COMPARISON OF NON‐GAUSSIAN QUANTITATIVE GENETIC MODELS FOR MIGRATION AND STABILIZING SELECTION

The balance between stabilizing selection and migration of maladapted individuals has formerly been modeled using a variety of quantitative genetic models of increasing complexity, including models based on a constant expressed genetic variance and models based on normality. The infinitesimal model can accommodate nonnormality and a nonconstant genetic variance as a result of linkage disequilibrium. It can be seen as a parsimonious one‐parameter model that approximates the underlying genetic details well when a large number of loci are involved. Here, the performance of this model is compared to several more realistic explicit multilocus models, with either two, several or a large number of alleles per locus with unequal effect sizes. Predictions for the deviation of the population mean from the optimum are highly similar across the different models, so that the non‐Gaussian infinitesimal model forms a good approximation. It does, however, generally estimate a higher genetic variance than the multilocus models, with the difference decreasing with an increasing number of loci. The difference between multilocus models depends more strongly on the effective number of loci, accounting for relative contributions of loci to the variance, than on the number of alleles per locus.     

Analysis of genetic structure in soil populations of Rhizobium leguminosarum recovered from the USA and the UK

Although many studies have shown that animal-associated bacterial species exhibit linkage disequilibrium at chromosomal loci, recent studies indicate that both animal-associated and soil-borne bacterial species can display a nonclonal genetic structure in which alleles at chromosomal loci are in linkage equilibrium. To examine the situation in soil-borne species further, we compared genetic structure in two soil populations of Rhizobium leguminosarum bv. trifolii and two populations of R. leguminosarum bv. viciae from two sites in Oregon, with genetic structure in R. leguminosarum bv. viciae populations recovered from peas grown at a site in Washington, USA, and at a site in Norfolk, UK. A total of 234 chromosomal types (ET) were identified among 682 strains analysed for allelic variation at 13 enzyme-encoding chromosomal loci by multilocus enzyme electrophoresis (MLEE). Chi-square tests for heterogeneity of allele frequencies showed that the populations were not genetically uniform. A comparison of the genetic diversity within combined and individual populations confirmed that the Washington population was the primary cause of genetic differentiation between the populations. Each individual population exhibited linkage disequilibrium, with the magnitude of the disequilibrium being greatest in the Washington population and least in the UK population of R. leguminosarum bv. viciae. Linkage disequilibrium in the UK population was created between two clusters of 9 and 23 ETs, which, individually, were in linkage equilibrium. Strong linkage disequilibrium between the two major clusters of 8 and 12 ETs in the Washington population was caused by the low genetic diversity of the ETs within each cluster relative to the inter-cluster genetic distance. Because neither the magnitude of genetic diversity nor of linkage disequilibrium increased as hierarchical combinations of the six local populations were analysed, we conclude that the populations have not been isolated from each other for sufficient time, nor have they been exposed to enough selective pressure to develop unique multilocus genetic structure.     

Social heterosis and the maintenance of genetic diversity at the genome level

Social heterosis is when individuals in groups or neighbourhoods receive a mutualistic benefit from across‐individual genetic diversity. Although it can be a viable evolutionary mechanism to maintain allelic diversity at a given locus, its efficacy at maintaining genome‐wide diversity is in question when multiple loci are being simultaneously selected. Therefore, we modelled social heterosis in a population of haploid genomes of two‐ or three‐linked loci. With such linkages, social heterosis decreases gametic diversity, but maintains allelic diversity. Genomes tend to survive as complimentary pairs, with alternate alleles at each locus (e.g. the pair AbC and aBc). The outcomes of selection appear similar to fitness epistasis but are novel in the sense that phenotypic interactions occur across rather than within individuals. The model’s results strongly suggest that strong linkage across gene loci actually increases the probability that social heterosis maintains significant genetic diversity at the level of the genome.     

