17. Mathematical Methods for Identifying Representative Reserve Networks
303
when applied to binary (i.e., presence-absence) data (Andelman and Meir, 2000).
Moreover, for any particular set of species or ecosystems, determining the optimal
balance of reserve clustering and separation to parameterize a simulated annealing
algorithm requires detailed empirical data on species life history and/or the spatial
distribution of catastrophes, which often do not exist.
Species/Biological Dynamics
The basic data used with reserve siting algorithms usually consist of presenceabsence data (or more often, simply presence data) for particular species and/or
vegetation types. The former (and to a lesser extent, the latter) can change.
Species appear and disappear from sites independently of whether sites are in, or
not in, reserve systems (e.g., Margules et al. 1994), and the frequency with which
this happens depends on numerous factors. This means that static approaches may
yield reserve networks that may not protect as much biodiversity as one might
think. The future of these sorts of problems lies in integrating spatial population
modeling with reserve network siting approaches, a significant challenge, both in
terms of data acquisition and model complexity (see Andelman et al., 2000, for a
recent review).
Landscape Change, Economic and Social Uncertainty
In most cases, it is not possible to both design and implement reserve networks
instantly. Even if an optimal set of sites has been identified, it will take decades of
negotiation and land purchases to translate that design into a set of reserves on the
ground. In the meantime, degrading processes will continue to operate at various
spatial scales. If sites are lost before implementation is complete, then efforts to
find the optimal reserve system will probably fail. This means, as time passes, not
only will the species composition of a site change, the carrying capacity of the site
for particular species (i.e., site quality) may also be modified, and some sites may
be destroyed entirely. Key sites may be lost before they become available for
conservation action, and if these key sites are integral to the overall reserve
network goals, then the final system may be poor when measured against the
initial goals. Ideally, then, we seek a dynamic theory of reserve design. Such a
theory must explicitly consider many stochastic events: the chance of site destruction and degradation, the chance a site becomes available for sale, the dynamics of
the financial system providing capital to buy and manage reserves, and the
strength of public interest in conservation relative to other land uses. Combining
all these factors in a single model would be almost impossible. Nevertheless,
incorporating some of these factors in a model is essential. For example, given
temporal variation in site availability, for small problem sets, Possingham and
colleagues (1993) used stochastic dynamic programming and found it was possible to determine which sites should be acquired, if and when they become
available.
Here, we have merely attempted to introduce some of the complexities that will
enter into practical reserve design problems, along with some of the mathematical
303
when applied to binary (i.e., presence-absence) data (Andelman and Meir, 2000).
Moreover, for any particular set of species or ecosystems, determining the optimal
balance of reserve clustering and separation to parameterize a simulated annealing
algorithm requires detailed empirical data on species life history and/or the spatial
distribution of catastrophes, which often do not exist.
Species/Biological Dynamics
The basic data used with reserve siting algorithms usually consist of presenceabsence data (or more often, simply presence data) for particular species and/or
vegetation types. The former (and to a lesser extent, the latter) can change.
Species appear and disappear from sites independently of whether sites are in, or
not in, reserve systems (e.g., Margules et al. 1994), and the frequency with which
this happens depends on numerous factors. This means that static approaches may
yield reserve networks that may not protect as much biodiversity as one might
think. The future of these sorts of problems lies in integrating spatial population
modeling with reserve network siting approaches, a significant challenge, both in
terms of data acquisition and model complexity (see Andelman et al., 2000, for a
recent review).
Landscape Change, Economic and Social Uncertainty
In most cases, it is not possible to both design and implement reserve networks
instantly. Even if an optimal set of sites has been identified, it will take decades of
negotiation and land purchases to translate that design into a set of reserves on the
ground. In the meantime, degrading processes will continue to operate at various
spatial scales. If sites are lost before implementation is complete, then efforts to
find the optimal reserve system will probably fail. This means, as time passes, not
only will the species composition of a site change, the carrying capacity of the site
for particular species (i.e., site quality) may also be modified, and some sites may
be destroyed entirely. Key sites may be lost before they become available for
conservation action, and if these key sites are integral to the overall reserve
network goals, then the final system may be poor when measured against the
initial goals. Ideally, then, we seek a dynamic theory of reserve design. Such a
theory must explicitly consider many stochastic events: the chance of site destruction and degradation, the chance a site becomes available for sale, the dynamics of
the financial system providing capital to buy and manage reserves, and the
strength of public interest in conservation relative to other land uses. Combining
all these factors in a single model would be almost impossible. Nevertheless,
incorporating some of these factors in a model is essential. For example, given
temporal variation in site availability, for small problem sets, Possingham and
colleagues (1993) used stochastic dynamic programming and found it was possible to determine which sites should be acquired, if and when they become
available.
Here, we have merely attempted to introduce some of the complexities that will
enter into practical reserve design problems, along with some of the mathematical