Interactive effects of temporal correlations, spatial heterogeneity and dispersal on population persistence

It is an ecological truism that population persistence depends on a population's growth rate when rare. To understand the interplay between temporal correlations, spatial heterogeneity and dispersal on persistence, an analytic approximation for this growth rate is derived for partially mixing populations. Partial mixing has two effects on population growth. In the absence of temporal correlations in relative fitness, greater movement to patches with, on average, higher relative fitness increases population growth rates. In the absence of spatial heterogeneity in the average relative fitnesses, lower dispersal rates enhance population growth when temporal autocorrelations of relative fitness within a patch exceed temporal cross-correlations in relative fitness between patches. This approximation implies that metapopulations whose expected fitness in every patch is less than 1 can persist if there are positive temporal autocorrelations in relative fitness, sufficiently weak spatial correlations and the population disperses at intermediate rates. It also implies that movement into lower quality habitats increases the population growth rate whenever the net temporal variation in per capita growth rates is sufficiently larger than the difference in the means of these per capita growth rates. Moreover, temporal autocorrelations, whether they be negative or positive, can enhance population growth for optimal dispersal strategies.