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- Model description
We formulated a mathematical model in order to study the joint influence of demographic and genetic processes on metapopulation viability. Moreover, we explored the influence of habitat structure, matrix quality and disturbance on the interplay of these processes. We showed that the conditions that allow metapopulation persistence under the synergistic action of genetic and demographic processes depart significantly from predictions based on a mere superposition of the effects of each process separately. Moreover, an optimal dispersal rate exists that maximizes the range of survival rates of dispersers under which metapopulation persists and at the same time allows the largest sustainable patch removal and patch-size reduction. The relative impact of patch removal and patch-size reduction depends both on matrix quality and the dispersal strategy of the species: metapopulation persistence is more affected by patch-size reduction (patch removal) for low (high)-dispersing species, in presence of a low (high) quality matrix. Avoidance of inbreeding, through increased dispersal when the rate of inbreeding in a population is large, has positive effects on low-dispersing species, but impairs the persistence of high-dispersing species. Finally, size heterogeneity between patches largely influences metapopulation dynamics; the presence of large patches, even at the expense of other patches being smaller, can have positive effects on persistence in particular for species of low dispersing ability.
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- Model description
Habitat fragmentation is recognized to have major effects on species persistence due in particular to the isolation between population fragments (Davies et al., 2001), which has negative demographic and genetic consequences (Gaggiotti & Hanski, 2004).
Dispersal of individuals between habitat patches can have positive effects on the long-term persistence of fragmented populations, a process known as the rescue effect. Populations can be rescued demographically, as immigrant individuals increase the size of the recipient population (Casagrandi & Gatto, 1999, 2002a) or, genetically, as migration can result to a significant reduction of inbreeding depression (Saccheri et al., 1998; Richards, 2000; Couvet, 2002).
However, emigration could lead to a demographic deficit, due to the mortality of emigrant individuals during dispersal, which may not be compensated by immigration. The intensity of this phenomenon is mediated by the resistance of the matrix, i.e. the nonhabitat portion surrounding habitat patches, to interpatch movement: the increased mortality of dispersers within a low-quality matrix can contribute significantly to patch isolation and, therefore, increase the probability of extinction (Vandermeer & Carvajal, 2001).
The fact that the matrix is an adverse habitat for the species is a common phenomenon (Hanski & Ovaskainen, 2000), in particular when the matrix is a human-dominated area. In such a case, the low survival of dispersing individuals can be for example due to negative effects of agriculture on wildlife – associated with pesticides and/or the rarity of palatable food – or hunting (Donald & Evans, 2006; see also Woodroffe & Ginsberg, 1998, for large carnivores).
Species at higher trophic levels and with large body sizes can be especially vulnerable to the loss of emigrants within the matrix for two main reasons (Ewers & Didham, 2005). First, the usually low reproductive rates of these species cannot compensate the high mortality during dispersal resulting to declining populations. Second, these species have high requirements in terms of habitat area and are, consequently, more heavily affected by isolation. A single patch, which would be large enough to maintain a minimum viable population – supposed to amount to a thousand of individuals (Lande, 1995) – will be impossible to find, except in few areas in the world; see the example of grizzly bears in Yellowstone (Miller & Waits, 2003).
Hence, the outcome of these antagonistic effects, and consequently the dispersal rates that allow metapopulation persistence, would jointly depend on the state of the matrix, the structure and the size of suitable patches as well as the biological characteristics of the species (e.g. reproductive rate and dispersal ability; With, 2004).
Although impressive efforts have been made to model metapopulation dynamics, there is still a clear dichotomy in the factors being taken into account. On the one hand, studies analysing the effects of disturbances on metapopulations in relation to the size and the growth rate of the populations (Hastings & Wolin, 1989), patch quality (Hanski, 1994), matrix quality (Vandermeer & Carvajal, 2001) or all of these factors together (Casagrandi & Gatto, 1999) neglect the genetic effects of fragmentation, while on the other hand, studies exploring the genetic processes associated with fragmentation do not usually incorporate demographic and habitat considerations (Mills & Allendorf, 1996; Couvet, 2002; Glémin et al., 2003). Higgins & Lynch (2001) investigated the interaction of environmental, genetic and demographic stochasticity on metapopulation persistence. They showed that the incorporation of deleterious mutations accumulation changes significantly the predictions concerning the influence of dispersal and metapopulation structure on metapopulation persistence. However, they did not include in their model the effects of matrix quality, i.e. the consequences from the imbalance between emigration and immigration.
Our study is an attempt for a more synthetic view that explores the interplay of demographic and genetic processes in relation to habitat and matrix structure. We begin by assuming that both habitat patches and the matrix are homogeneous. Population dynamics within a habitat patch is modelled as the outcome of reproductive potential of the species and the balance between emigration and immigration. These demographic processes are influenced by underlying genetic processes, i.e. fitness depends on the frequency of deleterious mutations, and the dispersal rate may change according to the level of inbreeding within patches (referred to as avoidance of inbreeding). Patch and matrix quality are reflected on the carrying capacity of habitat patches and the survival rate of dispersing individuals respectively.
In order to highlight the synergistic action of demographic and genetic processes on metapopulation persistence, we compare our conclusions with the predictions of two models that consider each process separately: (i) a deterministic demographic model (Casagrandi & Gatto, 2002b), which ignores both the effects of inbreeding on population growth rate and the relationship between inbreeding and dispersal; and (ii) an infinite island model, widely used in theoretical genetic studies (Couvet, 2002; Whitlock, 2002; Glémin et al., 2003) that ignores the imbalance between emigration and immigration.
We then explore the consequences of heterogeneity in habitat patches. Heterogeneity can have contrasting effects on metapopulation dynamics (Ewers & Didham, 2005). For instance, Day & Possingham (1995) showed that according to the colonization rate, the variability in patch size can either decrease or increase the probability of metapopulation extinction relative to an equal patch-size metapopulation.
Finally, our model allows us to examine the relative influence of different types of habitat disturbance (e.g. removal of entire patches vs. reduction in patch size) on metapopulation persistence. Useful conclusions for the conservation of fragmented populations are extracted.