Effect of delay on the emergent stability patterns in generalized Lotka–Volterra ecological dynamics

Abstract

Understanding the conditions of feasibility and stability in ecological systems is a major challenge in theoretical ecology. The seminal work of May in 1972 and recent developments based on the theory of random matrices have shown the existence of emergent universal patterns of both stability and feasibility in ecological dynamics. However, only a few studies have investigated the role of delay coupled with population dynamics in the emergence of feasible and stable states. In this work, we study the effects of delay on generalized Loka–Volterra population dynamics of several interacting species in closed ecological environments. First, we investigate the relation between feasibility and stability of the modelled ecological community in the absence of delay and find a simple analytical relation when intra-species interactions are dominant. We then show how, by increasing the time delay, there is a transition in the stability phases of the population dynamics: from an equilibrium state to a stable non-point attractor phase. We calculate analytically the critical delay of that transition and show that it is in excellent agreement with numerical simulations. Finally, following a similar approach to characterizing stability in empirical studies, we investigate the coefficient of variation, which quantifies the magnitude of population fluctuations. We show that in the oscillatory regime induced by the delay, the variability at community level decreases for increasing diversity. This article is part of the theme issue ‘Emergent phenomena in complex physical and socio-technical systems: from cells to societies’.

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“…To solve this disagreement, some authors have proposed generalizations of the original work of May (1972) that account for non-random among-species interactions (Yodzis, 1981;Rooney et al, 2006), or the stabilizing role of dispersal and spatial heterogeneity (Plitzko and Drossel, 2015;Gravel et al, 2016). Other approaches have suggested that the disagreement is caused by a focus on asymptotic resilience in theoretical studies (Pimm, 1984;McCann, 2000;Saeedian et al, 2022), which is biased by rare species (Haegeman et al, 2016). Our results adhere to this point of view, by showing that more complex systems (i.e., ecological and spatial networks, as opposed to single species and locations) are inevitably less variable, if using normalized estimates that correct for inherent effects on system size of system complexity.…”

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“…Saeedian et al's article Effect of delay on the emergent stability patterns in Lotka-Volterra ecological dynamics [175] finds itself at the ecosystem scale. They tackle the problem of ecosystem stability when the realistic feature of delayed interactions between species is incorporated in a generalized Lotka-Volterra model.…”