Linking Land-Use Projections and Forest 

Fragmentation Analysis

Linking Land-Use Projections and Forest 

Fragmentation Analysis

Andrew J. Plantinga, Ralph j. alig, henry eichman, and david j. lewis

U.S. Department of Agriculture Forest Service

A Technical Document Supporting 

the USDA Forest Service Interim Update of the 2000 RPA Assessment

A Technical Document Supporting 

the USDA Forest Service Interim Update of the 2000 RPA Assessment
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multiple use management of the Nation’s forest resources for sustained yields of wood,

water, forage, wildlife, and recreation. Through forestry research, cooperation with the

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Authors

Andrew J. Plantinga is an associate professor, Department of Agricultural and 

Resource Economics, Oregon State University, Corvallis, OR 97331; Ralph J. 

Alig is a team leader and research forester, U.S. Department of Agriculture, Forest 

Service, Pacific Northwest Research Station, Forestry Sciences Laboratory, 3200 

SW Jefferson Way, Corvallis, OR 97331; Henry Eichman is an economist, U.S. 

Department of the Interior, Bureau of Land Management, Prineville District, 3050 

NE Third, Prineville, OR 97754; David J. Lewis is an assistant professor, Department of Agricultural and Applied Economics, University of Wisconsin, Madison, 

WI 53706.
Abstract

Plantinga, Andrew J.; Alig, Ralph J.; Eichman, Henry; Lewis, David J. 2007. 

Linking land-use projections and forest fragmentation analysis. Res. Pap. PNWRP-570. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific 

Northwest Station. 41 p.

An econometric model of private land-use decisions is used to project land use 

to 2030 for each county in the continental United States. On a national scale, forest 

area is projected to increase overall between 0.1 and 0.2 percent per year between 

now and 2030. However, forest area is projected to decrease in a majority of regions, including the key forestry regions of the South and the Pacific Northwest 

Westside. Urban area is projected to increase by 68 million acres, and cropland, 

pasture, rangeland, and Conservation Reserve Program land is projected to decline 

in area. Regional econometric models are needed to better represent region-specific 

economic relationships. County-level models of forest fragmentation indices are 

estimated for the Western United States. The core forest model is found to perform 

better than the model of like adjacencies for forest land. A spatially detailed analysis of forest fragmentation in Polk County, Oregon, reveals that forests become 

more fragmented even though forest area increases. By linking the land-use projection and forest fragmentation models, we project increases in the average county 

shares of core forest in 8 of the 11 Western States. The average like adjacency 

measure increases in six of the states. The aggregate and spatially detailed fragmentation methods are compared by projecting the fragmentation indices to 2022 

for Polk County, Oregon. Considerable differences in the results were produced 

with the two methods, especially in the case of the like adjacency metric. 

Keywords: Land use, forest-land area, forest fragmentation, spatial analysis.
Contents

1 Chapter 1: Introduction

4 Chapter 2: National Econometric Model

4 Methods

4 Econometric Land-Use Model

6 Land-Use Projection Model

8 Projection Results

12 Chapter 3: Western Fragmentation Model

12 Data and Methods

17 Results

19 Discussion

22 Chapter 4: Spatially Explicit Fragmentation Analysis

22 Methods

25 Results

29 Chapter 5: Linkage of Land-Use Projections and Fragmentation Models

29 County Projections of Fragmentation Metrics

30 Comparison of Fragmentation Projections by Using Spatially Explicit 

 and Aggregate Methods

34 Chapter 6: Summary and Conclusions

37 Metric Equivalents

37 Acknowledgments

37 References

40 Appendix: Variable Measurement and Data Sources
Linking Land-Use Projections and Forest Fragmentation Analysis

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Chapter 1: Introduction

The fragmentation of forests into smaller patches affects habitat quality and thus 

biological diversity, and increases the likelihood of invasion by exotic species. Forest 

fragmentation is widely considered to be a primary threat to terrestrial biodiversity 

(Armsworth et al. 2004) and is a pervasive feature of U.S. forests. Riitters et al. 

(2002) found that approximately 62 percent of forest patches in the lower 48 States 

are located within 164 yards of the nearest edge. Forest fragmentation can result 

from land-use intensification, such as housing development, or from natural causes, 

such as expansion of nonforest plant communities. The overall simplification of 

biological communities may reduce, and make more costly, the goods and services 

that humans derive from ecosystems.

Although the ecological effects of forest fragmentation have received substantial attention, an understanding of the economic drivers of fragmentation is less 

developed. Land-use studies supporting the 2005 Renewable Resources Planning 

Act (RPA) Assessment update indicated that tens of millions of acres of private 

forest land in the United States could be converted to urban and developed uses 

over the next 50 years (e.g., Alig and Plantinga 2004, Alig et al. 2004), resulting 

in more forested areas being surrounded by nonforest areas, or adjacent to houses, 

streets, parking lots, and malls. The U.S. population is projected to grow by another 

120 million people by 2050, with relatively fast growth rates in the Western United 

States. These results indicate the importance of understanding economic determinants of forest fragmentation in the context of demands on and supplies of renewable resources from the Nation’s forests and rangelands.

Questions to answer concerning forest fragmentation include (1) Where, how 

much, and how is forest fragmentation happening (e.g., natural vs. human causes)? 

(2) What factors are causing forest fragmentation? (3) Are fragmentation trends 

changing (e.g., accelerating)? (4) What are prospective changes in forest fragmentation? (5) What incentives or associated policies could effectively be used to address 

fragmentation? Our study addresses a number of the questions posed above in the 

context of forests in the Western United States. We focus on forest fragmentation 

resulting from land use,1 directing our attention to the effect of human land uses 

on forest fragmentation.2 Land-use changes can result when supplies of land for 

 1 Because forest harvesting is often followed by reforestation (Alig and Butler 2004), effects of such 

age-class fragmentation are often not as severe in the longer term as, for example, conversion of 

forests to other land uses such as urban development.

2 We omit from the analysis fragmentation resulting from natural processes such as succession. 

Moreover, land-cover changes (e.g., timber harvesting) that do not involve changes in land use are 

not treated as fragmentation. 

Land use changes can 

result when supplies 

of land for different 

uses change in 

response to economic 

incentives, changing 

laws and regulations, 

and environmental 

conditions, interacting 

with shifts in demands 

for land in response 

to changes in 

socioeconomic factors 

such as population and 

personal income.
Research Paper PNW-RP-570

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different uses change in response to economic incentives, changing laws and regulations, and environmental conditions, interacting with shifts in demands for land 

in response to changes in socioeconomic factors such as population and personal 

income. Most public forests are unfragmented, whereas urbanization and increasing 

intensity of land use may lead to more fragmentation of private lands. We, therefore, focus our analysis on the link between land-use changes on private lands and 

forest fragmentation.

Our study of forest fragmentation supports the Sustainable Wood Production 

Initiative (SWPI) (Deal and White 2005) and the 2005 update of the 2000 RPA 

assessment (USDA Forest Service 2001), which was prepared in response to the 

mandate in the Forest and Rangeland Renewable Resources Planning Act of 1974, 

P.L. 93-378, 88 Stat. 475, as amended (RPA). Both the SWPI and RPA Assessments 

seek to better understand the major economic, ecological, and social issues affecting sustainable forestry. The 1974 RPA legislation established a periodic reporting 

requirement and broadened the resource coverage from timber alone to all renewable resources (e.g., fish and wildlife) from U.S. forests and associated issues such 

as fragmentation of forested landscapes. Fragmentation concerns are now also 

being reflected in the design of conservation policies in the most recent U.S. Farm 

Bill. For example, reducing forest fragmentation is a primary goal in the Wildlife 

Habitat Incentives Program as administered by several states. Likewise, many 

wildlife conservation plans adopted or proposed by nongovernmental agencies such 

as Partners-In-Flight have explicit goals related to the reduction of forest fragmentation. 

Conservation and management of U.S. forests is based in part on international 

protocols (e.g., Montreal Process), which are intended to provide a common understanding of what is meant by sustainable forest management and to provide a 

common framework for describing, assessing, and evaluating a country’s progress 

toward sustainability at the national level. For example, one criterion is maintenance and enhancement of long-term multiple socioeconomic benefits to meet the 

needs of societies. Clearly, the provision of these benefits is affected by forest fragmentation. However, the associated indicators, such as one for forest fragmentation 

(Riitters et al. 2002), offer little information about population and income and other 

drivers of change in resource conditions. In our study, we augment efforts such 

as the Montreal Process by reporting on important drivers of change in resource 

conditions and how issues such as urbanization crosscut or affect many measures of 

U.S. renewable resource condition, particularly forest fragmentation.

The design of our study is illustrated in figure 1 (the ovals represent components of the study; the boxes are inputs and outputs). The first component is a 
Linking Land-Use Projections and Forest Fragmentation Analysis

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national-level land-use projection model based on an econometric analysis of land 

use changes among crop, pasture, forest, urban, Conservation Reserve Program, 

and range categories. The econometric model is estimated with data on nonfederal 

land and explains land-use changes in terms of economic returns and site characteristics such as land quality. The projection model is used to generate land-use 

projections, by county, to 2030. We use forest fragmentation metrics (the share of 

the landscape in core forest and the percentage of like adjacencies) to characterize 

the amount of forest fragmentation in the Western United States. A statistical analysis is undertaken to explain the observed variation across counties in these metrics. 

These results support a linking of the land-use projections and the aggregate 

fragmentation analysis, allowing us to estimate how the fragmentation metrics may 

change as the shares of land in different uses differ. Chapter 4 contains a spatially 

explicit analysis of forest fragmentation in Polk County, Oregon. Projections of 

fragmentation metrics are generated and compared to those produced by the aggregate data approach used in chapter 3. This comparison sheds light on tradeoffs 

between precision and costs of data collection, assembly, and processing at different 

scales of inquiry. We conclude by summarizing key findings and offering suggestions for further research. 

