Spatial patterns emerging from a stochastic process near criticality

Abstract

There is mounting empirical evidence that many communities of living organisms display key features which closely resemble those of physical systems at criticality. We here introduce a minimal model framework for the dynamics of a community of individuals which undergoes local birth-death, immigration and local jumps on a regular lattice. We study its properties when the system is close to its critical point. Even if this model violates detailed balance, within a physically relevant regime dominated by fluctuations, it is possible to calculate analytically the probability density function of the number of individuals living in a given volume, which captures the close-to-critical behavior of the community across spatial scales. We find that the resulting distribution satisfies an equation where spatial effects are encoded in appropriate functions of space, which we calculate explicitly. The validity of the analytical formulae is confirmed by simulations in the expected regimes. We finally discuss how this model in the critical-like regime is in agreement with several biodiversity patterns observed in tropical rain forests.

Asymmetric stochastic resetting: Modeling catastrophic events

“…Instead, B(x) is linear on the population size, because the model assumes that the source of stochasticity is only due to individual random births and deaths. This framework has been used to explain some macro-ecological patterns in species-rich ecosystems [39,40]. In this case the asymmetric resetting describes how the population size plummets to a smaller size in the aftermath of environmental catastrophic events.…”

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

“…On this perspective, some experimental field works on plant biodiversity [42][43][44][45] have shown that the diversity within an ecosystem tends to be correlated positively with the community-level stability (measured as the inverse of the CV in community biomass) while it is only weakly correlated with CV for year to year variation in biomass of individual species (e.g. see Figures (6) and ( 9) in [44]). Also, some other studies on controlled microcosm experiments [46][47][48][49][50][51] have suggested that individual specie population-level variation is relatively uninfluenced by diversity, whereas community-level variations tends to decrease with increased diversity.…”

“…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).…”

Effective Resource-Competition Model for Species Coexistence

“…Instead of looking at what specific traits facilitate species' survival, this approach highlights the general features which tend to make species more similar to each other. This framework has the merit to predict several patterns in agreement with the empirical data [35][36][37][38][39][40]. However, it lacks a convincing mechanism of coexistence, which is usually maintained only by an external source of individuals.…”