can support and extend 

gradient modeling. FM simulates the establishment, 

growth, and death of individual trees on a tree-sized plot, 

which is considered to be homogeneous. A key attribute 

of the FM model is that it simulates feedbacks. Trees 

are affected by the environment and in turn, trees affect 

the environment. Species tolerances to environmental 

conditions are formalized in the model as heuristic, 

unimodal response curves; species replacements during 

succession or with climate change are a function of 

their relative positions with respect to the centers of 

the response functions. Gap-phase models such as 

FM are not spatially explicit, in that they simulate the 

dynamics of individual stands at specific locations in a 

landscape rather than the pattern of vegetation continuously across space. However, the FM model addresses 

spatial complexity by simulating arrays of individual 

plots in a rectangular grid across the landscape. The 

plots interact with one another via shading and seed 

sources. This relaxes the assumption of a homogeneous 

stand and allows for spatial interactions that modify the 

microenvironment within a stand (Smith and Urban 

1988, Urban and others 1991).

Gap models such as FM are an ideal means by which 

to strengthen and extend the predictions of gradient 

modeling (Figure 12) because they simulate feedbacks 

between vegetation and the environment. Species are 

ranked by tolerances to environmental conditions, explicitly linking the simulation to niche characterization. Gap 

models simulate regeneration, growth, and death of trees 

based on the interaction between the optima and tolerances with respect to environmental conditions present 

Figure 12. Gap-phase ecosystem dynamics models simulate growth, death, regeneration, and stand structure based on initial 

vegetation and biophysical conditions. They are based on mechanistic relationships between biological response variables 

and environmental drivers. In the conceptual model here, biotic responses (green boxes) are predicted as functions (pink 

boxes) of climate and soil characteristics (yellow boxes). The climate and soil characteristics at each simulated plot can be 

measured in the field. Gap models require a statement of initial vegetation conditions for initialization, which can be measured 

on a sample of plots. Extending predictions across space requires estimates of initial vegetation and biophysical conditions 

for unsampled plots. Imputation of multi-scale biophysical models is perhaps the best means of gaining these estimates of 

driving variables across space. Ecosystem models also require explicit information about the functional nature of vegetation 

response to each driving variable. These functional relationships must be based on empirical data from the system of interest. 

Extensive samples of vegetation across biophysical gradients, coupled with gradient modeling, provide information needed to 

quantify mechanistic relationships between specific environmental drivers and vegetation response.
26 USDA Forest Service RMRS GTR-194. 2007

at the site and changes in those conditions through time 

due to biotic interactions, climate change, or disturbance. These attributes of gap models can circumvent 

some limitations of gradient modeling, most notably 

the difficulty of dealing with temporal disequilibrium 

between current vegetation and the environment.

Conversely, gradient modeling offers solutions to the 

major challenges facing implementation of gap models 

across complex landscapes (Figure 12). Gap models 

rely on a quantitative understanding of the optima, tolerance, and performance of each species along biophysical 

gradients. Specifically, gap models use relationships 

between soil moisture, precipitation, snow pack, solar 

radiation and growth, mortality, and regeneration. 

Gradient modeling provides critical parameters by 

estimating the optima and tolerances of each species 

for growth, regeneration, and occurrence along each 

biophysical gradient. Large, representative samples 

taken across the full span of biophysical gradients, 

followed by multi-scale gradient modeling, are the best 

means to minimize the uncertainty associated with these 

critical relationships.

Gap-phase models have been implemented within 

landscape applications (Shugart and Seagle 1985, Urban 

and others 1991, Mladenoff and Baker 1999) but have 

used aggregation techniques that involve information loss 

and error propagation (Rastetter and others 1992, King 

1991). The uncertainties in aggregation to a landscape 

mosaic can be partially obviated by using multi-scale 

gradient imputation models (Cushman and McGarigal 

2003, Ohmann and Gregory 2002). Gap-phase models 

can produce expected future stand structure and composition for grids of forest plots. Gradient imputation on the 

simulated future plot values provided by the gap models 

can then be used to infer future vegetation composition 

and structure as a function of spatial location and biophysical gradients at each plot-sized cell in a landscape. Thus, 

by combining gap-phase futuring of permanent forest 

plots with gradient imputation, it is possible to simulate 

vegetation dynamics continuously across complex landscapes (e.g., Spies and others 2002).

Landscape-Level Disturbance Modeling

A major limitation of ecosystem modeling is the difficulty of addressing large-scale disturbance. Ecosystem 

dynamics models excel at predicting the effects of 

processes acting at the gap and stand scale, but they 

have difficulty addressing broad-scale, contagious 

spatial processes such as wildfire. Although some gapphase models simulate disturbance (e.g., Shugart and 

Noble 1981, Bonan and Shugart 1989, Miller and Urban 

2000), they do not simulate the propagation of fire across 

landscapes (Miller 2003). Instead, disturbance is represented in ecosystem models by linking multiple plots 

within a spatial network and using aggregate results 

(Urban and others 1991, Acevedo and others 1996). 

Interaction among cells, a key to successful simulation 

of contagious processes, is limited. Attempts to fully 

incorporate spatial interactions in a mechanistic framework encounter not only logistical problems associated 

with limits on data and computing resources, but also a 

host of inherent problems that may be intractable.

Limitations of mechanistic fire modeling

Keane and Finney (2003) describe in detail the 

components that a mechanistic fire effects simulation 

model (FESM) would need in order to predict fire occurrence, spread, and intensity across large landscapes and 

incorporate both succession after fire and repeated fire 

events. The program outlined is ambitious and suggests 

that robust mechanistic simulation of landscape-level 

fire effects is still out of reach. Drawing on Keane and 

Finney’s (2003) exposition, we recognize the following 

impediments to broad-scale mechanistic fire modeling: 

Fully physical fire models that mechanistically represent the three-dimensional fire environment do 

not run in real time even on small patches (Linn and 

others 2005). Thus, we are a long way from having 

computing resources adequate for landscape physical 

modeling. Current fire-behavior and fire-spread models rely on empirical approximations of crown and 

surface fire behavior (e.g., Finney 2003), and they 

have a maximum resolution of 30 m—too coarse to 

accurately capture the combustion process and the 

spatial heterogeneity of fuels.

