Richard Church, David Stoms, Frank Davis, and B.J. Okin
We present the details of a general spatial model that was developed for the selection of biodiversity management areas in the Sierra-Nevada Region. This model is loosely integrated with a GIS system. The basic modeling approach begins by first identifying those plant communities that are vulnerable due to land use activities in current management plans. The level of vulnerability is assessed for each element of interest on a spatial basis using ARC/INFO. The planning problem involves selecting an efficient set of watersheds for biodiversity management through specially developed heuristics and the Optimization Subroutine Library of IBM. Results of this approach are given for the northern region of the Sierra Nevada of California. The BMAS model represents a significant advance in GIS-based conservation planning, both in sophistication of the algorithms used and in the integration of cultural and land use data with biological data.
Protecting biodiversity has been the subject of a number of research projects and will continue to be of interest worldwide. Such interest is predicated on the loss of species due to land use changes and habitat losses as well as estimates for global climate change and increased variation within local climates. Researchers have discussed a variety of methods to protect habitats and biodiversity within a region; such methods include developing reserves and corridors, changing land use patterns, managing the landscape within limits to protect biodiversity, and managing captive breeding and release programs. Within a region, practically all of these techniques might be used to protect the natural environment and its diversity. To address regional biodiversity and plan for its protection, it is necessary to maintain up-to-date and accurate data on a wide variety of data coverages. Because of the detail and amount of such data as well as the importance of the spatial relationships inherent in location and proximity, it is natural to take advantage of GIS systems. We view the use of GIS as not only valuable, but for all intents and purposes, indispensable.
Much of the Sierran Region has been subjected to primary economic activities involving timber harvesting, grazing, recreation, mining, and water resource development. The impacts of such activities have been considerable. For example, aquatic biodiversity has been severely impacted by water impoundments and diversions, logging and grazing of riparian habitats, and the introduction of non-native species (Moyle and Randall 1996). In the Sierran foothills, long term (>150 years) livestock grazing has profoundly altered herb layer composition, aided the invasion of exotic plant species, degraded or eliminated riparian vegetation, and reduced soil fertility.. Ongoing rapid urbanization is spawning an extensive and possibly unmanageable urban-wildland interface. Even though middle and upper montane westside forests are relatively intact there is very little structurally complex forest left (11% of total). For the eastside of the Sierras, late seral conditions remain on only 7% of this forest type. Montane and subalpine meadows have been subject to long term sheep and cattle grazing. The legacy of grazing has altered soils, vegetation composition and hydrology in many meadow ecosystems.
We define Biodiversity Management Areas as specially designated public or private lands with an active ecosystem management plan in operation whose primary purpose is to contibute to regional maintenance of native genetic, species and community levels of biodiversity, and the processes that maintain that biodiversity. The primary management goal in each BMA is to sustain native biodiversity. The purpose of this paper is to describe the model used to select BMAs.
Biological conservation strategies have traditionally centered on biological reserves, where a reserve is "an area with an active management plan in operation that is maintained in its natural state and within which natural disturbance events are either allowed to proceed without interference or are mimicked through management. The viability of a reserve system is measured on the size, shape, and connectedness of these remnant habitat areas.
In much of the Sierra Nevada large portions of public and private land are managed for renewable natural resources such as livestock forage, timber, and recreation. The prevailing land cover types of the Sierra Nevada are managed forest, rangeland and alpine ecosystems that sustain many if not most elements of native biodiversity while also supporting natural resource-based economies. Thus, a Sierran BMA system would not function as an archipelago of biological reserves. However, a BMA system could provide "core habitat areas" of higher habitat quality for many species and/or sanctuaries for species and habitat types that are negatively impacted by human activities.
The BMA strategy is not intended to provide a comprehensive reserve system for the Sierra Nevada that will ensure against the extinction of species or ecosystems (Davis et al. 1996). Developing and evaluating such a system is beyond the scope of available data and resources, and would require us to make many assumptions about ecosystem processes and management of non-BMA lands that would be tenuous at best. Instead, we view instituting a system of biodiversity management areas that represent all major ecosystems as just one component of an overall biodiversity conservation strategy for the Sierra Nevada.
