The stochastic community and the logistic-J distribution

A new formal model called the multispecies logistical (MSL) system produces species/abundance distributions that are compared statistically with those found in natural communities. The system, which is able to handle thousands of individuals from hundreds of species, iteratively selects random pairs of individuals and transfers a unit of biomass (or energy) between the respective species. Several elaborations of the model, including those with trophic compartments, appear to produce the same distribution. The theoretical distribution underlying the MSL system is a hyperbolic section, here called the logistic-J distribution. In the study reported here, the logistic-J distribution has been fitted to the species-abundance histograms of 125 randomly selected taxocoenoses. Since the overall chi square score of the logistic-J achieved near-optimality in this study, it cannot be distinguished statistically from the J-curves observed by field biologists. For comparison, the log-series distribution was given the same test and scored significantly higher (more poorly) than the mean logistic-J score. If there is a single, major distribution underlying natural communities, it is not the log-series distribution. Nor, owing to a mathematical error in its formulation, can it be the lognormal distribution. In the MSL system each species follows a “stochastic orbit” about the mean abundance producing, in consequence, the logistic-J distribution. Such orbits are produced by any system in which the probabilities of reproduction and death are approximately equal. Accordingly, the “stochastic communities hypothesis” is proposed here as the overall mechanism governing abundances in all natural communities. It is not a single mechanism, per se, but the net effect of all environmental influences.