Even if these resource limitations were to be overcome, two other problems might be intractable.

There will likely always be a lack of good data at 

the scale of the landscape application. Keane and 

Finney (2003) suggest that five major processes 

should be included in a mechanistic landscape 

model: climate, fire, insect, disease, seed dispersal, 

and hydrology. Just looking at climate data, top 

down approaches usually couple coarse predictions 

from global circulation models to mesoscale gridded 

mechanistic climate models, such as RegCM2 

(Giorgi and others 1993, Luce and others 1999), 

MM5 (Grell and others 1994), or RAMS (Pielke 

and others 1992). The predictions of these gridded 

weather estimates are then used to compute sitespecific weather through interpolation (Luce and 

others 1999) or finer-scale mechanistic modeling 

(Running and others 1987). However, with up 

to four orders of estimation in this process, the 

1.

2.

a)
USDA Forest Service RMRS GTR-194. 2007 27

site-level error rates are likely to be unacceptably 

high, particularly in complex mountainous 

topography.

Even with data as accurate as reasonably possible, 

sensitive dependence on initial conditions (Ruelle 

1991) may rapidly degrade the accuracy of such 

a mechanistic model with multiple non-linear 

dependencies. For example, both fireline intensity 

and fire spread depend nonlinearly on the packing 

ratio of combustible fuels and its variability at fine 

scales (Rothermel 1972). In turn, fireline intensity is 

a key predictor of crown-fire initiation and spread, 

which can influence ecosystem properties for 

decades into the future. Data are lacking as to how 

serious this problem is, but ongoing experiments 

suggest that ecosystem-scale fire effects are very 

sensitive to small adjustments in fire-behavior 

parameters (Stocks and others 2004, Linn and 

others 2005).

Extreme events, which are the principal drivers of 

ecosystem change, are associated with coarse-scale 

controls. Even given error-free fine-scale modeling, 

there is a scale mismatch between driver and response. Extreme weather events, characterized by low 

relative humidity, high temperature, and high winds, 

trigger and maintain large high-severity fires (Johnson 

and Wowchuk 1993, Agee 1997, Skinner and others 

1999, Baker 2003, Gedalof and others 2005). Some 

success in prediction of total area burned has been 

achieved with fire behavior simulated at coarse resolution, assuming a homogeneous fuel environment 

at a scale matching climatic controls (Lenihan and 

others 2003), but these authors did not simulate fire 

spread nor did they incorporate the sub-cell heterogeneity associated with mountain landscapes.

Successful ignition, represented as fire starts, is a 

limiting factor whose accurate implementation is beyond the capacity of current mechanistic modeling. 

Broad-scale atmospheric conditions conducive to dry 

lightning have been identified (Rorig and Ferguson 

1999), but individual fire starts have not been directly linked to them. Thus, ignition is usually simulated 

with stochastic methods (Keane and others 1996, 

Keane and Long 1998).

Mechanistic fire modeling across large landscapes 

may be inherently intractable, as it encounters the 

“middle-number” problem (Allen and Hoekstra 

1992). Allen and Hoekstra (1992) compare landscape 

modeling to statistical thermodynamics, wherein the 

number of individual molecules that interact is astronomical, therefore impossible to model individually, 

b)

3.

4.

5.

but accessible using aggregate statistics. Analogously, 

aggregating ecosystem and landscape attributes to 

coarse scales (resolutions of multiple km) enables 

broad-scale modeling (e.g., Keane and Long 1998, 

Lenihan and others 1998) but cannot reproduce landscape variation at meaningful scales for contagious 

processes such as fire.

Because all of these limitations cannot be solved 

without major scientific advances, we submit that a 

stochastic paradigm, using aggregate properties of fire 

regimes and ensemble modeling, though eschewing the 

direct representation of fire behavior and fire spread, 

provides the best approach to landscape fire modeling.

Stochastic landscape dynamics simulators

Stochastic models exploit aggregate statistical properties of disturbance processes, rather than attempting to 

predict individual events and their behavior mechanistically. Fire, in particular, is appropriately modeled as a 

stochastic process, of which each fire history, whether 

from field observations or simulations, is just one realization (Lertzman and others 1998, Falk 2004, McKenzie 

and others 2005). Landscape dynamics simulators do not 

simulate fire behavior per se. Instead they use empirical 

models to estimate fire frequency, size, spread behavior, 

and intensity along biophysical gradients. These statistical relationships are used to populate landscapes with 

fire events that match expected patterns and frequency. 

Via “ensemble” simulations (see above), they are able 

to simulate properties of fire regimes accurately and 

can incorporate seasonal to multi-decadal climatic variability in the form of altered fire patterns. Rather than 

attempting to use coarse climatic predictions to mechanistically produce fires, these predictions are used to 

infer changes in fire regime.

Dynamic landscape simulation models have been 

used to explore synergistic effects of long-term climatic 

change and fire on landscape-level patterns of vegetation (Baker and others 1991, Keane and others 1996, 

Gardner and others 1999, He and Mladenoff 1999a, 

Hargrove and others 2000). A thorough review of landscape dynamics simulation models is found in Mladenoff 

and Baker (1999). The LANDIS (Mladenoff and 

others 1996), SIMPPLLE (Chew and others 2004) and 

RMLANDS (http://www.umass.edu/landeco/research/

rmlands/rmlands.html) models simulate fire, wind 

throw, and “harvest” on landscape pattern and structure. 

