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The statistical mechanics of community assembly and species distribution

Theoretically, communities at or near their equilibrium species number resist entry of new species. Such 'biotic resistance' recently has been questioned because of successful entry of alien species into diverse natural communities. Data on 10,409 naturalizations of 5350 plant species over 16 sites dispersed globally show exponential distributions for both species over sites and sites over number of species shared. These exponentials signal a statistical mechanics of species distribution, assuming two conditions. First, species and sites are equivalent, either identical ('neutral'), or so complex that the chance a species is in the right place at the right time is vanishingly small ('idiosyncratic'); the range of species and sites in our data disallows a neutral explanation. Secondly, the total number of naturalisations is fixed in any era by a 'regulator'. Previous correlation of species naturalization rates with net primary productivity over time suggests that regulator is related to productivity. We conclude that biotic resistance is a moving ceiling, with resistance controlled by productivity. The general observation that the majority of species occur naturally at only a few sites but only a few at many now has a quantitative [exponential] character, offering the study of species' distributions a previously unavailable rigor.