Self-organized criticality in phylogenetic-like tree growths

A simple stochastic model of Darwinistic evolution generating phylogenetic-like trees is developed. The model is based on a branching process taking competition-correlation effects into account. In presence of finite and short range correlations, the process self-organizes into a critical steady-state in which intermittent bursts of activity of all sizes are generated. On a geological-like time scale, this behaviour agrees with punctuated equilibrium features of biological evolution. The simulated phylogenetic-like trees are found to be self-similar. The dynamics of the transient regimes show a power law decrease of the order parameter towards the 0(+) value which characterizes an unstable critical state. The genetic range k of competition-correlations between living species is found to be a relevant parameter which determines the universality class of the evolution process. An infinite competition-correlation range destroys however the self-organized critical behaviour. The fractal dimension D-f of the phylogenetic-like trees increases from 2.0 to infinity as k goes from 1 to infinity. The critical exponent tau of avalanche size-distribution decreases from about 3/2 (for k = 1) and reaches about 1.2 for k = 10. A hyperscaling relation seems to relate the various universality classes. Through a mean-field theory, we mention that the evolution process is much more complex than a simple uncorrelated branching process.