LANDSIM (Roberts 1996) uses life history and vital 

attributes to drive succession in polygons. DISPATCH 

(Baker 1992, 1993) uses stochastic simulation of fire 

occurrence and spread based on dynamically simulated 

weather, fuel loadings, and topographic setting, and then 
28 USDA Forest Service RMRS GTR-194. 2007

simulates forest succession in change of cover type and 

stand age. Fire-BGC (Keane and others 1996) aggregates 

stand-level output of the ecosystem dynamics model 

Forest-BGC and applies disturbance stochastically 

using random ignitions. This model comes closest of 

any to date in linking mechanistic stand-level ecosystem 

dynamics to landscape disturbance; a revision is now 

complete and being applied across the northwestern 

United States (personal communication, Robert Keane, 

Rocky Mountain Research Station).

Fire regimes are defined in terms of probability 

distributions of size, frequency, and severity. Statistical 

models can be used to estimate expected values of fireregime parameters (McKenzie and others 2004, Duffy 

and others 2005, Gedalof and others 2005, Littell and 

others, submitted) as functions of climatic variability, 

using historical records. They can be extrapolated with 

some confidence to predict future fire-size and frequency 

distributions under changing climatic regimes, and 

to a certain extent past fire regimes can inform likely 

changes associated with potential future climates. If, for 

instance, hot dry years are associated with increases in 

fire size, frequency, or both, then a warmer and dryer 

future climate can be expected to produce similar results. 

Alternatively, instead of being constrained in advance, 

fire-size distributions may arise from deterministic or 

stochastic rules applied during the simulation of a fire 

event. For example, in grid-based cellular automata 

models, fire susceptibility in a cell adjacent to a burning 

cell may be “on” or “off,” or probabilistic. An interesting hybrid model is MC1 (Bachelet and others 2001a, 

Lenihan and others 2003), in which the flammable 

proportion of a cell is determined by biomass and fuel 

moisture thresholds during the event but constrained at 

the upper end by natural fire rotation.

An ideal landscape dynamics model would preserve 

the empirical detail provided by gradient models and 

the mechanism/response paradigm associated with the 

ecosystem dynamics models. However, as we noted 

above, the aggregate properties of a landscape subject to 

physical and ecological mechanisms are best captured 

with a stochastic approach, because of the logistical and 

technical limitations of mechanistic modeling at broad 

spatial scales. Stochastic landscape dynamics models, 

however, simulate the patch dynamics associated with 

each disturbance regime, a different organizational level 

than species-level responses to biophysical gradients. 

Stochastic landscape dynamics models address different 

entities (patches instead of organisms) at different scales 

(patches vs. plots), creating an obstacle to model integration, as discussed in more detail in the following section. 

Also, most landscape dynamics models under-represent 

variability in fire severity through space, because most 

are patch-based and force fire to spread along polygon 

boundaries or from cell to cell, ignoring spatial variability 

in biophysical gradients. Within-cell heterogeneity in fire 

severity can have significant effects on stand- and community-level succession (Turner and others 2003), and 

vegetation succession provides important constraints on 

future fire. Unlike some other sources of error, the biases 

associated with this underestimation of variance are not 

correctable with the ensemble approach to modeling. 

In the next section, we propose an approach to integrate 

gradient, ecosystem dynamics, and landscape dynamics 

models to overcome these difficulties.
USDA Forest Service RMRS GTR-194. 2007 29

The overall goal of the integrated modeling program 

described in this document is to obtain fine-scale predictions of ecosystem attributes across large geographical 

areas and project them over time under changing climate 

and disturbance regimes. The effort aims to extend plotlevel measurements of vegetation composition and 

structure across space with gradient imputation, and 

through time with mechanistic ecosystem and stochastic 

landscape dynamics models. The challenge is to integrate 

these three different modeling approaches to account for 

non-equilibrium relationships between current vegetation and biophysical drivers, spatial complexity across 

broad landscapes, and the large differences in scale of 

processes that drive local vegetation response to biophysical conditions and disturbance processes such as timber 

harvest and wildfire. The integration will depend on the 

adequacy of three major components, discussed in the 

sections below. This research agenda is ambitious and 

full implementation under a single funding source is 

highly unlikely. However, the agenda consists of a series 

of interrelated tasks that could be addressed incrementally under a series of independently funded research 

projects. For example, the base empirical data required to 

anchor the analysis may be collected as parts of existing 

or future broad-scale vegetation monitoring programs, 

such as FIA and CVS. Numerous researchers are actively 

engaged in addressing many of the issues we identified 

in gradient modeling, ecosystem dynamics modeling, 

and landscape simulation. Progress in these areas is 

approaching the point where one or several formal integration efforts will be able to combine methods between 

these components to achieve reliable predictions of 

forest vegetation across complex landscapes and over 

time under altered climate and disturbance regimes.

The Empirical Anchor

The most fundamental requirement for successful 

integration is the adequacy of empirical data relating 

species distribution, growth, and regeneration to biophysical drivers and disturbance history. This empirical data 

anchor has three components.

First, it is essential to base the modeling efforts on 

large and representative samples of vegetation composition and structure along gradients of biophysical 

condition and disturbance history. These data should 

include species, size, and condition of each individual 

tree in the plot, including seedlings, the density and 

volume of woody debris in several size classes, and 

the cover of shrubs, forbs, and grasses by species and 

non-vegetation cover by type (e.g., rock, soil, water). 

Rates of growth for each species should be measured 

by computing annual increment from cores and diameters of canopy dominant trees. Grid-based efforts 

such as FIA (Rudis 2003) sample biophysical conditions across broad spatial and ecological gradients, via 

massive replication of vegetation plots. These plots 

would be distributed on a grid across large geographical 

areas. Sample sizes in the hundreds to thousands would 

be ideal to cover the range of biophysical conditions 

and temporal disequilibria of vegetation. This magnitude of data collection is realistic, as the FIA system 

includes tens of thousands of vegetation plots on which 

much of the required data have already been collected. 