A number of questions need to be answered in order to develop the best startegy for biodiversity management in the Sierras. Such questions include:
Through the use of the model presented in the next section, we have addressed these issues and others in the SNEP study.
Assume that we have forecast both land use and activities for a region. This forecast would include land use changes by small watersheds or planning units. Given land use and the presence and extent of communities, habitats, and species, we can determine the extent to which various species, communities, endemic plants, old growth stands, etc. (called elements) are at risk now or in the future. We will call such elements at risk as being vulnerable. In order to reduce vulnerability, it is necessary to select BMAs in such a manner that sufficient distribution of that element is included among the selected BMAs. Selecting enough area for a vulnerable element, may mean that several watersheds or planning units need to be selected for BMAs. Some areas may be more suitable for selection than others. For example, if an area already has a dense human population or extensive road network and depending on the vulnerable element, the area may not be very suitable for targeting it for biodiversity management activities. Consequently, we would want to select those areas that are most compatible with our objective of improving the future of a given element and most compatible with existing land use.
It is necessary to select enough area for biodiversity management options that we keep elements from being considered vulnerable. Since we might consider hundreds of elements to be vulnerable and we can select from among hundreds of planning units for targeted action, the problem is relatively complex. We can represent this decision problem as an integer-linear programming model where the objective is to optimize the selection of suitable areas for biodiversity management such that enough area is selected for each element to keep it from being considered vulnerable. In order to formulate this model consider the following notation:
In order to formulate this model consider the following notation:
We can formulate the Biodiversity Management Area Selection (BMAS) Model in the following manner:
The above model deals with biodiversity management area selection (BMAS). This model involves selecting the most suitable and most compatible planning units that overlap with vulnerable elements. Enough area covering each vulnerable element must be selected to remove it from being vulnerable. This is established in the constraints of type (1). Either a planning unit is selected as a BMA or it is not. This is enforced by the definition of the integer decision variables and formalized in constraints (2). The objective function contains a number of terms. The first term is strictly an area term, so there will always be some concern for minimizing the total area selected for biodiversity management options. With the exception of the first term of the objective, each additional term involves a measurement of the suitability and potential effectiveness for that area to be used as a biodiversity management area. For each term, e.g. rj, a high value reflects low compatibility or potential as a BMA and a low value is indicative of being very suitable and compatible with targeting as a BMA. Specifically, rj and Hdj are terms which measure habitat quality, while the terms, Plaj and PPIj are terms which reflect the suitability of an area based on management and cost concerns. The objective involves minimizing the total area selected as well as optimizing the suitability of those areas selected by minimizing any such incompatibility.
The purpose of the BMAS model is to help guide in the selection of areas which can be valuable in a core of management areas for biodiversity. The major objective is to identify areas that are both appropriate for the protection and enhancement of biodiversity, but also identify enough area to represent at least a minimum amount of a given element's distribution. This is an important departure from many of the biodiversity -reserve design models that have been developed in the past. For example, many of the reserve design models have an objective of including each element at least once or a prespecified number of times. Picking polygons that include an element does not address whether that element is widely abundant or whether enough area is available within that area alone for biodiversity protection and representation. The use of a model which optimizes the number of distinct areas which include an element is valuable, but without related analyses which involve total area involved or needed by a given element, is limited and can be misleading.
If we change the Mink values to the number of times an element is to be represented and change the ajk coefficients to represent the presence of an element (or not) in a given planning unit, the above BMAS model can represent reserve design models based on the species covering approach. This means that the BMAS model is a relatively general model construct and can represent reserve design models like that of Margules et al. (1991). Consequently, developing techniques for solving the BMAS model is an improtant research objective.
