Exponential diversity-dependent diversification emerges from an individual-based model with Lotka-Volterra competition

A long-standing question in macroevolution is whether diversification is governed by the same processes that structure diversity at ecological scales, particularly competition. This competition has led to the development of a model where diversification rates depend on diversity, analogous to density-dependence in population growth models. Various versions of this model have been widely used for inference, where the rate of speciation and/or extinction can be either a linear or a power function of species number. It is, however, unknown if either approximates the diversification process that arises from the general ecological setting proposed to lead to diversity-dependence. This is of concern for inference, as failure to include a model that appropriately represents the hypothesized scenario is likely to lead to erroneous inference. Here we use an individual-based model adapted from adaptive dynamics, where fitness is governed by resource availability and the density of competitors, to determine the shape of the diversity-dependence functions. We find that the diversity-dependent rate of speciation produced by the individual-based model is best approximated by an exponential function of species diversity, consistent with a view of macroevolution where diversity increases rapidly after mass extinctions or when new adaptive space becomes available. Although we do find diversity-dependence in the extinction rate, it remains low over the entire process and erases its own signal, so it cannot be recovered from reconstructed phylogenies. The support for a linear relationship for diversity-dependent diversification found in many empirical phylogenies suggests that either our adaptive dynamics model of speciation is inadequate or there is too little information contained in reconstructed phylogenies. We indeed find evidence for the latter when pruning extinct species from our simulated phylogenies, but this does not rule out the former. ### Competing Interest Statement The authors have declared no competing interest.