Alternatively, in areas where gridded plots are incomplete or to augment the grid to obtain data for specific 

areas of interest, one could design a sample a priori to 

capture key biophysical gradients. For example, Littell 

and others (2005) used digital terrain models and GISbased modeling of environmental gradients to locate 

plots that filled the hyperspace of biophysical gradients 

expected to be key predictors of the response (in this 

case annual growth of montane Douglas-fir).

The second essential component is the adequacy of 

biophysical data. Plot-level biophysical variables would 

include soil depth and texture, slope, elevation, aspect, 

parent material, and microclimate records from portable 

weather stations (e.g., Hobo http://www.microdaq.com

/occ/hws/index.php). The microclimate data would 

include photosynthetically active radiation, daily precipitation, maximum temperature, minimum temperature, 

relative humidity, soil moisture, and April 1 snow-water 

equivalent. Gradient modeling and geostatistics can then 

be used to infer microclimate characteristics continuously across complex landscapes at a fine spatial scale. 

This obviates major scaling and extrapolation problems 

with downscaling regional climate models to landscape 

scales. There is no need to extrapolate across scale; rather 

the task is to model microclimate based on biophysical 

gradients and then impute it at its native scale to unsampled locations within the spatial domain of the sampling 

network. Also, plot-level biophysical data is not a sufficient predictor set, as biophysical factors from a range of 

scales simultaneously influence vegetation response. In 

addition, synoptic biophysical data is required to impute 

vegetation composition and structure to unsampled 

The Challenge of Integration
30 USDA Forest Service RMRS GTR-194. 2007

locations across the landscape. Thus, indices derived 

at multiple spatial scales from remotely sensed multispectral imagery and DEM will be essential for gradient 

modeling and imputation.

Accurate and spatially comprehensive information about disturbance history is the final component 

of essential empirical information. Disturbance history 

should include the dates of previous disturbances and 

their types, severities, and extents across the landscape. 

The availability of these data is currently limited for 

most landscapes and this is among the most substantial challenges facing this integrated modeling effort. 

Spatially comprehensive disturbance history is difficult to obtain. Most methods of estimating disturbance 

history, such as fire scars and charcoal analysis, do not 

produce spatially complete inferences of the disturbance 

histories of specific landscapes. These efforts are usually 

based on sparse samples across broad spatial extents and 

do not readily produce spatially synoptic estimates of 

fire history in terms of dates, extents and severities of 

past fires. Geostatistical modeling of fire scar chronologies is technically possible but logistically prohibitive 

in most landscapes. Stand age as a surrogate for disturbance history is more promising in areas of high intensity 

fire regime. However, in mixed- and low-severity fire 

regimes stand age is not a reliable surrogate for time since 

last disturbance. In addition, in complex mountainous 

landscapes, fire regime is expected to vary substantially based on topography, microclimate, barriers, and 

refugia, making the utility of stand age questionable as a 

surrogate for disturbance history. In many forested landscapes management history has had a major influence 

on the development of current vegetation. It is essential 

to obtain accurate maps of past management activities. 

Spatial databases describing management history should 

include the date, type, and perimeter of past management activities. Most public land management agencies 

have reasonably complete and accurate records of this 

kind. The integrated research agenda outlined in the 

final section of this document describes steps to improve 

the sufficiency of each component of the empirical data 

that is the core of this modeling paradigm.

Gradient Modeling and Ecosystem 

Modeling on Grids

Linking multi-scale gradient modeling with gap 

dynamics models is the second major component of the 

integrated modeling effort. Once the range of environmental hyperspace has been sampled, gradient models 

relating responses of interest (e.g., species distribution, 

growth, and establishment) to biophysical drivers and 

disturbance history can be built at multiple geographic 

scales. With sufficient sampling across gradient space, 

imputation can provide unbiased estimates across the 

landscape at a fine spatial resolution (Ohmann and 

Gregory 2002). Simultaneously, the gradient models 

can provide species-specific parameters for ecosystem 

dynamics models. Ecosystem dynamics models then 

can project plot-level vegetation on the sampled grid 

into the future, accounting for growth, mortality, and 

succession. These futured plot-level vegetation data 

then provide the training set to build gradient models 

for imputing future vegetation condition across the full 

landscape. This integration offers a means to extend 

non-equilibrium predictions across space and through 

time, wherein gradient models provide species response 

parameters, ecosystem models project future conditions 

on the sampled plots, and imputation provides spatial 

prediction of current and expected future vegetation 

composition and structure at a fine spatial scale (Figure 

13). Importantly, climate change can be incorporated 

directly in the gradient and ecosystem dynamics models 

(Figure 13). This integration facilitates prediction of 

expected changes in vegetation composition and structure across complex landscapes under changing climatic 

conditions at a fine spatial scale.

Linking Gradient, Ecosystem, and 

Landscape Models

The final component of the integration is the linkage 

of stochastic landscape-dynamics models with gradient 

models of vegetation response to biophysical conditions and disturbance history. Multi-scale gradient 

modeling and imputation, linked to gap-phase ecosystem 

dynamics, can predict species distributions, growth, 

regeneration, succession, and fuels at a fine spatial scale 

and then can impute these variables with known error 

characteristics across large landscapes. However, neither 

approach is sufficient to address large-scale disturbance 

processes. Large-scale disturbances, such as wildfire 

and timber harvest, are the dominant proximate drivers 

of landscape-level vegetation dynamics in the western 

United States. However, they are not predictable based 

on the fine-scale relationships between vegetation and 

biophysical conditions at specific locations on the landscape, and thus beyond the scope of gradient and gap 

dynamics models. These disturbances are largely related 

to processes acting at much broader spatial and temporal 

scales. For example, timber harvest may be determined 

by a complex political and economic process that may 

or may not relate to the biophysical drivers and current 

vegetation condition of a given harvested stand. The 

size, frequency, and severity of wildfire is often related 

to extreme fire weather events within the constraints of 
USDA Forest Service RMRS GTR-194. 2007 31

