Prediction of rates of inbreeding in populations undergoing index selection

For populations undergoing mass selection, previous studies have shown that the rate of inbreeding is directly related to the mean and variance of long-term contributions from ancestors to descendants, and thus prediction of the rate of inbreeding can be achieved via the prediction of long-term contributions. In this paper, it is shown that the same relationship between the rate of inbreeding and long-term contributions is found when selection is based on an index of individual and sib records (index selection) and where sib records may be influenced by a common environment. In these situations, rates of inbreeding may be considerably higher than under mass selection. An expression for the rate of inbreeding is derived for populations undergoing index selection based on variances of (one-generation) family size and incorporating the concept of long-term selective advantage. When the mating structure is hierarchical, and when half-sib records are included in the index, the correlation between parental breeding values and the index values of their offspring is higher for male parents than female parents. This introduces an important asymmetry between the contributions of male and female ancestors to the evolution of inbreeding which is not present when selection is based on individual and/or full-sib records alone. The prediction equation for index selection accounts for this asymmetry. The prediction is compared to rates of inbreeding calculated from simulation. The prediction is good when family size is small relative to the number selected. The reasons for overprediction in other situations are discussed.     

Prediction of Response to Selection and Inbreeding Coefficient under Assortative Mating

A method for predicting response to selection and inbreeding coefficient under the continuous use of assortative mating was derived. Using the method, numerical computation was carried out, and the utility of assortative mating in the selection programmes was evaluated. It was shown that the continuous use of assortative mating could not produce an appreciable additional increase in intermediate- or long-term selection response.     

Stabilizing selection of protein function and distribution of selection coefficient among sites

In this study, I take a new approach to modeling the evolutionary constraint of protein sequence, introducing the stabilizing selection of protein function into the nearly-neutral theory. In other words, protein function under stabilizing selection generates the evolutionary conservation at the sequence level. With the help of random mutational effects of nucleotides on protein function, I have derived the distribution of selection coefficient among sites, called the S-distribution whose parameters have clear biological interpretations. Moreover, I have studied the inverse relationship between the evolutionary rate and the effective population size, showing that the number of molecular phenotypes of protein function, i.e., independent components in the fitness of the organism, may play a key role for the molecular clock under the nearly-neutral theory. These results are helpful for having a better understanding of the underlying evolutionary mechanism of protein sequences, as well as human disease-related mutations.     

Contrasting the efficacy of selection on the X and autosomes in Drosophila

To investigate the relative efficacy of both positive and purifying natural selection on the X chromosome and the autosomes in Drosophila, we compared rates and patterns of molecular evolution between these chromosome sets using the newly available alignments of orthologous genes from 12 species. Parameters that may influence the relative X versus autosomal substitution rates include the relative effective population sizes, the male and female germline mutation rates, the distribution of allelic effects on fitness, and the degree of dominance of novel mutations. Our analysis reveals that codon usage bias is consistently greater for X-linked genes, suggesting that purifying selection consistently has greater efficacy on the X chromosome than on the autosomes across the Drosophila phylogeny. However, our results are less consistent with respect to the efficacy of positive selection, with only some lineages showing a higher substitution rate on the X chromosome. This suggests that either the distribution of selective effects of mutations or other relevant parameters are sufficiently variable across species to tip the balance in different ways in individual lineages. These data suggest that rates of substitution are not solely governed by adaptive evolution. This genome-wide analysis provides a clear picture that the efficacy of selection varies intragenomically and that this effect is markedly more consistent across the phylogeny in the case of purifying selection. Our results also suggest that simple models that predict systematic differences in rates of evolution between the X and the autosomes can only be made to be compatible with these Drosophila data if the relevant population genetic parameters that drive substitution rates differ among species and chromosomal contexts.     

Coalescent process with fluctuating population size and its effective size

We consider a Wright-Fisher model whose population size is a finite Markov chain. We introduce a sequence of two-dimensional discrete time Markov chains whose components describe the coalescent process and the fluctuation of population size. For the limiting process of the sequence of Markov chains, the relationship of the expectation of coalescence time to the harmonic and the arithmetic means of population sizes is shown, and the Laplace transform of the distribution of coalescence time is calculated. We define the coalescence effective population size (cEPS) by the expectation of coalescence time. We show that cEPS is strictly larger (resp. smaller) than the harmonic (resp. arithmetic) mean. As the population size fluctuates more quickly (resp. slowly), cEPS is closer to the harmonic (resp. arithmetic) mean. For the case of a two-valued Markov chain, we show the explicit expression of cEPS and its dependency on the sample size.     

