Genetic load in subdivided populations: interactions between the migration rate, the size and the number of subpopulations

We assess the relative importance of migration rate, size and number of subpopulations on the genetic load of subdivided populations. Using diffusion approximations, we show that in most cases subdivision has detrimental effects on fitness. Moreover, our results suggest that fitness increases with subpopulation size, so that for the same total population size, genetic load is relatively lower when there are a small number of large subpopulations. Using elasticity analysis, we show that the size of the subpopulations appears to be the parameter that most strongly determines genetic load. interconnecting subpopulations via migration would also be of importance for population fitness when subpopulations are small and gene flow is low. Interestingly, the number of subpopulations has minor influence on genetic load except for the case of both very slightly deleterious mutations and small subpopulations. Elasticities decrease as the magnitude of deleterious effects increases. In other words, population structure does not matter for very deleterious alleles, but strongly affects fitness for slightly deleterious alleles.     

Average number of nucleotide differences in a sample from a single subpopulation: a test for population subdivision

Unbiased estimates of θ = 4Nµ in a random mating population can be based on either the number of alleles or the average number of nucleotide differences in a sample. However, if there is population structure and the sample is drawn from a single subpopulation, these two estimates of θ behave differently. The expected number of alleles in a sample is an increasing function of the migration rates, whereas the expected average number of nucleotide differences is shown to be independent of the migration rates and equal to 4N_Tµ for a general model of population structure which includes both the island model and the circular stepping-stone model. This contrast in the behavior of these two estimates of θ is used as the basis of a test for population subdivision. Using a Monte-Carlo simulation developed so that independent samples from a single subpopulation could be obtained quickly, this test is shown to be a useful method to determine if there is population subdivision.     

Does harvest affect genetic diversity in grey wolves?

Harvest can affect vital rates such as reproduction and survival, but also genetic measures of individual and population health. Grey wolves (Canis lupus) live and breed in groups, and effective population size is a small fraction of total abundance. As a result, genetic diversity of wolves may be particularly sensitive to harvest. We evaluated how harvest affected genetic diversity and relatedness in wolves. We hypothesized that harvest would (a) reduce relatedness of individuals within groups in a subpopulation but increase relatedness of individuals between groups due to increased local immigration, (b) increase individual heterozygosity and average allelic richness across groups in subpopulations and (c) add new alleles to a subpopulation and decrease the number of private alleles in subpopulations due to an increase in breeding opportunities for unrelated individuals. We found harvest had no effect on observed heterozygosity of individuals or allelic richness at loci within subpopulations but was associated with a small, biologically insignificant effect on within‐group relatedness values in grey wolves. Harvest was, however, positively associated with increased relatedness of individuals between groups and a net gain (+16) of alleles into groups in subpopulations monitored since harvest began, although the number of private alleles in subpopulations overall declined. Harvest likely created opportunities for wolves to immigrate into nearby groups and breed, thereby making groups in subpopulations more related over time. Harvest appears to affect genetic diversity in wolves at the group and population levels, but its effects are less apparent at the individual level given the population sizes we studied.     

Properties of a neutral allele model with intragenic recombination

An infinite-site neutral allele model with crossing-over possible at any of an infinite number of sites is studied. A formula for the variance of the number of segregating sites in a sample of gametes is obtained. An approximate expression for the expected homozygosity is also derived. Simulation results are presented to indicate the accuracy of the approximations. The results concerning the number of segregating sites and the expected homozygosity indicate that a two-locus model and the infinite-site model behave similarly for 4Nu less than or equal to 2 and r less than or equal to 5u, where N is the population size, u is the neutral mutation rate, and r is the recombination rate. Simulations of a two-locus model and a four-locus model were also carried out to determine the effect of intragenic recombination on the homozygosity test of Watterson (Genetics 85, 789-814; 88, 405-417) and on the number of unique alleles in a sample. The results indicate that for 4Nu less than or equal to 2 and r less than or equal to 10u, the effect of recombination is quite small.     

Coexistence of cytoplasmic incompatibility and male-killing-inducing endosymbionts, and their impact on host gene flow

Male-killing (MK) and cytoplasmic incompatibility (CI) inducing bacteria are among the most common endosymbionts of arthropods. Previous theoretical research has demonstrated that these two types of endosymbionts cannot stably coexist within a single unstructured host population if no doubly infected host individuals occur. Here, we analyse a model of two host subpopulations connected by migration. We demonstrate that coexistence of MK- and CI-inducing endosymbionts is possible if migration rates are sufficiently low. In particular, our results suggest that for coexistence to be possible, migration rates into the subpopulation infected predominantly with MK-inducing endosymbionts must be considerably low, while migration rates from the MK- to the CI-infected subpopulation can be very high. We also analyse how the presence of MK- and CI-inducing endosymbionts affects host gene flow between the two subpopulations. Employing the concept of the 'effective migration rate', we demonstrate that compared with an uninfected subdivided population, gene flow is increased towards the MK-infected island, but decreased towards the CI-infected island. We discuss our results with respect to the butterfly Hypolimnas bolina, in which infection polymorphism of CI- and MK-inducing Wolbachia has been reported across South-Pacific island populations.     

