Segregation and the evolution of sex under overdominant selection

The segregation of alleles disrupts genetic associations at overdominant loci, causing a sexual population to experience a lower mean fitness compared to an asexual population. To investigate whether circumstances promoting increased sex exist within a population with heterozygote advantage, a model is constructed that monitors the frequency of alleles at a modifier locus that changes the relative allocation to sexual and asexual reproduction. The frequency of these modifier alleles changes over time as a correlated response to the dynamics at a fitness locus under overdominant selection. Increased sex can be favored in partially sexual populations that inbreed to some extent. This surprising finding results from the fact that inbred populations have an excess of homozygous individuals, for whom sex is always favorable. The conditions promoting increased levels of sex depend on the selection pressure against the homozygotes, the extent of sex and inbreeding in the population, and the dominance of the invading modifier allele.     

Effect of dominance on heterozygosity and the fixation probability in a subdivided population

Under the assumptions of a subdivided population and the presence of dominance for fitness, the expected sum of heterozygosity in the total population during the lifetime of mutant was investigated. It was shown analytically and by computer simulations that in the island model the effect of dominance on the expected sum of heterozygosity decreases as the migration rate decreases and is lost almost completely when the migration rate is very low. In addition to the expected sum of heterozygosity, the fixation probability of mutant was also investigated. The effect of dominance on the fixation probability also decreases as the migration rate decreases but is not completely lost when the migration rate is very low.     

Consequences of population structure on genes under balancing selection

This paper describes a new approach to modeling population structure for genes under strong balancing selection of the type seen in plant self-incompatibility systems and the major histocompatibility complex (MHC) system of vertebrates. Simple analytic solutions for the number of alleles maintained at equilibrium and the expected proportion of alleles shared between demes at various levels are derived and checked against simulation results. The theory accurately captures the dynamics of allele number in a subdivided population and identifies important values of m (migration rate) at which allele number and distribution change qualitatively. Starting from a panmictic population, as migration among demes decreases a qualitative change in dynamics is seen at approximately m(crit) approximately equal to the square root of(s/4piNT) where NT is the total population size and s is a measure of the strength of selection. At this point, demes can no longer maintain their panmictic allele number, due to increasing isolation from the total population. Another qualitative change occurs at a migration rate on the same order of magnitude as the mutation rate, mu. At this point, the demes are highly differentiated for allele complement, and the total number of alleles in the population is increased. Because in general u < m<(crit) at intermediate migration rates slightly fewer alleles may be maintained in the total population than are maintained at panmixia. Within this range, total allele number may not be the best indicator of whether a population is effectively panmictic, and some caution should be used when interpreting samples from such populations. The theory presented here can help to analyze data from genes under balancing selection in subdivided populations.     

A novel solution for the time-dependent probability of gene fixation or loss under natural selection

Kimura proposed a solution for the time-dependent probability of fixation, or loss, of a gene under selection. Example calculations suggest the formulas are prone to numerical inaccuracies. An alternative solution is proposed; the correctness of the solution is confirmed by numerically solving the Kolmogorov backward equation and by simulation.     

A unified treatment of the probability of fixation when population size and the strength of selection change over time

The fixation probability is determined when population size and selection change over time and differs from Kimura's result, with long-term implications for a population. It is found that changes in population size are not equivalent to the corresponding changes in selection and can result in less drift than anticipated.     

The network structure affects the fixation probability when it couples to the birth-death dynamics in finite population

The study of evolutionary dynamics on graphs is an interesting topic for researchers in various fields of science and mathematics. In systems with finite population, different model dynamics are distinguished by their effects on two important quantities: fixation probability and fixation time. The isothermal theorem declares that the fixation probability is the same for a wide range of graphs and it only depends on the population size. This has also been proved for more complex graphs that are called complex networks. In this work, we propose a model that couples the population dynamics to the network structure and show that in this case, the isothermal theorem is being violated. In our model the death rate of a mutant depends on its number of neighbors, and neutral drift holds only in the average. We investigate the fixation probability behavior in terms of the complexity parameter, such as the scale-free exponent for the scale-free network and the rewiring probability for the small-world network.     

Quantitative variability and multilocus polymorphism under epistatic selection

We study multilocus polymorphism under selection, using a class of fitness functions that account for additive, dominant, and pairwise additive-by-additive epistatic interactions. The dynamic equations are derived in terms of allele frequencies and disequilibria, using the notions of marginal systems and marginal fitnesses, without any approximations. Stationary values of allele frequencies and pairwise disequilibria under weak selection are calculated by regular perturbation techniques. We derive conditions for existence and stability of the multilocus polymorphic states. Using these results, we then analyze a number of models describing stabilizing selection on additive characters, with some other factors, and determine the conditions under which genetic quantitative variability is maintained.     

