A computational view of population genetics

Abstract

This paper contributes to the study of nonlinear dynamical systems from a computational perspective. These systems are inherently more powerful than their linear Ž . counterparts such as Markov chains , which have had a wide impact in computer science, and they seem likely to play an increasing role in the future. However, there are as yet no general techniques available for handling the computational aspects of discrete nonlinear systems, and even the simplest examples seem very hard to analyze. We focus in this paper on a class of quadratic systems that are widely used as a model in population genetics and also in genetic algorithms. These systems describe a process where random matings occur between parental chromosomes via a mechanism known as ''crossover'': i.e., children inherit pieces of genetic material from different parents according to some random rule. Our

The power of randomization by sex in multilocus genetic evolution

“…At the start of each trial, an initial population of parents was generated by drawing alleles at each of the L loci at random for each parent without replacement from a store of alleles at equal frequencies. Next, an offspring was generated from two random parents using the Poisson model of recombination [ 41 , 42 ], according to which a crossover occurs between neighboring positions with probability p ≤1/2, independently of crossovers at other positions. Finally, an offspring survived with probability .…”

Optimal Recombination in Genetic Algorithms

“…in terms of optimization time). The theoretical methods proposed in [17] and [41] may be helpful in runtime analysis of GAs with optimal recombination. All of the polynomially solvable cases of the optimal recombination problems considered above rely upon the efficient deterministic algorithms for the Max-Flow/Min-Cut Problem (or the Maximum Matching Problem in the unweighted case).…”

How to analyse evolutionary algorithms

“…Some other results are obtained under unrealistic assumptions like the model of evolutionary algorithms working with populations of infinite size. Only Rabani, Rabinovich, and Sinclair [57] estimate the effect of such an assumption rigorously. However, their paper investigates a stochastic process without fitness-based selection.…”