The effect of positive assortative mating at one locus on a second linked locus

Summary Considerations proceed from a model of positive assortative mating based on genotype at one locus, with an arbitrary number of alleles, assuming no selection, mutation, or migration, hypothetically infinite population size, and discrete non-overlapping generations. From these conditions, inferences are made about the genotypic structure at a linked locus, as well as about the corresponding 2-locus gametic structure.The following main results are presented: in the course of the generations, the genotypic structure at the second locus and the 2-locus gametic structure always tend to a limit responsive to the initial conditions concerning the joint genotypic structure at the two loci and the degree of assortativity and linkage. A complete, analytical representation of the limits is given. In particular, if assortative mating is only partial and at the same time linkage is not complete, a population is not able to maintain a permanent deviation of the gametic structure from linkage equilibrium, and thus the genotypic structure at the second locus tends to Hardy-Weinberg proportions. On the other hand, if initial linkage disequilibrium is combined with partial assortative mating and complete linkage (or with complete assortative mating and unlinked loci) the population maintains this disequilibrium and thus the genotypic structure at the second locus need not tend to Hardy-Weinberg proportions. It turns out that the conditions not only of complete linkage, but also of unlinked loci together with complete assortativity, imply no change in gametic structure from the initial structure.In order to demonstrate the influence of several parameters on the speed of convergence to and the magnitude of the respective limits, several graphs are included.     

Major histocompatibility complex variation in insular populations of the Egyptian vulture: inferences about the roles of genetic drift and selection

Insular populations have attracted the attention of evolutionary biologists because of their morphological and ecological peculiarities with respect to their mainland counterparts. Founder effects and genetic drift are known to distribute neutral genetic variability in these demes. However, elucidating whether these evolutionary forces have also shaped adaptive variation is crucial to evaluate the real impact of reduced genetic variation in small populations. Genes of the major histocompatibility complex (MHC) are classical examples of evolutionarily relevant loci because of their well-known role in pathogen confrontation and clearance. In this study, we aim to disentangle the partial roles of genetic drift and natural selection in the spatial distribution of MHC variation in insular populations. To this end, we integrate the study of neutral (22 microsatellites and one mtDNA locus) and MHC class II variation in one mainland (Iberia) and two insular populations (Fuerteventura and Menorca) of the endangered Egyptian vulture (Neophron percnopterus). Overall, the distribution of the frequencies of individual MHC alleles (n=17 alleles from two class II B loci) does not significantly depart from neutral expectations, which indicates a prominent role for genetic drift over selection. However, our results point towards an interesting co-evolution of gene duplicates that maintains different pairs of divergent alleles in strong linkage disequilibrium on islands. We hypothesize that the co-evolution of genes may counteract the loss of genetic diversity in insular demes, maximize antigen recognition capabilities when gene diversity is reduced, and promote the co-segregation of the most efficient allele combinations to cope with local pathogen communities.     

Development and characterization of microsatellite markers in Populus euphratica (Populaceae)

In this study, we developed 12 microsatellite loci for Populus euphratica and checked their variability in 27 individuals. The number of alleles for 12 loci ranged from five to nine, the observed and expected heterozygosities ranged from 0.32 to 0.48 and from 0.53 to 0.67. Frequencies of null alleles of all loci are not significantly greater than zero. None of the loci showed significant deviation from Hardy-Weinberg equilibrium. No significant linkage disequilibrium was observed between pairs of studied loci. These markers are useful in studies of population genetic structure of P. euphratica.     

The effects of multilocus balancing selection on neutral variability

We studied the effect of multilocus balancing selection on neutral nucleotide variability at linked sites by simulating a model where diallelic polymorphisms are maintained at an arbitrary number of selected loci by means of symmetric overdominance. Different combinations of alleles define different genetic backgrounds that subdivide the population and strongly affect variability. Several multilocus fitness regimes with different degrees of epistasis and gametic disequilibrium are allowed. Analytical results based on a multilocus extension of the structured coalescent predict that the expected linked neutral diversity increases exponentially with the number of selected loci and can become extremely large. Our simulation results show that although variability increases with the number of genetic backgrounds that are maintained in the population, it is reduced by random fluctuations in the frequencies of those backgrounds and does not reach high levels even in very large populations. We also show that previous results on balancing selection in single-locus systems do not extend to the multilocus scenario in a straightforward way. Different patterns of linkage disequilibrium and of the frequency spectrum of neutral mutations are expected under different degrees of epistasis. Interestingly, the power to detect balancing selection using deviations from a neutral distribution of allele frequencies seems to be diminished under the fitness regime that leads to the largest increase of variability over the neutral case. This and other results are discussed in the light of data from the Mhc.     

