From theoretical ecology to statistical physics and back: self-similar landscape metrics as a synthesis of ecological diversity and geometrical complexity

Biological diversity would apparently seem the most intuitive and easily studied of ecological concepts. The first and obvious way to study it simply consists in counting the number of species present at a given location. However, it has rapidly become clear that diversity measurements are a far interesting and richer task than simple estimation of the number of species present. After the Second World War, several diversity indices have been proposed in order to quantify several aspects of biological diversity and their ecological implications. Since many theoretical foundations of biological diversity evolved at the cross-roads of theoretical ecology and statistical physics, in this paper I summarize the influences of statistical physics which mostly contributed to the understanding of biological diversity. Particularly, this review focuses on the observation that, despite the use of the same formalism, the ecological concept of diversity and the concept of geometrical complexity of strange attractors in statistical physics are based on very different theoretical assumptions. That is, ecologists do not simply rely on physical notation, but they generally reelaborates the theoretical foundation of statistical physics in an (ecological) meaningful way.