|The primary objective of this study was to integrate biological and economic models in an optimizing framework to address economic issues related to efficiency. The resulting model was used to estimate the productive capacity for three outputs (timber, Great Horned Owls, and common porcupines) on a forested landscape over a period of time. The wildlife species were selected to represent competing conservation objectives; their habitat needs are different. The productive capacity solutions show maximum possible combinations of the outputs, ignoring landowner types and objectives. Current management under existing landownership was evaluated by simulating different landowner objectives and constraints. They were compared to the productive capacity solutions. This research builds upon the growing body of research that attempts to demonstrate tradeoffs between conservation and financial land use objectives.
The project activities were to:
· Develop a prototype model of single species-the northern flying squirrel (Glaucomys sabrinus)-on 10,000-hectare (ha) landscape in the Oregon Cascade Range (Calkin, in press).
· Develop population equations for two species, the Great Horned Owl (Bubo virginianus), and the population size of the common porcupine (Erethizon dorsatum) (Nalle, 2001).
· Develop an optimization model and estimate the production possibility frontier on 1.7 million ha landscape in the Oregon Cascade Range and simulate a prospective future forest management in study area (Nalle, 2001).
The full study area was a 1.7 million ha forested landscape in the Oregon Cascade Range. Current management is polarized; roughly 50 percent of the area is managed for timber production (private lands) and the other 50 percent is solely used for natural resource protection (public lands). We modeled three outputs from this landscape: (1) the present value of timber production; (2) the population size of the Great Horned Owl; and (3) the population size of the common porcupine. These species were selected because of their negligible predator-prey interaction, expected dependence on different types of spatial forest age structure, and sufficient knowledge for population modeling.
Wildlife responses to landscape change were measured with a spatially-explicit, individually-based species simulator model called PATCH (Schumaker, 1998). PATCH uses species life history characteristics, habitat preferences, and movement behavior to stochastically simulate individual animals as they move about a landscape, breed, and die. A proxy for PATCH that quickly predicted populations as a function of habitat attributes was used in the optimization. There were three steps involved in using PATCH: (1) acquire data for habitat preferences and life history parameters required to model a species; (2) generate the time-series of habitat quality maps resulting from land management activities for input into PATCH; and (3) develop a fast proxy that is highly correlated to PATCH to use in the optimization model.
Life History and Habitat Preference Data. Basic habitat suitability data for each of the two species were habitat maps of the current landscape with a habitat score assigned to each management unit. These were developed by expert opinion from a team of wildlife biologists1.
Habitat Maps. To evaluate the effect of timber harvest and forest aging on habitat quality, it was necessary to determine the relation between habitat scores and the vegetative cover on the landscape. To accomplish this, the following regression model was estimated for each of the two species, s = 1, 2:
|where:||Hsj = habitat score for species s in unit j|
| ||Cjk = area of conifer forest in age class k in unit j|
| ||Rmj = set of units in ring m about unit j|
The ring structure was constructed to capture the spatial influence of habitat in neighboring areas on the ability of unit j to support each species. It was assumed that habitat quality within a site was a function of that site's vegetative cover, as well as the vegetative cover in nearby areas. Data for the regression were habitat scores and vegetative cover from a remotely-sensed image of the landscape in 1995 (Pacific Northwest Ecosystem Research Consortium Web Site). Regression coefficients are reported in (Nalle, 2001). This equation predicted 76 percent (R2 = 0.76) of the variation in owl habitat scores and 88 percent of the variation in porcupine scores. Residuals for each unit were retained and used in the computation of habitat scores on a changing landscape because these captured unexplained variation that the biologists considered, but for which no quantitative data were available.
