  Recently there has been growing interest in the use of Maximum Relative
Entropy (MaxREnt) as a tool for statistical inference in ecology. In contrast,
here we propose MaxREnt as a tool for applying statistical mechanics to
ecology. We use MaxREnt to explain and predict species abundance patterns in
ecological communities in terms of the most probable behaviour under given
environmental constraints, in the same way that statistical mechanics explains
and predicts the behaviour of thermodynamic systems. We show that MaxREnt
unifies a number of different ecological patterns: (i) at relatively local
scales a unimodal biodiversity-productivity relationship is predicted in good
agreement with published data on grassland communities, (ii) the predicted
relative frequency of rare vs. abundant species is very similar to the
empirical lognormal distribution, (iii) both neutral and non-neutral species
abundance patterns are explained, (iv) on larger scales a monotonic
biodiversity-productivity relationship is predicted in agreement with the
species-energy law, (v) energetic equivalence and power-law self-thinning
behaviour are predicted in resource-rich communities. We identify mathematical
similarities between these ecological patterns and the behaviour of
thermodynamic systems, and conclude that the explanation of ecological patterns
is not unique to ecology but rather reflects the generic statistical behaviour
of complex systems with many degrees of freedom under very general types of
environmental constraints.
