Statistical mechanics unifies different ecological patterns

The Maximum Entropy Theory of Ecology (METE) is a unified theory of biodiversity that predicts a large number of macroecological patterns using only information on the species richness, total abundance, and total metabolic rate of the community. We evaluated four major predictions of METE simultaneously at an unprecedented scale using data from 60 globally distributed forest communities including over 300,000 individuals and nearly 2000 species. METE successfully captured 96%...

The Maximum Entropy Theory of Ecology (METE) predicts a universal species-area relationship (SAR) that can be fully characterized using only the total abundance (N) and species richness (S) at a single spatial scale. This theory has shown promise for characterizing scale dependence in the SAR. However, there are currently four different approaches to applying METE to predict the SAR and it is unclear which approach should be used due to a lack of empirical evaluation. Specifi...

Scaling laws in ecology, intended both as functional relationships among ecologically-relevant quantities and the probability distributions that characterize their occurrence, have long attracted the interest of empiricists and theoreticians. Empirical evidence exists of power laws associated with the number of species inhabiting an ecosystem, their abundances and traits. Although their functional form appears to be ubiquitous, empirical scaling exponents vary with ecosystem ...

We typically observe large-scale outcomes that arise from the interactions of many hidden, small-scale processes. Examples include age of disease onset, rates of amino acid substitutions, and composition of ecological communities. The macroscopic patterns in each problem often vary around a characteristic shape that can be generated by neutral processes. A neutral generative model assumes that each microscopic process follows unbiased stochastic fluctuations: random connectio...

We show that the naive application of the maximum entropy principle can yield answers which depend on the level of description, i.e. the result is not invariant under coarse-graining. We demonstrate that the correct approach, even for discrete systems, requires maximization of the relative entropy with a suitable reference probability, which in some instances can be deduced from the symmetry properties of the dynamics. We present simple illustrations of this crucial yet surpr...

We discuss the relevance of studying ecology within the framework of Complexity Science from a statistical mechanics approach. Ecology is concerned with understanding how systems level properties emerge out of the multitude of interactions amongst large numbers of components, leading to ecosystems that possess the prototypical characteristics of complex systems. We argue that statistical mechanics is at present the best methodology available to obtain a quantitative descripti...

Studies on distribution, abundance and diversity of species revealed fascinating universalities in macroecology. Many of these patterns, like the species-area and range-abundance relationship or the year-to-year fluctuations in population sizes are expressed as power-law distributions, and indicate thus scale-invariance. The species abundance distribution (SAD) apparently shows this scale-free nature only for rare species, and its mathematical form is much debated. In the pre...

Understanding the assembly of ecosystems to estimate the number of species at different spatial scales is a challenging problem. Until now, maximum entropy approaches have lacked the important feature of considering space in an explicit manner. We propose a spatially explicit maximum entropy model suitable to describe spatial patterns such as the species area relationship and the endemic area relationship. Starting from the minimal information extracted from presence/absence ...

This book brings new mathematical rigour to the ongoing vigorous debate on how to quantify biological diversity. The question "what is diversity?" has surprising mathematical depth, and breadth too: this book involves parts of mathematics ranging from information theory, functional equations and probability theory to category theory, geometric measure theory and number theory. It applies the power of the axiomatic method to a biological problem of pressing concern, but the ne...

A central issue in ecology today is that of the factors determining the relative abundance of species within a natural community. The proper application of the principles of statistical physics to the problem of species abundance distributions (SADs) has enabled us to identify the fundamental ecological principles responsible for the near universal features observed. These principles are (i) a limit on the number of individuals in an ecological guild and (ii) per capita birth...