Statistical mechanics unifies different ecological patterns

The simplest theories often have much merit and many limitations, and in this vein, the value of Neutral Theory (NT) has been the subject of much debate over the past 15 years. NT was proposed at the turn of the century by Stephen Hubbell to explain pervasive patterns observed in the organization of ecosystems. Its originally tepid reception among ecologists contrasted starkly with the excitement it caused among physicists and mathematicians. Indeed, NT spawned several theore...

Natural ecosystems are characterized by striking diversity of form and functions and yet exhibit deep symmetries emerging across scales of space, time and organizational complexity. Species-area relationships and species-abundance distributions are examples of emerging patterns irrespective of the details of the underlying ecosystem functions. Here we present empirical and theoretical evidence for a new macroecological pattern related to the distributions of local species per...

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 for both species over sites and sites over number of species shared. These exponentials signal a statistical mechanics of species ...

Understanding the behaviors of ecological systems is challenging given their multi-faceted complexity. To proceed, theoretical models such as Lotka-Volterra dynamics with random interactions have been investigated by the dynamical mean-field theory to provide insights into underlying principles such as how biodiversity and stability depend on the randomness in interaction strength. Yet the fully-connected structure assumed in these previous studies is not realistic as reveale...

One of the first successes of neutral ecology was to predict realistically-broad distributions of rare and abundant species. However, it has remained an outstanding theoretical challenge to describe how this distribution of abundances changes with spatial scale, and this gap has hampered attempts to use observed species abundances as a way to quantify what non-neutral processes are needed to fully explain observed patterns. To address this, we introduce a new formulation of s...

Disordered systems theory provides powerful tools to analyze the generic behaviors of highdimensional systems, such as species-rich ecological communities or neural networks. By assuming randomness in their interactions, universality ensures that many microscopic details are irrelevant to system-wide dynamics; but the choice of a random ensemble still limits the generality of results. We show here, in the context of ecological dynamics, that these analytical tools do not requ...

Whether or not biodiversity dynamics tend toward stable equilibria remains an unsolved question in ecology and evolution with important implications for our understanding of diversity and its conservation. Phylo/population genetic models and macroecological theory represent two primary lenses through which we view biodiversity. While phylo/population genetics provide an averaged view of changes in demography and diversity over timescales of generations to geological epochs, m...

In this paper we review various information-theoretic characterizations of the approach to equilibrium in biological systems. The replicator equation, evolutionary game theory, Markov processes and chemical reaction networks all describe the dynamics of a population or probability distribution. Under suitable assumptions, the distribution will approach an equilibrium with the passage of time. Relative entropy - that is, the Kullback--Leibler divergence, or various generalizat...

Entropy measures of probability distributions are widely used measures in ecology, biology, genetics, and in other fields, to quantify species diversity of a community. Unfortunately, entropy-based diversity indices, or diversity indices for short, suffer from three problems. First, when computing the diversity for samples withdrawn from communities with different structures, diversity indices can easily yield non-comparable and hard to interpret results. Second, diversity in...

In this paper an alternative approach to statistical mechanics based on the maximum information entropy principle (MaxEnt) is examined, specifically its close relation with the Gibbs method of ensembles. It is shown that the MaxEnt formalism is the logical extension of the Gibbs formalism of equilibrium statistical mechanics that is entirely independent of the frequentist interpretation of probabilities only as factual (i.e. experimentally verifiable) properties of the real w...