Figure 13. Integrating gap-phase ecosystem dynamics models with gradient modeling and simulation. We begin with a large 

sample of vegetation plots distributed across a landscape (A). Gradient models (B) are then used to quantify relationships 

between growth and mortality of trees by species and size by biophysical condition. Current vegetation and composition 

across the landscape are then mapped (C) with gradient imputation. The gap dynamics model (D) is used to project the future 

condition of vegetation (E) based on growth, mortality and succession in each of these plots. Gradient modeling (F) is then 

used to associate vegetation composition and structure with biophysical gradients, and gradient imputation (G) is used to infer 

expected composition and structure of vegetation across the full landscape. Changes in climate across time-steps (H) can be 

inserted into the ecosystem dynamics model and gradient model to project how changes in microclimate at each plot affects 

expected future patterns of vegetation in the imputed landscape.
32 USDA Forest Service RMRS GTR-194. 2007

biophysical context, past disturbance history, and current 

vegetation and fuels. Fire is also spatially contagious. 

Thus the occurrence of fire at a given location at a given 

time is not predictable based on the biophysical and 

vegetational characteristics of that specific location.

As discussed in the landscape dynamics modeling 

section above, we believe that stochastic models that 

simulate area, frequency, shape, and intensity of wildfires under alternative climatic scenarios provide the 

most reliable means to project effects of changing 

climate regimes on wildfire. By linking these landscapelevel disturbance simulations with gradient modeling 

and gap-phase ecosystem modeling, it may be possible 

to obtain a broad integration of the processes that drive 

the relationships between forests, climate and fire, and 

the ability to produce expectations about the effects of 

future changes in climate and disturbance regime on 

forest ecosystems across space and through time.

The challenge lies in the fact that stochastic landscape 

dynamics models simulate patches, while ecosystem 

and gradient models predict vegetation composition 

and structure within stands. This disjunction in organizational level is the major challenge in uniting these 

models to predict the effects of altered climate and fire 

regimes on vegetation composition and structure across 

broad landscapes. It is essential to translate the patchdynamics predictions of stochastic landscape dynamics 

models back down to stand level vegetation and composition. As discussed in the integrated research agenda 

below, this may be accomplished by using appropriate 

transfer functions. The stochastic landscape models 

produce perimeters of disturbance polygons (e.g., timber 

harvest, insects, wildfire). Disturbance effects on vegetation can be inferred using empirically derived transfer 

functions, developed from large samples of plots across 

biophysical context and disturbance history, or appropriate submodels, such as FOFEM (Peterson and Ryan 

1986, http://fire.org). Through these transfer functions 

the local effects of broad-scale disturbance on vegetation composition and structure can be inferred. Figure 14 

illustrates the approach we suggest for integrating landscape, ecosystem, and gradient models.
USDA Forest Service RMRS GTR-194. 2007 33

Figure 14. Integrating stochastic landscape dynamics with gradient and gap models. The approach is the same as outlined in 

Figure 13, with the addition of climate affects on fire regime (H), stochastic simulation of landscape disturbance, including fire 

and timber harvest (B), and transfer functions or submodels (C) to translate from the patch mosaic produced by the landscape 

model to vegetation composition and structure within stands. At each time-step the sequence of steps is: (A) begin with a 

large sample of vegetation plots distributed across a landscape, (B) simulate disturbances with the landscape model, (C) 

infer effects of these disturbances on existing vegetation in sampled plots, (D) grow sampled plots with ecosystem dynamics 

model, (E) apply gradient models to predict vegetation composition, structure, and growth based on biophysical and disturbance factors, and (F) impute gradient models to produce spatially explicit predictions of vegetation composition and structure 

across the landscape. This imputed landscape is then the initial condition for the next time-step and the process continues 

iteratively. Changes in climate across time-steps (G) influences fire regime parameters (H), transfer functions (C), ecosystem 

dynamics models (D), biophysical gradient models (E), and imputation across the landscape (F), as described more fully in 

the integrated research agenda section below.
34 USDA Forest Service RMRS GTR-194. 2007

Step 1—Multi-scale Gradient Modeling

Questions

What are the multi-scale relationships between topography and microclimatic variability (e.g., temperature, 

humidity, soil moisture, and snow pack)?

How does microclimatic variability affect the distribution of individual tree species, the composition of 

plant communities, growth at the species and community levels, and regeneration?

To what extent is current vegetation prediction affected by disturbance history?

How do fine and coarse fuel loads and their rates of 

accumulation depend on energy, temperature, humidity, water, snow-pack, soils, and topography in 

interaction with vegetation condition and age?

What is the relative importance of spatial dependence 

vs. non-spatial biophysical variables for predicting 

the response of individual tree species and the plant 

community?

What is the relative predictive power of coarser-scale 

predictors, such as DAYMET, PRISM, and MTCLIM, 

compared to plot-derived measurements of energy, 

temperature, humidity, water, snowpack, soils, and 

topography?

Can we successfully aggregate predictions from plotlevel measurements to the scale of coarser (DAYMET, 

etc.) grids?

Data

Plot-level measurements of topography, vegetation 

composition and structure, annual growth, microclimate, seedling establishment, snow-water equivalent, 

and soils.

Topographical variables for each plot DEM include 

slope, aspect, elevation, profile curvature, tangent 

curvature, topographical wetness index, and others at 

a range of radii (approximately 100, 200...1,000 m), 

that spans the plausible range of influence of local topography on microclimate and vegetation.

Disturbance history data such as fire perimeter and 

cutting history maps, plot level evidence of past fire 

dates and intensities, beetle infestations, and timber 

harvest.

A large sample of plots, distributed representatively 

across the full combination of biophysical gradients. 

1.

2.

3.

4.

5.

6.

7.

1.

2.

3.

4.

Existing re-measure plot grids should be utilized to 

gain the benefit of prior investment and data collection. FIA and related sample grids such as the National 

Vegetation Pilot provide sufficient replication and 

geographic coverage, and they are ideal as a base for 

these analyses. Plot structures should be augmented 

to better capture spatial autocorrelation factors critical to successful imputation.

