Allele frequencies in multidimensional Wright-Fisher models with a general symmetric mutation structure

The diffusion form of a multiple-allele Wright-Fisher model of allele frequencies of types A₁,…,A_K at a neutral locus where there are general symmetric mutation rates of M_ij (=M_ji) from A_i → A_j is studied. A convenient recurrence relationship for the moments of linear forms in the allele frequencies is found. A formula is derived for the expected homozygosity in the transient and stationary models, which is applied to general stepwise mutation models where mutation over more than one step is possible. The probability that two randomly chosen genes are j steps apart at time t in the stepwise mutation model is found to have a reasonably simple form if conditioning is on the initial allele frequencies arranged in order of magnitude. Of interest is a new geometric charge state model, mutation over several steps roughly corresponding to independent charge changes. The expected homozygosity and expected distance between two randomly chosen genes is tabulated in this model.     

The frequency spectrum of a mutation,and its age,in a general diffusion model

General formulae are derived for the probability density and expected age of a mutation of frequency x in a population, and similarly for a mutation with b copies in a sample of n genes. A general formula is derived for the frequency spectrum of a mutation in a sample. Variable population size models are included. Results are derived in two frameworks: diffusion process models for the frequency of the mutation; and birth and death process models. The coalescent structure within the mutant gene group and the non-mutant group is considered.     

Allele frequencies of 6 autosomal STR loci in the Xibo nationality with phylogenetic structure among Chinese populations

In the present study, we investigated the genetic polymorphisms of 6 autosomal STR loci Hum-CSF1PO, D13S317, D5S818, D16S539, TH01, and TPOX in the Xibo population of Liaoning, northeastern China as well as its genetic relationships with other populations in China. No significant deviations from Hardy-Weinberg equilibrium could be found for all loci. Allele frequencies in the Xibo population ranged from 0.001 to 0.507. Among all the 6 loci, D16S539 had the highest polymorphism (PIC = 0.8632), whereas TPOX had the lowest (PIC = 0.5179). A phylogenic tree was constructed using Poptree 2 software. In the phylogenic tree, Xibo population has a distant relationship with the other populations.     

The rate of multi-step evolution in Moran and Wright-Fisher populations

Several groups have recently modeled evolutionary transitions from an ancestral allele to a beneficial allele separated by one or more intervening mutants. The beneficial allele can become fixed if a succession of intermediate mutants are fixed or alternatively if successive mutants arise while the previous intermediate mutant is still segregating. This latter process has been termed stochastic tunneling. Previous work has focused on the Moran model of population genetics. I use elementary methods of analyzing stochastic processes to derive the probability of tunneling in the limit of large population size for both Moran and Wright-Fisher populations. I also show how to efficiently obtain numerical results for finite populations. These results show that the probability of stochastic tunneling is twice as large under the Wright-Fisher model as it is under the Moran model.     

Equilibrium correlations in a model for multidimensional epistasis

We investigate a statistical model for multidimensional epistasis. The genotype is devided into subsequences, and within each subsequence mutations which occur in a prescribed order are beneficial. The bit-string model used to represent the genotype, may be cast in the form of a ferromagnetic Ising model with a staggered field. We describe the actual correlations between mutations at different sites, within an equilibrium population at a given tolerance, which we define to be the temperature of the statistical ensemble.     

宋朝中国人的姓氏分布与群体结构分化

姓氏是一种十分有用的文化遗传因子,它的传递方式类似于Ｙ染色体的表现。１０００年前宋朝（公元９６０￣１１７９年）中国人姓氏频率的分布,是一组十分吻合Ｋａｒｌｉｎ－ＭｃＧｒｅｇｏｒ的中性等位基因分布理论的随机数据。１６个省区的姓氏种类丰度的相对参数α和迁移率的相对参数ｖ的分析,反映了这一时期的中国人群的迁移和人群间混合的程度。姓氏遗传距离和现状聚类图的分析,表明在１０００年前的宋朝中国人群已经形成了南     

Chaotic dynamics of allele frequencies in condition-dependent mating systems

I study the dynamics of allele frequencies in sexually reproducing populations where the choosy sex has a preference for condition-dependent displays of the opposite sex. The condition of an individual is assumed to be shaped by frequency-dependent selection. For sufficiently strong preferences the dynamics becomes increasingly complex, and periodic orbits and chaos are observed. Moreover, multiple attractors can exist simultaneously. The results hold also when the choosy sex is allowed to maintain a moderate level of assortative mating. Complex dynamics, a well studied phenomenon in a purely ecological setting, has been rarely observed in ecologically motivated population genetic models.     

