Random Walks, Fractals and the Origins of Rainforest Diversity

Rain forests are legendary because of their extreme species richness. In the richest rain forests every second tree on a hectare is a different species. As a consequence, most species are rare. Using field data from studies in different parts of the world, we show that species-rich plots often display a distribution of number of species $N_s(I)$ represented by $I$ individuals with a power-law shape $N_s(I) \procto I^{-\beta}$ with $\beta \approx 1.5$. Power laws are characteristic (but not exclusive) of systems poised close to critical points and this is supported by the analysis of the gap distribution over space in the Barro Colorado Island forest, which has been shown to be fractal. Here we propose a new model of rainforest dynamics which is able to account for a wide set of observations, strongly suggesting that indeed rain forests would be organized close to instability points, showing strongly path-dependent dynamics.