We suggest developing these approaches on one or 

several pilot grids, e.g., the National Vegetation Pilot 

grid located in the Idaho Panhandle National Forests. 

These grids should be augmented to ensure that 

rare types and disturbance histories are adequately 

sampled.

The following climatological/ecological variables on 

each plot, weekly, monthly, seasonally, annually, for 

five years:

ambient temperature

solar radiation (incident, diffuse)

humidity

precipitation

snow pack

soil depth and texture

At the end of the five-year period vegetation conditions on the plots should be remeasured, including 

measurement of annual increment of canopy dominant trees, seedlings, and coarse and fine fuels.

Analysis

Gradient modeling appropriate for identifying driver-response relationships (Table 1) for example CCA, 

GLM, GAM.

A combination of multiple scale variables, partial 

bivariate scaling (Thompson and McGarigal 2002), 

and hierarchical variance partitioning (Cushman and 

McGarigal 2003) to optimize scaling relationships 

across independent variables and incorporate the influence of spatial dependence.

Data splitting or Monte Carlo resampling methods to 

evaluate the predictive power of the models, and formal accuracy assessment involving ROC, Kappa, and 

other appropriate tests.

Expected products

Multi-scale gradient models predicting microclimate 

from topographical data.

5.

6.

a)

b)

c)

d)

e)

f)

7.

1.

2.

3.

1.

An Integrated Research Agenda
USDA Forest Service RMRS GTR-194. 2007 35

Multi-scale gradient models predicting species occurrence, growth and regeneration, forest structure, and 

fuels.

Importance

These models in themselves will be useful to managers 

by providing quantitative predictions of relationships 

between biophysical gradients and the responses of 

forest ecosystems.

Gradient models are the basis for gradient imputation, in which the expected condition of vegetation is 

mapped at a fine spatial resolution across landscapes.

Gradient models will provide species-specific parameters for ecosystem dynamics models. Specifically, 

they will provide growth, mortality, and regeneration 

curves for each species across each dimension of the 

biophysical niche.

2.

1.

2.

3.

Figure 15. Gradient modeling produces statistical models of relationships between species distributions, community structure, 

growth, and other dependent variables and gradients of biophysical driving variables and disturbance history. These gradient 

models are non-spatial and limited to the single instance in time at which their data was gathered. Temporal factors such 

as disturbance history are included as explanatory variables. These are reasonable time-proxies, giving gradient models 

temporal depth looking backward in time, but with limited ability to project change into the future. Thus, looking forward in 

time, the gradient method produces predictions that have zero dimension in the Time-by-Space scale space (a point in the 

two-dimensional space on the left).
36 USDA Forest Service RMRS GTR-194. 2007

Step 2—Gradient Imputation

Questions

What is the spatial structure of microclimatic gradients across complex landscapes?

What is the spatial pattern of vegetation composition 

and structure, growth, and regeneration across complex landscapes?

What is the accuracy of these imputed maps of microclimate and forest structure for each dependent 

variable?

Data

Multi-scale data derived from DEM including slope, 

aspect, elevation, profile curvature, tangent curvature, 

topographical wetness index, and others at a range of 

radii. These will be produced by moving window algorithms for each variable at the same radii as used 

in Step 1.

Remotely sensed data and GIS data:

Spectral data from TM imagery and, ideally, recent 

images from spring and summer.

Spectral data from Quickbird if available and NAIP 

color imagery. These provide much higher spatial 

resolution than TM imagery, which could be critical 

in producing powerful imputation models.

GIS layers showing stand histories, past disturbances, soil, geology, and hydrology.

Analysis

Gradient imputation to derive expected values for 

each dependent variable at each location in the landscape based on the multi-scale gradient models. The 

1.

2.

3.

1.

2.

a)

b)

c)

1.

models used for imputation will include both the 

biophysical driving variables used in Step 1 and the 

synoptic scale GIS and remote sensing variables collected for this Step, including disturbance history.

The imputation methods will include gradient nearest 

neighbor and k-nearest neighbor for canonical ordination, or analogous methods for GLM and GAM.

Quantify spatial patterns of each dependent variable 

across the landscape using landscape pattern analysis 

software such as FRAGSTATS.

Expected products

Predicted values of each dependent variable mapped 

across complex landscapes.

These variables will include microclimate and vegetation. Predicted microclimate variables include 

growing degree days, spring snow-water equivalent, expected temperature, and soil moisture regime. 

Predicted vegetation variables will include occurrence 

probability and basal area by tree species, stand age, 

canopy closure, cover by shrub species, and coarse 

and fine fuels.

Importance

These spatially explicit, fine-scale, broad-extent predictions of forest composition, structure, growth, and 

regeneration will provide managers more detail about 

the condition of forest resources across complex landscapes than has been possible in the past.

Such information is essential to quantify the site-level and cumulative effects of management actions and 

natural disturbances.

2.

3.

1.

2.

1.

2.

Figure 16. Gradient models predict the value of a dependent variable as a function of n-dimensional environmental data. 

These models are multi-scale and multi-dimensional in ecological space (Figure 15). Gradient imputation links the model in 

ecological space to the structure of biophysical gradients across the landscape, thereby extending the gradient approach in 

the spatial dimension. Output maps provide quantitative estimates of the distribution of each variable across the landscape, 

providing spatially explicit information about resource conditions at multiple spatial scales.
USDA Forest Service RMRS GTR-194. 2007 37

Step 3—Linking ecosystem dynamics to 

gradient imputation

Questions

How can parameters for stand-level, plant-based 

ecosystem dynamics models (growth, mortality, regeneration, competition, soil, climate) be developed 

using multi-scale gradient models?

What are the initial conditions for each cell on complex landscapes?

How reliably can we integrate predictions of future 

vegetation on plots with gradient imputation to predict future vegetation across complex landscapes?