National land-use

projection model 

Projections of county

land use shares

Spatially explicit

fragmentation analysis

Projections of fragmentation metrics

for Polk County, Oregon

Evaluation of methods

Western county

fragmentation analysis

County projections of

fragmentation metrics

Figure 1—An illustration of the study design.
Research Paper PNW-RP-570

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Chapter 2: National Econometric Model

Lubowski et al. (2006) conducted a national-scale analysis of the cost of sequestering carbon in forests. As part of this project, Lubowski (2002) developed a nationalscale econometric model of land use. Lubowski estimated the probabilities for 

transitions between six major land-use categories. The transition probabilities are 

functions of net financial returns to the alternative uses, soil quality, and estimated 

parameters. The first step in the present research is to incorporate the econometric 

results into a land-use projection model. The projection model is an algorithm that 

projects changes in land use, beginning with 1997 base year conditions. The model 

treats crop and timber prices as endogenous, thereby accounting for feedback 

effects of land-use change on the prices of key commodities. The following sections 

describe Lubowski’s econometric model and the algorithm used for the land-use 

projections and present and discuss national and regional land-use projections to 

2030. 

Methods

Econometric Land-Use Model

The National Resources Inventory (NRI) is the primary data set used by Lubowski 

(2002) to estimate a national econometric land-use model. The NRI is a panel 

survey of land use and land characteristics on nonfederal lands conducted at 5-year 

intervals from 1982 to 1997 over the entire United States, excluding Alaska. Data 

include approximately 844,000 plot-level observations, each representing a land 

area given by a sampling weight. The NRI provides information on three land-use 

transitions over the periods 1982-87, 1987-92, and 1992-97. The Lubowski analysis 

focuses on the lower 48 States and six major land uses: crops, pasture, forest, urban, 

range, and Conservation Reserve Program (CRP).3 The land base in the study 

comprises 1.4 billion acres, representing about 74 percent of the total land area and 

about 91 percent of nonfederal land in the contiguous United States. 

The dependent variable in the econometric model is the choice of land use in 

year t+5 (t = 1982, 1987, 1992) at each NRI plot, and the independent variables 

are the land use in year t, the land quality rating of the plot, and proxies for the 

expected net returns from the land-use alternatives as of year t. By assembling data 

 3 Lands in “rural roads and transportation” uses are likely to change through a different decisionmaking process than profit maximization by private landowners, and are omitted. Streams 

and water bodies, marshlands, and barren lands are also excluded, as these uses are unlikely to 

differ over time. Finally, lands classified under unspecified “miscellaneous” uses are omitted.
Linking Land-Use Projections and Forest Fragmentation Analysis

5

from a variety of private and public sources, Lubowski (2002) constructed countylevel estimates of annual net returns (per acre) for crops, pasture, forest, range, 

and urban uses for all 3,014 counties in the 48 contiguous states.4 The net returns 

to cropland and timber are weighted averages of net returns to specific crops and 

forest types, where the weights reflect current cropping patterns and forest type 

distributions (see the appendix for more details). The land quality measure is the 

land capability class (LCC) rating of the NRI plot. The LCC rating is a composite 

index representing 12 factors (e.g., soil type, slope) that determine the suitability 

of the land for agriculture. It also serves as a proxy measure for forest productivity. 

The LCC rating ranges from I to VIII, where I indicates the greatest potential for 

intensive agricultural uses. For the econometric analysis, the eight LCC categories 

are combined to produce four land quality classes. 5

Landowners are assumed to have static expectations of future net financial 

returns and to allocate their land to the use generating the highest return net of conversion costs. Net financial returns are assumed to have deterministic and random 

components. The deterministic component includes the county net return, land 

quality class dummy variables (LQ), and the interaction between the two variables. 

This specification allows for plot-level deviations from the average county return. 

Certain distributional assumptions (see Train 2003) are imposed on the random 

components of net returns to yield a nested logit model for estimation. Three nests 

include land uses with similar land quality requirements: crops, pasture, and CRP; 

forest and range; and urban.6 Details on the econometric estimation and results 

are available in Lubowski (2002) and Lubowski et al. (2006). The analysis yields 

probabilities for transitions between each of the six land uses. These probabilities 

are functions of independent variables and estimated parameters,

Pijkt = P(βˆ

jk ,NRit, LQi

) (1)

where Pijkt denotes the probability that plot i transitions from use j to k during the

interval beginning in year t, β

ˆ

jk is a vector of estimated parameters for the j to k

transition, NRit is a vector of net returns to the six uses in year t and for the county 

 4 Net returns estimates are, thus, constructed for all of the land-use categories, except for 

CRP, which is modeled by using a different procedure discussed in Lubowski (2002). 

5 Land quality class 1 includes LCC I and II land, land quality class 2 includes LCC III and IV 

land, land quality class 3 includes LCC V and VI land, and land quality class 4 includes LCC 

VII and VIII land.

6 Crops, pasture, and CRP lands tend to have relatively high quality (in terms of the LCC rating), whereas forest and range lands have relatively low quality. There is little correspondence 

between urban uses and land quality and so urban is placed in a separate nest.
Research Paper PNW-RP-570

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where plot i is located, and LQi is a vector of land quality class dummy variables 

for plot i.

7

Land-Use Projection Model

The key inputs to the land-use projection model are the transition probabilities in 

(1) and plot-level data on land use, net returns, and soil quality from the NRI. The 

projection model operates at the NRI plot level and begins in the base year 1997. 

To simplify notation, we denote the years 1997, 2002, and 2007, etc., as t = 0, 1, 

2, etc. Based on the sampling design, each NRI plot is associated with a certain 

number of acres. We define Aijt as the number of acres associated with plot i in use 

j in time t. In the initial period, each plot is in one of the six uses as indicated in the 

1997 NRI data. Thus, Aij0 equals the acres represented by plot i if the plot is in use 

j in time 0, and equals 0 otherwise. Given a sequence of transition probabilities, we 

can compute how this land will be distributed across the six use categories at each 

time in the future. We can then express the area of land represented by plot i that 

transitions (transition acres) from use j to k during the interval beginning in t as 

TAijkt = Pijkt • Aijt. As well, the acres of land represented by plot i in use j at time t+1 

are given by,

Aijt+1 = ∑kTAikjt = ∑kPikjt • Aikt (2)

This expression reflects the first-order Markov structure of our model.

The transition probabilities in the base year are computed with the 1997 values 

of the net returns (and the time-independent coefficients, β

ˆ

jk , and variables, LLCi

). 

With the initial acres Aij0, we can estimate the acres in each use in time 

1 by using the relationship in (2). The induced change in land use implies a change 

in the supply of land-based commodities and services and, hence, changes in related 

prices and the net returns from each use. We model these endogenous price effects 

for forest and cropland, and assume the net returns to pasture, range, urban, and the 

CRP remain constant throughout the simulation. Pasture and CRP account for 

a small share of the total land base. Rangeland is a major component of the land 

base (about 30 percent initially), but we were unable to find any information on 

markets (specifically, demand elasticities) for forage, the principal output of rangeland. Finally, the probabilities for transitions into urban uses were found to be 

insensitive to changes in urban rents, indicating that these transition probabilities 

would tend to remain the same even with endogenous price effects. 

7 Conversion costs are not measured explicitly, but rather are reflected in constant terms 

specific to each land-use transition.

The key inputs to the 

land-use projection 

model are the 

transition probabilities 

in (1) and plot-level 

data on land use, 

net returns, and soil 

quality from the NRI. 
Linking Land-Use Projections and Forest Fragmentation Analysis

7

Consistent with the model of landowner behavior underlying the econometric 

analysis, cropland and forest commodities are supplied inelastically. Thus, we 

can use crop and timber yields, measured in output per acre, to translate land-use 

changes into output changes. After aggregating output changes to the appropriate 

level, we compute corresponding price changes by using own-price demand elasticities estimated in previous econometric studies.8

 Changes in cropland area result 

in immediate changes in crop output because crops are assumed to be harvested in 

the same year that they are planted. In the case of forests, timber harvests will be 

delayed for a period of years while the forest stand grows to maturity. For afforested 

lands, we assume that harvests are delayed for the period of one optimal rotation, 

after which time the forest is “fully regulated” and provides a constant annual flow 

of timber.9 Likewise, all land originally in forest (i.e., in t = 0) is assumed to have 

a fully regulated structure. When these lands are converted to nonforest uses, we 

assume that only a portion of the timber (20 percent) is merchantable.

The assumption of a fully regulated forest will clearly overstate the timber supply from private forests. It is well documented that nonindustrial private landowners, who own almost 80 percent of the private forest in the United States, frequently 

manage their lands for nontimber outputs such as recreation (Butler and Leatherberry 2004). To account for these alternative management objectives, we assume 

that a fixed percentage of forest land in each timber production region (see footnote 

4) is never harvested, while the remaining forest is harvested in the manner described above. The no-harvest percentages are determined by calibrating the model 

to regional timber harvest data for 1997.10 The no-harvest percentages range from 6 

percent in the South Central region to 62 percent in the Pacific Southwest region.

Once we have computed the price changes resulting from the land-use changes 

between periods 0 and 1, we can form new measures of net returns in period 1. 

Specifically, we apply the national or regional percentage price change to the 

8 For crop commodities, we use a national-level demand elasticity for raw food inputs by 

food processors (Goodwin and Brester 1995). We apply this elasticity (-0.661) separately to 

each of the 25 crop commodities in our model. For timber, we use demand elasticities for 

seven timber production regions—Pacific Northwest (-0.300), Pacific Southwest (-0.497), 

Rocky Mountains (-0.054), North Central (-0.141), Northeast (-0.029), South Central (-0.193), 

Southeast (-0.285)—from the Timber Assessment Market Model (Adams and Haynes 1996). 

These elasticities apply to a composite timber type representative of the species found within 

the region. In general, we would expect the mixes of crop and timber types to change in 

response to price changes. However, we assume for simplicity that the crop and timber type 

shares remain constant over time. 

9 Specifically, if t*

 is the optimal rotation length, then there is an equal area of forest in each 

age category in the interval [0, t

* ]. Each year, timber of age t*

, or 1/t

*

 of the forest area, is 

harvested.

10 These data were provided to the authors by Dr. Darius Adams in the Department of Forest 

Resources at Oregon State University.
Research Paper PNW-RP-570

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county-level prices used to compute net returns. With the period 1 net returns, 

we recalculate the transition probabilities and repeat the procedure. This stage 

of the simulation ends when the crop and forest net returns have converged (i.e., 

period-to-period changes in prices are near zero). The converged net returns are 

equilibrium values that reflect all anticipated supply adjustments in agricultural and 

forest commodity markets. This process is atemporal; it represents an instantaneous 

adjustment to a new market equilibrium. For this reason, we hold urban land constant during this stage of the simulation. Urban land will increase over time with 

factors such as population growth—as it does in the second stage of the algorithm 

discussed below—but should not affect the immediate adjustment in net returns to 

cropland and forests.

