The demography of a metapopulation in an environment changing in time and space

The persistence of populations living in heterogeneous environments crucially depends on the interaction between changes of the environment in space and time, and the way individuals move between locations. Here an approximation for the multiplicative growth rate of a metapopulation is derived, as a function of the properties of the spatial heterogeneity and temporal change in local habitat quality, and the dispersal pattern. This analysis reveals that the growth rate depends on (i) the geometric mean of the average growth rate in the metapopulation, (ii) whether individuals tend to be more numerous in high quality demes and (iii) temporal fluctuations in the spatial distribution of individuals. The two latter effects had been previously identified but mostly in simulation studies. Here I identify them in a unified analytical framework which helps clarifying previous studies. This analysis reveals that the shape of temporal variability interacts with the dispersal rate to determine the growth of the metapopulation, and in particular that the effects of dispersal depend on the level of temporal correlation of the environment.