A standardized genetic differentiation measure

Interpretation of genetic differentiation values is often problematic because of their dependence on the level of genetic variation. For example, the maximum level of GST is less than the average within population homozygosity so that for highly variable loci, even when no alleles are shared between subpopulations, GST may be low. To remedy this difficulty, a standardized measure of genetic differentiation is introduced here, one which has the same range, 0-1, for all levels of genetic variation. With this measure, the magnitude is the proportion of the maximum differentiation possible for the level of subpopulation homozygosity observed. This is particularly important for situations in which the mutation rate is of the same magnitude or higher than the rate of gene flow. The standardized measure allows comparison between loci with different levels of genetic variation, such as allozymes and microsatellite loci, or mtDNA and Y-chromosome genes, and for genetic differentiation for organisms with different effective population sizes.     

The Island Model of Population Differentiation: A General Solution

The island model deals with a species which is subdivided into a number of discrete finite populations, races or subspecies, between which some migration occurs. If the number of populations is small, an assumption of equal rates of migration between each pair of populations may be reasonable approximation. Mutation at a constant rate to novel alleles may also be assumed.-A general solution is given for the process of population divergence under this model following subdivision of a single parental population, expressed in terms of the observed average frequency of heterozygotes within and between subpopulations at a randomly chosen set of independently segregating loci. No restriction is imposed on the magnitude of the migration or mutation rates involved, nor on the number of populations exchanging migrants.-The properties of two fundamental measures of genetic divergence are deduced from the theory. One is a parameter related to varphi, the coefficient of kinship, and the other, gamma, measures the rate of mutational divergence between the sub-populations.     

Heterosis or Neutrality?

Various statistics have been proposed on an ad hoc basis to test whether alleles at a locus are selectively neutral. By considering population models in which selection operates, this paper shows that the population homozygosity is a powerful test statistic for testing departures from neutrality, in the direction of heterozygote advantage or disadvantage. The sample homozygosity plays a similar role when only sample data are available. Some numerical examples are included, showing the application of the test.—An analysis is made of the effect of heterosis on such quantities as the expected number of alleles in the population or sample, the effective number of alleles, the expected homozygosity, and on the population and sample allele frequency distributions generally.     

Nonequilibrium migration in human history

A nonequilibrium migration model is proposed and applied to genetic data from humans. The model assumes symmetric migration among all possible pairs of demes and that the number of demes is large. With these assumptions it is straightforward to allow for changes in demography, and here a single abrupt change is considered. Under the model this change is identical to a change in the ancestral effective population size and might be caused by changes in deme size, in the number of demes, or in the migration rate. Expressions for the expected numbers of sites segregating at particular frequencies in a multideme sample are derived. A maximum-likelihood analysis of independent polymorphic restriction sites in humans reveals a decrease in effective size. This is consistent with a change in the rates of migration among human subpopulations from ancient low levels to present high ones.     

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.     

Genetic variation,population structure and identification of yellow catfish, <Emphasis Type="Italic">Mystus nemurus</Emphasis> (C&;V) in Thailand using RAPD,ISSR and SCAR marker

Random amplified polymorphic DNA (RAPD) and inter-simple sequence repeat (ISSR) markers were used to investigate the genetic structure of four subpopulations of Mystus nemurus in Thailand. The 7 RAPD and 7 ISSR primers were selected. Of 83 total RAPD fragments, 80 (96.39%) were polymorphic loci, and of 81 total ISSR fragments, 75 (92.59%) were polymorphic loci. Genetic variation and genetic differentiation obtained from RAPD fragments or ISSR fragments showed similar results. Percentage of polymorphic loci (%P), observed number of alleles, effective number of alleles, Nei’s gene diversity (H) and Shannon’s information index revealed moderate to high level of genetic variations within each M. nemurus subpopulation and overall population. High levels of genetic differentiations were received from pairwise unbiased genetic distance (D) and coefficient of differentiation. Mantel test between D or gene flow and geographical distance showed a low to moderate correlation. Analysis of molecular variance indicated that variations among subpopulations were higher than those within subpopulations. The UPGMA dendrograms, based on RAPD and ISSR, showing the genetic relationship among subpopulations are grouped into three clusters; Songkhla (SK) subpopulation was separated from the other subpopulations. The candidate species-specific and subpopulation-specific RAPD fragments were sequenced and used to design sequence-characterized amplified region primers which distinguished M. nemurus from other species and divided SK subpopulation from the other subpopulations. The markers used in this study should be useful for breeding programs and future aquacultural development of this species in Thailand.     