In the second stage of the algorithm, we compute the time path of land-use 

changes. Specifically, we recalculate the transition probabilities for the initial period 

by using the converged net returns for cropland and forests and the observed net 

returns for the other uses. Beginning with the initial acres in each use (Aij0 ), we use 

(2) to compute the sequence of land-use transitions (TAijkt) through time. Unlike in 

the first stage of the algorithm, the net returns remain at their equilibrium values 

throughout this stage. 

Projection Results

Lubowski (2002) developed two sets of econometric results. One set uses data on 

transitions from all three periods and the other uses data only on transitions from 

the final period (1992–97). We generated projections with both sets of estimates, but 

present here only the results based on the 1992-1997 parameters as similar results 

are obtained. Table 1 shows the national-level changes.11 Forest area is projected 

to increase between 0.1 and 0.2 percent per year from 1997 to 2030. The largest 

increases occur between now and 2010 and, then, gradually decline. Urban land 

shows the largest increase of any use category. The overall net increase in national 

forest area represents a 4.7 percent increase between 1997 and 2030, in contrast to 

a 1.5 percent decrease projected by Alig et al. (2003) using a mixture of databases. 

The NRI data on land use transactions among major land uses analyzed in the current study allow projections of net changes as well as gross land-use changes, e.g., 

the total amount of forest area projected to be deforested.

Urban area increases by approximately 2 million acres per year throughout 

the projection period, for a total gain of 68 million acres by 2030. This represents 

an average annual increase of 2.7 percent. The increases in forest and urban area 

11 Some of the following results were presented in an earlier publication by Alig and Plantinga 

(2004).
Linking Land-Use Projections and Forest Fragmentation Analysis

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Table 1—Land-use projections for the contiguous United States, 1997 to 2030

 Land uses

Year Cropland Pasture Forest Urban CRP Rangeland Total

Area projections 1,000 acres

1997 376,383 119,513 404,680 75,924 32,696 404,824 1,414,019

2002 369,364 129,912 408,668 86,056 27,262 392,758 1,414,019

2010 362,828 125,431 414,652 103,007 22,661 385,440 1,414,019

2020 354,061 119,016 419,905 123,777 19,098 378,162 1,414,019

2030 344,911 113,209 423,464 143,969 16,789 371,677 1,414,019

Change, 1997-2030 -31,472 -6,303 18,784 68,045 -15,907 -33,147

Annual change 1,000 acres per year

1997-2002  -1,404 2,080 798 2,026 -1,087 -2,413

2002-2010  -817 -560 748 2,119 -575 -915

2010-2020  -877 -642 525 2,077 -356 -728

2020-2030  -915 -581 356 2,019 -231 -648

Annual percent change Percent per year

1997-2002  -0.4  1.7  0.2 2.7 -3.3 -0.6

2002-2010 -0.2  -0.4  0.2 2.5 -2.1 -0.2

2010-2020 -0.2  -0.5 0.1 2.0 -1.6 -0.2

2020-2030 -0.3 -0.5 0.1 1.6 -1.2 -0.2

CRP = Conservation Reserve Program.

come at the expense of cropland, pasture, CRP, and rangeland, which are projected 

to decline, respectively, by 31.4, 6.3, 15.9, and 33.1 million acres by 2030. With the 

exception of pasture area, which increases initially, the largest declines in these 

categories occur between now and 2010.

Table 2 disaggregates the national projections by RPA regions.12 Forest area is 

projected to decrease in a majority of regions, including the key forestry regions of 

the South and the Pacific Northwest Westside.The table reveals increases in forest area in five regions (Pacific Northwest East, Mountain, Northern Plains, Corn 

Belt, and South Plains) and declines in forest area in six regions (Pacific Southwest, 

Pacific Northwest West, Lake States, Northeast, Southeast, and South Central). The 

largest increases are projected in the Mountain, North Plains, Cornbelt, and South 

12 The regions include the following states or the indicated portions thereof: PSW (CA), 

PNWW (western OR and WA), PNWE (eastern OR and WA), Mountain (AZ, CO, ID, MT, 

NM, NV, UT, WY), Northern Plains (KS, NB, ND, SD), South Plains (western OK and TX), 

Lake States (MI, MN, WI), Corn Belt (IA, IL, IN, MO, OH), South Central (AL, AR, KY, LA, 

MS, eastern OK, TN, eastern TX), Northeast (CT, DE, MA, MD, ME, NH, NJ, NY, PA, RI, 

VT, WV), and Southeast (FL, GA, NC, SC, VA).

Forest area is projected 

to decrease in a 

majority of regions, 

including the key 

forestry regions of the 

South and the Pacific 

Northwest Westside.
Research Paper PNW-RP-570

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Plains regions, and are accompanied by large declines in rangeland in the Mountain 

and South Plains regions and cropland in the North Plains and Cornbelt regions. 

The largest declines in forest area are projected in the Northeast, Southeast, and 

South Central regions. In all regions, the area of urban land increases significantly. 

Cropland area declines in all but the South Plains and South Central regions. 

Pasture and rangeland gain or lose area depending on the region.

We project relatively large increases in forest area in regions—Mountain, North 

Plains, Cornbelt, and South Plains—not normally considered to have active margins 

between forest and nonforest uses. We consider two possible explanations. First, the 

Table 2—Regional land-use projections for the contiguous United States, 1997 to 2030

 Land uses

Region Cropland Pasture Forest Urban CRP Rangeland

Change, 1997-2030 1,000 acres

Pacific Southwest  -1,742 1,402 -594 5,748 -114 -4,701

Pacific Northwest West -545 -932 -1,883 3,120 8 232 

Pacific Northwest East  -3,113 2,793 2,048 2,634 -1,289 -3,072 

Mountain  -3,098 7,408 10,313 8,942 -2,912 -20,653 

Northern Plains -12,123 8,179 5,703 6,298 -3,407 -4,651 

Lake States  -3,978 -282 -1,240 5,290 -1,423 1,633

Corn Belt  -8,441 -4,494 5,416 7,365 -3,171 3,325

Northeast  -3,988 -1,860 -2,980 7,073 19 1,735 

Southeast  -224 -3,158 -3,606 6,996 -780 772 

South Plains  739 440 8,005 5,083 -2,009 -2,259 

South Central  5,041 -15,800 -2,399 9,496 -829 4,492 

All regions -31,472 -6,303 18,784 68,045 -15,907 -33,147

Percentage change, 

1997-2030 Percent

Pacific Southwest  -18.1 133.7 -4.3 119.8 -65.7 -25.7

Pacific Northwest West -39.1 -58.8 -12.0172.6 724.4 389.7 

Pacific Northwest East  -34.5 178.0 21.1 416.5 -86.0 -20.4 

Mountain  -8.4 88.3 40.1 185.9 -46.0 -11.1 

Northern Plains  -13.8 111.1 170.5294.1 -39.7 -6.5 

Lake States  -9.8 -3.3 -2.6 82.6 -56.3 N/A

Corn Belt  -9.6 -21.6 18.5 73.4 -66.4 3,800.5

Northeast  -24.8 -24.7 -3.8 51.6 9.8 N/A 

Southeast  -1.2 -23.7 -4.8 45.8 -66.1 23.9 

South Plains  2.1 2.8 199.8 83.2 -40.0 -11.3 

South Central  15.4 -47.0 -2.3 93.0 -34.2 350.2 

All regions -8.4 -5.3 4.6 89.6 -48.7 -8.2
Linking Land-Use Projections and Forest Fragmentation Analysis

11

econometric results that underlie the projections were part of a national analysis. 

In particular, a single set of parameters was estimated to characterize the observed 

land-use patterns. The model may be able to accurately represent land-use trends at 

a national scale because it reflects the central tendency of the data. However, it may 

be less accurate at a regional level because the model is not specified to capture 

regional differences in the underlying relationships. This represents a potential 

limitation of the fragmentation analyses presented in chapters 3 and 4, which draw 

on regional land-use projections. 

To a significant degree, the projections are a reflection of the land-use transitions between 1992 and 1997.13 Thus, a second possibility is that the regional projections simply mimic the land-use changes that actually occurred during this period. 

Table 3 presents some evidence in support of this explanation. For each region, it 

shows the acres of land that moved from pasture to forest, from range to forest, 

and from forest to nonforest uses (cropland, pasture, urban, etc.). In the Mountain 

region, a relatively large amount of rangeland (820,000 acres) converted to forest 

between 1992 and 1997, while a smaller area of land left forest (462,000 acres). 

A similar pattern is seen in the Cornbelt and South Plains regions, except in these 

cases there were relatively large amounts of pasture transitioning to forest. In some 

regions where we project declines in forest, such as the Northeast and Southeast, the 

flow of land out of forest between 1992 and 1997 exceed the flow of land into forest. 

Table 3—Observed land-use transitions to and from forest, 1992 to 1997

 Land-use transitions

Region Pasture to forest Range to forest Forest to nonforest

 1,000 acres

Pacific Southwest  19 398 741

Pacific Northwest West  17  0 148

Pacific Northwest East 11  93 32

Mountain  13 820 462

Northern Plains  20  42 56 

Lake States  583  0 404

Corn Belt  1,128  7 608

Northeast  972  0 1,376

Southeast  732 105 2,555

South Plains  358  99 74

South Central  2,254  23 1,876 

13 Land-use classification is complicated in some regions when relatively small changes in 

vegetation composition can shift land between uses classes; especially between forestry and 

pasture or rangeland. Regions where this occurs include the Mountains and Plains regions.
Research Paper PNW-RP-570

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Chapter 3: Western Fragmentation Model

In this chapter, we present aggregate models of forest fragmentation for 11 Western 

States. Using county-level data, we estimate models of two fragmentation indices, 

the share of the county in core forest, and the percentage of neighboring parcels that 

are also forested (like adjacencies). The explanatory variables describe county landuse shares, forest ownership, land quality, topography, the likelihood of changes in 

forest area, and the income distribution of a county’s residents. The purpose of this 

analysis is to identify the determinants of forest fragmentation by using aggregate 

data and to develop a model that can be used to project fragmentation indices. The 

fragmentation indices used as dependent variables summarize the spatial configuration of land use within the county. In chapter 4, we present an analysis of forest 

fragmentation for a single county that accounts for land-use decisions on individual 

parcels. This approach offers more precision than the methods described here, but 

this precision comes at a higher cost in terms of managing large data sets, using 

specialized software, and requiring greater computing time. If readily available 

aggregate data can be used to model forest fragmentation, then reliable projections 

of forest fragmentation can be made at low cost and over large geographical areas.

