Solution of the spatial neutral model yields new bounds on the Amazonian species richness

Abstract

Neutral models, in which individual agents with equal fitness undergo a birth-death-mutation process, are very popular in population genetics and community ecology. Usually these models are applied to populations and communities with spatial structure, but the analytic results presented so far are limited to well-mixed or mainland-island scenarios. Here we combine analytic results and numerics to obtain an approximate solution for the species abundance distribution and the species richness for the neutral model on continuous landscape. We show how the regional diversity increases when the recruitment length decreases and the spatial segregation of species grows. Our results are supported by extensive numerical simulations and allow one to probe the numerically inaccessible regime of large-scale systems with extremely small mutation/speciation rates. Model predictions are compared with the findings of recent large-scale surveys of tropical trees across the Amazon basin, yielding new bounds for the species richness (between 13100 and 15000) and the number of singleton species (between 455 and 690).

Spatial Patterns Emerging from a Stochastic Process Near Criticality

“…These flows of probability among microstates break detailed balance and time symmetry and produce macroscopic nonequilibrium behavior. A common way to overcome these hurdles is to formulate some kind of effective Langevin equation which describes the dynamics of the mesoscopic variables of interest, losing track, however, of the underlying microscopic dynamics [13][14][15]. Nonetheless, in this paper we study a model which, despite violating microscopic detailed balance [16,17], allows one to study analytically (stationary) out-of-equilibrium properties of spatial patterns.…”

Stochastic Spatial Models in Ecology: A Statistical Physics Approach

“…where in each time window there is a preference for a randomly chosen species. Different works have recently analyzed this type of models, showing that time-dependent habitat preference greatly improves predictions of empirical ecological patterns with respect to purely neutral theories [31,[85][86][87]. In particular, it has been claimed that these models provides more realistic estimates of dynamical quantities, such as average species persistence times and distributions of species turnover [88], compared with their neutral counterparts.…”

“…We have verified in simulations (not shown) that keeping ν constant (rather than Aν constant) small deviations from perfect collapse are observed. We conclude this section mentioning that a heuristic expression for the SAD has been recently derived for the voter model with speciation following a completely different approach [31,32]. Let us define P (x, t) as the distribution of the number of individual of a given species at time t. If we approximate x as a continuous quantity, we can heuristically write a Fokker-Planck equation for the evolution of P (x, t)…”

“…We then discuss its predictions of macroecological patterns: the SAR, and the SAD. For the latter, we compare two recent analytical approaches [30][31][32] with novel computational results. We mainly discuss the twodimensional case due to its ecological relevance, but also briefly present the one-dimensional case for comparison.…”

Spatial patterns emerging from a stochastic process near criticality

“…These flows of probability among microstates break detailed balance, time symmetry and produce macroscopic non-equilibrium behavior. A common way to overcome these hurdles is to formulate some kind of effective Langevin equation which describes the dynamics of the mesoscopic variables of interest, loosing track, however, of the underlying microscopic dynamics [13][14][15]. Nonetheless, in this paper we study a model which, despite violating microscopic detailed balance [16,17], allows one to study analytically (stationary) out-of-equilibrium properties of spatial patterns.…”