Unfortunately, the BMAS model is related to the class of n-p hard problems that can be found in the integer programming literature (like the travelling salesman problem). This can be easily demonstrated as the BMAS model can be transformed into an equivalent multi-dimensional knapsack problem. Basically, worst-case instances of large n-p hard problems may require an inordinate amount of computer time to solve optimally. Our use of a general purpose Optimization Subroutine Library (OSL by IBM) to solve moderate sized BMAS problems has been modestly successful at best. Consequently, most of our research has been focused on the design of a robust heuristic to solve the BMAS problem. Our heuristic is based on the combination of several well-known methods including greedy, interchange, and multiple drops and adds (which represents a form of strategic oscillation). The details of the approach are given in Okin et al. (1995). In testing the heuristic against known bounded solutions for selected problems, heuristic performance was consistently within 2% of optimality.
The SNEP area was divided into six separate planning regions whose boundaries were defined by major river drainages. This division was made to capture latitudinal and longitudinal gradients in Sierran habitats (see Davis et al. 1996). Watersheds make logical units for BMAs because they are readily located on the ground, are appropriate physiographic units for managing ecosystem and hydrologic processes, and may be large enough to support viable populations of many plant and animal species. We used the Calwater planning watersheds as our basic BMA unit (which average 3000 ha (7,000 ac) in size). The areal extent of every plant community types in each watershed was calculated by intersecting the watershed boundaries with a map of plant community types (Davis and Stoms 1996). The vegetation map was prepared at 1:100,000 scale for the gap analysis of the Sierra Nevada. In general, there are several community types per watershed.
In each region we defined a starting BMA system based on maps of land ownership and management. (For example, one alternative is to consider all parks, designated nature reserves, and ungrazed designated wilderness areas as BMA lands.) Next we established a target level for representing plant community types in BMAs. This level can be set for each individual element, but for simplicity we used the same target level, for example, 10% of the mapped distribution, for every plant community type. By overlaying the map of existing BMAs on the map of plant community types we determined which types are not adequately represented and how much additional BMA land is needed for each type. This forms the basis of the Mink values.
Our purpose is not to identify the optimal sites for a Sierra BMA system. The BMAS model allows us to explore some of the likely dimensions of plausible, alternative BMA systems for the Sierra Nevada to answer the set of questions posed above. Alternatives can be generated readily by changing the model inputs: e.g., assumptions about current management, target levels for reducing vulnerability, the land base from which new BMA's can be selected, the weights in the objective function, the suitability factors, or the biodiversity elements to be represented.
Detailed results of the BMAS model applied to the Sierra Nevada can be found in the SNEP final report (Davis et al. 1996). Here we limit our presentation to one example alternative solution of the BMAS model for the northern subregion of the Sierra Nevada (Figure 1). This alternative identifies the most suitable BMA core which contains at least 10% representation of the distribution of each vulnerable element. For this alternative, we assumed that only designated reserves, parks, and wilderness areas which are not grazed are currently managed for biodiversity (approximately 2% of the subregion). With these assumptions and targets, 54 of the 59 plant community types in the subregion would be considered vulnerable. The model selected 55 out of 776 watersheds as new BMAs, totaling 189,000 ha. Private land comprised 41% of the new areas, whereas 48% of the subregion as a whole is privately owned. Thus, the suitability objective in the model, which is weighted against private ownership, helped direct selection towards public lands but because the foothill areas are so predominately in private ownership, several community types could only be found there.
Figure 1: An example BMAS solution for the northern subregion of the Sierra-Nevada Region. Selected watersheds are outlined in red. This alternative was based on a target level of 10% protection for every native plant community type.
The model was also quite efficient in selecting watersheds. The combined area of new and existing BMAs was only 10.8% of the land area. The additional 0.8% beyond the 10% target of this alternative is due to the requirement that entire planning watersheds be selected, even if only part would have been required to meet the Mink constraint. Furthermore, five community types already exceed the 10% representation requirement and were not considered vulnerable. Note that there is a moderate level of natural clustering of several of the watersheds that are selected by the model. This apparent clustering we attribute to the underlying spatial autocorrelation of both the distributions of plant communities and of the suitability factors, at least at the resolution of the planning watersheds used in the analysis. As the target level is increased to 25% representation, the clumping seems even more pronounced, although we have not formally measured this spatial pattern. If this clumping pattern is real, it suggests that the aggregation of selected watersheds in the 10% solution is limited primarily by the Mink constraint.
