Dynamic processes in complex communities: interplay of noise, nonlinearity, and network structure

Abstract

Mathematical modeling of spatial ecological systems has signi cantly contributed to our understanding of population dynamics, species distribution across space, collective behavior, and ecological stability. The theory of dynamical systems and diverse numerical methods are instrumental in studying spatial population models. In this thesis, we study various mathematical models of spatial ecological systems to understand the e ect of demographic and environmental stochasticity, dispersal network topology, species movement patterns, and arrangement of landscape on ecosystem dynamics. Noise-induced symmetry breaking has barely been unveiled on ecological grounds, though its occurrence may elucidate mechanisms responsible for maintaining biodiversity and ecosystem stability. We study an ecological network model and demonstrate that the interplay of network structure and noise intensity manifests a transition from homogeneous steady state to inhomogeneous steady states, resulting in noise-induced symmetry breaking. Further, we move beyond dyadic couplings and consider the higher-order species interactions in an ecological network. We study the synchrony patterns and observe that higher-order interactions bring about signi cant changes in collective behavior compared to the conventional pairwise interaction. We also nd the region where the synchronous state is stable using the master stability function. The ability of species to move between fragmented landscapes is an essential factor in ascertaining the dynamics and spatial distribution of populations. Further, the e ect of resource pulses on ecological processes due to environmental variation in the context of foraging strategies remains largely unexplored. Considering resource pulses, we analyze the uni ed impact of foraging behavior and species life-history traits on the structure and dynamics of ecosystems. We nd that a Levy walk is consistently e ective as a movement strategy. We also nd that the optimal foraging behavior shifts from Brownian to ballistic as the mortality rate of grazers increases. In addition, our study comprehends how climate warming and spatial separation between habitat patches inuence species collective dynamics. We nd that rising habitat temperature has the potential to destabilize ecological dynamics, and density-dependent species dispersal can mitigate these adverse e ects. Moreover, long-range dispersal works out as the driving force for species persistence in extreme temperature conditions of habitat.