Dispersal-induced synchrony, temporal stability, and clustering in a mean-field coupled Rosenzweig–MacArthur model

Abstract

In spatial ecology, dispersal among a set of spatially separated habitats, named as metapopulation, preserves the diversity and persistence by interconnecting the local populations. Understanding the effects of several variants of dispersion in metapopulation dynamics and to identify the factors which promote population synchrony and population stability are important in ecology. In this paper, we consider the mean-field dispersion among the habitats in a network and study the collective dynamics of the spatially extended system. Using the Rosenzweig–MacArthur model for individual patches, we show that the population synchrony and temporal stability, which are believed to be of conflicting outcomes of dispersion, can be simultaneously achieved by oscillation quenching mechanisms. Particularly, we explore the more natural coupling configuration where the rates of dispersal of different habitats are disparate. We show that asymmetry in dispersal rate plays a crucial role in determining inhomogeneity in an otherwise homogeneous metapopulation. We further identify an unusual emergent state in the network, namely, a multi-branch clustered inhomogeneous steady state, which arises due to the intrinsic parameter mismatch among the patches. We believe that the present study will shed light on the cooperative behavior of spatially structured ecosystems.Maintaining species diversity and persistence regionally in fragmented landscapes is a challenging task in spatial ecology. Often population dispersal among a set of spatially separated habitats, named as metapopulation, preserves the diversity and persistence by interconnecting the local populations. Ecologists studied the effects of dispersal in metapopulation dynamics to identify the factors which promote the population synchrony and population stability. In fact, various dispersal strategies have been used to identify the significance of dispersal in long term persistence of populations. Here, we analyze the mean- field coupled Rosenzweig–MacArthur (RM) model with various dispersal assumptions. We exhibit the behavioral aspect of vegetation and herbivore dispersal in terms of oscillation quenching mechanisms. Further, using this mechanism, we emphasize the simultaneous occurrence of synchrony and stability through spatial and environmental heterogeneity in a network of many (more than two) interacting patches. Also, new collective behavior, like multi-branch and multi-cluster inhomogeneous steady states, arises that will broaden our understanding of real ecosystems.