Patterns of relative species abundance in rainforests and coral reefs

A formidable many-body problem in ecology is to understand the complex of factors controlling patterns of relative species abundance (RSA) in communities of interacting species. Unlike many problems in physics, the nature of the interactions in ecological communities is not completely known. Although most contemporary theories in ecology start with the basic premise that species interact, here we show that a theory in which all interspecific interactions are turned off leads to analytical results that are in agreement with RSA data from tropical forests and coral reefs. The assumption of non-interacting species leads to a sampling theory for the RSA that yields a simple approximation at large scales to the exact theory. Our results show that one can make significant theoretical progress in ecology by assuming that the effective interactions among species are weak in the stationary states in species-rich communities such as tropical forests and coral reefs.
A variety of patterns have been observed in the RSA distributions, which are measures of the number of species having a given number of individuals, of ecological communities. In particular, tropical forests1, 2, 3, 4, 5 and coral reefs6, 7 exhibit contrasting RSA patterns. In tropical-tree communities there are fewer rare species in the local community than in the metacommunity, whereas the opposite pattern is found in coral reefs. Reference 6 reported log-series-like RSA distributions in local communities, and log-normal-like RSA distributions when a geographically widespread set of coral-reef communities was pooled to estimate the RSA distribution for the metacommunity. In contrast, local tropical-tree communities exhibit log-normal-like RSA distributions, which become more log-series-like at large landscape scales1, 2, 3, 4, 5. The log-series RSA distribution has a larger proportion of rare species than the log-normal. Here we consider two distinct types of community structure: first, a relatively small semi-isolated local community surrounded by a very large metacommunity acting as a source of immigrants, as in Hubbell's theory1, and, second, spatially isolated island communities whose assemblage acts as the metacommunity8, 9. For the tropical forest, the timescale for species turnover in the metacommunity is very long compared to the characteristic timescale for immigration, leading to an effectively frozen metacommunity acting as a backdrop for immigration. In coral reefs, in contrast, each local community receives immigrants from all the surrounding semi-isolated local communities, within each of which the species abundances are not frozen in time. We present a simple unified theory for understanding the RSA patterns of tropical forests and coral reefs.