Prediction of effects of genetic drift on variance components under a general model of epistasis

For a model of diallelic loci with arbitrary epistasis, Barton and Turelli [2004. Effects of genetic drift on variance components under a general model of epistasis. Evolution 58, 2111-2132] gave results for variances among and within replicate lines obtained by inbreeding without selection. Here, we discuss the relation between their population genetic methods and classical quantitative genetic arguments. In particular, we consider the case of no dominance using classical identity by descent arguments, which generalizes their results from two alleles to multiple alleles. To clarify the connections between the alternative methods, we obtain the same results using an intermediate method, which explicitly identifies the statistical effects of sets of loci. We also discuss the effects of population bottlenecks on covariances among relatives.     

Equine plasminogen polymorphism: allelic frequencies in 23 breeds

A modified procedure for detection of the two alleles of equine plasminogen using Western blotting methods following polyacrylamide gel isoelectric focusing is described. Gene frequencies in 23 breeds and Equus przewalskii are provided.     

Proportions of different habitat types are critical to the fate of a resistance allele

We describe a simple deterministic theoretical framework for analysing the gene frequency evolution of two alternative alleles at a single genetic locus in a habitat comprising two environments in which the genotypes have different relative fitnesses. We illustrate this for adaptation of pest insects, where one allele (resistance to toxins expressed in transgenic crops) is favoured in one environment (transgenic plants) and the other allele (susceptibility to toxins) is favoured in the other environment (‘refuges’ of non-transgenic plants). The evolution of allele frequencies depends on selection pressure because of relative sizes of the environments and relative fitnesses of the genotypes in each environment. We demonstrate that there are critical threshold proportions for habitat division that determine equilibrium allele frequencies. The stability of the system depends on relationships between the relative genotype fitnesses. In some cases, the division of the habitat in exactly the threshold proportions removes selection pressure and maintains polymorphism at all allele frequencies.     

Temporal variation of allele frequencies in populations of Akodon dolores (Rodentia,Cricetidae)

Summary Six population samples of the South American cricetid rodent Akodon dolores were collected at the same site at six-month intervals over a three year period. Changes in density were detected. Seven out of 18 loci analyzed by means of starch gel electrophoresis were polymorphic. Only two of these loci (Est-4 and G6pdh) showed statistically significant variation in allele frequencies following a seasonal pattern. There was no correlation between allele frequencies and population density. When animals were grouped into two classes according to body weight, a clear difference in allele distribution at the Est-4 and G6pdh loci was observed between individuals 39 g or less and those heavier than 39 g. As the first group comprises predominantly younger animals, the data indicate that changes in the age-structure of population, rather than density variations, are responsible for the cyclic pattern of allele frequencies fluctuations.     

Density-dependent selection migration model with non-monotone fitness functions

This paper studies the classical single locus, diallelic selection model with diffusion for a continuously reproducing population. The phase variables are population density and allele frequency (or allele density). The genotype fitness depend only on population density but include one-hump functions of the density variable. With mild assumptions on genotype fitnesses, we study the geometry of the nullclines and the asymptotic behavior of solutions of the selection model without diffusion. For the diffusion model with zero Neumann boundary conditions, we use this geometric information to show that if the initial data satisfy certain conditions then the corresponding solution to the reaction-diffusion equation converges to the spatially constant stable equilibrium which is closest to the initial data.Research partially supported by NSF grant DMS-8920597Research supported by funds provided by the USDA-Forest Service, Southeastern Forest Experiment Station, Pioneering (Population Genetics of Forest Trees) Research Unit, Raleigh, North Carolina     

Evidence for a predominant role of oxidative damage in germline mutation in mammals

Spontaneous copying errors in replication often are assumed to be the main source of germline mutations in humans and other mammals. However, when laboratory data on context-dependent patterns of oxidative DNA damage are compared with patterns of mutation inferred from mammalian sequence evolution, the strength of the correlation suggests that damage is the main source of mutations. Analysis of damage susceptibility holds promise for improving models of mutational specificity.     

