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Register a new userSex-ratio bias induced by mutation
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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.
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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, does not influence the stationary states, but nevertheless leads to a qualitative change of dynamics. For instance, such a dynamic transition can be between the convergence to a stationary state and a strong increase without stationary states, or between the convergence to one stationary state and that to a different state. This effect is illustrated for a dynamical system describing two symbiotic populations, one of which exhibits a growth rate larger than the other one. We show that, although the stationary states of the dynamical system do not depend on the growth rates, the latter influence the boundary of the basins of attraction. This change of the basins of attraction explains this unusual effect of the quantitative change of dynamics by growth rate variation.
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 rate is sufficiently high, the master type no longer survives and gets replaced by a wide range of mutant types, thus destroying the quasi-species. It is the so-called error catastrophe. But natural selection acts on phenotypes, not genotypes, and huge amounts of genotypes yield the same phenotype. An important consequence of this is the appearance of beneficial mutations which increase the fitness of mutants. A model has been recently proposed to describe quasi-species in the presence of beneficial mutations. This model lacks the error catastrophe of Eigens model and predicts a steady state in which the viral population grows exponentially. Extinction can only occur if the infectivity of the quasi-species is so low that this exponential is negative. In this work I investigate the transient of this model when infection is started from a small amount of low fitness virions. I prove that, beyond an initial regime where viral population decreases (and can go extinct), the growth of the population is super-exponential. Hence this population quickly becomes so huge that selection due to lack of host cells to be infected begins to act before the steady state is reached. This result suggests that viral infection may widespread before the virus has developed its optimal form.
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 presented as opposing explanations for the existence of sex. Here, we develop and analyze evolutionary models based on the asexual and sexual replication pathways in Saccharomyces cerevisiae (Bakers yeast), and show that sexual replication can both purge deleterious mutations in a static environment, as well as lead to faster adaptation in a dynamic environment. This implies that sex can serve a dual role, which is in sharp contrast to previous theories.
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 (or diversity); and 2) selection which acts in the opposite sense by limiting the entropy explosion. Selection wins this competition if mutations performed at birth are few enough. By slowly increasing the average number m of mutations, however, the population suddenly undergoes a mutational degradation precisely at a transition point mc. Above this point, the bad alleles spread over the genetic pool of the population, overcoming the selection pressure. Individuals become selectively alike, and evolution stops. Only below this point, m < mc, evolutionary life is possible. The finite-size-scaling behaviour of this transition is exhibited for large enough chromosome lengths L. One important and surprising observation is the L-independence of the transition curves, for large L. They are also independent on the population size. Another is that mc is near unity, i.e. life cannot be stable with much more than one mutation per diploid genome, independent of the chromosome length, in agreement with reality. One possible consequence is that an eventual evolutionary jump towards larger L enabling the storage of more genetic information would demand an improved DNA copying machinery in order to keep the same total number of mutations per offspring.
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 Differential Hebbian Learning framework, coupled with a homeostatic mechanism to derive two self-consistency equations that lead to increased responses to the same stimulus. Although all our simulations are done with simple Leaky-Integrate and Fire neurons and standard Spiking Time Dependent Plasticity learning rules, our results can be easily interpreted in terms of rates and population codes.
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