Quantifying the impact of ecological memory on the dynamics of interacting communities

Abstract

Ecological memory refers to the influence of past events on the response of an ecosystem to exogenous or endogenous changes. Memory has been widely recognized as a key contributor to the dynamics of ecosystems and other complex systems, yet quantitative community models often ignore memory and its implications. Recent studies have shown how interactions between community members can lead to the emergence of resilience and multistability under environmental perturbations. We demonstrate how memory can complement such models. We use the framework of fractional calculus to study how the outcomes of a well-characterized interaction model are affected by gradual increases in ecological memory under varying initial conditions, perturbations, and stochasticity. Our results highlight the implications of memory on several key aspects of community dynamics. In general, memory slows down the overall dynamics and recovery times after perturbation, thus reducing the system's resilience. However, it simultaneously mitigates hysteresis and enhances the system's capacity to resist state shifts. Memory promotes long transient dynamics, such as long-standing oscillations and delayed regime shifts, and contributes to the emergence and persistence of alternative stable states. Collectively, these results highlight the fundamental role of memory on ecological communities and provide new quantitative tools to analyse its impact under varying conditions.

Extending the Monod model of microbal growth with memory

“…The growth rate depends on an average of resource concentrations outside the cell, including potentially less-limiting concentrations from the recent past, instead of just current resource concentrations outside the cell. We refer to a as the memory element (or cell memory) following previous interpretations in the literature (Amirian et al, 2020;Khalighi et al, 2022). The appropriate value of a for a particular species will be determined by statistical data analysis incorporating a population model, presented below.…”