Legendre transformation and information geometry for the maximum entropy theory of ecology

Reinterpreting Maximum Entropy in Ecology: a null hypothesis constrained by ecological mechanism

Simplified mechanistic models in ecology have been criticized for the fact that a good fit to data does not imply the mechanism is true: pattern does not equal process. In parallel, the maximum entropy principle (MaxEnt) has been applied in ecology to make predictions constrained by just a handful of state variables, like total abundance or species richness. But an outstanding question remains: what principle tells us which state variables to constrain? Here we attempt to solve both problems simultaneously, by translating a given set of mechanisms into the state variables to be used in MaxEnt,…

A strong test of the Maximum Entropy Theory of Ecology

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% and 89% of the variation in the species abundance distribution and the individual size distribution, but performed poor…

Resilience reconsidered: Case histories from disease ecology

We expand the current understanding of ecological resilience to include the nested hierarchy of cognitive submodules that particularly, if not uniquely, delineates human ecosystems. These modules, ranging from the immune system to the local social network, are embedded in a cultural milieu which, to take the perspective of the evolutionary anthropologist Robert Boyd, ''is as much a part of human biology as the enamel on our teeth''. We begin by extending recent treatments of cognitive process as associated with characteristic information sources to a certain class of ecosystems through a gener…

From Ecology to Finance (and Back?): Recent Advancements in the Analysis of Bipartite Networks

Bipartite networks provide an insightful representation of many systems, ranging from mutualistic networks of species interactions to investment networks in finance. The analysis of their topological structures has revealed the ubiquitous presence of properties which seem to characterize many - apparently different - systems. Nestedness, for example, has been observed in plants-pollinator as well as in country-product trade networks. This has raised questions about the significance of these patterns, which are often believed to constitute a genuine signature of self-organization. Here, we revi…

What constrains food webs? A maximum entropy framework for predicting their structure with minimal biases

Food webs are complex ecological networks whose structure is both ecologically and statistically constrained, with many network properties being correlated with each other. Despite the recognition of these invariable relationships in food webs, the use of the principle of maximum entropy (MaxEnt) in network ecology is still rare. This is surprising considering that MaxEnt is a statistical tool precisely designed for understanding and predicting many different types of constrained systems. Precisely, this principle asserts that the least-biased probability distribution of a system's property, c…

广义最大熵：何时以及为何需要它

Generalized Maximum Entropy: When and Why you need it

本文探讨了在强相关系统中Shore-Johnson公理的强系统独立性假设失效时，从业者应何时及为何放弃Shannon熵，转而采用单参数Uffink-Jizba-Korbel（UJK）广义熵族，并通过经济学与生态学应用及数学模型展示了广义最大熵方法的优势。