Mutant gene frequencies in cats of the greater London area

Summary The frequencies of seven mutant genes of the domestic cat have been estimated by sampling the population of greater London, specific areas of the capital and adjoining counties. An attempt was made to diversify the method of sampling by concentrating upon certain categories of cats. In addition to the usual sightings of cats in streets and open spaces, surveys were made of cats attending a veterinary clinic, those staying at a boarding cattery, those exhibited in the household pet classes at a cat show and those in rescue centres. Although there are inconsistencies, the general impression from frequencies in present and earlier observations is that the lighter phenotypes (mackerel tabby, blue dilution and orange) are favoured by human preference, as opposed to the darker phenotypes (blotched tabby, black and non-orange). Reasons are discussed for thinking that, while human preference may be a factor in the evolution of the feline polymorphism, it is not the fundamental cause.     

A stochastic model for the mutation-selection balance in an infinite asexual population with a genome of fixed size

A stochastic model is presented which describes the evolution of a genome of a haploid species in an infinite population. The genome is a finite set of elements. The elements are divided into different classes according to their effect on the fitness of the organism. Repeated mutations of the genome elements are permitted, in particular positive mutations are introduced. The distribution of the deleterious elements in the genome with respect to the impact on the fitness is given after the replication step. The steady state is fully described including the distribution and the fitness.     

Complex dynamics occur in a single-locus, multiallelic model of general frequency-dependent selection

We examine the characteristics of non-equilibrium dynamics produced by a simple well-known model of frequency-dependent selection at a single diploid locus. An examination of the parameter space of this “pairwise-interaction model” (PIM) revealed non-equilibrium dynamics for polymorphisms of 3, 4 and 5 alleles; both allele-frequency cycling and aperiodic trajectories were detected. We measured the number, cycle length and domains of attraction of the various attractors produced by the model. The domains of attraction tended to be smaller, and the cycles longer, for systems with larger number of alleles. Fitnesses that parametrized negative frequency-dependent selection were more likely to allow cycling, and these cycles also had larger domains of attraction. Aperiodic trajectories were detected only in cases with 4 or 5 alleles. The genetic cycles produced by the model do not have periods as short as those predicted in ecological models with cycling (such as predator–prey population cycles, etc.). Consequently, in a real-world system, PIM allele-frequency cycling is likely to be indistinguishable from stable equilibria when observed over short time scales.     

Selection, mutation and sexual reproduction in an infinite haploid population with a genome of finite length

We present a model which describes mutation, selection and sexual reproduction in an infinite haploid population with a finite genome. Each generation is described using an approximation which assures a certain persistent form of the distribution of the number of deleterious elements. The steady state exists and is determined. In addition, we conclude that the introduction of sexual reproduction increases the mean fitness in the equilibrium.     

A continuous migration model with stable demography

A probability model of a population undergoing migration, mutation, and mating in a geographic continuum R is constructed, and an integrodifferential equation is derived for the probability of genetic identity. The equation is solved in one case, and asymptotic analysis done in others. Individuals at x, y R in the model mate with probability V(x, y) dt in any time interval (t, t + dt). In two dimensions, if V(x,y) = V(x–y) where V(x) V(x/)/ ² approaches a delta function, the equilibrium probability of identity vanishes as 0. The asymptotic rate at which this occurs is discussed for mutation rates u u _o > 0 and for Cu , > 0, and u 0.Partially supported by NSF grant MCS79-03472Research was partially supported by Task Agreement No. DE-AT06-76EV71005 under Contract No. DE-AM06-76RL02225 between the U.S. Dept. Energy and the University of Washington     

Altruism and antagonistic pleiotropy in Penna ageing model

The Penna ageing model is based on mutation accumulation theory. We show that it also allows for self-organization of antagonistic pleiotropy which helps at young age at the expense of old age. This can be interpreted as emergence of altruism.