The Distribution of Abundance in Neutral Communities

Abstract

The patterns of abundance generated by a simple stochastic birth-death-immigration model are described in order to characterize the diversity of neutral communities of ecologically equivalent species. Diversity is described by species number S and the variance of frequency or log abundance q∼. The frequency distribution of abundance is very generally lognormal, skewed to the left by immigration and resembling descriptions of natural communities. Increased immigration and community size always cause S to increase. Their effect on q∼ is more complicated, but given biologically reasonable assumptions, S and q∼ will be positively correlated in most circumstances. Larger samples contain more species; the graph of log S on log individuals, equivalent to a species-area curve, is generally convex upward but becomes linear with a slope of about +0.25 when immigration is low and births exceed deaths. When individuals invade a new, vacant environment, both S and q∼ increase through time. Thus, a positive correlation between S and q∼ will usually be generated when sites of differing size or age are surveyed. At equilibrium, communities maintain roughly constant levels of S and q∼ but change in composition through time; composition may remain similar, however, for many generations. Many prominent patterns observed in natural communities can therefore be generated by a strictly neutral model. This does not show that community structure is determined exclusively by demographic stochasticity, but rather demonstrates the necessity for an appropriate null model when functional hypotheses are being tested.

Keywords: abundance; biodiversity; neutral model; species diversity; species‐area relationship.