By **Vandewalle N. and Ausloos M.**

Recent progress of both statistical physics and computer modelling give us new instruments in order to study biological processes and related natural pattern formations. Various biologically motivated models have been invented like the Kauffman's cellular automaton [1] or the recent evolution model of Bak and Sneppen [2]. Such models are always defined by simple rules and the simulated patterns show intriguingly complex features of real biological systems. These models allow one to investigate the biological processes in physics terms. Hence specific processes responsible for the complexity can be pinned point.

Self-organized criticality (also called the edge of chaos) is found to be a paradigm in the study of such models. This suggests that in nature non-linear processes organize biological systems into structures that appear to have order on all length scales [1-3]. These computational and physical results agree with recent concepts like punctuated equilibrium [4,5].

Particularly, we extended the Bak and Sneppen model of evolution to a branching process allowing the study of phylogenetic-like trees. Interaction-competitions were considered between genetically low differentiated species. We found that this competition-correlation model self-organizes into a steady-state made of intermittent avalanches of all sizes including catastrophic ones. This behaviour is close to the Bak and Sneppen result and is similar to the features of real biological evolution observed on geological time scales. The critical exponent values of this competition-correlation model are different from the Bak and Sneppen values. Moreover, the simulated phylogenetic trees are found to be self-similar and the critical exponents are found to obey the hyperscaling relations of percolation theory. This suggests possible applications of such models to phylogenetic tree data analysis.

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