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METAPOPULATION MODELS |
We believe the concept of the metapopulation and metapopulation dynamics may provide insights into the persistence and conservation of species faced with habitat fragmentation as a consequence of military training or other land use (see Predicting the results of training and land management actions). Accordingly, we are developing a metapopulation model for the Red-Cockaded Woodpecker which has viable populations at several Southeastern Military Bases (see Managing species across multiple installations) and the Karner Blue Butterfly at Fort McCoy, Wisconsin (See Managing species on a single installation). Here we present some background on the concept of the metapopulation and introduce our model to address the regional persistence of the red-cockaded woodpecker on military installations across the Southeastern United States.
Andrewartha and Birch introduced the concept of the metapopulation as early as 1954 when they wrote (Andrewartha and Birch 1954; p. 657) that "A natural population occupying any considerable area will be made up of a number of ... local populations or colonies. In different localities the [demographic] trends may be going in different directions as the same time." However, Levins (1970; p. 105) first used the term metapopulation to describe his concept of "a population of populations which go extinct locally and recolonize," and he introduced (Levins 1969, 1970) a succinct mathematical description of the metapopulation:
dp/dt = m p (1 - p) - e p ,
where p is the proportion (fraction) of population centers (e.g., habitat "islands" or patches), m is the migration (colonization) rate, and e is the rate at which local populations go extinct.
At equilibrium p* = 1 - e/m. The metapopulation will persist (i.e., p* > 0) only if e < m.
The Levins concept and model has become the classical metapopulation. More recently, Hanski and Gilpin (1991; p. 7) defined a metapopulation as a "[s]et of local populations which interact via individuals moving among populations." Hanski and Simberloff (1997; p. 11) defined a metapopulation as a "[s]et of local populations within some larger area, where typically migration from one local population to at least some other patches is possible."
Minimally then, a metapopulation is a collection of relatively isolated, spatially distributed, local populations bound together by occasional dispersal between populations. These relatively long distance dispersal events may be infrequent, but must occur often enough to provide for recolonization of populations that have suffered local extinction. The regional metapopulation persists in the face of local extinctions precisely because of sufficient dispersal among populations. If dispersal among populations is so frequent that local extinctions do not occur, the concept of the metapopulation is superfluous, and the regional population is better thought of simply as a single spatially (albeit patchily) distributed population. One the other hand, if dispersal is too infrequent, and the probability of local extinction is non-zero, the regional metapopulation cannot persist and will go extinct.
Human alteration of the landscape frequently leads to the fragmentation and isolation (insularization) of once contiguous wildlife habitat. The similarity between discontinuous patches of fragmented habitat and the relatively isolated local populations of a metapopulation is obvious. In principle at least, metapopulation dynamics could provide for the regional persistence of a species occupying a network of discontinuous habitat patches or islands. Not surprisingly, conservation biology has turned to metapopulation dynamics as a possible solution to the persistence of species in fragmented landscapes. However, the many assumptions which provide for the simplicity and elegance of Levins classical metapopulation model (e.g., equally spaced same-size populations) are probably too restrictive for application to a specific species and landscape or region where, for example, patch size and inter-patch distance may be quite variable. The assumptions of the Levins model can be, and have been, relaxed in a variety of interesting and useful ways (e.g., see Hanski 1991). Nevertheless, these models still usually assume that the regional or landscape population is in fact a metapopulation. Insular populations recently formed by habitat fragmentation may not function as metapopulation in the classical sense, but may instead represent a nonequilibrium metapopulation (Harrison and Taylor 1997). Indeed, they may not represent a metapopulation at all, but rather exist as a simple set of noninteracting isolated populations.
Consequently, while we approach the question of regional persistence of the red-cockaded woodpecker from the perspective of metapopulation dynamics, we do not assume the existence of a metapopulation. Rather we ask: Can the red-cockaded woodpecker be managed as a regional metapopulation? Or, must the species be managed as a set of isolated (closed) populations? Similarly, our regional model for the red-cockaded woodpecker uses a patch-based approach in which we model the changes in number of active colonies at each red-cockaded woodpecker population center (e.g., military base or national forest) across the Southeast. We explicitly model the individual local extinction probabilities of these sites, and the rates of colonization from other sites. We can then ask whether the aggregate properties of the populations are consistent with metapopulation dynamics, without assuming a priori the existence of a metapopulation.
REFERENCES
Andrewartha, H. G., and L. C. Birch. 1954. The Distribution and Abundance of Animals. The University of Chicago Press, Chicago, Illinois.
Harrison, S., and A. D. Taylor. 1997. Empirical evidence for metapopulation dynamics. pp. 27–42. In I. A. Hanski and M. E. Gilpin (eds.), Metapopulation Biology. Academic Press, San Diego, Californina.
Hanski, I. 1991. Single-species metapopulation dynamics: concepts, models, and observations. Biological Journal of the Linnean Society 42:17–38.
Hanski, I., and M. Gilpin. 1991. Metapopulation dynamics: brief history and conceptual domain. Biological Journal of the Linnean Society 42:3–16.
Hanski, I., and D. Simberloff. 1997. The metapopulation approach, its history, conceptual domain, and application to conservation. pp. 5–26. In I. A. Hanski and M. E. Gilpin (eds.), Metapopulation Biology. Academic Press, San Diego, Californina.
Levins, R. 1969. Some demographic and genetic consequences of environmental heterogeneity for biological control. Bulletin of the Entomological Society of America 15:237–240.
Levins, R. 1970. Extinction. pp. 77–107. In M. Gesternhaber (ed.), Some Mathematical Problems in Biology. American Mathematical Society, Providence, Rhode Island.
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