Quantifying the impact of ecological memory on the dynamics of interacting communities
Fig 7
Impact of memory on the dynamics of an empirically parameterized bistable community.
(A-B) Dynamics of a bistable community composed of Bacteroides uniformis (BU) and Bacteroides thetaiotaomicron (BT), as simulated from a gLV model fitted to a set of empirical time series by Venturelli et al. [39] in which we have introduced memory effects (Eq (2) in the Methods). (A) Dynamics for the same initial conditions as one of the empirical time series used to fit the model. The original empirical data are indicated by squares and (truncated) error bars centered on the squares, representing the mean and standard deviation across biological replicates, respectively. (B) Dynamics for initial conditions leading to the alternative stable state dominated by BU. (A) and (B) illustrate that increasing memory lengthens the convergence time to the stable state, although it may hasten it in initial stages. (C-D) For each matrix entry in (E-F), a pulse perturbation is applied to the growth rate of BU (C), which temporarily displaces the community away from its original stable state dominated by BT (D). Convergence is achieved once species abundances reach an arbitrarily set convergence interval (in purple). (E-F) Recovery time to stable state after perturbation as a function of memory strength in BU and BT (the upper-left cell corresponds to the memoryless case). Both color and matrix entries indicate the recovery time after a pulse perturbation starting from the BT-dominated stable state, as illustrated in (C-D). (E) Recovery times are measured using a loose convergence interval (Bray-Curtis dissimilarity of 0.02 or lower between the community’s current state and its initial stable state), thus capturing the early stages of the recovery. Recovery time decreases with increasing memory, i.e., memory effects increase resilience. (F) Recovery times are now measured using a much tighter convergence interval (Bray-Curtis dissimilarity of 7e − 4 or lower), thus capturing the later stages of the recovery. Recovery time now decreases with increasing memory, i.e., memory effects decrease resilience. Hence, as for the two-species Gonze model in S8 Fig, the effect of memory on resilience depends on the time scale considered: memory hastens the recovery at first (E) but slows it down further in time (F).