Increased persistence via asynchrony in oscillating ecological populations with long-range interaction

Abstract

Understanding the influence of structure of dispersal network on the species persistence and modeling a much realistic species dispersal in nature are two central issues in spatial ecology. A realistic dispersal structure which favors the persistence of interacting ecological systems has been studied in [Holland \& Hastings, Nature, 456:792--795 (2008)], where it is shown that a randomization of the structure of dispersal network in a metapopulation model of prey and predator increases the species persistence via clustering, prolonged transient dynamics, and amplitudes of population fluctuations. In this paper, by contrast, we show that a deterministic network topology in a metapopulation can also favor asynchrony and prolonged transient dynamics if species dispersal obeys a long-range interaction governed by a distance-dependent power-law. To explore the effects of power-law coupling, we take a realistic ecological model, namely the Rosenzweig-MacArthur model in each patch (node) of the network of oscillators, and show that the coupled system is driven from synchrony to asynchrony with an increase in the power-law exponent. Moreover, to understand the relationship between species persistence and variations in power-law exponent, we compute correlation coefficient to characterize cluster formation, synchrony order parameter and median predator amplitude. We further show that smaller metapopulations with less number of patches are more vulnerable to extinction as compared to larger metapopulations with higher number of patches. We believe that the present work improves our understanding of the interconnection between the random network and deterministic network in theoretical ecology.