The Proxy. The proxy for PATCH quickly estimates population sizes for each species that would be found from simulation. The optimization model used the proxy to identify a set of solutions likely to be on or near the Productin Possiblity Frontier (PPF). The following regression was performed for each of the two species in each of the 10 decades:
|where:||k = 1, ..., 7, the number of forest age classes|
| ||pst = normalized population size from PATCH for species s in decade t|
| ||Hsjt = normalized habitat score as predicted for species s in unit j at time t|
| ||Cjkt = area of conifer forest in unit j and age class k at time t|
Researchers obtained data by randomly selecting a set of 40 landscapes (ranging from 2 to 100 percent of the study area), subjecting each landscape to 20 time-series of randomly drawn management regimes that varied in harvest intensity, and by running PATCH simulations. Because the sample landscapes were of different sizes, all variables were normalized by their area. Coefficient estimates and validation procedures are reported (Nalle, 2001).
With an out-of-sample data set, the equations predicted more than 97 percent of the variation in population sizes (for both species). Furthermore, when regressing predicted proxy population sizes (found during optimization) and observed sizes from PATCH simulation results (using solutions from optimization), slopes were no different than unity (p-values > 0.35 for both species over all time periods).
We developed a PPF for the three modeled outputs on the landscape with detailed spatial resolution across multiple time periods. The PPF marks the boundary between feasible and infeasible combinations of various outputs. Along the frontier, no single output can be increased without simultaneously requiring a reduction of some other output. The PPF is useful in two ways. First, it can help identify opportunities for improving current land-use and management, which may fall well inside the PPF, allowing either enhanced natural resource protection or increased commodity production without harming the other goal. Second, it illustrates the tradeoffs between goals once the choice of a land-use/land management decision has eliminated the potential for a "win-win" solution.
The landscape was overlaid with a uniform grid of 0.70 km2 to approximate the average territory size for each species (Bigger and Vesely, 2000), yielding 28,251 management units. On each management unit in each time period, a decision was made to either harvest timber (clear-cut) or leave the unit untouched. If a unit was harvested, profits (or losses) from timber operations were realized and the age class of the management unit was set to zero. A planning horizon of 100 years (10 periods) was chosen to model benefits to current and future generations, and the passage of time was simulated by advancing each unit's age class by 10 years per period. Timber prices were determined in each decade from projected demand equations for western Oregon (Adams, et al., 2001). To simulate competitive market equilibrium outcomes, the value of timber production was measured by summing together discounted consumer and producer surpluses over time with an annual discount rate of four percent.
The PPF was found by solving a series of integer programs. Specifically, the value of timber production was maximized, subject to thresholds on the geometric mean population size of each species. The integer program was resolved by increasing one species' population threshold while keeping the other threshold fixed. A boundary point along the frontier was located once the set of threshold values could not be satisfied. To trace out the entire frontier, this process was repeated by selecting a new fixed threshold for one species and incrementally increasing the remaining threshold until a new boundary point was located.
The formal optimization model used to find the PPF was:
|for j||= 1,…, M management units, t = 1,…, T decades, and s = 1, 2 species where:|
|xjt||= 1 if unit j is assigned clear-cut timber harvest in decade t, 0 otherwise|
|hjt||= clear-cut timber harvest volume for unit j harvested at decade t|
|Qt||= total harvest volume in decade t such that Qt = Mj=1hjtxjt|
|Dt(q)||= timber demand price as a function of total harvest volume|
|cj||= harvest and haul cost for unit j|
|VjT||= land and standing timber value of unit j in the final period T|
|pˆst||= predicted population size for species s at decade t|
|p¯st||= threshold value for species s|
The objective function shown in equation 3 consists of 2 parts: (1) the discounted value of timber harvest (area under the timber demand function minus harvest and haul costs) across time periods in the planning horizon; and (2) the value of land and timber at the end of the planning horizon assuming steady-state management beyond this point. Equation 4 constrains the geometric mean of each population time-series to meet or exceed a threshold value. The geometric mean was used to measure aggregate population size because of its sensitivity to extinction (and near-extinction) events.