How will altered climate affect the response of vegetation across the simulated landscape?

Data

Initial vegetation condition among sampled plots.

Initial microclimate and biophysical characteristics of 

each plot.

Empirical models of growth, death, and regeneration 

responses by species, age, and competitive position, 

across biophysical gradient space. This is provided by 

Step 1.

Empirical models of microclimate across biophysical 

gradient space. This is provided by Step 1.

Expected initial condition of cell across the simulated landscape, in terms of species composition, age, 

biophysical context, and microclimate, provided from 

Step 2.

Analysis

Use gradient models of growth, mortality, and regeneration by species, age, and competitive position, 

across biophysical gradient space to quantify response 

functions in a forest dynamics model, such as FM.

Use imputation results from Step 2 to provide the biophysical context and microclimate for each cell across 

the landscape.

1.

2.

3.

4.

1.

2.

3.

4.

5.

1.

2.

Simulate changes in forest composition and structure 

in sampled plots under an equilibrium climate.

Simulate changes in forest composition and structure under four alternative climate change scenarios: 

1) warmer/wetter, 2) warmer/drier, 3) colder/wetter, 

4) colder/drier.

Use the results of 3 and 4 as input into gradient models 

to produce imputed expectations of the composition 

and structure of vegetation across the full landscape 

under each scenario.

Quantify expected changes in vegetation composition and structure under current and altered climate 

regimes in the absence of exogenous disturbance. 

Quantify changes in the spatial configuration of the 

vegetation mosaic using landscape pattern analysis 

tools such as FRAGSTATS.

Expected products

Predictions of future vegetation on measured plots 

accounting for succession and climatic change.

Prediction of future vegetation across complex 

landscapes under alternative climate regimes in the 

absence of disturbance.

Importance

The forest dynamics model will explicitly address 

nonequilibrium dynamics of existing vegetation due 

to succession and interspecific interactions.

The linkage of the forest dynamics model with gradient imputation will allow projection of growth, 

mortality, and succession across landscapes at fine 

spatial scale.

Simulation under current and altered climate regimes 

will provide an estimate of impact possible from altered climate due to autogenous community-level 

processes.

Mapping expected future fine-scale vegetation across 

complex landscapes will provide managers with improved information about expected condition of forest 

resources in the coming decades.

3.

4.

5.

6.

1.

2.

1.

2.

3.

4.
38 USDA Forest Service RMRS GTR-194. 2007 Figure 17. The gradient models provide parameter values and functional forms for the ecosystem dynamics models (pink boxes above). This anchors the ecosystem dynamics models with empirically derived growth, regeneration, and mortality parameters. Gradient imputation provides the initial conditions of driving variables (yellow boxes) on each cell. Ecosystem dynamics models are then run across all measured vegetation plots, providing expected future vegetation. Altered climatic scenarios can be readily implemented by changing climate inputs. At each time-step, the results of the ecosystem dynamics model are returned as the training data for the gradient models and a map of vegetation composition and structure at that time-step is created through gradient imputation. By linking ecosystem dynamics models to gradient models with imputation, it is possible to span the space x time scale space, integrating spatial and temporal complexity in forest responses to biophysical drivers.
USDA Forest Service RMRS GTR-194. 2007 39

Step 4—Linking landscape dynamics 

simulation to ecosystem and 

gradient models

4a implementing alternative disturbance 

regimes in a landscape dynamics model

Questions

What is the relationship between climate, weather, 

microclimate, vegetation, topography, and fire regime 

in terms of frequency, size, and severity of fires?

How do insect outbreaks and expected future land use 

confound these relationships?

How can these relationships be translated into input 

for landscape dynamics models such that uncertainties and error propagation are minimized?

How will expected fire regimes, management, and 

insect outbreaks under different climate affect forest 

ecosystems on complex landscapes?

Data

Predictive models of the responses of fire regimes to 

climate.

Extent and pattern of expected land use change.

Method for estimating insect disturbance (quantitative or heuristic).

Initial vegetation conditions (imputed from gradient 

models) and ecosystem model outputs at appropriate 

time-steps.

Analysis

Use a landscape dynamics simulation model, such as 

RMLands, to simulate current and alternative disturbance regimes.

Define current disturbance regime based on frequency, extent, pattern, and severity of each disturbance 

type by biophysical context.

Define alternative disturbance regimes based on expected changes to frequency, extent, severity, and 

pattern of each disturbance type across biophysical 

gradients.

Alternative scenarios should include the warm/

wet, warm/dry, cold/wet, cold/dry scenarios used in 

Step 3.

1.

2.

3.

4.

1.

2.

3.

4.

1.

2.

3.

4.

Apply estimated parameters of disturbance regimes 

to the landscape dynamics simulation model for current and alternative scenarios.

Initialize each scenario with current vegetation and 

biophysical conditions.

Simulate each scenario with multiple runs (minimum 

of 100 over 500+ years), at a relatively short timestep (5-20 years).

Characterize change in landscape pattern of cover 

types and successional stages under each scenario 

using landscape pattern analysis software such as 

FRAGSTATS and multivariate landscape trajectory 

analysis (Cushman and McGarigal 2007, in press).

Expected products

Quantification of range of variation in patch mosaic 

consisting of cover types and successional stages under the current climate.

Range of variation of vegetation mosaic under alternative future climates.

Predicted effects of altered disturbance regimes on 

the area and configuration of cover types and successional stages, enabling managers to infer the effects 

of alternative management at the stand level.

Importance

Information about the range of variation of cover type 

and successional stage mosaic under current climatic 

conditions will provide critical information for evaluating the current condition with respect to historic 

ranges and desired future conditions.

Information about expected ranges of variation of 

cover types and successional stages under possible 

future climatic regimes will provide managers critical information about the possible extent and nature 

of changes in forest ecosystems resulting from altered 

climate and disturbance regimes.

