Breaking records in the evolutionary race

Joachim Krug and Kavita Jain

Physica A: Statistical Mechanics and its Applications, 2005, vol. 358, issue 1, 1-9

Abstract: We explore some aspects of the relationship between biological evolution processes and the mathematical theory of records. For Eigen's quasispecies model with an uncorrelated fitness landscape, we show that the evolutionary trajectories traced out by a population initially localized at a randomly chosen point in sequence space can be described in close analogy to record dynamics, with two complications. First, the increasing number of genotypes that become available with increasing distance from the starting point implies that fitness records are more frequent than for the standard case of independent, identically distributed random variables. Second, fitness records can be bypassed, which strongly reduces the number of genotypes that take part in an evolutionary trajectory. For exponential and Gaussian fitness distributions, this number scales with sequence length N as N, and it is of order unity for distributions with a power law tail. This is in strong contrast to the number of records, which is of order N for any fitness distribution.

Keywords: Biological evolution; Punctuated equilibrium; Record dynamics; Extremal statistics; Quasispecies model (search for similar items in EconPapers)
Date: 2005
References: View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:358:y:2005:i:1:p:1-9

DOI: 10.1016/j.physa.2005.06.002

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