Effective Resource-Competition Model for Species Coexistence

Abstract

Local coexistence of species in large ecosystems is traditionally explained within the broad framework of niche theory. However, its rationale hardly justifies rich biodiversity observed in nearly homogeneous environments. Here we consider a consumer-resource model in which effective spatial effects, induced by a coarse-graining procedure, exhibit stabilization of intra-species competition. We find that such interactions are crucial to maintain biodiversity. Herein, we provide conditions for several species to live in an environment with a very few resources. In fact, the model displays two different phases depending on whether the number of surviving species is larger or smaller than the number of resources. We obtain conditions whereby a species can successfully colonize a pool of coexisting species. Finally, we analytically compute the distribution of the population sizes of coexisting species. Numerical simulations as well as empirical distributions of population sizes support our analytical findings.

Cross-feeding shapes both competition and cooperation in microbial ecosystems

“…More ambitiously, if will be interesting to extend our calculation to derive dynamical mean-field equations [32,39]. Another promising direction is to understand how space and migration modify the intuitions found here [40][41][42]. Finally, we would like to explore if we can exploit the mean-field equations derived here to understand ecoevolutionary dynamics in the presence of cross-feeding [43].…”

Well-mixed Lotka-Volterra model with random strongly competitive interactions

“…As yet, there is no single, well-established theory allowing us to understand such systems and to integrate the plethora of empirical data coming from a growing number of controlled experiments. In particular, a quantitative general framework able to discriminate between the niche theory [3,4]-based on a limited number of niches, each occupied by a single species according to the competitive exclusion principle [5] -and neutral models [6] -which focus on general features contributing to making species more similar to the others -is still missing. Mechanisms according to which individuals shape and re-organize their niche have been studied both at equilibrium and in outof-equilibrium settings, using for instance time series and ecological successions principles.…”

Effect of delay on the emergent stability patterns in Generalized Lotka-Volterra ecological dynamics

“…A fascinating aspect in the study of biological and ecological systems is the emergence of ubiquitous patterns that do not depend on the specific details of the system under study [1][2][3][4][5][6][7] In this context, one of the main problems of theoretical ecology is the search for key mechanisms leading to the emergence and maintenance of biodiversity. The conditions for many species to coexist in spite of changing environment or perturbations are tightly connected to the problem of understanding when and how ecological systems are feasible (i.e., all solutions are positive at large times) and asymptotically stable (i.e., the real parts of all the eigenvalues of the Jacobian are negative).…”