Main

Early ideas were based on competitive exclusion, in which two (or more) species compete for shared resources but only the more proficient survives3, and the number of coexisting species, n, does not exceed the number of available resources, k. But these ideas based on competitive exclusion cannot explain how rich ensembles of species can coexist on a limited number of resources (that is, n>k), as in aquatic ecosystems.

A solution to this biodiversity problem has been suggested by Huisman and Weissing2 in the form of a model demonstrating the possibility of coexistence of two or more competitors under conditions of fluctuating (periodic or chaotic) community dynamics, a finding central to contemporary ecological theory4. However, we believe that their solution to the n>k puzzle has long been known5,6,7,8,9,10,11,12,13.

It was first inferred from a computer simulation over 25 years ago5 that two species can coexist on one biotic resource, with coexistence occurring along what appeared to be a periodic orbit, as was also shown by Huisman and Weissing2. This was confirmed analytically and expanded to cover the more general case of n species coexisting on one biotic resource9. The fact that coexistence depends on the nonlinearity of the species-specific growth functions and on the lack of system equilibrium — the central issue discussed by Huisman and Weissing2 — has also been demonstrated earlier8. The plankton paradox (whereby n>k) was thus resolved about two decades after it was first posed as a biodiversity problem.