Evolutionary dynamics on strongly correlated fitness landscapes

Abstract

We study the evolutionary dynamics of a maladapted population of self-replicating sequences on strongly correlated fitness landscapes. Each sequence is assumed to be composed of blocks of equal length and its fitness is given by a linear combination of four independent block fitnesses. A mutation affects the fitness contribution of a single block leaving the other blocks unchanged and hence inducing correlations between the parent and mutant fitness. On such strongly correlated fitness landscapes, we calculate the dynamical properties like the number of jumps in the most populated sequence and the temporal distribution of the last jump which is shown to exhibit a inverse square dependence as in evolution on uncorrelated fitness landscapes. We also obtain exact results for the distribution of records and extremes for correlated random variables.

Nonlinear Deterministic Equations in Biological Evolution

“…The above equations can be written down in a manner analogous to the above cases. Since selection occurs before recombination, on replacing X i (t) by W i X i (t)/W(t) on the RHS of (40)- (43), the evolution equations with selection and recombination are obtained. Finally the unidirectional mutation scheme is implemented.…”

“…More often however the fitness landscapes are complex and one has to specify all the a L fitnesses. These fitnesses can be assumed to be independent random variables [22] or they may have correlations [39,43]. An important feature of generic fitness landscapes is the presence of epistasis which is a measure of the nonlinear contribution of locus fitness to the sequence [29].…”

Extreme value distributions for weakly correlated fitnesses in block models

“…In this article, we focus on the extreme value distribution for nonindependent and identically distributed (ni.i.d.) random variables (for some results on nonindependent and nonidentically distributed fitnesses, see [6,23]). Such ni.i.d.…”

A Model with Darwinian Dynamics on a Rugged Landscape

“…Because the connection between Darwinian dynamics and physical evolution is less obvious than in the case of annealing, the implications of physics to such problems has been much less studied. Although there have been statistical mechanical models of evolution (see, for example [35][36][37][38][39][40]) using the knowledge of universal glassy features has been much less exploited [5].…”