Europhys. Lett, 44 (5), pp. 546-551 (1998)
A solvable model of the evolutionary loop
Laboratoire de Physico-Chimie Théorique, CNRS URA 1382, ESPCI
10, rue Vauquelin, F-75231 Paris Cedex 05, France
Dipartimento di Fisica and Unità INFM, Università "Federico II"
Mostra d'Oltremare, Pad. 19, I-80125 Napoli, Italy
(received 22 June 1998; accepted in final form 5 October 1998)
PACS. 02.50Ey - Stochastic processes.
PACS. 05.40 - Fluctuation phenomena, random processes, and Brownian motion.
PACS. 87.10 - General, theoretical and mathematical biophysics (including logic of biosystems, quantum biology, and relevant aspects of thermodynamics, information theory, cybernetics, and bionics).
A model for the evolution of a finite population in a rugged fitness landscape is introduced and solved. The population is trapped in an evolutionary loop, alternating periods of stasis to periods in which it performs adaptive walks. The dependence of the average rarity of the population (a quantity related to the fitness of the most adapted individual) and of the duration of stases on population size and mutation rate is calculated.