Effective size and F-statistics of subdivided populations for sex-linked loci.

For a population subdivided into an arbitrary number (s) of subpopulations, each consisting of different numbers of separate sexes, with arbitrary distributions of family size and variable migration rates by males (dm) and females (df), the recurrence equations for inbreeding coefficient and coancestry between individuals within and among subpopulations for a sex-linked locus are derived and the corresponding expressions for asymptotic effective size are obtained by solving the recurrence equations. The usual assumptions are made which are stable population size and structure, discrete generations, the island migration model, and without mutation and selection. The results show that population structure has an important effect on the inbreeding coefficients in any generation, asymptotic effective size, and F-statistics. Gene exchange among subpopulations inhibits inbreeding in initial generations but increases inbreeding in later generations. The larger the migration rate, the greater the final inbreeding coefficients and the smaller the effective size. Thus if the inbreeding coefficient is to be restricted to a specific value within a given number of generations, the appropriate population structure (the values of s, dm, and df) can be obtained by using the recurrence equations. It is shown that the greater the extent of subdivision (large s, small dm and df), the larger the effective size. For a given subdivided population, the effective size for a sex-linked locus may be larger or smaller than that for an autosomal locus, depending on the sex ratio, variance and covariance of family size, and the extend of subdivision. For the special case of a single unsubdivided population, our recurrence equations for inbreeding coefficient and coancestry and formulas for effective size reduce to the simple expressions derived by previous authors.     

Use of a genetic marker to examine genetic interaction among subpopulations of pink salmon (Oncorhynchus gorbuscha)

In 1979 and 1981, a genetic marker was bred into one of the five identifiable subpopulations of pink salmon [Oncorhynchus gorbuscha (Walbaum)] in the Auke Lake drainage in Southeast Alaska. As a result of the marking effort, the frequencies of two malate dehydrogenase (MDH-B1, 2^*) alleles were changed in the marked subpopulation, but not in other subpopulations that spawn at different times or places. Between 1983 and 1989, the marker allele frequencies were monitored in many of these subpopulations and in early- and late-run pink salmon spawning in nearby Waydelich Creek, located approximately 1km away. Changes in allele frequencies at MDH-B1, 2^*, used to obtain direct estimates of average migration rates (m) from the marked to the unmarked subpopulations, revealed little or no introgression into early subpopulations or into nearby Waydelich Creek. Moreover, spatially distinct late-run Auke Creek subpopulations were not immediately overrun by the more abundant marked subpopulation. These observations suggest that genetic isolation exists between temporally distinct spawning runs and that small temporal and spatial (or ecological) differences contribute to population structure. These observations should be considered in taking actions that affect conservation and harvest management or extensive culture of salmonids.     

From the Apennines to the Alps: colonization genetics of the naturally expanding Italian wolf (Canis lupus) population

Wolves in Italy strongly declined in the past and were confined south of the Alps since the turn of the last century, reduced in the 1970s to approximately 100 individuals surviving in two fragmented subpopulations in the central-southern Apennines. The Italian wolves are presently expanding in the Apennines, and started to recolonize the western Alps in Italy, France and Switzerland about 16 years ago. In this study, we used a population genetic approach to elucidate some aspects of the wolf recolonization process. DNA extracted from 3068 tissue and scat samples collected in the Apennines (the source populations) and in the Alps (the colony), were genotyped at 12 microsatellite loci aiming to assess (i) the strength of the bottleneck and founder effects during the onset of colonization; (ii) the rates of gene flow between source and colony; and (iii) the minimum number of colonizers that are needed to explain the genetic variability observed in the colony. We identified a total of 435 distinct wolf genotypes, which showed that wolves in the Alps: (i) have significantly lower genetic diversity (heterozygosity, allelic richness, number of private alleles) than wolves in the Apennines; (ii) are genetically distinct using pairwise F(ST) values, population assignment test and Bayesian clustering; (iii) are not in genetic equilibrium (significant bottleneck test). Spatial autocorrelations are significant among samples separated up to c. 230 km, roughly correspondent to the apparent gap in permanent wolf presence between the Alps and north Apennines. The estimated number of first-generation migrants indicates that migration has been unidirectional and male-biased, from the Apennines to the Alps, and that wolves in southern Italy did not contribute to the Alpine population. These results suggest that: (i) the Alps were colonized by a few long-range migrating wolves originating in the north Apennine subpopulation; (ii) during the colonization process there has been a moderate bottleneck; and (iii) gene flow between sources and colonies was moderate (corresponding to 1.25-2.50 wolves per generation), despite high potential for dispersal. Bottleneck simulations showed that a total of c. 8-16 effective founders are needed to explain the genetic diversity observed in the Alps. Levels of genetic diversity in the expanding Alpine wolf population, and the permanence of genetic structuring, will depend on the future rates of gene flow among distinct wolf subpopulation fragments.     