Population genetics of polymorphism and divergence under fluctuating selection

Current methods for detecting fluctuating selection require time series data on genotype frequencies. Here, we propose an alternative approach that makes use of DNA polymorphism data from a sample of individuals collected at a single point in time. Our method uses classical diffusion approximations to model temporal fluctuations in the selection coefficients to find the expected distribution of mutation frequencies in the population. Using the Poisson random-field setting we derive the site-frequency spectrum (SFS) for three different models of fluctuating selection. We find that the general effect of fluctuating selection is to produce a more "U"-shaped site-frequency spectrum with an excess of high-frequency derived mutations at the expense of middle-frequency variants. We present likelihood-ratio tests, comparing the fluctuating selection models to the neutral model using SFS data, and use Monte Carlo simulations to assess their power. We find that we have sufficient power to reject a neutral hypothesis using samples on the order of a few hundred SNPs and a sample size of approximately 20 and power to distinguish between selection that varies in time and constant selection for a sample of size 20. We also find that fluctuating selection increases the probability of fixation of selected sites even if, on average, there is no difference in selection among a pair of alleles segregating at the locus. Fluctuating selection will, therefore, lead to an increase in the ratio of divergence to polymorphism similar to that observed under positive directional selection.     

The probability of fixation of a single mutant in an exchangeable selection model

The Cannings exchangeable model for a finite population in discrete time is extended to incorporate selection. The probability of fixation of a mutant type is studied under the assumption of weak selection. An exact formula for the derivative of this probability with respect to the intensity of selection is deduced, and developed in the case of a single mutant. This formula is expressed in terms of mean coalescence times under neutrality assuming that the coefficient of selection for the mutant type has a derivative with respect to the intensity of selection that takes a polynomial form with respect to the frequency of the mutant type. An approximation is obtained in the case where this derivative is a continuous function of the mutant frequency and the population size is large. This approximation is consistent with a diffusion approximation under moment conditions on the number of descendants of a single individual in one time step. Applications to evolutionary game theory in finite populations are presented.      

A method for estimating the intensity of overdominant selection from the distribution of allele frequencies

A method is proposed for estimating the intensity of overdominant selection scaled by the effective population size, S = 2Ns, from allele frequencies. The method is based on the assumption that, with strong overdominant selection, allele frequencies are nearly at their deterministic equilibrium values and that, to a first approximation, deviations depend only on S. Simulations verify that reasonably accurate estimates of S can be obtained for realistic sample sizes. The method is applied to data from several loci in the major histocompatibility complex (Mhc) in numerous human populations. For alleles distinguished by both serological typing and the sequence of the peptide-binding region, our estimates of S are comparable to those obtained by analysis of DNA sequences in showing that selection is strongest on HLA-B and weaker on HLA-A, HLA-DRB1, and HLA-DQA1. The intensity of selection on HLA-B varied considerably among populations. Two populations, Native American and Inuit, showed an excess rather than a deficiency in homozygosity. Comparable estimates of S were obtained for alleles at Mhc class II loci distinguished by serological reactions (serotyping) and by differences in the amino acid sequences of the peptide-binding region (molecular typing). A comparison of two types of data for DQA1 and DRB1 showed that serotyping led to generally lower estimates of S.     

Membrane fluidity and the probability of complement fixation

We develop a mathematical theory of the role of membrane fluidity in the initiation of the IgG mediated complement cascade. The basic assumption is that C1q must be at least doubly bound to activate C1r, but that once C1q is doubly bound, C1r still requires some mean finite time tau to become enzymatically active. If C1q dissociates during this time interval, C1r cannot be activated. We consider the consequences of the simplest model of fluidity--one in which the difference between "fluid phase" lipids and "non-fluid phase" lipids is to allow protein mobility, but not a change in protein conformation. We show that under these conditions fluidity will effect C1r activation only if the rate of formation of multiply bound C1q is limited by diffusion in the membrane. If diffusion in the membrane is not rate-limiting, then, within the framework of this model, fluidity has no effect whatsoever on C1r activation. Thus, an experimental determination that C1q binding is not rate-limited by diffusion in the surface, but that fluidity does effect activation, would suggest a protein conformational change resulting perhaps from altered lipid composition. If diffusion in the surface does rate limit multiple C1q binding, we predict the possibility of an optimum diffusion coefficient for activation. For suitably chosen and reasonable parameter values this optimum will occur in the range (10(-11) less than or equal to D less than or equal to 10(-8) cm2/sec. We predict further, under these circumstances, a precipitous drop in the probability of activation above the optimum. The abrupt switch from a high probability of activation to essentially no probability of activation suggests the possibility of a very sensitive control mechanism exploitable by relatively small changes in membrane lipid composition.     

