M ar 2 01 8 Entropy evaluation sheds light on ecosystem complexity

Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Environmental changes and human activity threaten the fauna of many geographical areas. We exploit the entropy definition from thermodynamics to assess ecosystem stability. In particular, we study a minimal ecosystem on a lattice in which two species struggle for survival. Entropy is measured both in the Shannon-Fano approximation and through a new least entropy principle, based on Maximum Entropy algorithm, that enables the entropy computation in a variational framework. The comparison between the two entropies allows us to measure the degree of long-range ordering in the system. Furthermore, entropy sheds new light on three different phase transitions the system undergoes by tuning animal phenotypes, two being of second order and one of first order. In the latter, the whole ecosystem transits abruptly into an extinction state, causing an ecological catastrophe very difficult to predict, since no precursors indicate the imminent disaster.