The Impact of Habitat Impermanence on Metapopulation Viability and Size

Habitat is often impermanent causing the amount and spatial distribution of habitat patches available to species to vary through time. Theory calls for metrics that fully account for the impact of habitat impermanence on metapopulations, yet all use averages that homogenize spatiotemporal impacts of habitat impermanence in some manner. We develop a novel modelling approach using a deterministic variation of the widely used spatially realistic Levins model paired with a continuous time Markov chain to capture the stochastic impacts of habitat impermanence on finite metapopulations. From this model we derive analytic expectations of metapopulation viability and size by weighting landscape capacities and equilibrium occupancies by the quasi-equilibrium distribution of habitat configurations exhibited by landscapes characterized by a simplest form of habitat impermanence (i.e. random and independent habitat patch loss and gain at constant rates). These provide expectations of metapopulation viability and size in absence of transient metapopulation dynamics. We then show how dispersal and colonization/extinction rates, relative to rates of habitat change, separately impact metapopulation viability and size. Using simulations of our model, we show the measures we propose invariably improve estimation of metapopulation viability and size from earlier estimates, but ultimately overestimate both when species less able to keep pace with rates of change from habitat impermanence in the landscapes they occupy. Our research identifies the importance of fully accounting for spatial habitat configurations through time, and highlights the importance of transient dynamics as rates of habitat impermanence increase.