Butler et al. (2004) and Alig et al. (2005) estimated aggregate models of forest 

fragmentation in western Washington and western Oregon. The dependent variables used to describe forest fragmentation in these studies included spatial metrics 

(percentage edge, share of like adjacencies) and aggregate land-use variables (share 

of nonforest). Both studies use data defined at the census tract scale and consider 

models with combined and individual spatial metrics. In both studies, population 

density, share of land in agricultural use, and the distance to highways had statistically significant coefficients. The Butler et al. study also found the share of federal 

land and slope to be statistically significant. They concluded that their composite 

index of forest fragmentation is a viable alternative to the multiple metric method 

used to describe components of forest fragmentation, and that the empirical model 

conforms to land-use theory. The Alig et al. study found distance to urban centers 

and the spatial configuration of land quality to be statistically significant across all 

their models. They found that including the spatial configuration of land quality 

increased the fit by more when the dependent variable represented a spatial pattern 

rather than an aggregate land-use share. 

Data and Methods

Our study area consists of 11 Western States (Washington, Oregon, California, 

Idaho, Nevada, Montana, Wyoming, Utah, Arizona, Colorado, and New Mexico). 
Linking Land-Use Projections and Forest Fragmentation Analysis

13

Counties containing no forest land were eliminated, giving us a total of 372 observations for analysis.

The dependent variables in our study are the share of the county in core forest 

and the percentage of like adjacencies (neighbors that are like the subject) for forest. 

These indices are derived from the U.S. Geological Survey National Land Cover 

Data for the early 1990s.1 Data representing fragmentation from natural processes 

are excluded, and temporary land-cover changes (e.g., from timber harvesting) are 

not treated as fragmentation. The data are delineated in a 100-foot grid. A core 

forest parcel is defined as a forest parcel at least 100 feet from a nonforest edge. 

The core forest variable equals the number of core forest parcels in a county divided 

by the total number of parcels in the county (times 100 to convert the variable to a 

percentage). It indicates both the amount of forest land in a county and the extent 

to which these parcels form relatively large blocks of forest. For example, a county 

would have a low value of this index if it had a large area of forest that is severely 

fragmented or if it had a small area that formed forest blocks. The core forest share 

ranges from 0 to 93.5 percent, with a mean of 32.4 percent. Table 4 provides summary statistics for the variables used in this study.

The percentage of like adjacencies for forest is defined as,

 , (3)

where I = 1,..., N indexes the forested parcels in a county and ADJij is an indicator 

variable that takes the value 1 if the jth parcel adjacent to parcel i is forested and 

the value 0 if it is not. Adjacency is defined by using an eight-neighbor rule2 and, 

thus, the term in parentheses equals the share of parcels adjacent to parcel i that are 

also forested. These proportions are then averaged over all forested parcels in the 

county. The percentage of like adjacencies measures the contiguity of forest parcels. It equals 0 if forest parcels are maximally dispersed and tends toward 100 as a 

county becomes entirely forested. The percentage of like adjacencies ranges from 

 1 We thank Jennifer Swenson for computing these indices. Because the indices represent 

forest fragmentation within counties, the metrics may be artificially truncated at the county 

boundaries. For example, if contiguous forest blocks span county boundaries, the indices will 

overstate the degree of fragmentation. We do not make adjustments for this problem, but note 

that the influence of borders is diminished with large counties and small parcel sizes (100-foot 

grid, in our case).

2 In a 3 by 3 grid, the center parcel is adjacent to eight neighbors. 

100

N

1

8 ∑

8

j=1

∑

N

i=1

ADJij
Research Paper PNW-RP-570

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0 to 99.998 percent. The mean is 98.2 percent, indicating that most forest parcels in 

the study region are surrounded by other forested parcels. The correlation coefficient for the core forest and like adjacencies measures is 42 percent, indicating that 

the two measures move together but represent different features of fragmentation.

Variation in the county forest fragmentation indices is explained by using a set 

of independent variables. These variables can be grouped to represent four general 

factors hypothesized to influence the spatial arrangement of forest land. The first 

group measures the aggregate allocations of land to forest and alternative uses. The 

second group accounts for effects of public ownership of forests. The third group 

measures the influence of land quality, which influences the feasibility of forest 

and other uses. Finally, the last group summarizes the effect of economic factors 

such as net returns to alternative land uses. The selection of variables reflects an 

effort to obtain a predictive model while also yielding insights into the important 

determinants of forest fragmentation. It is important to emphasize that we model 

Table 4—Ranges and expected signs of variables used in the aggregate forest fragmentation models

 Expected sign

Variable Minimum Mean Maximum Core Like adjacencies

Share of core forest parcels 0  32.4  93.5 N/A N/A

Share of like adjacent parcels 0  98.2 100.0 N/A N/A

Share of crops 0 9.2  74.4 - -

Share of pasture 0 2.5  15.3 - -

Share of forest 0  14.2  87.3 + +

Share of urban 0 2.9  58.2 - -

Share of Conservation Reserve Program 0 1.0  14.7 - -

Share of range 0  26.6  90.5 - -

Share of federal forest land 0  22.4  79.0 + +

Share of nonfederal public forest land 0 2.3 42.6 + +

Share of nonfederal land in LCC I 0  .7  19.5 + +

Share of nonfederal land in LCC II 0 4.3  40.5 + +

Share of nonfederal land in LCC III 0  12.4  63.7 + +

Share of nonfederal land in LCC IV 0  15.1  70.7 + +

Share of nonfederal land in LCC V 0 1.2  16.8 + +

Share of nonfederal land in LCC VI 0  28.2  80.8 + +

Share of nonfederal land in LCC VII 0  33.8  94.4 + +

Share of nonfederal land in LCC VIII 0 4.3  42.0 + +

Range of elevation (in feet) 155.0  1,714.0 4,393.0 - -

Agriculture-to-forest transition probability 0 0 .3 + +

Only public forest 0 .1 1.0 + +

Forest-to-agriculture transition probability 0 0  0 - -

Forest-to-urban transition probability 0 0 .1 - -

Share of wealthy households  0 2.3  17.0 - -

The selection of 

variables reflects 

an effort to obtain a 

predictive model while 

also yielding insights 

into the important 

determinants of forest 

fragmentation.
Linking Land-Use Projections and Forest Fragmentation Analysis

15

the cross-sectional variation in forest fragmentation. As such, we are interpreting 

forest fragmentation as a static outcome (i.e., as a state of the landscape). If repeated 

observations of the fragmentation metrics were available, one could model the 

dynamic process that leads to fragmentation.

To account for the effect of human land uses on forest fragmentation, the 

county shares of nonfederal land in forest, crops, pasture, urban, CRP, and range 

were included as explanatory variables. Data on areas of land in these six major 

land-use categories were extracted from the 1997 NRI survey results, and land-use 

shares were calculated as a percentage of total county acreage.3 We expect that, 

overall, the forest share will have a positive effect on the fragmentation metrics because both indices tend toward 100 as a county becomes entirely forested. However, 

depending on how forest land is arranged spatially, it is possible for a county with a 

greater share of land in forest to have more fragmented forests than another county 

with less forest land. We expect land in other uses to have a negative effect on the 

fragmentation indices overall, although, as above, the land-use share variables do 

not measure the spatial configuration of land uses. Including the county land-use 

shares in the model enables us to project fragmentation by using the land-use 

projections from chapter 2.

The NRI data used to measure the land-use shares account only for nonfederal 

land. We included the shares of federal and nonfederal public forest land (e.g., state 

and municipal forest land) as additional explanatory variables. Public forest areas 

were taken from the U.S. Forest Service Forest Inventory Analysis (FIA) Integrated 

Database (RPA 2002 Tabler/Mapmaker Version 1.0) and calculated as a percentage of total county acreage. The observations are from different FIA survey years 

ranging from the late 1980s to the mid 1990s. We expect public forests, whether in 

federal or nonfederal ownerships, to be unfragmented relative to private forests because development and other nonforest uses are typically prohibited on these lands. 

These variables would also control for nonhuman causes of forest fragmentation 

(e.g., transition zones between forest and nonforest plant communities) to the extent 

that these effects are systematic across public forests. Overall, we expect the shares 

of public forest land to be positively related to the fragmentation metrics. 

Land capability class shares were included to capture variation within the 

county in land quality. The areas of land in each of the eight LCC classes were 

3 The land-use shares, and some of the other variables discussed below, are measured a few 

years after the fragmentation indices. Aggregate land-use measures change very slowly and, 

thus, we do not expect this to be a problem.
Research Paper PNW-RP-570

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extracted from the 1997 NRI database and then normalized on the area of nonfederal land in each county. Alig et al. (2005) found that indices summarizing the spatial 

configuration of land quality are an important determinant of forest fragmentation. 

It was too costly to construct such measures for this study. However, if our nonspatial LCC variables, which are readily computed from NRI data, are significant 

predictors of forest fragmentation, models of forest fragmentation can be developed 

at lower cost. Overall, we expect a negative relationship between high-quality land 

and the fragmentation metrics because high-quality land tends to be allocated to 

intensive agricultural uses such as crops and pasture. We include dummy variables 

for LCC classes II through VIII (class I is the omitted category). Because class I is 

the highest quality land, we expect positive signs on the remaining categories. That 

is, increasing the share of land in lower quality classes raises the fragmentation 

metrics relative to class I lands.

To capture the variability of land quality within each county, a variable 

measuring the range in elevation is included. We conjecture that counties with a 

large range in elevation should have greater variability in land quality and, as a 

result, more fragmented forests. The elevation data were extracted from a global 

scale Digital Elevation Model in ArcGIS4 and calculated as the difference (in feet) 

between the maximum and minimum elevations within each county.

Average land-use transition probabilities were calculated for the counties in 

the study area from the econometric results in chapter 2. The probabilities are for 

the period 1992 to 1997 and for transitions on nonfederal land from agriculture to 

forest, forest to agriculture, and forest to urban. These probabilities incorporate 

the effects of land rents on land-use transitions involving forest land. Land rents, 

in turn, reflect the drivers of land-use change such as commodity price changes, 

population growth, and public infrastructure investment.5 We expect counties with 

high probabilities for transitions from agriculture to forest to have a higher proportion of core forest and forest parcels with like adjacencies. In this case, conversion 

of agricultural land to forest may join existing forest parcels, thereby increasing 

the value of the fragmentation indices. For the opposite reason, counties with high 

probabilities for transitions from forest to agriculture and urban uses should have 

more fragmented forests. 

