Numéro
J. Phys. I France
Volume 6, Numéro 4, April 1996
Page(s) 599 - 606
DOI https://doi.org/10.1051/jp1:1996232
DOI: 10.1051/jp1:1996232
J. Phys. I France 6 (1996) 599-606

Speciations and Extinctions in a Self-Organizing Critical Model of Tree-Like Evolution

M. Kramer, N. Vandewalle and M. Ausloos

S.U.P.R.A.S., Institut de Physique B5, Sart Tilman, Université de Liège, B-400 Liège, Belgium



(Received 4 December 1994, revised 15 December 1995 and accepted 5 January 1996)

Abstract
We study analytically a simple model of a self-organized critical evolution. The model considers both extinction and speciation events leading to the growth of phylogenetic-like trees. Through a mean-field like theory, we study the evolution of the local configurations for the tree leaves. The fitness threshold, below which life activity takes place through avalanches of all sizes is calculated. The transition between speciating (evolving) and dead trees is obtained and is in agreement with numerical simulations. Moreover, this theoretical work suggests that the structure of the tree is strongly dependent on the extinction strength.

Résumé
Nous étudions analytiquement un modèle simple d'évolution auto-organisée critique. Le modèle considère des extinctions et des spéciations conduisant à une croissance d'arbre phylogénétiques. Nous étudions ici par une théorie de champ moyen l'évolution des configurations des extrémités de l'arbre. Le seuil critique de "fitness" en-dessous duquel des explosions d'activité biologique de toutes tailles se produisent est calculé. La transition entre arbres croissants et arbres éteints est également obtenue en accord avec les simulations. En outre, ce travail théorique suggère que la structure des arbres générés dépend fortement du paramètre d'extinctions.



© Les Editions de Physique 1996

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