Spatially structured populations in patchy habitats show much variation in migration rate, from patchy populations in which individuals move repeatedly among habitat patches to classic metapopulations with infrequent migration among discrete populations. To establish a common framework for population dynamics in patchy habitats, we describe an individual-based model (IBM) involving a diffusion approximation of correlated random walk of individual movements. As an example, we apply the model to the Glanville fritillary butterfly (Melitaea cinxia) inhabiting a highly fragmented landscape. We derive stochastic patch occupancy model (SPOM) approximations for the IBMs assuming pure demographic stochasticity, uncorrelated environmental stochasticity, or completely correlated environmental stochasticity in local dynamics. Using realistic parameter values for the Glanville fritillary, we show that the SPOMs mimic the behavior of the IBMs well. The SPOMs derived from IBMs have parameters that relate directly to the life history and behavior of individuals, which is an advantage for model interpretation and parameter estimation. The modeling approach that we describe here provides a unified framework for patchy populations with much movements among habitat patches and classic metapopulations with infrequent movements.Keywords: patchy population, metapopulation, individual-based model, stochastic patch occupancy model, Glanville fritillary butterfly, SPOMSIM.* E-mail: otso.ovaskainen@helsinki.fi. † E-mail: ilkka.hanski@helsinki.fi. Populations and metapopulations inhabiting fragmented landscapes show much variation in migration rate among habitat patches. In one extreme, termed the patchy population model (Harrison 1991), individuals move frequently among habitat patches and may reproduce in several patches during their lifetime. In the other extreme, most individuals remain all their life in the natal population, and movements among populations are infrequent, though migration rate is high enough to allow eventual recolonization of habitat patches where a local population has gone extinct (the classic metapopulation model; Levins 1969). Clearly, it would be helpful to have a theoretical framework that allows the full range of migration rate to be modeled. One such modeling framework is called structured metapopulation models, which are structured by the distribution of local population sizes (Hastings and Wolin 1989;Gyllenberg and Hanski 1992;Lande et al. 1998Lande et al. , 1999Casagrandi and Gatto 1999;Saether et al. 1999) or by a simple classification of population sizes (Hanski 1985;Hastings 1991;Hanski and Zhang 1993). Local dynamics and migration are modeled mechanistically, and there are no restrictions on the rate of migration; the consequences of emigration and immigration on local dynamics are fully accounted for. However, these models make the simplifying island model assumptions of global migration among infinitely many identical habitat patches (the assumption of identical patches was relaxed by Gyll...
I analyze stochastic patch occupancy models (SPOMs), which record habitat patches as empty or occupied. A problem with SPOMs has been that if the spatial structure of a heterogeneous habitat patch network is taken into account, the computational effort needed to analyze a SPOM grows as a power of 2n, where n is the number of habitat patches. I propose a computationally feasible approximation method, which approximates the behavior of a heterogeneous SPOM by an "ideal" metapopulation inhabiting a network of identical and equally connected habitat patches. The transformation to the ideal metapopulation is based on weighting the individual patch occupancies by the dynamic values of the habitat patches, which may be calculated from the deterministic mean-field approximation of the original SPOM. Conceptually, the method resembles the calculation of the effective size of a population in the context of population genetics. I demonstrate how the method may be applied to SPOMs with flexible structural assumptions and with spatially correlated and temporally varying parameter values. I apply the method to a real habitat patch network inhabited by the Glanville fritillary butterfly, illustrating that the metapopulation dynamics of this species are essentially driven by temporal variability in the environmental conditions.
We modeled hierarchical multiscale colonization-extinction dynamics of two aphid species living in a shared host plant. We parameterized the model with data collected at the level of individual ramets of the host plant, with the plants being organized as groups within islands. As expected, the extinction rates and per capita colonization rates decreased with increasing spatial scale. The per capita colonization rates were greater for winged than for unwinged individuals, but as the unwinged individuals were much more abundant, they actually performed most of the colonizations. Colonizations and extinctions were negatively correlated, so that when the colonization rate in a given island was high, the extinction rate in the same island was low. There was a clear indication of interspecific interaction, with the presence of one species increasing the extinction rate and decreasing the colonization rate of the other species. Further simulation results based on the parameterized model show a contrasting pattern between the two species, with Metopeurum fuscoviride (with relatively stable dynamics) being favored by a highly aggregated distribution of the ramets, whereas for Macrosiphoniella tanacetaria (with a high turnover rate), an equally high persistence time follows if the plants are distributed in a segregated manner over several islands.
Functional connectivity is a fundamental concept in conservation biology because it sets the level of migration and gene flow among local populations. However, functional connectivity is difficult to measure, largely because it is hard to acquire and analyze movement data from heterogeneous landscapes. Here we apply a Bayesian state-space framework to parameterize a diffusion-based movement model using capture-recapture data on the endangered clouded apollo butterfly. We test whether the model is able to disentangle the inherent movement behavior of the species from landscape structure and sampling artifacts, which is a necessity if the model is to be used to examine how movements depend on landscape structure. We show that this is the case by demonstrating that the model, parameterized with data from a reference landscape, correctly predicts movements in a structurally different landscape. In particular, the model helps to explain why a movement corridor that was constructed as a management measure failed to increase movement among local populations. We illustrate how the parameterized model can be used to derive biologically relevant measures of functional connectivity, thus linking movement data with models of spatial population dynamics.
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