4 We thank Scott Walker for providing these data.

5 Another alternative approach, which we leave for future investigation, would be to enter 

county land rents directly into the regression equation. This might reduce collinearity with 

some of the other variables in the model.
Linking Land-Use Projections and Forest Fragmentation Analysis

17

The transition probabilities reflect the influence of market forces on landuse change. Because public forests are typically managed for reasons other than 

maximizing financial returns (e.g., provision of wildlife habitat and recreation), the 

forest-to-agriculture and forest-to-urban transition probabilities are not applicable 

to these lands. In a small number of counties, all forests are publicly owned. We 

construct a dummy variable for these counties, denoted DPublic, and enter it in the 

model as follows,

β1DPublic + (1-DPublic )(β2PFA+ β3PFU) , (4)

where PFA and PFU are the forest to agriculture and forest to urban transition probabilities and β1, β2, β3

 are the corresponding coefficients. The influence of having 

only public forests is measured by β1 , which we expect to be positively signed. 

The effects of the transition probabilities are measured only for counties with some 

private forest land because (1-DPublic )(β2PFA+ β3PFU)=0 for counties with only 

public forests.

Finally, a variable measuring the share of wealthy households was included 

to test the relationship between income and the resulting lifestyle choices that 

may influence forest fragmentation. Higher incomes could increase the demand 

for large-lot housing amenities such as privacy and forested settings. Therefore, 

counties with a large share of higher income households would be associated with 

fragmented forests. The share of wealthy households is calculated as the percentage 

of households in a county with income three or more times the national median 

household income ($30,056 in 1989). The income data are from the U.S. Bureau of 

the Census.

We use standard multiple linear regression models to quantify the relationships 

between the explanatory variables and the two forest fragmentation measures. The 

dependent variables in our models are shares and, therefore, lie in the unit interval. 

Predictions from a model estimated with ordinary least squares, however, may fall 

outside the unit interval. We did not encounter this problem in projecting the fragmentation indices and, therefore, did not pursue alternative estimation approaches. 

White’s (1980) estimate of the covariance matrix was used. This provides consistent 

estimates of standard errors in the presence of unknown heteroskedasticity.

Results 

The estimation results for the core forest model are presented in table 5. The 

adjusted R-squared statistic indicates that the explanatory variables explain 
Research Paper PNW-RP-570

18

approximately 93 percent of the variation in the dependent variable. Among the 

land-use share variables, only the forest share is significantly related to the percentage of the county in core forest. As expected, the sign of the coefficient is positive. 

We find also, and as expected, a positive and significant relationship between core 

forest and shares of land in public uses. Many of the land quality variables are 

significantly different from zero and, as expected, positive. Higher shares of land 

in lower LCC classes increase the amount of core forest relative to the highest 

LCC class. The range in elevation and the share of wealthy households do not have 

significant effects on the core forest share. Among the transition probabilities, only 

the agriculture-to-forest transition probability has a significant effect. As expected, 

counties with a higher probability of agricultural land moving to forest have more 

core forests.

Table 5—Estimation results for the core forest model

Variable	 	 	 	 Coefficient	 Standard error	 	 t-value	 	 P-value

Intercept  -36.11**  16.38 -2.21 0.028

Share of crops 0.03  0.04 0.63 0.528

Share of pasture 0.24  0.16  1.47 0.142

Share of forest 0.89**  0.04 25.53 <0.001

Share of urban  -0.07  0.09 -0.75 0.454

Share of Conservation Reserve Program  -0.050.17 -0.32  0.752

Share of range 0.01  0.03  0.43 0.667

Share of federal forest land 0.84**  0.03 27.08 <0.001

Share of nonfederal public forest land 0.19**  0.09  2.13  0.034

Share of nonfederal land in LCC II 0.34*  0.19  1.82  0.069

Share of nonfederal land in LCC III 0.30*  0.16  1.82  0.069

Share of nonfederal land in LCC IV 0.35**  0.17  2.11  0.036

Share of nonfederal land in LCC V 0.21  0.20  1.01  0.311

Share of nonfederal land in LCC VI 0.36**  0.16  2.23  0.027

Share of nonfederal land in LCC VII 0.36**  0.16  2.21  0.028

Share of nonfederal land in LCC VIII 0.24  0.17  1.47  0.143

Per-county range of elevation  .001  .001  1.00  0.32

Agriculture-to-forest transition probability  27.89**  9.43  2.96  0.003

Only public forest  -2.05  2.81 -0.73  0.466

Forest-to-agriculture transition probability  76.25  295.12  0.26  0.796

Forest-to-urban transition probability  -33.92 75.72 -0.45  0.654

Share of wealthy households  .09  .35 .26  0.793

Adjusted R2 = 0.93, n = 372.

** P < 0.05.

* P < 0.10.

LCC = land capability class.
Linking Land-Use Projections and Forest Fragmentation Analysis

19

6 The earlier studies by Butler et al. (2004) and Alig et al. (2005) did not include a variable for 

elevation range.

The estimation results for the like adjacencies model are presented in table 6. 

The adjusted R-squared statistic for this model is 23 percent. Four of the coefficients on the land-use share variables are significantly different from zero at the 

10 percent level or lower. As expected, like adjacencies are increasing in the forest 

share and declining in the agricultural and urban shares. Unexpectedly, we found a 

positive and significant relationship with the pasture share. None of the coefficients 

on the public land or the land quality variables are significantly different from zero. 

However, the coefficient on the elevation range variable is significantly different 

from zero. The sign is positive, indicating that greater elevation range is associated 

with less fragmentation. We expected the opposite relationship.6 The agricultureto-forest and forest-to-urban transition probabilities had negative and significant effects on like adjacencies. Although the second relationship has the anticipated sign, 

the first is contrary to our expectations. Finally, the like adjacencies are increasing 

in the share of wealthy households. Again, the sign of this coefficient is opposite 

from what we expected.

Comparing the results for the models, we find that the coefficients on only two 

variables were significantly different from zero in both models. The share of land 

in forest is positively related to the core forest and like adjacency metrics. The 

agriculture-to-forest transition probability has a significant effect on both fragmentation measures, but the signs of the effects differ between the two models. It has a 

positive effect on core forest and a negative effect on like adjacencies.

Discussion 

The results of this analysis are mixed. The core forest model has a good fit and the 

coefficients of many explanatory variables are significant and have the expected 

signs. In contrast, the variables in the like adjacency model have relatively low explanatory power and many of the coefficients have unexpected signs. These results 

highlight the challenges inherent in estimating aggregate models of forest fragmentation. Forest fragmentation is the outcome of a spatial process. We have attempted 

to model fragmentation by using aggregate data that necessarily mask underlying 

spatial relationships. Moreover, we have used relatively large observational units 

(counties) in order to consider a large geographical area (11 Western States). Given 

our study area, it was infeasible to construct explanatory variables that summarize 

spatial patterns, such as the land-quality metrics used in Alig et al. (2005). Rather, 

Among the land-use 

share variables, only 

the forest share is 

significantly related to 

the percentage of the 

county in core forest. 

As expected, the sign 

of the coefficient is 

positive. We find also, 

and as expected, a 

positive and significant 

relationship between 

core forest and shares 

of land in public uses. 
Research Paper PNW-RP-570

20

we relied on aspatial measures of land use, ownership, land quality, and land-use 

transition probabilities.

The share of land in forest was found to have a positive and significant effect on 

the percentage of the landscape in core forest and the percentage of like adjacencies 

for forest. This finding is related to a concept in landscape ecology referred to as 

the percolation threshold (Grimmett 1989). In the context of forest land, the idea is 

that once forests occupy a critical share of a landscape (approximately 60 percent), 

the number of spatially isolated patches drops at a fast rate with the addition of new 

forests. Thus, we find that an increase in the forest share, all else equal, increases 

both the fragmentation indices.7

7 The foregoing discussion suggests a nonlinear relationship between the fragmentation 

indices and the forest share. We estimated models that included the square of the forest share 

and found negative and significant coefficients on this variable. Otherwise, the results were 

similar.

Table 6—Estimation results for the like adjacency model

Variable	 	 	 	 Coefficient	 Standard error	 	 t-value	 	 P-value

Intercept 113.06**  14.62 7.73 <0.001

Share of crops -0.12* 0.07 1.84  0.066

Share of pasture 0.26* 0.15 1.67  0.096

Share of forest 0.04** 0.01 2.88  0.004

Share of urban -0.18** 0.04 -4.15 <0.001

Share of Conservation Reserve Program -0.28 0.28 -0.98  0.329

Share of range 0.004  0.01 0.37  0.71

Share of federal forest land 0.01  0.01 0.79  0.431

Share of nonfederal public forest land 0.05 0.04 1.33  0.185

Share of nonfederal land in LCC II -0.16 0.16 -1.00 0.319

Share of nonfederal land in LCC III -0.10 0.15 -0.66 0.507

Share of nonfederal land in LCC IV -0.08 0.14 -0.55 0.582

Share of nonfederal land in LCC V -0.02 0.15 -0.12 0.904

Share of nonfederal land in LCC VI -0.15 0.14 -1.03 0.303

Share of nonfederal land in LCC VII -0.09 0.14 -0.65 0.517

Share of nonfederal land in LCC VIII -0.15 0.14 -1.06 0.291

Per-county range of elevation 0.002** 0.001 3.47 <0.001

Agriculture-to-forest transition probability -16.50** 8.33 -1.98 0.048

Only public forest -5.24 4.25 -1.23 0.218

Forest-to-agriculture transition probability -714.68 577.65 -1.24 0.217

Forest-to-urban transition probability -115.41*  62.82 -1.84 0.067

Share of wealthy households 0.21* 0.11 1.81 0.072

Adjusted R2 = 0.23, n = 372.

* P < 0.05.

