Extinction and self-organized criticality in a model of large-scale evolution

A simple model of large-scale biological evolution is presented. This model involves an $N$-species system where interactions take place through a given connectivity matrix, which can change with time. True extinctions, with removal of less-fit species, occur followed by episodes of diversification. An order parameter may be naturally defined in the model. Through the dynamical equations, the system moves towards the critical threshold, which triggers the extinctions. The frequency distribution $N\left(s\right)\mathrm{}$ of extinctions of size $s$ follows a power law $N\left(s\right)\mathrm{}\approx s^{-\alpha }$ with $\alpha \approx 2.3$, close to known palaeobiological evidence.