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The role of between-patch dynamics in a metapopulation: a discrete-time modelling approach

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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.

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Acknowledgements

This research is supported under NSF Grant DMS - 1817124 Metacommunity Dynamics: Integrating Local Dynamics, Stochasticity, and Connectivity. The authors would also like to thank the anonymous reviewers for providing detailed comments that helped improve and clarify this manuscript.

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Authors and Affiliations

  1. Department of Environmental Science and Policy, University of California, Davis, California, USA

    Nathan G. Marculis & Alan Hastings

  2. Department of Mathematics, University of California, Davis, California, USA

    Jorge Arroyo-Esquivel

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  1. Nathan G. Marculis
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  2. Jorge Arroyo-Esquivel
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  3. Alan Hastings
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Correspondence to Nathan G. Marculis.

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Marculis, N.G., Arroyo-Esquivel, J. & Hastings, A. The role of between-patch dynamics in a metapopulation: a discrete-time modelling approach. Theor Ecol 14, 161–172 (2021). https://doi.org/10.1007/s12080-020-00486-3

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