Due to the large number of decision variables and the non-linear constraint structure, heuristic solution methods were required. To solve the model, a hybrid method was developed that combined the strengths of Simulated Annealing and Tabu Search (Metropolis, et al., 1989; Kirkpatrick, et al., 1989; Glover and Laguna, 1989a; and Glover and Laguna, 1989b). The hybrid found solutions of statistically similar quality to either heuristic but did so approximately 50 times faster. Also, because many millions of iterations were required to solve each optimization problem, and because PATCH itself is complex and requires many iterations, a fast proxy for PATCH results was developed based on spatial habitat attributes and lagged PATCH population sizes. To verify accuracy of the PPF boundary points, these solutions were run in PATCH.
Figure 1. Estimates of Maximum Potential Combinations
The solutions shown in Figures 1 (a), (b), and (c), are an estimate of the set of maximum potential combinations of the modeled outputs. Because porcupines prefer younger forests, timber production and healthy porcupine populations are complementary to a large degree. On the other hand, because this species of owl (Great Horned Owl) prefers older forests for nesting (but to some extent can tolerate a mix of younger and older forests), timber production and owls are for the most part competitive. Figure 1(a) shows that the timber production value increases with porcupine population up to 19,500 porcupines, the point of maximum timber harvest value. Beyond this point, further increases in the porcupine population require harvesting stands prior to the financially optimal rotation age resulting in decreased value of timber harvest. Figure 1(b) shows that increasing the owl population above 3,800 requires limiting timber production value. To maintain low levels of the owl population, the average harvest age of a management unit decreases but a small amount of mature forest is retained. Figure 1(c) shows the relation between owl and porcupine populations. There is always a tradeoff between populations of the two species because of their very different habitat preferences. This is important because timber production, which can result in a patchwork of habitat over short distances (though weighted toward younger forests), sometimes has a complementary or neutral effect on some species populations.
The preceding analysis assumes that every management unit within the landscape has equal potential to be used for timber production or species conservation. In reality, different landowners have different management objectives that greatly affect the land-use/land management decisions chosen for different parcels. To simulate current management, net present value of timber was maximized on private land (about 45 percent if the area) and timber harvest was disallowed on federal land. We maximized Equation 3, subject to:
where P is the subset of the management units that are federally owned. The findings of this analysis are labeled as points in Figures 1 (a), (b), and (c). The management pattern resulted in timber harvest value of $21.06 billion, porcupine geometric mean population of 14,121, and owl geometric mean population of 8,503.
As shown, results from current management remain well inside the PPF when the owl is taken into consideration. From Figure 1(b), owls can be maximally increased 38 percent to 11,751 individuals by moving horizontally from the point of current management to the PPF. This does not affect the number of porcupines or timber value due to the complementarity of the two. Alternatively, without changing the number of owls, the timber value can be maximally increased 14 percent to $23.9 billion by moving vertically from the point of current management to the PPF in Figure 1(b). This corresponds to an upslope move along the PPF in Figure 1(a) to $23.9 billion and 18,071 porcupines, and a vertical move in Figure 1(c) from current management to the PPF (a 28 percent increase in porcupines). Furthermore, the analysis reveals that both economic and ecological objectives could be increased (timber value from 0 to 14 percent, owls from 0 to 38 percent, and porcupines from 0 to 28 percent) by changing current policy to permit some timber harvests on public lands in exchange for enhanced owl protection on some private lands.
Owl habitat maps in the 5th decade corresponding to 3 outcomes are shown in Figure 2 (A). In Figure 2(A), the PPF solution that has the highest timber value (owl population = 3,800, porcupine population = 19,500, timber value = 24.3), in (B) the current management simulation (owl population = 8,500, porcupine population = 14,120, timber value = 21.1), and in (C) the PPF solution that supports the same owl population as current management (owl population = 8,500, porcupine population = 18,150, timber value = 23.9). In the current management simulation, timber production occurs only on private land, which is concentrated in the western half of the study area, while owl habitat develops in the eastern half. This pattern makes financial sense when timber production is the only objective that can be seen by observing the PPF solution. The highest timber value also concentrates timber production in the west and owl habitat in the east. Timber harvest and haul costs are lower in the west because wood processing facilities lie along the western boundary of the study area and slope is lower in the west. Site productivity is also higher in the west, contributing to higher timber harvest volumes. However, a comparison of the current management simulation to the PPF solution that supports the same owl population shows that the best spatial configuration of timber harvest changes when owl habitat becomes a higher priority management objective. In the PPF solution, timber harvest and owl habitat are more dispersed over the landscape than in the current management scenario.
