Quantifying the impact of ecological memory on the dynamics of interacting communities
Fig 1
Schematic illustration of a three-species community in the presence of memory and perturbations.
(A) Mutual interaction model introduced by Gonze et al. [25] to illustrate the emergence of alternative stable states in human gut microbial communities. The model describes the dynamics of species abundances Xi as functions of growth rates bi, death rates ki, and inhibition functions fi, where Kij and n denote interaction constants and Hill coefficients, respectively. (B) Standard perturbations include pulse, periodic, and stochastic variation in species immigration, death, or growth rates. Such perturbations may trigger shifts between alternative states. (C) Memory (bolded circles) can be incorporated into dynamical models by substituting the integer-order derivatives with fractional derivatives of order μi (see [37] and Methods). As decreasing μi values correspond to increasing memory, memory is measured as 1 − μi. When all community members have the same memory (μi = μ for all i), the system is said to have commensurate memory, otherwise incommensurate. Increasing memory changes community dynamics, in particular by introducing inertia and modifying the stability landscape around stable states. (D) Ecological memory can change the system dynamics under perturbations.