Statistical mechanics unifies different ecological patterns

Degree distributions have been widely used to characterize biological networks including food webs, and play a vital role in recent models of food web structure. While food webs degree distributions have been suggested to follow various functional forms, to date there has been no mechanistic or statistical explanation for these forms. Here I introduce models for the degree distributions of food webs based on the principle of maximum entropy (MaxEnt) constrained by the number ...

Recent theoretical progress in nonequilibrium thermodynamics, linking the physical principle of Maximum Entropy Production ("MEP") to the information-theoretical "MaxEnt" principle of scientific inference, together with conjectures from theoretical physics that there may be no fundamental causal laws but only probabilities for physical processes, and from evolutionary theory that biological systems expand "the adjacent possible" as rapidly as possible, all lend credence to th...

Diversity is a fundamental feature of ecosystems, even when the concept of ecosystem is extended to sociology or economics. Diversity can be intended as the count of different items, animals, or, more generally, interactions. There are two classes of stylized facts that emerge when diversity is taken into account. The first are Diversity explosions: evolutionary radiations in biology, or the process of escaping 'Poverty Traps' in economics are two well known examples. The sec...

Ecosystems are among the most interesting and well-studied examples of self-organized complex systems. Community ecology, the study of how species interact with each other and the environment, has a rich tradition. Over the last few years, there has been a growing theoretical and experimental interest in these problems from the physics and quantitative biology communities. Here, we give an overview of community ecology, highlighting the deep connections between ecology and st...

In this report, I will review some of the most used models in theoretical ecology along with appealing reformulations and recent results in terms of diversity, stability, and functioning of large well-mixed ecological communities.

Many species of plants are found in regions to which they are alien and their global distribution has been found to exhibit several remarkable patterns,characterised by exponential functions of the kind that could arise through versions of MacArthur's broken stick. We show here that these various patterns are all quantitatively reproduced by a simple algorithm, in terms of a single parameter- a single stick to be broken. This algorithm admits a biological interpretation in te...

Statistical Physics has proved essential to analyze multi-agent environments. Motivated by the empirical observation of various non-equilibrium features in Barro Colorado and other ecological systems, we analyze a plant-species abundance model, presenting analytical evidence of scale-invariant plant clusters and non-trivial emergent modular correlations. Such first theoretical confirmation of a scale-invariant region, based on percolation processes, reproduces the key feature...

Zipf's law, and power laws in general, have attracted and continue to attract considerable attention in a wide variety of disciplines - from astronomy to demographics to software structure to economics to linguistics to zoology, and even warfare. A recent model of random group formation [RGF] attempts a general explanation of such phenomena based on Jaynes' notion of maximum entropy applied to a particular choice of cost function. In the present article I argue that the cost ...

This thesis focuses on the applications of mathematical tools and concepts brought from nonequilibrium statistical physics to the modeling of ecological problems. The first part provides a short introduction where the theoretical concepts and mathematical tools that are going to be used in subsequent chapters are presented. Firstly, the different levels of description usually employed in the models are explained. Secondly, the mathematical relationships among them are prese...

The method of optimizing entropy is used to (i) conduct Asymptotic Hypothesis Testing and (ii) determine the particle distribution for which Entropy is maximized. This paper focuses on two related applications of Information Theory: Statistics and Statistical Mechanics.