Extinctions and taxonomy in a trophic model of coevolution

We investigate the statistics of extinction sizes and the taxonomy in a trophic model of evolution recently proposed [Phys. Rev. Lett. 82, 652 (1999)]. By further exploring the parameters of this model, we find that the distribution of extinction sizes N(s) shows typically a characteristic maximum before developing the power-law behavior N(s) approximate to s(-alpha) with alpha approximate to 2, in agreement with empirical observations. Furthermore, the derivation of the alpha = -2 exponent given by Drossel [Phys. Rev. Lett. 81, 5011 (1998)] for this model is completed. The extinction sizes in each trophic level are also analyzed; one finds that at the fourth level and up (l greater than or equal to 4) the extinction size statistics is a power law with exponent alpha(1) similar or equal to 1.4, and exponential-like at the second level, also in agreement with some empirical data not previously explained by current models. On the other hand, in contrast to the observed power-law distribution of the number of species in genera, numerical simulations yield an exponential law. A modification of the model is presented that provides an approximate potential behavior for taxonomy, and some consequences for future modeling are outlined.