The current version of the BMAS model does not consider the spatial pattern of the selected watersheds. Based on general principles of conservation biology one could argue that larger, better connected BMAs would tend to maintain biodiversity better than small, poorly connected systems (Reid and Murphy 1995). On the other hand, there is evidence that populations in several scattered sites are less vulnerable to large-scale environmental disturbances than populations in a single larger site (Harrison and Quinn 1989). Obviously, it would be useful to incorporate spatial considerations in the BMAS model in order to explore these issues more analytically. Continguity is difficult to incorporate as a suitability factor, however, because it is not a property than can be measured a priori for a watershed but is dynamic in that it changes as its neighbors are selected. The BMAS model used here provides solutions that are the most efficient solutions only in terms of requiring the least area. Thus the solutions can be considered planning benchmarks in terms of the area requirements for representative BMA systems. Any additional constraints such as spatial design will increase the area of the solution.
Financial support for this research was provided by the USFS Sierra Nevada Ecosystem Project. Computing support was provided by a grant from the IBM Corporation Environmental Research Program. We gratefully acknowledge Michael Bueno and Joe Walsh of UCSB for assistance and many individuals from SNEP for supplying data. We particularly appreciate the productive discussions with Norm Johnson which refined the model and the BMAS alternatives considered.
Davis, F. W. and Stoms, D. M. (1996) Sierran vegetation: A gap analysis. In Sierra Nevada Ecosystem Project: Final Report to Congress, vol. II, Assessments and Scientific Basis for Management Options, in press.
Davis, F. W., Stoms, D. M., Church, R. L., Okin, W. J., and Johnson, N. L. (1996) Selecting biodiversity management areas. In Sierra Nevada Ecosystem Project: Final Report to Congress, vol. II, Assessments and Scientific Basis for Management Options, in press.
Harrison, S., and Quinn, J. F.. (1989) Correlated environments and the persistence of metapopulations. Oikos 56: 293-298.
Margules, C. R., Pressey, R. L., and Nicholls, A. O. (1991) Selecting nature reserves. Pp. 90-97 in, C. R. Margules and M. P. Austin, eds., Nature conservation: cost effective biological surveys and data analysis. Melbourne: CSIRO.
Moyle, P. I., and Randall, P. J. (1996) Biotic integrity of watersheds. In Sierra Nevada Ecosystem Project: Final Report to Congress, vol. II, Assessments and Scientific Basis for Management Options, in press.
Okin, W. J. (1996) Solving the Biodiversity Management Area Selection Problem, Masters Thesis, University of California Santa Barbara, in progress.
Reid, T. S., and Murphy, D. D. (1995) Providing a regional context for local conservation action. Bioscience Supplement: S84-S90.
Richard L. Church, Professor
Department of Geography
University of California, Santa Barbara
Santa Barbara, CA 93106-4060
Voice: (805) 893-4217
Fax: (805)-893-3146
e-mail: church@geog.ucsb.edu
David M. Stoms, Assistant Research Scientist
Institute for Computational Earth System Science
University of California, Santa Barbara
Santa Barbara, CA 93106-3060
Voice: (805) 893-7655
Fax: (805)-893-3146
e-mail: stoms@geog.ucsb.edu
Frank W. Davis, Professor
Department of Geography
University of California, Santa Barbara
Santa Barbara, CA 93106-4060
Voice: (805) 893-3438
Fax: (805)-893-3146
e-mail: fd@geog.ucsb.edu
William J. Okin, Graduate Student Researcher
Department of Geography
University of California, Santa Barbara
Santa Barbara, CA 93106-4060
e-mail: okin@geog.ucsb.edu
