Objective: The overall objective of the research was the development and evaluation of methods for conservation decision-making in the face of incomplete information. For concreteness, the project was organized around the reserve site selection, in which the problem is to select a subset of potential sites for the establishment of biological reserves. The research was initially intended to focus on three issues: (1) estimating the probability that a species is present within a site; (2) identifying the subset of sites with maximal expected species coverage; and (3) exploring the use of species number as a proxy for other measures of biological diversity. In the course of the project, it was decided to focus on (2) and (3), as (1) had already received attention in the conservation literature.
The accomplishments and research results of the project were as follows.
1. We developed and applied a method for incorporating cost information into the reserve site selection problem. The reserve site selection problem involves selecting a subset of potential sites for the establishment of biological reserves. The objective is to select sites to maximize the coverage of the target species, where a species is said to be covered if it is contained in one or more of the selected sites. In the field of Operations Research, this problem is called the maximal coverage problem. As it is typically formulated in conservation, the constraint imposed in the maximal coverage problem is expressed in terms of the number of sites that can be selected. This constraint is reasonable when the cost of establishing a reserve is the same for each potential site. However, when there are differences in cost, then greater coverage may be achieved by establishing more sites where costs are low. The resulting optimization problem can be solved by expressing the constraint in terms of economic cost. This is described in Ando, et al. (1998), where we use data on the distribution of endangered species within all U.S. counties to show that substantial gains in efficiency, as measured by species coverage per dollar, can be gained by taking explicit account of differences in land values.
2. We developed and illustrated methods for accommodating uncertainty about species incidence in the reserve site selection problem. The common assumption in the reserve site selection problem is that the distribution of species within potential reserve sites is known. In practice, this is not the case. When only incidence probabilities are available, a reasonable goal is to maximize the expected number of species covered. We refer to this as the maximal expected coverage problem. Earlier methods for dealing with this kind of uncertainty involve assuming that a species is present in a site if the probability that it is present exceeds some threshold and that it is absent if this probability fails to exceed this threshold. In Polasky, et al. (2000), we use data on the distribution of vertebrate species in the State of Oregon to show that these earlier methods fail to identify the optimal solution. The maximal expected coverage problem is a nonlinear binary integer programming problem that is difficult to solve. In Camm, et al. (in press), we develop a linear integer programming approximation and show that it works well on the Oregon data.
3. We developed and illustrated a method for assessing the value of additional information in the reserve site selection problem. Additional information about species distributions has value in the maximal expected coverage problem in the sense that it can lead to improved expected coverage. In designing surveys to gain this additional information, it is necessary to know a priori what the expected improvement is. This information is needed to determine the appropriate level of survey effort (which comes at some cost) and to choose between alternative survey plans. In Polasky and Solow (in press), we showed how to formulate this problem under a Bayesian framework. Through some illustrative examples, we showed that the value of alternative survey plans depends on the prior species incidence probabilities, the quality of the survey information, and the number of sites that can be selected. The contribution of this work is to provide a formal basis for assessing the value of information in the maximal expected coverage problem.
4. The goal of maximizing the number of conserved species has been criticized for failing to account for taxonomic differences between species. However, the informational requirements for maximizing alternative measures of biological diversity are extremely high for practical use in reserve site selection. In Polasky, et al. (2001), we used distributional and taxonomic data on 147 bird genera to study whether genera number serves as a reasonable proxy for a specific measure of taxonomic diversity. For this measure, the diversity of a collection of taxonomic units (in this case, genera) is given by the length of the phylogenetic tree connecting then. In this case, we found that reserve sites selected to maximize the coverage of bird genera do not result in a high level of taxonomic diversity and vice versa. This casts doubt on the use of species number as a proxy for taxonomic diversity.
In addition to these broader accomplishments, progress was made on a number of narrower technical issues. These include: (1) the development of a quick estimator of the expected number of new species that will be discovered by further sampling (Solow and Polasky, 2000);
(2) a study of the effect of dependence on the standard estimate of species coverage (Solow, 2000); and (3) the development of an index of the contribution of spatial variability to species accumulation curves (Smith, et al., 2000).
Finally, the project supported the Ph.D. thesis project of John Bartlett at the University of Maine under the Direction of Dr. Raymond O'Connor. Bartlett's thesis project was aimed at identifying pathways by which human activities shape the environmental determinants of biological diversity.
Conclusions: This project was motivated by the lack of existing methods for dealing with uncertainty in the reserve site selection problem and in related problems in conservation decision making. The project was extremely successful in developing and evaluating new methods for this problem. The methods developed in the course of this project allow conservation decision makers to take explicit account of uncertainty about species ranges in designing reserve networks. These methods also allow the decision maker to assess a priori the value to reserve site selection of additional information about uncertain species ranges. When this information is collected through directed sampling, these methods also allow the decision maker to optimize sampling for reserve site selection.
Publications and Presentations: Total Count: 12
Polasky S, Csuti B, Vossler C, Meyers S. A comparison of taxonomic distinctness versus richness as criteria for setting conservation priorities for North American birds. Biological Conservation, Volume 97, Issue 1, January 2001, Pages 99-105.
Solow A, Polasky S. A quick estimator for taxonomic surveys. Ecology 1999.
Smith W, Solow A, Chu C. An index of the contribution of spatial heterogeneity to the species accumulation curve. Ecology 2000.
Polasky S, Camm J, Solow A, Csuti B, White D, Ding R. Choosing reserve networks with incomplete species information. Biological Conservation, Volume 94, Issue 1, June 2000, Pages 1-10.
Camm J, Norman S, Polasky S, Solow A. Nature reserve site selection to maximize expected species covered. Operations Research 2000 (submitted for publication).
Polasky S, Camm J, Garber-Yonts B. Selecting biological reserves cost-effectively: an application to terrestrial vertebrate conservation in Oregon. Land Economics 2001, Volume: 77 , Number: 1 (FEB) , Page: 68-78.
Ando A, Camm J, Polasky S, Solow A. Species distributions, land values, and efficient conservation. Science 1998;279:2126-2128.
Solow A. The effect of dependence on coverage estimation. Environmetrics 2000 (in press).
Polasky S, Solow A. The value of information in reserve site selection. Biodiversity and Conservation 2001, Volume: 10 , Number: 7 (JUL) , Page: 1051-1058.
Csuti B. Decision-making under uncertainty in the conservation of biological diversity. Presented at the 1998 Annual Meeting of the Society for Conservation Biology, Sydney, Australia, 1998.
Camm J. Decision-making under uncertainty in the conservation of biological diversity. Presented at the 1998 INFORMS National Meeting, Seattle, WA, 1998.
Solow A. Decision-making under uncertainty in the conservation of biological diversity. Presented at the 2000 Annual Meeting of the American Statistical Association, Indianapolis, IN, 2000.