** P < 0.10.

LCC = land capability class.
Linking Land-Use Projections and Forest Fragmentation Analysis

21

Other variables also have significant effects on forest fragmentation. In the core 

forest model, these include the public ownership and land-quality variables and the 

agriculture-to-forest transition probability. In the like adjacencies model, the crop 

and urban shares and the forest-to-urban transition probability had negative and significant effects. Three variables (pasture share, elevation range, and agriculture-toforest transition probability) had significant effects but coefficients with unexpected 

signs. There are plausible explanations for the positive effect of elevation range 

and the negative effect of the agriculture-to-forest transition probability. Counties 

with large elevation ranges may have high mountains. In this case, agricultural and 

urban uses may be infeasible owing to steep slopes or prohibited by statute and, 

thus, forests may be less fragmented. Transitions from agriculture to forest may 

create isolated forest parcels, which could lower the like adjacencies variables. 

The pasture share may proxy for county characteristics in a way that is difficult to 

identify. This illustrates an inherent problem with aggregate data models and with 

our use of relatively large observational units. With smaller units, the predictive 

power of aggregate forest fragmentation models increases (Butler et al. 2004).

Our use of data on Western counties gives rise to other challenges with developing aggregate models of forest fragmentation. According to the data on like 

adjacencies, forest fragmentation is not a pervasive feature of Western forests. For 

approximately 69 percent of the counties, the like adjacencies measure exceeds 

99 percent. For 88 percent, the measure exceeds 95 percent. This indicates that a 

large majority of the forest parcels in our study area are surrounded by other forest 

parcels (i.e., are core forest). The lack of variation in the like adjacencies variable 

makes it difficult to find significant explanatory variables. The fact that most forest 

parcels are core forest implies that the percentage of a county in core forest will 

closely correspond to the total share of the county in forest. Thus, our model is 

similar to a forest land shares model (e.g., Ahn et al. 2000) and may not provide 

many insights into the determinants of forest fragmentation. 
Research Paper PNW-RP-570

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Chapter 4: Spatially Explicit 

Fragmentation Analysis

In this chapter, we predict changes in forest fragmentation by using spatially 

explicit simulations. This approach differs markedly from the analysis in chapter 3, 

which uses an aggregate model of forest fragmentation. The analysis in this chapter 

uses the econometrically estimated transition probabilities, discussed in chapter 2, 

in a landscape simulation employing geographic information system (GIS) data on 

land use and parcel characteristics. We summarize the spatial pattern of the simulated landscapes by using the same forest fragmentation indices used in the aggregate model. This allows us to compare predictions of forest fragmentation measures 

produced with the two approaches. This comparison is the subject of chapter 4.

Methods

We conducted the analysis of forest fragmentation in Polk County, Oregon, by 

using the methods developed in Lewis (2005). Polk County is located in the Willamette Valley west of Salem, Oregon. We analyzed a 304,692-acre section of 

the county.1 According to the Oregon Rural Lands Database (ORLD) (Oregon 

Department of Land Conservation and Development, n.d.), 41.5 percent of the 

land in our study area was in forest in 1998, 55.2 percent was in agricultural uses, 

2.5 percent was in urban uses, and 0.8 percent was in other uses (table 7). The 

land-use transition probabilities for Polk County were extracted from the land-use 

projection model discussed in chapter 2.2 The probabilities account for endogenous 

price feedbacks and, thus, are the same ones used (for Polk County) to produce the 

projections in chapter 2. There is very little land in the rangeland and Conservation 

Reserve Program (CRP) categories in Polk County. As well, the GIS data we used 

in the simulations do not identify pasture as a separate category. Therefore, we 

combined these uses with cropland and created a new category for all agricultural 

land. The transition probabilities indicate the probability that land moves from one 

 1 The total land area of Polk County is 474,296 acres. We analyzed a portion of the county 

because our GIS data are available in U.S. Geological Survey quads, and we considered only 

those quads contained entirely in the county. 

 2 We used the model parameters estimated in the national econometric analysis and the 

independent variables for Polk County to compute the transition probabilities. Separate 

probabilities are obtained for starting and ending use and land quality class, corresponding to 

the LQ variable used in the econometric analysis (see page 4). Given the national scope of the 

econometric analysis, we cannot account for all of the factors that influence land-use decisions 

in Polk County, including localized land-use regulations. However, our purpose in this section 

is to compare projections using different methods. In this regard, it is most important that we 

model a consistent set of land-use determinants. 

We summarize the 

spatial pattern of the 

simulated landscapes 

by using the same 

forest fragmentation 

indices used in the 

aggregate model. 

This allows us to 

compare predictions 

of forest fragmentation 

measures produced 

with the two 

approaches.
Linking Land-Use Projections and Forest Fragmentation Analysis

23

Table 7­—Simulation results for Polk County, Oregon

Categories Forest share Core forest share Like adjacencies

Initial values (1998)

Forest 41.5 35.3 94.3

Agriculture 55.2 48.3 95.7

Urban 2.5  2.0 93.6

Mean simulated values (2022)

Forest 42.6 32.6 91.1

Agriculture 39.4 28.9 90.3

Urban 17.3  9.8 82.7

Note: 0.8 percent of the land is in uses other than forest, agriculture, and urban in 1998 and 2022. 

use to another over the period 1997 to 2002. These 5-year probabilities are reported 

in the top half of table 8. The probability that high-quality (class 1) agricultural land 

remains in agriculture is 91.7 percent, compared to 94.8 percent for class 2 agricultural land. The probability that agricultural land transitions to forest is 4.3 percent 

for class 1 land and 2.1 percent for class 2 land. We would expect class 1 agricultural land to have a lower probability of converting to forest than class 2 land. We 

find that class 1 land is more likely to transition to forest because of the relatively 

high probability that class 1 pasture, which is included in the agriculture category, 

transitions to forest. The probabilities that class 1 and 2 agricultural land transitions 

to urban use are 4.1 percent and 3.1 percent, respectively. The transition probabilities for class 3 and 4 agricultural land are unimportant for our analysis because 

little agricultural land is found in these categories. The results for land initially in 

forest reveal very small probabilities for forest-to-agriculture conversions. Forest 

land has the highest probabilities of remaining in forest (between 94.6 percent and 

97.7 percent) and converting to urban use (between 1.8 percent and 5.2 percent). 

Finally, we do not observe land transitioning from urban to other uses. Therefore, 

the urban-to-urban transition probability is assumed to equal one.

The simulations are conducted over the 25-year period, 1997 to 2022. Thus, we 

are ultimately interested in the likelihood that a parcel beginning the simulation 

in one use moves into the other uses by the end of the simulation. Assuming that 

the 5-year transition probabilities apply in each of the intervening periods, we can 

compute the transition probabilities for the 25-year period by iterative multiplication of the transition probability matrices for each land quality class. The results 

are presented in the bottom half of table 8. The results show, for example, that class 

1 land in agriculture in 1997 has only a 64.8 percent probability of still being in 
Research Paper PNW-RP-570

24

agriculture by 2022 and 16.0 percent and 19.1 percent probabilities of being in forest 

and urban, respectively. The probability that forest land remains forested after 25 

years ranges from 75.7 percent to 89.6 percent.

Landscape simulations were conducted by using GIS data for Polk County. 

We obtained spatial data layers from the ORLD that categorize the landscape by 

agriculture, forest, and urban use and land quality classes 1, 2, 3, and 4.3 By overlaying these data, we identified unique parcels that match the transition probabilities. For example, a given parcel may be identified as class 2 land that is initially 

in agriculture. In this case, we assume the parcel has a 76.6 percent probability of 

remaining in agriculture over the 25-year horizon and 8.8 percent and 14.6 percent 

Table 8—Land-use transition probabilities for Polk County, Oregon

 Ending use

Land quality Agriculture Forest Urban

 

Five-year transition probability (1997-2002)

Initial use is agriculture

1 .917  .043  .041

2 .948  .021  .031

3 .863  .099  .038

4 .863  .099  .038

Initial use is forest

1 .002  .946  .052

2 .002  .954  .043

3 .003  .975  .021

4 .005  .977  .018

 Twenty-five-year transition probabilities (1997-2022)

Initial use is agriculture

1 .648  .160 .191

2 .766  .088 .146

3 .482  .356 .162

4 .483  .358 .159

Initial use is forest

1 .009  .757 .234

2 .010  .792 .199

3 .011  .885 .103

4 .018  .896 .086

3 A third data layer on land ownership is used to eliminate public lands, as the transition probabilities primarily represent land-use changes on private land.
Linking Land-Use Projections and Forest Fragmentation Analysis

25

probabilities of converting to forest and urban use, respectively (table 8). The 

landscape simulations are conducted by using a random number generator. The 

number generator randomly selects a value from the uniform distribution defined 

on the unit interval. For the parcel discussed above, if the selected value is below 

0.766, the parcel remains in agriculture, if it falls between 0.766 and 0.854 the 

parcel is converted to forest, and if it is between 0.854 and 1.0 the parcel converts to 

urban. For every parcel on the landscape, we match the land quality and initial land 

use of the parcel to the relevant transition probabilities and repeat the simulation 

procedure. The result is a simulated landscape that is consistent with the underlying 

transition probabilities assumed to govern land-use change.4

Given the probabilistic nature of the transition rules, there are a large number 

of landscapes that are consistent with the rules. Generating all of these landscapes5

would be time consuming and produce results that are difficult to interpret. We 

handled this challenge in two steps. First, we summarized the spatial pattern of 

forest land by using fragmentation metrics computed with the Fragstat software. 

The use of fragmentation metrics reduces the number of unique outcomes because 

many different landscapes will produce the same value of a given fragmentation 

index. The fragmentation metrics include the percentage of the landscape by use, 

the percentage of the landscape in core forest (defined as a forest patch more than 

100 feet from the nearest nonforest edge), and the percentage of like adjacencies for 

forest. The latter metrics are computed in the same way as those used in the aggregate fragmentation analysis. Second, we ran 500 simulations in order to characterize the range of possible outcomes.6

 In particular, we computed empirical frequency 

distributions defined over values of the fragmentation indices.

Results

Simulation results are presented in table 7 and figures 2 through 4. We project an 

increase in forest area from 41.5 percent of the land base to 42.6 percent, on average, by 2022. Figure 2 shows that the distribution of the forest share is roughly 

symmetrical, with values ranging from approximately 40 percent to 44.5 percent. 

The share of land in urban use is projected to increase substantially, from 2.5 

percent to 17.3 percent, while the agricultural land share declines from 55.2 percent 

4 The probabilities are from an econometric analysis employing data from a random sample of 

plots. This prevents us from accounting for factors such as spatial correlation among land-use 

decisions and parcelization. 

