Statistical mechanics of relative species abundance

The persistence of bipartite ecological communities with Lotka-Volterra dynamics

The assembly and persistence of ecological communities can be understood as the result of the interaction and migration of species. Here we study a single community subject to migration from a species pool in which inter-specific interactions are organised according to a bipartite network. Considering the dynamics of species abundances to be governed by generalised Lotka-Volterra equations, we extend work on unipartite networks to we derive exact results for the phase diagram of this model. Focusing on antagonistic interactions, we describe factors that influence the persistence of the two guilds, locate transitions to multiple-attractor and unbounded phases, as well as identifying a region of parameter space in which consumers are essentially absent in the local community.

Ecological communities with Lotka-Volterra dynamics

Ecological communities in heterogeneous environments assemble through the combined effect of species interaction and migration. Understanding the effect of these processes on the community properties is central to ecology. Here we study these processes for a single community subject to migration from a pool of species, with population dynamics described by the generalized Lotka-Volterra equations. We derive exact results for the phase diagram describing the dynamical behaviors, and for the diversity and species abundance distributions. A phase transition is found from a phase where a unique globally attractive fixed point exists to a phase where multiple dynamical attractors exist, leading to history-dependent community properties. The model is shown to possess a symmetry that also establishes a connection with other well-known models.

SPECIES-AREA RELATIONSHIP FOR POWER-LAW SPECIES ABUNDANCE DISTRIBUTION

We studied the mathematical relations between species abundance distributions (SADs) and species-area relationships (SARs) and found that a power-law SAR can be generally derived from a power-law SAD without a special assumption such as the "canonical hypothesis". In the present analysis, an SAR-exponent is obtained as a function of an SAD-exponent for a finite number of species. We also studied the inverse problem, from SARs to SADs, and found that a power-SAD can be derived from a power-SAR under the condition that the functional form of the corresponding SAD is invariant for changes in the number of species. We also discuss general relationships among lognormal SADs, the broken-stick model (exponential SADs), linear SARs and logarithmic SARs. These results suggest the existence of a common mechanism for SADs and SARs, which could prove a useful tool for theoretical and experimental studies on biodiversity and species coexistence.

The statistical mechanics of community assembly and species distribution

• Theoretically, communities at or near their equilibrium species number resist entry of new species. Such 'biotic resistance' recently has been questioned because of successful entry of alien species into diverse natural communities. • Data on 10,409 naturalizations of 5350 plant species over 16 sites dispersed globally show exponential distributions both for species over sites and for sites over number of species shared. These exponentials signal a statistical mechanics of species distribution, assuming two conditions. First, species and sites are equivalent, either identical ('neutral') or so complex that the chance a species is in the right place at the right time is vanishingly small ('idiosyncratic'); the range of species and sites in our data disallows a neutral explanation. Secondly, the total number of naturalizations is fixed in any era by a 'regulator'. • Previous correlation of species naturalization rates with net primary productivity over time suggests that the regulator is related to productivity. • We conclude that biotic resistance is a moving ceiling, with resistance controlled by productivity. The general observation that the majority of species occur naturally at only a few sites, and only a few species occur at many sites, now has a quantitative (exponential) character, offering the study of species' distributions a previously unavailable rigor.

An investigation into the population abundance distribution of mRNAs, proteins, and metabolites in biological systems

MOTIVATION

Distribution analysis is one of the most basic forms of statistical analysis. Thanks to improved analytical methods, accurate and extensive quantitative measurements can now be made of the mRNA, protein and metabolite from biological systems. Here, we report a large-scale analysis of the population abundance distributions of the transcriptomes, proteomes and metabolomes from varied biological systems.

RESULTS

We compared the observed empirical distributions with a number of distributions: power law, lognormal, loglogistic, loggamma, right Pareto-lognormal (PLN) and double PLN (dPLN). The best-fit for mRNA, protein and metabolite population abundance distributions was found to be the dPLN. This distribution behaves like a lognormal distribution around the centre, and like a power law distribution in the tails. To better understand the cause of this observed distribution, we explored a simple stochastic model based on geometric Brownian motion. The distribution indicates that multiplicative effects are causally dominant in biological systems. We speculate that these effects arise from chemical reactions: the central-limit theorem then explains the central lognormal, and a number of possible mechanisms could explain the long tails: positive feedback, network topology, etc. Many of the components in the central lognormal parts of the empirical distributions are unidentified and/or have unknown function. This indicates that much more biology awaits discovery.

Rank abundance relations in evolutionary dynamics of random replicators

We present a nonequilibrium statistical mechanics description of rank abundance relations (RAR) in random community models of ecology. Specifically, we study a multispecies replicator system with quenched random interaction matrices. We here consider symmetric interactions as well as asymmetric and antisymmetric cases. RARs are obtained analytically via a generating functional analysis, describing fixed-point states of the system in terms of a small set of order parameters, and in dependence on the symmetry or otherwise of interactions and on the productivity of the community. Our work is an extension of Tokita [Phys. Rev. Lett. 93, 178102 (2004)], where the case of symmetric interactions was considered within an equilibrium setup. The species abundance distribution in our model come out as truncated normal distributions or transformations thereof and, in some case, are similar to left-skewed distributions observed in ecology. We also discuss the interaction structure of the resulting food-web of stable species at stationarity, cases of heterogeneous cooperation pressures as well as effects of finite system size and of higher-order interactions.