Revising the tolerance-fecundity trade-off; or, on the consequences of discontinuous resource use for limiting similarity, species diversity, and trait dispersion

The recently proposed tolerance-fecundity trade-off model represents a step forward in the study of seed size diversity in plant communities. However, it uses an oversimplified picture of seed tolerance, with an infinitely sharp threshold: the probability that a seed tolerate a given stress level is either 1 or 0. This invites a revision of the model, presented here. We demonstrate that this simplification has large impacts on model behavior, including altering predictions regarding limiting similarity, raising expected diversity levels, and lessening expected spacing between species along the trait axis. Such dramatic impacts ultimately stem from the fact that a discontinuity in the probability of tolerating a site drastically reduces competition between similar species. This is one example of a class of models with a nondifferentiable peak in the competition kernel, which we recently showed is produced by resource use unrealistically modeled as discontinuous and affects fundamental predictions regarding limiting similarity. This article illustrates those general results and offers a revised model of the tolerance-fecundity trade-off.