5 If there are X parcels and Y uses, then there are YX possible landscape configurations.

6 Extensive diagnostics, discussed in Lewis (2005), were done to determine the appropriate 

number of simulations.
Research Paper PNW-RP-570

26

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

39.9540.3340.71

41.09

41.47

41.8442.2242.6042.9843.36

43.73

44.1144.49

Percentage of the landscape in forest

Frequency (percent)

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

29.97

30.34

30.72

31.09

31.47

31.84

32.21

32.59

32.96

33.34

33.71

34.08

34.46

Percentage of the landscape in core forest

Frequency (percent)

Figure 3—The percentage of the landscape in the core forest from simulation results for Polk County, Oregon, 2022.

Figure 2—The percentage of the landscape in forest from simulation results for Polk County, Oregon, 2022.
Linking Land-Use Projections and Forest Fragmentation Analysis

27

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

90.4890.57

90.66

90.7490.83

90.92

91.0191.09

91.18

91.2791.3691.44

91.53

Percentage of the like adjacencies for forest parcels

Frequency (percent)

Figure 4—The percentage of the like adjacencies for forest from simulation results for Polk County, Oregon, 2002.

to 39.4 percent. Despite the increase in forest area, we project the percentage of the 

landscape in core forest to decline from 35.3 percent to 32.6 percent, on average, 

with values ranging from approximately 30.0 percent to 34.5 percent (fig. 3). Likewise, the percentage of like adjacencies for forest is projected to decline from 94.3 

percent to 91.1 percent, on average, with values ranging from about 90.5 percent to 

91.5 percent (fig. 4).

These results show that increases in forest area need not reduce the degree of 

forest fragmentation.7 The forest share increases by 1.1 percentage points, but we 

find that the expected share of the landscape in core forest declines by 2.7 percentage points, suggesting that some of the new forest parcels are relatively small or 

isolated from existing forest patches. Another possibility is that fragmentation 

results from the conversion of existing forest land to urban use, which increases by 

almost 15 percentage points over the projection period. Moreover, the statistics in 

table 7 reveal that urban land in Polk County becomes more dispersed over time. 

Using the same definition of a core parcel as used for forest land, we computed 

 7 Our simulation results depend to some degree on initial landscape conditions. See Lewis and 

Plantinga (in press) for a treatment of this issue.

These results show 

that increases in forest 

area need not reduce 

the degree of forest 

fragmentation.
Research Paper PNW-RP-570

28

the share of core urban land. In 1998, 80 percent of the urban land was in core (2 

percent divided by 2.5 percent), but by 2022, this share has dropped to 57 percent. 

Similarly, the percentage of like adjacencies for urban land was 93.6 percent in 

1998, declining to 82.7 percent by 2022. The increase in urban area, coupled with 

more dispersed urban land, can account for the increase in forest fragmentation. A 

similar explanation can be offered for the change in the percentage of like adjacencies for forest, which is projected to decline by 3.2 percentage points. 
Linking Land-Use Projections and Forest Fragmentation Analysis

29

Chapter 5: Linkage of Land-Use Projections 

and Fragmentation Models

In this chapter, we link the land-use projections and the aggregate fragmentation 

analysis. The shares of land in crops, pasture, forest, urban, Conservation Reserve 

Program, and range are included as explanatory variables in the fragmentation 

models. Thus, we can estimate how the fragmentation metrics will change as 

the shares of land in different uses change. We use projections of county landuse shares to estimate the share of land in core forest and the percentage of like 

adjacencies for forest in 2030. As well, we project these indices for Polk County, 

Oregon, to the year 2022 to compare the results from the aggregate and spatially 

explicit analyses.

County Projections of Fragmentation Metrics 

Using observed and projected values of the county land-use shares, we used the 

estimated parameters in tables 5 and 6 to compute fragmentation metrics for 1997 

and 2030. We present the results in two ways. First, we computed percentage 

changes (1997 to 2030) in average state-level values. The state averages are formed 

by averaging the predicted values over counties within each state. The core forest 

measure is projected to increase in 8 of the 11 states (table 9). Declines are found in 

Table 9—Projected changes in the core forest and like adjacency metrics 

for Western States, 1997 to 2003

State Core forest share Like adjacencies for forest

 

 Percentage change, 1997-2030

Arizona  12.3 0.2

California  -4.4  -0.8

Colorado 3.2 0.2

Idaho 6.4 1.1

Montana  5.9 0.0

Nevada 7.2 0.0

New Mexico  22.8 0.9

Oregon -2.5-0.8

Utah 2.9 -0.2

Washington -4.0 -0.2

Wyoming 11.6 -0.1

Note: To arrive at these figures, we first averaged the county-level measures to obtain a state average for 1997 

and 2030. Then, we computed the percentage change in the state average.

The core forest 

measure is projected 

to increase in 8 of the 

11 states. Declines 

are found in the 

three Pacific States 

(California, Oregon, 

and Washington) 

and relatively large 

increases are found 

for Arizona and New 

Mexico. 
Research Paper PNW-RP-570

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the three Pacific States (California, Oregon, and Washington) and relatively large 

increases are found for Arizona and New Mexico. To some degree, the changes in 

the core forest metric correspond to the projected changes in the share of land in 

forest. The three Pacific States have negative or small positive projected changes 

in the forest share. Relatively large percentage increases in forest are projected for 

Arizona and New Mexico. For the like adjacency measure, small changes in the 

state averages (between -0.8 percent and 1.1 percent) are projected. Increases are 

projected in four states, with the largest percentage gains in Idaho and New Mexico 

(table 9). As indicated in table 6, increases in crop and urban shares reduce the 

like adjacency measure and increases in forest and pasture increase it. Differences 

among the state-level changes in like adjacencies are due to the specific patterns of 

land-use change. 

The second way to present the results is with maps revealing changes for each 

county (figs. 5 and 6). For the core forest metric, declines in the metric for counties 

in western Oregon and Washington are apparent. The increases in Arizona and 

New Mexico are not as readily seen because of the way in which the categories 

are defined. For the like adjacency metric, increases are apparent for counties in 

California, Nevada, Oregon, and Washington, and declines can be seen in Arizona, 

Montana, Wyoming, and New Mexico. 

Comparison of Fragmentation Projections by Using 

Spatially Explicit and Aggregate Methods

The spatially explicit and aggregate approaches to projecting fragmentation metrics 

rely on the same transition probabilities derived from econometric analysis of 

National Resources Inventory data (chapter 2). Moreover, the aggregate model of 

forest fragmentation is estimated with observations on western counties, including 

Polk County, Oregon. Therefore, we can compare the projection results for Polk 

County generated with the two approaches. But, first, we must make some adjustments to the fragmentation metrics. Public forest lands are included in the countylevel measures used in chapter 2, but excluded from the measures used in chapter 4. 

If we assume that all public forests are core forest and have 100 percent like adjacencies, then the initial percentage of all private lands in Polk County in core forest 

is 42.0 percent and the initial percentage of like adjacencies for these forests is 96.6 

percent.8 These figures differ from those computed for the 304,692-acre section of 

 8 The core forest share of all land in Polk County is 53.7 percent. We subtract the public forest 

land share (11.7 percent) to obtain 42 percent. The like adjacency measure for all forest is 97.3 

percent. Public forests represent 19.6 percent of all forests and so the like adjacency measure 

for private lands is given by (97.3 – 19.6)/80.4 = 96.6 percent.
Linking Land-Use Projections and Forest Fragmentation Analysis

31

Figure 5—The share of the landscape in core forest in Western U.S. counties, 1997 and 2030.
Research Paper PNW-RP-570

32

Figure 6—The percentage of like adjacencies for forest in Western U.S. counties, 1997 and 2030. 
Linking Land-Use Projections and Forest Fragmentation Analysis

33

Polk County analyzed above. As noted in chapter 4, the initial core forest and like 

adjacency measures are 35.3 percent and 94.3 percent, respectively.9

Because the initial values differ, we compare percentage changes in the fragmentation metrics. Based on the aggregate model, we project that the core forest 

share of private lands in Polk County will decline by 4.0 percent by 2022. The 

corresponding figure from the spatially explicit analysis ranges from 2.4 to 15.1 

percent, with a mean value of 7.6 percent. Thus, the prediction from the aggregate 

model falls within the range of outcomes generated with the spatially explicit 

analysis (fig. 3). However, the predicted 4.0 percent decline is an “outlier” in the 

sense that it is found in the tail of the distribution. Ninety-five percent of the distribution is found between 4.5 percent and 11.4 percent. Using the aggregate model, 

we project only a 0.1 percent decline in the like adjacency measure for all private 

forests in Polk County by 2022. The spatially explicit analysis yields declines in the 

range of 3.0 to 4.0 percent and, thus, we find that the two methods produce considerably different results. Nevertheless, given the differences in the methods used, it 

is noteworthy that the projected changes in the fragmentation metrics have the same 

sign and are the same order of magnitude in percentage terms.

9 There may simply be differences in the fragmentation of forests within and outside the section of the county considered. 
Research Paper PNW-RP-570

34

Chapter 6: Summary and Conclusions

We use an econometric model of private land-use decisions to project land use to 

2030 for each county in the continental United States. We assume that net financial 

returns to urban, pasture, and range remain constant through time, but allow crop 

and forest returns to adjust endogenously to the projected changes in land use. 

On a national scale, forest area is projected to increase between 1997 and 2030, 

representing a change overall between 0.1 and 0.2 percent per year. Urban area is 

projected to increase by 68 million acres over this period, with annual increases 

ranging from 1.6 to 2.7 percent. Cropland, pasture, rangeland, and Conservation 

Reserve Program land is projected to decline by 2030.

The national projections were disaggregated by Resources Planning Act (RPA) 

regions. Increases in forest area are projected for the Corn Belt, Mountain, Pacific 

Northwest East, Northern Plains, and South Plains. The largest increases occur in 

the Mountain and South Plains regions (10.3 and 8.0 million acres, respectively). 

Declines are found for the other regions, with the largest occurring in the Southeast 

and Northeast (3.6 and 3.0 million acres, respectively). The finding of forest area 

increases in predominately agricultural regions was unexpected. However, the 

National Resources Inventory data for the period 1992 to 1997, which were used in 

the estimation of the econometric model, reveal significant shifts of rangeland to 

forest in the Mountain region and pasture to forest shifts in the Corn Belt and South 

Central regions. Additional research is warranted along with augmentation of landuse data pertaining to transitions among major land uses. First, regional econometric models can be estimated that might better represent relationships specific to 

the region. Second, the land-use projection model can be modified to account for 

endogenous price responses to changes in pasture and rangeland. This would likely 

reduce transitions into forest by raising the opportunity costs of converting pasture 

and rangeland. 

