1. New England Complex Systems Institute, Cambridge, Massachusetts 02138, USA
2. Universidade Estadual de Campinas, Unicamp, Campinas, São Paulo 13083-970, Brazil
3. University of Arizona, Tucson, Arizona 85719, USA
4. Boston University, Boston, Massachusetts 02215, USA

Correspondence to: Y. Bar-Yam¹ Correspondence and requests for materials should be addressed to Y.B.-Y. (Email: yaneer@necsi.edu).

Abstract

In recent years, strikingly consistent patterns of biodiversity have been identified over space, time, organism type and geographical region^{1, 2}. A neutral theory (assuming no environmental selection or organismal interactions) has been shown to predict many patterns of ecological biodiversity^{2, 3}. This theory is based on a mechanism by which new species arise similarly to point mutations in a population without sexual reproduction. Here we report the simulation of populations with sexual reproduction, mutation and dispersal. We found simulated time dependence of speciation rates, species–area relationships and species abundance distributions consistent with the behaviours found in nature^{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}. From our results, we predict steady speciation rates, more species in one-dimensional environments than two-dimensional environments, three scaling regimes of species–area relationships and lognormal distributions of species abundance with an excess of rare species and a tail that may be approximated by Fisher's logarithmic series. These are consistent with dependences reported for, among others, global birds⁴ and flowering plants⁵, marine invertebrate fossils⁶, ray-finned fishes⁷, British birds^{8, 9} and moths¹⁰, North American songbirds¹¹, mammal fossils from Kansas¹² and Panamanian shrubs¹³. Quantitative comparisons of specific cases are remarkably successful. Our biodiversity results provide additional evidence that species diversity arises without specific physical barriers^{6, 11, 14}. This is similar to heavy traffic flows, where traffic jams can form even without accidents or barriers¹⁵.

1. New England Complex Systems Institute, Cambridge, Massachusetts 02138, USA
2. Universidade Estadual de Campinas, Unicamp, Campinas, São Paulo 13083-970, Brazil
3. University of Arizona, Tucson, Arizona 85719, USA
4. Boston University, Boston, Massachusetts 02215, USA

Correspondence to: Y. Bar-Yam¹ Correspondence and requests for materials should be addressed to Y.B.-Y. (Email: yaneer@necsi.edu).

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