Chromosome Length Scaling in Haploid, Asexual Reproduction

We study the genetic behaviour of a population formed by haploid individuals which reproduce asexually. The genetic information for each individual is stored along a bit-string (or chromosome) with L bits, where 0-bits represent the wild-type allele and 1-bits correspond to harmful mutations. Each newborn inherits this chromosome from its parent with some few random mutations: on average a fixed number m of bits are flipped. Selection is implemented according to the number N of 1-bits counted along the individual's chromosome: the smaller N the higher the probability an individual has to survive a new time step. Such a population evolves, with births and deaths, and its genetic distribution becomes stabilised after many enough generations have passed. The question we pose concerns the procedure of increasing L. The aim is to get the same distribution of relative genetic loads N/L among the equilibrated population, in spite of a larger L. Should we keep the same mutation rate m/L for different values of L? The answer is yes, which intuitively seems to be plausible. However, this conclusion is not trivial, according to our simulational results: the question involves also the population size.