Rate of Decrease of Genetic Variability in a Two-Dimensional Continuous Population of Finite Size

The rate of decay of genetic variability was investigated for two-dimensional continuous populations of finite size. The exact value of the rate involves a rather complicated expression (formula (4-1)). However, numerical examples indicate that in a population habitat size LxL and density D, the rate is approximately equal to (see PDF) where sigma(2) is the variance of dispersion distance assuming isotropical migration. The value given in (2) is equal to that of a panmictic population of size DL(2). It is remarkable that whether the rate assumes the value given by (1) or by (2) depends only on Dsigma(2) (a local property), which is independent of the habitat size. Since, in a one-dimensional population, this depends on both Dsigma(2) and the habitat size, there is an essential difference between the two types of population structure.-The function giving the probability of two homologous genes separated by a given distance being different alleles was also obtained, (formula (5-1)).     

Relationship between Migration and DNA Polymorphism in a Local Population

The expected amount of DNA polymorphism, measured in terms of the number of nucleotide differences between the two DNA sequences randomly sampled from subpopulations, was studied by using the stepping-stone model and the finite island model, under the assumption that the migration rate is not the same among different subpopulations. The results obtained indicate that the expected amount of DNA polymorphism in the subpopulation with lower migration rate is smaller than that of higher migration rate. This suggests that marginal populations tend to have lower level of DNA polymorphism than central populations if the migration rate in the marginal populations is lower than that of the central populations.     

DNA Polymorphism in a Subdivided Population: The Expected Number of Segregating Sites in the Two-Subpopulation Model

Using the two subpopulation model, the expected numbers of segregating sites in a number of DNA sequences randomly sampled from a subdivided population were examined for several types of population subdivisions. It is shown that, in the case where the pattern of migration is symmetrical such as the finite island model, the expected number of segregating sites is independent of the migration rate when two or three DNA sequences are randomly sampled from the same subpopulation, but depends on the migration rate when more than three DNA sequences are sampled. It is also shown that the population subdivision can increase the amount of DNA polymorphism even in a subpopulation in some cases.     

推测187份玉米自交系基因组血统与分子亲缘关系

为提高育种效率以及开展重要 QTL 和关键基因关联性分析研究, 以 187 份生产上重要玉米自交系为材料, 以 70 个均匀分布于全基因组简单重复序列(SSR)基因座鉴定出的290个等位基因多态性为分析数据, 采用联合连锁位点与混合模型分析, 推测这些自交系的基因组血缘构成以及分子亲缘关系, 并分析了全基因连锁不平衡。当亚群数目 K=5 时, 导致似然值 P 明显下降, 亚群数据 K > 6 时, 似然值 P 没有明显上升, 表明群体结构的亚群数 K 最佳推测为 6。六个亚群分别为 PA、BSSS (含 Reid)、PB、兰卡斯特 (Lancaster)、旅大红骨 (旅大红骨及其衍生系)、四平头 (唐四平头及其衍生系)。亚群间的Kullback-Leibler 距离自 0.13 至 1.06 不等, 平均为 0.599, 各亚群间区分度较好。全基因组连锁不平衡(LD)分析表明: 与四平头种质类群内相比, 遗传基础宽泛种质的基因组内存在 LD"区块"(LD block)少且小, 对重要 QTLs 与基因的关联性分析可以避免假阳性。本研究群体结构与基因组构成分析数据为这些材料育种应用与改良提供了重要信息, 也为基于这些材料的关联性分析奠定了分析基础。     

Linkage Disequilibrium in Subdivided Populations

The linkage disequilibrium in a subdivided populaton is shown to be equal to the sum of the average linkage disequilibrium for all subpopulations and the covariance between gene frequencies of the loci concerned. Thus, in a subdivided population the linkage disequilibrium may not be 0 even if the linkage disequilibrium in each subpopulation is 0. If a population is divided into two subpopulations between which migration occurs, the asymptotic rate of approach to linkage equilibrium is equal to either r or 2(m(1) + m(2)) - (m(1) + m(2))(2), whichever is smaller, where r is the recombination value and m(1) and m(2) are the proportions of immigrants in subpopulations 1 and 2, respectively. Thus, if migration rate is high compared with recombination value, the change of linkage disequilibrium in subdivided populations is similar to that of a single random mating population. On the other hand, if migration rate is low, the approach to lnkage equilibrium may be retarded in subdivided populations. If isolated populations begin to exchange genes by migration, linkage disequilibrium may increase temporarily even for neutral loci. If overdominant selection operates and the equilibrium gene frequencies are different in the two subpopulations, a permanent linkage disequilibrium may be produced without epistasis in each subpopulation.