Synchrony and perturbation transmission in trophic metacommunities

Abstract

In a world where natural habitats are ever more fragmented, the dynamics of metacommunities is essential to properly understand species responses to perturbations. If species' populations fluctuate asynchronously, the risk of their simultaneous extinction is low, thus reducing the species' regional extinction risk. We propose a metacommunity model consisting of two food chains connected by dispersal to study the transmission of small perturbations affecting populations in the vicinity of an equilibrium. We show that perturbing a species in one patch can lead to asynchrony between patches if the perturbed species is not the most affected by dispersal. Dispersal affects rare species the most, thus making biomass distribution critical to understand the response of trophic metacommunities to perturbations. We further partition the effect of each perturbation on species synchrony when several independent perturbations are applied. Our approach allows disentangling and predicting the responses of simple trophic metacommunities to perturbations, thus providing a theoretical foundation for future studies considering more complex spatial ecological systems.

Synchrony and Stability in Trophic Metacommunities: When Top Predators Navigate in a Heterogeneous World

“…Stochastic perturbations are defined by their standard deviation σ i and a white noise term dW i with mean 0 and variance 1. In addition, perturbations scale with each species' biomass with an exponent z depending on the type of perturbation considered (Haegeman and Loreau, 2011;Arnoldi et al, 2019): exogenous stochasticity (from harvesting for instance) corresponds to z = 0, demographic stochasticity (from birth-death processes) to z = 0.5, and environmental factors to z = 1 (see demonstration in Lande et al, 2003 and in the Supplementary Material of Quévreux et al, 2021a). Arnoldi et al (2019) showed that when a species is perturbed, the ratio of its biomass variance to perturbation variance increases with the species' biomass in the case of environmental perturbations, while it is independent of its biomass in the case of demographic perturbations.…”

“…Arnoldi et al (2019) showed that when a species is perturbed, the ratio of its biomass variance to perturbation variance increases with the species' biomass in the case of environmental perturbations, while it is independent of its biomass in the case of demographic perturbations. Therefore, Quévreux et al (2021a) and Quévreux et al (2021c) chose demographic perturbations in their analysis as these enabled them to perturb different species with the same relative intensity regardless of their abundance.…”

“…Synchrony in the metacommunity can be evaluated from the covariance between the temporal variations of the various species and patches, which are encoded in the variancecovariance matrix C * . If the metacommunity is at equilibrium and perturbations are small enough, we can linearise the system in the vicinity of the equilibrium to get Equation (2) where X i = B i − B * i is the deviation from equilibrium [see the Supplementary Material of Quévreux et al (2021a) for more mathematical details].…”

“…The metacommunity model used by Quévreux et al (2021a) and Quévreux et al (2021c) is based on the food chain model developed by Barbier and Loreau (2019), which corresponds to the "intra-patch dynamics" part of Equations ( 5a) and (5b), and integrates a dispersal term to consider a metacommunity with two patches (Figure 2A).…”

“…Therefore, the temporal variability of biomass, measured by coefficient of variation (CV), is a much better metric because it can be easily measured experimentally and gives access to synchrony (Vasseur and Fox, 2009;Fox et al, 2013). In addition, the CV of biomass in response to stochastic perturbations is a powerful theoretical tool used by Quévreux et al (2021a) to disentangle the different mechanisms governing synchrony as perturbations can affect particular species and are then transmitted across the metacommunity.…”