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A question in evolutionary biology is why the number of males is approximately equal to that of females in many species, and Fishers theory of equal investment answers that it is the evolutionarily stable state. The Fisherian mechanism can be given a concrete form by a genetic model based on the following assumptions: (1) Males and females mate at random. (2) An allele acts on the father to determine the expected progeny sex ratio. (3) The offspring inherits the allele from either side of the parents with equal probability. The model is known to achieve the 1:1 sex ratio due to the invasion of mutant alleles with different progeny sex ratios. In this study, however, we argue that mutation plays a more subtle role in that fluctuations caused by mutation renormalize the sex ratio and thereby keep it away from 1:1 in general. This finding shows how the sex ratio is affected by mutation in a systematic way, whereby the effective mutation rate can be estimated from an observed sex ratio.
In a standard bifurcation of a dynamical system, the stationary points (or more generally attractors) change qualitatively when varying a control parameter. Here we describe a novel unusual effect, when the change of a parameter, e.g. a growth rate,
Eigens quasi-species model describes viruses as ensembles of different mutants of a high fitness master genotype. Mutants are assumed to have lower fitness than the master type, yet they coexist with it forming the quasi-species. When the mutation ra
The two classic theories for the existence of sexual replication are that sex purges deleterious mutations from a population, and that sex allows a population to adapt more rapidly to changing environments. These two theories have often been presente
We discovered a dynamic phase transition induced by sexual reproduction. The dynamics is a pure Darwinian rule with both fundamental ingredients to drive evolution: 1) random mutations and crossings which act in the sense of increasing the entropy (o
Neural populations exposed to a certain stimulus learn to represent it better. However, the process that leads local, self-organized rules to do so is unclear. We address the question of how can a neural periodic input be learned and use the Differen