Synchrony and stability: towards understanding temporal and spatial dynamics of ecosystems

Abstract

Synchrony and stability are two important dynamical phenomena which are widely observed in population ecology. These two phenomena have great importance for better management of ecosystem functioning and theoretical understanding of these two phenomena in population dynamics is still demanding. In this thesis, various mathematical models of ecological systems and the concepts of nonlinear dynamics are taken into account, the relationship between synchrony and stability is characterized in terms of time and space. At first, using a minimal chemostat model, we show that the interaction between toxic and non-toxic phytoplankton species with changing competitive effects among species due to allelopathy helps to promote the stable coexistence of many species on a single resource and hence can be considered as an alternative solution of the paradox of plankton. Further, we demonstrate a framework for understanding the effect of dispersal in promoting synchrony and stability in ecosystems. Various network topologies in metapopulation models are taken into account, additional mortality driven by misdirected migration, failed migration and death due to overcrowding is addressed using different dispersal structures. The considered mean-field coupling enables various complex behaviours such as rhythmogenesis and birhythmicity, period-doubling of limit cycle and even chaotic oscillations. Importantly, both population synchrony and temporal stability, which are believed to be of conflicting outcomes of dispersion, can be simultaneously achieved by oscillation quenching mechanisms. Excitability is one of the interesting features of slow-fast dynamical systems that is characterized by the fact that a small perturbation in the input leads to a large excursion in phase space before coming to the rest state. There also exists examples of excitability and slow-fast time scales in ecosystems. Also, most of the spatially separated habitats where species live are highly dynamic rather than just static, we model the consumerresource interactions in a common dynamic environment along with dispersal in a ring type coupled network. Under different environmental conditions, the interplay between excitability and dispersal, as well as the interplay between dynamic environment and dispersal characterize the synchrony-stability relationship through oscillation quenching as well as oscillation generation mechanisms. Finally, emphasizing intrinsic heterogeneity via period mismatch and seasonal variation in the context of metapopulation dynamics, we address how dispersal, heterogeneity and seasonal fluctuations are associated with time-dependent habitats in promoting synchronization. Explicitly, by introducing heterogeneity in terms of time scale difference along with dispersal, we explore the quasiperiodic, phase-synchronization and entrainment behaviour with/without seasonal force. Indeed, we find that the right balance between seasonality, stochasticity and non-linearity can increase the persistence of metapopulation dynamics. Overall, we believe that our findings in terms of temporal and spatial dynamics provides a better understanding of population synchrony and stability in diverse ecological systems.