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Incorporating metapopulation dynamics of greater gliders into reserve design in disturbed landscapes
Ecology, March, 1999 by Michael A. McCarthy, David B. Lindenmayer
INTRODUCTION
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Since Andrewartha and Birch (1954) realized that simple models of population dynamics were inadequate for representing extinction and colonization of patches, concepts and models of metapopulation dynamics have continued to develop (Hastings and Harrison 1994, Hanski and Gilpin 1997). The earliest mathematical representation of metapopulation dynamics considered a large suite of identical patches (Levins 1970). Levins (1970) assumed that colonization and local extinction were uncorrelated among patches, habitat quality of patches remained constant, colonization of all empty patches was equally likely, and local population dynamics were ignored (Levins 1970). More recent developments have considered effects of different-sized patches (Hahski 1994), differences in the chance of migration between different pairs of patches (Hunski 1994), fluctuations in habitat quality over time (Possingham et al. 1994), a finite number of patches (Nisbet and Gurney 1982, Gilpin 1990, Hanski 1994), and local population dynamics (Hastings and Wolin 1989). Correlation between the population dynamics in patches has rarely been considered (Harrison and Quinn 1989, Gilpin 1990). For example, Lindenmayer and Possingham (1995) considered correlated disturbance events, which ultimately drove the simulated dynamics of a metapopulation of Leadbeater's possum (Gymnobelideus leadbeateri) in the forests of southeastern Australia. However, they did not consider spatial correlation in the disturbance process, with the implicit assumptions that all patches were uniformly affected by disturbance, and that the correlation between the incidence of disturbance was the same for near patches as for distant patches.
The most common generic software packages used for population viability analyses are based on meta-population models (see review by Lindenmayer et al. 1995a). Where the aim is to minimize the risk of extinction of particular species, metapopulation models can formalize arguments about whether to establish a single large, or several small, reserves (the SLOSS debate; Diamond 1975, Diamond and May 1976, Simberloff 1988, Gilpin 1990, Burgman et al. 1993, McCarthy et al. 1994, Lindenmayer et al. 1995a). The answer depends on a number of factors such as the risk of extinction of local populations, the rate of migration among populations, and the correlation among local extinction events (Burgman et al. 1993). In many instances, there is little choice about the location of reserves, so the SLOSS debate is irrelevant (Noss and Cooperrider 1994). However, this is not the case in parts of Australia, where new reserves may be established in timber production areas, with up to 15% of each forest type to be set aside (Commonwealth of Australia 1995). The reservation target of 15% is essentially arbitrary, but if areas are to be excluded from timber harvesting, it is important that they provide the maximum possible conservation value. In this case, issues associated with the size, number, and spatial configuration of reserves in a protected network are likely to be important. If reserves are clustered together, a single disturbance event such as a large fire may affect the entire reserve network simultaneously. In contrast, fragmentation of the reserve system may expose small, isolated populations to high risks of extinction.
A recent model has been developed that simulates fires in mountain ash forest as a set of spatially correlated events (McCarthy and Lindenmayer 1998). This model has been validated with data on the prevalence of multi-aged mountain ash forest, and has been shown to perform well, illustrating that the model adequately simulates the effects of fire on the age structure of mountain ash forest. This model may be used as a basis for simulating metapopulation dynamics that are spatially correlated.
The purpose of this paper is twofold. Firstly, we describe the development of a model of the metapopulation dynamics of the greater glider (Petauroides volans), an arboreal marsupial of forests in eastern Australia. The model accounts for spatially correlated disturbance by using the recently developed fire model (McCarthy and Lindenmayer 1998). Secondly, the metapopulation model is used to explore effects of reserve configuration (size and location of patches) on the risk of extinction of greater gliders in mountain ash forests. Risks of extinction in single patches are determined first, and then the risk of extinction within an actual area of timber production forest in the Central Highlands of Victoria is examined. Results of the model are compared with a theoretical generalization developed by Lande (1993), which relates the mean time to extinction in a single patch to a power of population size. Replication of the reserves across large areas is investigated by considering the risk of extinction in a number of independent patches, and by considering the mean time to extinction in the reserve network (see also Quinn and Hastings 1987). Within the Central Highlands region, there is scope for removing some areas of forest from timber production and including them in a reserve system (Lindenmayer and Possingham 1995). The model is used to determine the configuration of such a reserve network that would minimize the risk of extinction of greater gliders.
