Metapopulation Dynamics of Multiple Species: The Geometry of Competition in a Fragmented Habitat

Abstract

Populations of species living within a spatially fragmented habitat may be affected by interspecific competition on a regional time scale. Metapopulation theory is a potentially powerful tool for understanding the dynamics of such competing species, but metapopulation models with competition are often too complex to be useful as guides for empirical investigation. In this paper I employ two techniques from dynamical systems theory (perturbation expansion and the examination of invariant manifolds) in a qualitative and quantitative analysis of two-species competition within a metapopulation, with the goal of using geometric ideas to provide insight into how competition affects species living in a fragmented habitat. Four-state metapopulation competition models (where habitat patches may be occupied by either of two competing species, both, or neither) can be analyzed as perturbations of simpler three-state models (those without doubly occupied patches as one of the state variables). Symmetric competition for patches is always unstable in three-state Levins-type metapopulations, but generally stable in analogous mainland-island systems. The attracting manifold of a three-state system has the form of an invariant curve joining the two species' Levins equilibria. Under asymmetric competition for patches, coexistence is possible only if the inferior competitor possesses a higher equilibrium proportion of occupied patches in the absence of competition. Asymmetric competition changes the nature of the attracting manifold, with the limit case a curve that is locally tangent to a line parallel to the axis for the proportion of occupied patches of the inferior competitor. The interior equilibrium of a four-state model can be calculated as a perturbation expansion in a parameter ␣, the fraction of doubly occupied patches that contribute to recolonization. The perturbation method in conjunction with center manifold analysis proves that coexistence of like species within a metapopulation is possible if and only if there is recolonization from doubly occupied patches. Rescue effects may make competitive coexistence impossible via the creation of a saddle-point equilibrium having one-dimensional stable and unstable manifolds. Application of the theory to published data from several species of Daphnia in Fennoscandia shows good quantitative agreement with observations and makes several new qualitative predictions. The results are discussed in connection with ecological dynamics of similar forms, including those in the process of speciation.

Modeling competition, niche, and coexistence between an invasive and a native species in a two‐species metapopulation

“…Thus, providing evidence for niche partitioning is not sufficient to argue that it plays a large role in coexistence. We also show that theoretical models that inspire the patch-dynamic perspective often rely on assumptions unlikely to be met in metacommunities, and that models integrating doubly occupied sites and transient co-occurrence (Slatkin 1974, Taneyhill 2000 may provide parsimonious explanations to regional coexistence, even in the case of similar species.…”

“…Our system differs from this idealized situation in two ways: competition is not efficient enough to preclude co-occurrence within patches (70% of doubly occupied patches remain in this state from one year to the next), and species may compensate for differences in competitive replacement ability not only by colonization, but also by persistence and competitive preemption (here, A. marmorata has stronger replacement effects, and P. acuta stronger preemption effects). The available models that best capture these characteristics are metapopulation models of two competing species (Slatkin 1974, Taneyhill 2000 in which conditions for coexistence at the landscape scale are not as stringent as in classical competition-colonization metacommunity models. For example, competition may elevate the threshold colonization rate below which a species cannot persist, but this threshold does not have to exceed the colonization rate of the competitor (e.g., Taneyhill 2000).…”

“…The available models that best capture these characteristics are metapopulation models of two competing species (Slatkin 1974, Taneyhill 2000 in which conditions for coexistence at the landscape scale are not as stringent as in classical competition-colonization metacommunity models. For example, competition may elevate the threshold colonization rate below which a species cannot persist, but this threshold does not have to exceed the colonization rate of the competitor (e.g., Taneyhill 2000). Accordingly, our simulations suggest that although A. marmorata has a greater basal colonization rate than P. acuta, and P. acuta a higher basal local persistence rate than A. marmorata, these conditions were not required for them to coexist.…”

The roles of competition and habitat in the dynamics of populations and species distributions

“…Since the two species we studied have overlapping, but distinct, habitat preferences (Wiens 2012), our study also allows us to investigate how competition affects the relationship between occupancy and habitat covariates. This work is thus expected to inform general theory about competition and coexistence in multispecies metapopulation systems in fragmented habitat (Holt 1997, Nee et al 1997, Taneyhill 2000, Leibold et al 2004). It will also allow us to evaluate the effects of competition on species distributions, as well as conservation efforts directed at persistence of Northern Spotted Owls in the face of increasing Barred Owl populations (Kelly et al 2003, Gutie´rrez et al 2007.…”

Fisher waves and front roughening in a two-species invasion model with preemptive competition

“…However, recent developments emphasize the ecological realism of discrete individuals [7,8,9]. Our study analyzes front propagation when two plant species compete preemptively [10,11,12,13,14] for a common limiting resource. Discrete individuals of each species propagate clonally, so that competitive interactions are spatially localized.…”