This information will enable managers to anticipate 

changes in disturbance regimes and to take proactive 

measures to appropriately manage resources under 

changing ecological conditions.

5.

6.

7.

8.

1.

2.

3.

1.

2.

3.
40 USDA Forest Service RMRS GTR-194. 2007

Figure 18. Stochastic landscape simulation models provide a means to simulate how disturbance regimes affect the area and 

configuration of cover types and successional stages across complex landscapes and through time. The predictions are 

probabilistic and patch-based. Thus although they explicitly model broad-scale disturbance, they do so with different entities 

(patches instead of organisms) than the ecosystem and gradient models. A significant remaining challenge is to link patch 

level predictions of fire size, shape, and severity with the responses of organisms across complex biophysical gradients.
USDA Forest Service RMRS GTR-194. 2007 41

4b linking extent, frequency, and severity of 

fires to vegetation response at a fine spatial 

scale, continuously across the landscape

Questions

What are the relationships between type, extent, frequency, and severity of disturbance and fine-scale 

vegetation composition and structure across broad 

landscapes?

What are the uncertainties in predicting site-level 

changes in vegetation composition, structure, growth, 

mortality, and regeneration from the output of patchbased landscape dynamics models?

Does the integration of gradient models, ecosystem 

dynamic models, and landscape disturbance models 

improve our ability to predict the effects of changing 

biophysical conditions and disturbance regimes on 

forest vegetation, at a fine-spatial scale, across large 

spatial extents, and through time?

Data

Empirical measurements of fire impacts on vegetation. Requires measurement of vegetation response 

on a large number of fires of varying age, size, and 

severity across biophysical gradients.

Requires a large and representative sample of remeasure plots before and after disturbance within the 

perimeter of each fire.

These plots must cover the full combination of biophysical gradients and disturbance size, severity, and 

age in order to derive robust models.

A large investment to collect samples prior to fires, 

to populate the landscape with “pre-treatment” 

measurements.

1.

2.

3.

1.

2.

3.

4.

A large investment in post-fire remeasurements on 

these permanent plots to quantify fire impacts in the 

context of initial vegetation condition, biophysical 

context, and disturbance characteristics.

Analysis

Use gradient modeling to infer relationships between 

species response and type, size, intensity, biophysical 

context, and time since fire.

Apply these models to predict effects of simulated fires 

on vegetation condition across complex landscapes.

Predict post-fire vegetation response and recovery. 

This is done for each cell post-fire in the succeeding 

time-step. Within scenarios, this provides expected response of fine-scale vegetation across the full 

landscape to one realization of a disturbance regime. 

Across scenarios, this provides aggregate statistics 

of vegetation response to altered climate and fire 

regime.

Expected products

Spatially explicit predictions of expected future vegetation across complex landscapes under alternative 

climatic and disturbance regimes.

Importance

Effectively translating from the patch-mosaic dynamics of landscape simulation models back to fine-scale 

vegetation dynamics is the key to integrating biophysical modeling of individualistic vegetation response 

with large-scale disturbances.

This integration is essential if we are to successfully 

understand and predict the effects of climate change 

and disturbance regime change on forest ecosystems.

5.

1.

2.

3.

1.

1.

2.
42 USDA Forest Service RMRS GTR-194. 2007 Figure 19. Reliable predictions of the effects of management, climate, and disturbance regimes require the integration of broad-scale disturbance with ecological responses across biophysical gradients and over time. This can be done by linking gradient modeling, ecosystem dynamics modeling, and landscape dynamics modeling. However, this integration is challenging due to the qualitative difference between the entities being addressed (Figure 18). We therefore return full-cycle to the gradient modeling paradigm. With large samples of remeasure plots in areas that have received fire we can develop quantitative link functions (via regression, GLMs, and CCA) between fire size, shape, and biophysical context and the response of vegetation and other ecological factors at the site-level. The key ingredient for this analysis is pre-disturbance and post-disturbance sampling.
USDA Forest Service RMRS GTR-194. 2007 43

The response of forest ecosystems and fire regimes to 

global climate change will depend on factors at multiple 

scales and complex interactions among climate, fire, 

and vegetation. Altered fire regimes may have larger 

impacts on species distribution, migration, substitution, and extinction than the direct effects of climate 

change itself (Weber and Flannigan 1997, McKenzie 

and others 2004). An integrated approach is needed that 

addresses the nonequilibrium and often discontinuous 

dynamics of mechanisms and responses at biologically meaningful scales, including the critical scale of 

direct interactions between organisms and the environment. Our agenda links multi-scale gradient modeling, 

ecosystem dynamics modeling, and landscape simulation, to predict the changes to forest ecosystems from 

a changing biophysical environment and disturbance 

regimes.

Complete model integration brings us back fullcycle to the relationships between forest vegetation 

and biophysical gradients. Without a linkage to finescale vegetation and the biophysical limiting factors 

that govern its response, landscape disturbance models 

cannot reliably predict changes in species distributions, 

community structure, stand structure, and other critical 

attributes of forest ecosystems. Conversely, without 

addressing landscape dynamics, predictions of relationships between biophysical limiting factors and vegetation 

are confounded by disturbance. Wildfire is likely to be 

the proximate cause of ecosystem change in the context 

of climate change, and meaningful understanding must 

involve linking vegetation response to biophysical gradients with the effects of large-scale disturbance.

Synthesis of existing data sets will be helpful in guiding 

this effort but will not be sufficient. Successful integration of forest ecosystem dynamics, climate change, and 

disturbance regimes will require investment in sampling 

efforts to gather empirical data on species distributions, 

growth, regeneration, and fire histories across broad 

scales and over extensive biophysical gradients. As the 

effort will necessarily be large and involve integration 

of several major fields of research, it will also require 

collaboration among many partners. No one scientist, institution, or research discipline has the expertise 

required for this integration. Broad and magnanimous 

collaboration will be essential.

Conclusion
44 USDA Forest Service RMRS GTR-194. 2007

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