The study illustrates how analysis based on estimation of productive capacity for a site can be used to search for opportunities to improve current management. We found that it might be possible to increase owl populations by 30 percent over likely current management levels without reducing timber values or porcupine populations. It also may be possible to increase the timber by 13 percent and porcupines by 30 percent without reducing owl populations. Current management, in which private land is managed for timber in response to market incentives and federal land is managed almost exclusively for other forest uses, appears to be inefficient. Models such as this one may prove useful for identifying situations where the payoff for making the difficult policy changes to markets and/or to federal land management to encourage landscape-level management of forests is likely to be great.
Figure 2. Owl Habitat Maps
Incorporation of more realism in the wildlife models (e.g., predator/prey relations, more refined habitat preferences), the timber model (e.g., roading, site quality), and the vegetation model (e.g., disturbance regimes, more refined vegetation classes) will improve the practical usefulness of this approach. The model can be used to improve understanding of the tradeoffs between alternative conservation objectives by carefully selecting to model wildlife, that represents different conservation goals (e.g., old-forest-dependent endangered species versus large numbers of species with more general habitat needs). Finally, there are many forest uses, aside from wildlife and timber, that might be modeled using this framework (e.g., fire risk, recreation).
The analysis uses the PATCH wildlife population model, described in Schumaker (1998) as a set of population prediction equations and a heuristic optimization algorithm. Assumptions, performance criteria, test results, theory, statistical significance of parameter estimates, and mathematical formulations for the last two components of the model are briefly described above and described in detail (Nalle 2001). The prototype model has passed peer review (Calkin [in press]) and the full model components are now or soon will be undergoing peer review (Nalle, et al. 2002a, 2002b). Both models successfully passed Ph.D. thesis defense. The optimizations for the full model were run using MATLAB v5.3 executable code1. Solution run-times were approximately 30 to 90 minutes on a PC with two 700 MHz processors and 512 MB of RAM.
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Pacific Northwest Ecosystem Research Consortium, http://www.orst.edu/Dept/pnw-erc.
Bigger D, Vesely D. Life history database for vertebrates of the Willamette River Basin. Pacific Wildlife Research, Inc. Corvallis, OR, 2000.
Adams DM, Schillinger RA, Latta G, VanNalts A. Timber harvest projections for private land in western Oregon. Oregon State University Forest Research Lab. Corvallis, OR, 2001.
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|Publications and Presentations: Total Count: 21|
|Dissertation/Thesis||Nalle DJ. Estimating extinction risk with spatial and temporal measures. In: Optimizing spatial and temporal aspects of nature reserve design under economic and ecological objectives. Ph.D. Dissertation. Oregon State University, Corvallis, OR, 2001, 188 pp. ||not available |
|Dissertation/Thesis||Calkin DE. Land management with ecological and economic objectives: developing a production possibility set of wildlife species persistence and timber harvest value using simulated annealing. Ph.D. Dissertation, Oregon State University, Corvallis, OR, 2001, 84 pp. ||not available |
|Dissertation/Thesis||Nalle DJ. Locating production possibility frontiers of economic and ecological outputs over long horizons. In: Optimizing spatial and temporal aspects of nature reserve design under economic and ecological objectives. Ph.D. Dissertation. Oregon State University, Corvallis, OR, 2001, 188 pp. ||not available |
|Journal Article||Calkin DE, Montgomery CA, Schumaker NH, Polasky S, Arthur JL, Nalle DJ. Developing a production possibility set of wildlife species persistence and timber harvest value. Canadian Journal of Forestry Research. ||not available |
|Presentation||Polasky S, Montgomery CA. A framework for analyzing biodiversity conservation. Presented at the U.S. Department of Agriculture, Forest Service Seminar, National Headquarters, Washington, DC, April 1999. ||not available |