Standardizing selection and its consequences for genetic population structure

Type of selection for total fitness, specific for domestic animals and termed by us standardizing selection, is discussed. Consequences of such selection for the population structure genetic are considered taking a population of domestic pigs as an example. Examples of effective and ineffective standardizing selection are presented. Specific features of genetic determination of ten quantitative traits detected in analysis of standardizing selection are discussed.     

Burkholderia cepacia under different ecological conditions: the amount and variability of the bacterial population

In a series of prolonged experiments with the use of the bacteriological method and PCR analysis the amount and state of B. cepacia population, associated and not associated with infusoria Tetrahymena pyriformis, were dynamically evaluated under different conditions: in water, brain heart broth, soil extract and at different temperature (4 degrees C and 25 degrees C). In soil extract at 25 degrees C B. cepacia existed in the vegetative state for the period of up to 3 months, while at 4 degrees C, in the absence of protozoa, the transition of these microorganisms into the uncultivable forms occurred in 9 days, and they could be detected only with the use of PCR. Protozoa maintained the existence of the vegetative bacteria for as long as 2 months, and in 3-4 months uncultivable forms of B. cepacia cells were registered. In water at low temperature B. cepacia disappeared in 2 months, evidently, eaten up by infusoria. The population variability of B. cepacia under different conditions of their existence was established: S-R dissociation, a decrease in biochemical activity, growth deceleration. A high level of cytopathogenicity in B. cepacia pigment-forming clones was noted. In the process of transition into the uncultivable state pigment formation in B. cepacia population decreased up. The ecological plasticity and multi-pathogenicity of B. cepacia as phytopathogens and the causative agents of human diseases are discussed.     

Human population structure and the adaptive response to pathogen-induced selection pressures

The past few years of research in human evolutionary genetics have provided novel insights and questions regarding how human adaptations to recent selective pressures have taken place. Here, we review the advances most relevant to understanding human evolution in response to pathogen-induced selective pressures. Key insights come from theoretical models of adaptive evolution, particularly those that consider spatially structured populations, and from empirical population genomic studies of adaptive evolution in humans. We also review the CCR5-Δ32 HIV resistance allele as a case study of pathogen resistance in humans. Taken together, the results make clear that the human response to pathogen-induced selection pressures depends on a complex interplay between the age of the pathogen, the genetic basis of potential resistance phenotypes, and how population structure impacts the adaptive process in humans.     

Strong habitat selection and the development of population structure in a mosquito

Summary Remarkably simple and regular patterns of genic variation for two electrophoretically assayed loci are presented against a background of strong habitat selection, population isolation, and population structuring in the pitcher-plant mosquitoWyeomyia smithii. The genic variation assessed thus far comes from 29 local populations, all but one of which lie within the glaciated region of North America. Although the conclusions drawn from these patterns are still quite tentative, it appears that the fact that the same higher frequency electromorphs occurred everywhere for both loci may be due more to selection than drift. Drift or selection, acting alone or in concert may be responsible for the almost complete absence of electromorphs of intermediate frequency. A weak association was found between the two-locus genic variation and the well-studied diapause-development time variation in this species. It is suggested that a Wrightian interaction system and fluctuating-stabilizing selection might account for maintenance of the genic level polymorphism. The observations reported are circumstantially in accord with Wright's shifting balance process of evolution. Future studies in the older parts of the species range will put these hypotheses to a strong test.     

The fixation probability of a beneficial allele in a population dividing by binary fission

We derive formulae for the fixation probability, P, of a rare benefical allele segregating in a population of fixed size which reproduces by binary fission, in terms of the selection coefficient for the beneficial allele, s. We find that an earlier result P 4s does not depend on the assumption of binary fission, but depends on an assumption about the ordering of events in the life cycle. We find that P 2s for mutations occurring during chromosome replication and P 2.8s for mutations occurring at random times between replication events.