Self-similarity in the distribution and abundance of species

If the fraction of species in area A that are also found in one-half of that area is independent of A, the distribution of species is self-similar and a number of observed patterns in ecology, including the widely cited species-area relationship connecting species richness to censused area, follow. Self-similarity also leads to a species-abundance distribution, which deviates considerably from the commonly assumed lognormal distribution and predicts considerably more rare species than the latter. Because the abundance distribution is derived under the condition of self-similarity, it may be widely applicable beyond ecology.