|Presentation||Montgomery CA. Compatibility of timber and conservation: tracing the trade-off frontier. Presented at the Wood Compatibility Initiative Workshop, U.S. Department of Agriculture, Forest Service, Skamania, WA, December 5-7, 2001. ||not available |
|Presentation||Montgomery CA. Developing a production possibility set of wildlife species persistence and timber harvest value using simulated annealing: two case studies. Presented at the Annual Meeting of the Western Forest Economists, Wemme, OR, May 5-7, 2001. ||not available |
|Presentation||Nalle DJ. Efficient economic and ecological production. Presented at the Tahoe National Forest Seminar, U.S. Department of Agriculture, Forest Service, Nevada City, CA, December 2001. ||not available |
|Presentation||Nalle DJ. Empirically finding production possibility frontiers of economic and ecological landscape outputs. Presented at the Resource Economics Seminar, University of Nevada, Reno, NV, October 10, 2001. ||not available |
|Presentation||Nalle DJ. Finding efficient combinations of economic and ecological landscape uses. Presented at the General Meeting of the Institute for Operations Research and Management Science, Miami Beach, FL, November 5, 2001. ||not available |
|Presentation||Montgomery CA. Land management with biological and economic objectives. Presented at the Annual Meeting of the Allied Social Sciences Association, Atlanta, GA, January 4-6, 2002. ||not available |
|Presentation||Montgomery CA. Land management with biological and economic objectives. Presented at the Annual Meeting of the Association of Environmental and Resource Economics, Atlanta, GA, January 4-6, 2002. ||not available |
|Presentation||Calkin D. Land management with biological and economic objectives. Presented at the Annual Meetings of the Western Forest Economists, Wemme, OR, May 1999. ||not available |
|Presentation||Calkin D. Land management with biological and economic objectives. Presented at the Institute for Operations Research and Management Science Spring Meetings, Cincinnati, OH, May 1999. ||not available |
|Presentation||Montgomery CA. Land management with economic and biological objectives: two case studies. Presented at the Conservation Biology Seminar Series, University of Minnesota, St. Paul, MN, February 26, 2001. ||not available |
|Presentation||Nalle DJ, Arthur JL. Maximal species survivability as a function of timber harvest volume. Presented at the Spring Meetings of the Institute for Operations Research and Management Science, Salt Lake City, UT, May 2000. ||not available |
|Proceedings||Arthur JL, Calkin D, Montgomery CA, Nalle DJ, Polasky S, Schumaker NH. Balancing economics and conservation in forest land management. In: Proceedings of the 5th International Conference of the Decision Sciences Institute, Athens, Greece, July 1999 (abstract). ||not available |
|Proceedings||Montgomery CA. Compatibility of timber and conservation: tracing the tradeoff frontier. In: Johnson AC, Haynes RW, Monserud RA, eds. Proceedings of the Wood Compatibility Initiative Workshop, U.S. Department of Agriculture Forest Service, Pacific Northwest Research Station, Portland, OR. ||not available |
|Proceedings||Polasky S, Montgomery CA, Calkin D, Arthur JL, Nalle DJ, Schumaker NH. Land management with ecological and economic objectives. In: Proceedings of the U.S. Environmental Protection Agency Office of Economy and Environment and National Center for Environmental Research Workshop, Washington, DC, December 1999 (abstract). ||not available |
|Proceedings||Montgomery CA, Arthur JL, Nalle DJ, Polasky S, Schumaker N. Land management with ecological and economics objectives: developing a production possibility set of wildlife species persistence and timber harvest value. In: Proceedings of the 2002 Decision Making and Valuation for Environmental Policy Progress Review Workshop, Washington, DC, March 21-22, 2002. ||not available |
|Proceedings||Montgomery CA, Calkin D, Montgomery CA, Schumaker NH, Polasky S, Arthur JL, Nalle DJ. Modeling the compatibility of biological and economic objectives on a forested landscape. In: Proceedings of the 2000 International Institute of Fisheries Economics and Trade Conference, Corvallis, OR, July 2000 (abstract). ||not available |