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 coeffi-
cient 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.