中华绒螯蟹“长荡湖1号”连续3个世代的遗传多样性分析

为了解选育对中华绒螯蟹(Eriocheir sinensis)“长荡湖1号”遗传多样性的影响, 研究采用20个微卫星位点对“长荡湖1号”A系和B系各连续3个世代进行遗传多样性分析。结果如下: 20个微卫星标记在6个群体中共检测到551个等位基因, 各位点的平均等位基因数(N_a)和平均有效等位基因数(N_e)分别为27.55和13.61, 平均观测杂合度(H_o)和平均期望杂合度(H_e)分别为0.72和0.90, 平均香农信息指数(I)和多态信息含量(PIC)分别为2.73和0.89。在选育过程中, A系和B系3个世代的PIC均有下降趋势, 各群体的H_e和H_o均维持较高水平。A系子一代(G1)和子二代(G2)的有效群体数量(N_e)分别为72.7和111.8, B系G1和G2的有效群体数量分别为67.7和115.8, 均维持在较高水平。Hardy-Weinber平衡检验结果显示, 有72.5%的数据偏离Hardy-Weinber平衡, 表明选育群体的遗传结构处于相对不稳定的状态。A系和B系后代与G0的遗传距离均逐代增大, 其中A系从0.2455增大到0.2607, B系从0.1736增大到0.1751。各群体之间遗传分化指数(F_st)均小于0.05, 表明各群体间遗传分化程度微弱。AMOVA分析结果表明, “长荡湖1号”仅0.87%的变异存在于各群体间, 而99.13%的变异发生在群体内个体间。综上所述, 中华绒螯蟹“长荡湖1号”经过2代选育, 选育群体的遗传多样性和有效群体数量依然保持较高水平, 但群体遗传结构处于相对不稳定状态, 今后选育过程中应该保持足够的繁殖亲本数量和遗传多样性, 防止近交退化。     

The effective number of a population that varies cyclically in size. II. Overlapping generations

We consider haploid and dioecious age-structured populations that vary over time in cycles of length k. Results are obtained for both autosomal and sex-linked loci if the population is dioecious. It is assumed that k is small in comparison with numbers of haploid individuals (or of numbers of males and females) in any generation of a cycle. The inbreeding effective population size N(e) is then approximately given by the expression [T summation operator (k-1)(j=0)1/[N(e)(j)T(j)]](-1), where N(e)(j) and T(j) are, respectively, the effective population size and generation interval that would hold if the population was at all times generated in the same way as at time j. The constant T, which is the effective overall generation interval, is defined to be k times the harmonic mean of the quantities T(j). Our expressions for T and N(e), in terms of N(e)(j) and T(j), are general, but the N(e)(j)s are derived under the assumption that offspring are produced according to Poisson distributions.     

Gain and diversity in advanced generation coastal Douglas-fir selections for seed production populations

Sublines are used in the third-generation breeding and testing of coastal Douglas-fir in British Columbia, with the original intent of selecting only one genotype per subline for production populations (e.g., seed orchards) to eliminate relatedness among parents (therein called “1/SL”). We evaluated three additional selection scenarios that did not consider the subline structure. One of the scenarios strictly selected on the basis of the highest breeding values of the trees (“TOP”); another scenario used the TOP selections, but assigned the number of ramets per selection proportionally to the selection breeding value (“LIND”); lastly, a simulated annealing technique was applied to maximize gain under explicit constraints on coancestry (“OPTS”). All three alternative selection scenarios resulted in some relatedness and coancestry among selections, but the last two provided increases in average breeding values compared to those obtained by the 1/SL scenario. Effective population sizes (and consequently inbreeding coefficients) varied among the three selection scenarios. Effects of the various selections on merchantable volume at rotation age were determined using a linear regression model based on an individual tree model (TASS), which was first run to determine the relationship between merchantable volume and inbreeding (f). LIND and TOP selections yielded the highest breeding values but, due to the increased coancestry among selections, paid a penalty in the merchantable volume determination. OPTS maximized merchantable volume at rotation age 60 after including more than 13 selections with an increase of around 3% over that obtained by the 1/SL selection scenario, with an associated increase in Ne of 50%. Other implications of the three alternative selection scenarios are discussed.     

Three components of genetic drift in subdivided populations

Wright's metaphor of sampling is extended to consider three components of genetic drift: those occurring before, during, and after migration. To the extent that drift at each stage behaves like an independent random sample, the order of events does not matter. When sampling is not random, the order does matter, and the effect of population size is confounded with that of mobility. The widely cited result that genetic differentiation of local groups depends only on the product of group size and migration rate holds only when nonrandom sampling does not occur prior to migration in the life cycle.     

Sex-linked effective population size in control populations,with particular reference to honeybees (Apis mellifera L.)

Summary Sex-linked effective population size (Ne) is derived for a variety of control population structures relevant to normal diploid and/or, more importantly, to haplo-diploid species. For equal sex ratio, it is shown that the control population structure which doubles autosomal effective population size trebles sex-linked effective size. For haplo-diploid species where the number of males exceeds the number of reproductive females, several different control structures are described, which tend to increase effective population size by about 1/3. These would be suitable for stock maintenance of honeybees. Directional selection programmes employing within-family selection would maintain most of the minimum drift/inbreeding properties of these control populations.