We conducted an analysis of forest fragmentation in the Western United States. 

One of the primary goals was to determine if county-level forest fragmentation 

metrics can be modeled in terms of aggregate variables constructed from readily 

available data, in contrast to using spatial data that are more costly to obtain. For 

the core forest model, many of the proposed explanatory variables were significantly different from zero and have coefficient signs consistent with expectations. We 

found that the share of the county in core forest increases with the shares of land in 

private, federal, and other public forest. This finding may reflect the concept from 

landscape ecology of a percolation threshold. Once the area occupied by forest is 

sufficiently high, patches become connected and fragmentation is reduced. We also 

We found that the 

share of the county in 

core forest increases 

with the shares of land 

in private, federal, and 

other public forest. 

This finding may reflect 

the concept from 

landscape ecology of a 

percolation threshold. 

Once the area occupied 

by forest is sufficiently 

high, patches 

become connected 

and fragmentation is 

reduced.
Linking Land-Use Projections and Forest Fragmentation Analysis

35

found that the core forest percentage increased with lower quality land and a higher 

agriculture-to-forest transition probability.

The results for the like adjacency model are weaker. As expected, the like 

adjacency metric was positively related to the forest share and negatively related 

to the agricultural and urban shares and the forest-to-urban transition probability. 

However, we found positive effects from the pasture share, greater elevation range, 

and the share of wealthy households and a negative effect from the agricultureto-forest transition probability. The last four results are contrary to expectations. 

One of the challenges with modeling like adjacencies is that this variable exhibits 

relatively little variation in the Western United States. For approximately 69 percent 

of the counties, the like adjacencies measure exceeded 99 percent, indicating very 

little forest fragmentation (at least at the scale considered) in the majority of counties. This is an important empirical finding in its own right and motivates the search 

for alternative representations of forest fragmentation that may confirm this finding. 

Also, it may be of interest to compute the like adjacencies measure for other U.S. 

regions (e.g., the Midwest and Northeast) where it is expected to be lower.

Another challenge—common to both fragmentation models—is how to appropriately model an inherently spatial phenomenon by using aggregate variables. 

A promising approach is to include explanatory variables that summarize spatial 

pattern within the unit of observation (counties, in our case). Alig et al. (2005) 

found that indices summarizing the spatial configuration of land quality were a 

significant determinant of forest fragmentation. One might also use this approach 

to represent the spatial configuration of urban land, which is likely to be a factor in 

determining forest fragmentation but is unlikely to be correlated with traditional 

measures of land quality. Another strategy is to reduce the geographical scale of the 

observations (e.g., from counties to census tracts). However, this increases the cost 

of the analysis.

We conducted a spatially detailed analysis of forest fragmentation in Polk 

County, Oregon. This approach has much greater data requirements, and considerable computing resources are needed to conduct land-use simulations. One of the 

interesting findings is that forests in Polk County are projected to become more 

fragmented even though forest area increases. The amount of core forest, for 

example, will not necessarily increase if new forest parcels are isolated from existing or other new forest parcels. Moreover, there may be an overall decline in core 

forest if enough existing core forest parcels are converted to nonforest uses such as 

urban. This finding for Polk County is consistent with the aggregate fragmentation 

analysis. Although the county-level fragmentation metrics depended positively on 
Research Paper PNW-RP-570

36

shares of land in forest, other variables, such as urban shares, were found to have 

negative effects.

We linked the land-use projections and the analyses of forest fragmentation. 

County land-use shares were included in the aggregate forest fragmentation models, 

allowing us to determine how projected changes in land use would affect the fragmentation metrics. We found increases in the average county shares of core forest 

in 8 of the 11 Western States, with the largest percentage changes in New Mexico, 

Arizona, and Wyoming. The average like adjacency measure increased in six of the 

states. Declines were found in all of the Pacific Coast States. One of the valuable 

features of this approach is that we can examine changes in the spatial distribution 

of the fragmentation metrics by using geographic information system-based maps.

We compared the results of the aggregate and spatially detailed fragmentation analyses. In each case, we projected the fragmentation indices to 2022. Both 

approaches rely on the same land-use transition probabilities and measures of 

forest fragmentation, and evaluate conditions in Polk County, Oregon. We found 

considerable differences in the results produced with the two methods, especially in 

the case of the like adjacency metric. This finding may indicate that the aggregate 

data method, which does not account explicitly for spatial processes, is invalid. It 

should be noted, however, that we were unable to design a perfect test. Owing to the 

nature of the available data, the spatially detailed analysis considered only a portion 

of Polk County, whereas the aggregate model included the entire county. Additional 

research could evaluate aggregate fragmentation models estimated at a finer scale, 

such as census tracts (e.g., Alig et al. 2005, Butler et al. 2004). This would provide 

a closer correspondence between the geographical areas evaluated under the two 

approaches.

Forest fragmentation is an important cause of biodiversity loss in terrestrial 

ecosystems. We have developed a framework for modeling forest fragmentation 

at large scales and projecting changes in fragmentation under different economic 

and policy scenarios. Our analysis directly supports the Sustainable Wood Production Initiative and the RPA assessments, and expands efforts to define and develop 

protocols for sustainable forest management. Moreover, our approach offers promise for analyzing emerging policies designed to reduce forest fragmentation. Our 

econometric model quantifies the relationship between net returns to alternative 

land uses and land-use transitions. As such, the model can be used to simulate the 

effects of market-based policies, such as subsidies, encouraging conversion of land 

to forest or retention of land in forest. The effects on landscape-level indicators of 

forest fragmentation can then be measured by using the procedure discussed in 

Forest fragmentation 

is an important 

cause of biodiversity 

loss in terrestrial 

ecosystems. We have 

developed a framework 

for modeling forest 

fragmentation at 

large scales and 

projecting changes in 

fragmentation under 

different economic and 

policy scenarios.
Linking Land-Use Projections and Forest Fragmentation Analysis

37

chapter 4. Lewis and Plantinga (in press) developed an application of this approach 

to South Carolina. Using the models developed here, a national-scale policy analysis could be conducted.

Metric Equivalents

1 foot = 0.3048 meters

1 yard = 0.9144 meters

1 acre = 0.4047 hectares

Acknowledgments

The authors thank Brett Butler, Ruben Lubowski, Susan Stewart, and Eric White 

for helpful comments and suggestions.

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Appendix—Variable Measurement and Data Sources

Land Use

The land-use data used to estimate the econometric model are from the USDA National Resources Inventory (NRI). “Croplands” include row and close-grown crops, 

fallow, pasture and haylands in rotation with crops, permanent haylands, vineyards, 

orchards, and nurseries. “Pasture” includes land managed for introduced forage for 

livestock grazing. “Range” includes land under native or introduced forage suitable 

for grazing which, unlike pasture, receives only limited management. “Forests” are 

areas at least 1 acre in size and 100 feet in width that are at least 10 percent stocked 

with trees with the potential to reach 13 feet at maturity. This translates to a canopy 

cover of at least 25 percent. “Urban lands” include areas in residential, industrial, 

commercial, or institutional uses. Parcels below 10 acres, such as small parks and 

transport facilities, are also classed as urban if they are completely surrounded by 

urban lands. This definition excludes roads and other lands used for transportation 

in nonmetropolitan areas, as these are separately identified by the NRI. 

Net Returns for Rural Land Uses

Estimated annual cropland net returns per acre consist of two components: a 

weighted average of the net returns for 21 major crops and total federal farm program payments, excluding payments from the Conservation and Wetlands Reserve 

Programs.We used state-level marketing-year-average prices and county-level 

yields from the National Agricultural Statistics Service (NASS) for 21 major crops. 

Cash costs at the state and regional levels, respectively, are from the Census of 

Agriculture and Economic Research Service (ERS). County acreages from NASS 

and the Census of Agriculture provided weights. County-level estimates of total 

federal direct farm program payments per acre are from the Census of Agriculture 

and include receipts from deficiency payments, support price payments, indemnity 

programs, disaster payments, and soil and water conservation projects.

Annual net returns per acre for pasture were estimated by using yields from the 

National Cooperative Soil Survey (NCSS). We multiplied yields by the state price 

for “other hay” for NASS and deducted costs for hay and other field crops from the 

Census of Agriculture.

Annual net returns per acre for rangeland were estimated with forage yields 

from NCSS multiplied by state-level per head grazing rates from the ERS database 

on cash rents. 

Annual net returns per acre from forestry were constructed by annualizing at 

a 5 percent interest rate the estimated net present value of a weighted average of 
Linking Land-Use Projections and Forest Fragmentation Analysis

41

sawtimber revenues from different forest types. State-level stumpage prices were 

gathered from state and federal agencies and private data services. Regional timber 

yields for different forest types were obtained from Richard Birdsey of the USDA 

Forest Service. Regional replanting and management costs were derived from 

Moulton and Richards (1990). An infinite stream of timber revenues for each forest 

type was estimated by using the optimal rotation age from the Faustmann formula. 

County acreage and sawtimber output data from the Forest Inventory and Analysis 

and Timber Product Output surveys of the U.S. Forest Service provided weights for 

averaging across individual forest types and species, respectively.

Urban Net Returns

Annual urban net returns were estimated as the median value of a recently developed one-acre parcel used for a single-family home, less the value of structures, 

annualized at a 5 percent interest rate. Median county-level prices for single-family 

homes were constructed from the Census of Population and Housing Public Use 

Microdata Samples and the Office of Federal Housing Enterprise Oversight House 

Price Index. Regional data on lot sizes and values of land relative to structures 

were obtained from the Characteristics of New Housing Reports (C-25 series) and 

the Survey of Construction microdata from the Census Bureau. 

Pacific Northwest Research Station

Web site http://www.fs.fed.us/pnw

Telephone (503) 808-2592

Publication requests (503) 808-2138

FAX (503) 808-2130

E-mail pnw_pnwpubs@fs.fed.us

Mailing address Publications Distribution

	 	 Pacific Northwest Research Station

 P.O. Box 3890

	 	 Portland, OR 97208-3890
United States Department of Agriculture

Forest Service

Pacific northwest research station

PNW-RP-570

February 2007