1. Department of Physics, 104 Davey Laboratory, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
2. Department of Plant Biology, The University of Georgia, Athens, Georgia 30602, USA
3. The Smithsonian Tropical Research Institute, Box 2072, Balboa, Panama
4. International School for Advanced Studies (SISSA), Via Beirut 2/4, 34014 Trieste, Italy
5. INFM and The Abdus Salam International Center for Theoretical Physics, Trieste, Italy

Correspondence to: Jayanth R. Banavar¹Stephen P. Hubbell^2,3 Correspondence and requests for materials should be addressed to J.R.B. (Email: banavar@psu.edu) or S.P.H. (Email: shubbell@dogwood.botany.uga.edu).

Abstract

The theory of island biogeography¹ asserts that an island or a local community approaches an equilibrium species richness as a result of the interplay between the immigration of species from the much larger metacommunity source area and local extinction of species on the island (local community). Hubbell² generalized this neutral theory to explore the expected steady-state distribution of relative species abundance (RSA) in the local community under restricted immigration. Here we present a theoretical framework for the unified neutral theory of biodiversity² and an analytical solution for the distribution of the RSA both in the metacommunity (Fisher's log series) and in the local community, where there are fewer rare species. Rare species are more extinction-prone, and once they go locally extinct, they take longer to re-immigrate than do common species. Contrary to recent assertions³, we show that the analytical solution provides a better fit, with fewer free parameters, to the RSA distribution of tree species on Barro Colorado Island, Panama⁴, than the lognormal distribution^{5, 6}.

1. Department of Physics, 104 Davey Laboratory, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
2. Department of Plant Biology, The University of Georgia, Athens, Georgia 30602, USA
3. The Smithsonian Tropical Research Institute, Box 2072, Balboa, Panama
4. International School for Advanced Studies (SISSA), Via Beirut 2/4, 34014 Trieste, Italy
5. INFM and The Abdus Salam International Center for Theoretical Physics, Trieste, Italy

Correspondence to: Jayanth R. Banavar¹Stephen P. Hubbell^2,3 Correspondence and requests for materials should be addressed to J.R.B. (Email: banavar@psu.edu) or S.P.H. (Email: shubbell@dogwood.botany.uga.edu).