Self-consistent dispersal puts tight constraints on the spatiotemporal organization of species-rich metacommunities

Abstract

Biodiversity is often attributed to a dynamic equilibrium between the immigration and extinction of species. This equilibrium forms a common basis for studying ecosystem assembly from a static reservoir of migrants—the mainland. Yet, natural ecosystems often consist of many coupled communities (i.e., metacommunities), and migration occurs between these communities. The pool of migrants then depends on what is sustained in the ecosystem, which, in turn, depends on the dynamic migrant pool. This chicken-and-egg problem of survival and dispersal is poorly understood in communities of many competing species, except for the neutral case—the “unified neutral theory of biodiversity.” Employing spatiotemporal simulations and mean-field analyses, we show that self-consistent dispersal puts rather tight constraints on the dynamic migration–extinction equilibrium. When the number of species is large, species are pushed to the edge of their global extinction, even when competition is weak. As a consequence, the overall diversity is highly sensitive to perturbations in demographic parameters, including growth and dispersal rates. When dispersal is short range, the resulting spatiotemporal abundance patterns follow broad scale-free distributions that correspond to a directed percolation phase transition. The qualitative agreement of our results for short-range and long-range dispersal suggests that this self-organization process is a general property of species-rich metacommunities. Our study shows that self-sustaining metacommunities are highly sensitive to environmental change and provides insights into how biodiversity can be rescued and maintained.

Tipping points emerge from weak mutualism in metacommunities

“…Looking at the abundance distribution P[N ] at a dispersal rate close above λ c , we observe that when increasing the number of species, its shape transitions from a scaling P[N ] ∝ x N /N for small N , a common scaling in ecology often referred to as Fisher-log series (28,29), to an approximate Gaussian distribution [see Fig. 2(b), for details see (23) and Appendix 2]. In summary, our numerical and analytical results strongly suggest that despite the lack of bistability in the deterministic and well-mixed population dynamics, the metacommunity displays a tipping point accompanied by a regime of bistability.…”

“…S = 1, the growth and dispersal dynamics represented by Eq. (1) have been extensively studied for short-range dispersal in the context of directed percolation (21, 22) and for global dispersal in metapopulations (23–26). From these earlier studies we expect that for S = 1, increasing the dispersal rate leads to a continuous transition from a phase of zero population size (absorbing phase) to a phase of finite population sizes (active phase).…”

“…To get deeper insights into the exact form of the bifurcation, we employ a mean-field approximation of Eq. (1), that has been recently presented to approximate the stationary abundance distribution for metacommunities with competitive interactions (23). In short, by expressing the interaction term through the species-averaged abundance on a patch defined as and treating the mean-fields and as deterministic mean-field parameters, we can map the dynamics Eq.…”

“…(1) to the solvable problem of a Brownian particle in a fixed potential. Demanding that and are both equal in equilibrium (in the limit of an infinite number of species and patches) we can derive an analytic expression for the abundance distribution as a function of the mean species abundance and the control parameters r, K, a, S , and λ , which can be solved self-consistently [for a detailed derivation see (23) and Appendix 2]. In agreement with our numerical solution, our analytic mean-field approximation predicts bistability between the dispersal rate λ c [for an analytic expression see (23) and Appendix 2] and a lower dispersal rate λ t , which marks a point where a small decrease of the dispersal rate causes an abrupt shift from finite population size to extinction, often referred to as tipping point (10) [see dashed vertical lines in Fig.…”

“…Looking at the abundance distribution at a dispersal rate close above λ c , we observe that when in-creasing the number of species, its shape transitions from a scaling for small N , a common scaling in ecology often referred to as Fisher-log series (28, 29), to an approximate Gaussian distribution [see Fig. 2(b), for details see (23) and Appendix 2].…”