The role of between-patch dynamics in a metapopulation: a discrete-time modelling approach
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ORIGINAL PAPER
The role of between‑patch dynamics in a metapopulation: a discrete‑time modelling approach Nathan G. Marculis1 · Jorge Arroyo‑Esquivel2 · Alan Hastings1 Received: 22 April 2020 / Accepted: 30 September 2020 © Springer Nature B.V. 2020
Abstract We present a single-species metapopulation model structured by population size that is discrete in time. The novel formulation of our model allows for explicit incorporation of both the local, in space, dynamics and new details of the dispersal process. To study the impact of between-patch dynamics in the model, we construct various functions to describe density-dependent dispersal, recolonization, and between-patch stochasticity. Due to the complexity of the model, numerical simulations are used to obtain the distribution of the metapopulation. Moreover, we can use our model to predict the proportion of patches occupied, expected patch density, and variance in patch density. Our results provide insight into the influence that each of these processes play in the distribution of the metapopulation. In particular, our findings emphasize the benefit of explicitly modelling these processes. We consider two density-dependent dispersal strategies based upon individuals wanting to form average-sized patches and illustrate the differences in the metapopulation distributions. For recolonization of empty suitable patches, we look at two simplistic redistribution strategies modeled as either a continuous uniform or Laplace distribution. The between-patch stochasticity is modelled using redistribution kernels where we consider both thin-tailed and fat-tailed kernels. We find that the form of density-dependent dispersal has a major influence on the distribution of the metapopulation while recolonization is a key process for metapopulation persistence. In addition, fatter tails for the between-patch stochasticity can decrease the proportion of occupied patches and increase the expected patch density and variance in patch density. Keywords Metapopulation · Integrodifference equations · Dispersal · Recolonization · Stochasticity
Introduction Models for metapopulation dynamics have a rich history dating back to the original single-species model proposed by Levins (Levins , 1969a; Levins , 1969b). Many subsequent studies on single-species metapopulation dynamics realized the limitations of the Levins model and have incorporated more biological complexity (Levin and Paine , 1974; Hastings and Wolin , 1989; Gyllenberg and Hanski , 1997; Hanski , 1998). All of these models are continuous in time and assume a large, essentially infinite, number of local populations. An alternate approach (Hastings , 1993; Gyllenberg et al. , 1993; Gonzalez and Perry , 1993) of looking at the * Nathan G. Marculis [email protected] 1
Department of Environmental Science and Policy, University of California, Davis, California, USA
Department of Mathematics, University of California, Davis, California, USA
2
dynamics of two local populations connected by dispersal in discrete-time le
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