Soft selective sweep near a gene that increases plant height in wheat

Strong selection within a given population locally reduces genetic variability not only in the selected gene itself but also in neighbouring loci. This so-called hitch-hiking effect is related to the initial linkage disequilibrium between markers and the selected gene, and depends mainly on the number of copies of the beneficial allele at the start of the selection phase. Contrary to the classical case, in which selection acts on a single, newly arisen beneficial mutation, we considered selection from standing variation (soft selective sweeps) on a gene ( Rht-B1 ) with a major effect on plant height, a selected trait in an experimental wheat population grown for 17 generations, and we documented the evolution of gene diversity and linkage disequilibrium near this gene. As expected, Rht-B1 was found to be under strong selection ( s  = 0.15) and its variation in frequency accounted for 15% of the total trait evolution. This led to a smaller genetic effective population size at Rht-B1 ( N_eg  = 18) compared to the whole genome estimation ( N_eg  = 167). When compared with expectations under genetic drift only, no significant decrease in gene diversity was found at the closest loci. We computed expected di-locus frequencies for any linked marker– Rht-B1 pair due to hitch-hiking effects. We found that hitch-hiking was expected to affect the two most closely linked loci, but expected reduction in gene diversity was not greater than that due to genetic drift, which was consistent with the observations. Such limited effect was attributed to the low level of linkage disequilibrium (0.16) estimated after parental intercrosses, together with a relatively high initial frequency of the gene. This situation is favourable to candidate gene approaches where small linkage disequilibrium around selected genes is expected.     

Sexual and parental antagonism shape genomic architecture

Populations with two sexes are vulnerable to a pair of genetic conflicts: sexual antagonism that can arise when alleles have opposing fitness effects on females and males; and parental antagonism that arises when alleles have opposing fitness effects when maternally and paternally inherited. This paper extends previous theoretical work that found stable linkage disequilibrium (LD) between sexually antagonistic loci. We find that LD is also generated between parentally antagonistic loci, and between sexually and parentally antagonistic loci, without any requirement of epistasis. We contend that the LD in these models arises from the admixture of gene pools subject to different selective histories. We also find that polymorphism maintained by parental antagonism at one locus expands the opportunity for polymorphism at a linked locus experiencing parental or sexual antagonism. Taken together, our results predict the chromosomal clustering of loci that segregate for sexually and parentally antagonistic alleles. Thus, genetic conflict may play a role in the evolution of genomic architecture.     

Recombination and linkage disequilibrium among mitochondrial genes in structured populations of the gynodioecious plant Silene vulgaris

The impact of intergenic recombination on the population genetics of plant mitochondrial genomes is unknown. In an effort to study this in the gynodioecious plant Silene vulgaris three-locus PCR/RFLP genotypes (based on the mitochondrial genes atpA, cox1, and cob) were determined for 239 individuals collected from 20 North American populations. Seventeen three-locus PCR/RFLP genotypes were found. Recombination was indicated by observation of each of the four two-locus genotypes possible when the two most common alleles are considered for each of two loci. Based on these common alleles the absolute values of standardized linkage disequilibrium |D'| between pairs of loci range from 0.17 to 0.78. This indicates modest disequilibrium, rather than the maximum value expected in the absence of recombination |D'=1|, or the linkage equilibrium expected if recombination is pervasive (D'=0). Values of D' did not depend on which pair of loci contributed alleles to the analysis. The direction of D' obtained for the common atpA and cox1 alleles was comparable in sign and magnitude to that obtained by examining similar information obtained in a prior study of European samples. All three loci indicated a high degree of population structure (average FST=0.63), which would limit the within-population genetic diversity required for intergenic recombination to create novel genotypes, if most mating is local. Thus, population structure acts as a constraint on the approach to linkage equilibrium.     

The two-locus model of Gaussian stabilizing selection

We study the equilibrium structure of a well-known two-locus model in which two diallelic loci contribute additively to a quantitative trait that is under Gaussian stabilizing selection. The population is assumed to be infinitely large, randomly mating, and having discrete generations. The two loci may have arbitrary effects on the trait, the strength of selection and the recombination rate may also be arbitrary. We find that 16 different equilibrium patterns exist, having up to 11 equilibria; up to seven interior equilibria may coexist, and up to four interior equilibria, three in negative and one in positive linkage disequilibrium, may be simultaneously stable. Also, two monomorphic and two fully polymorphic equilibria may be simultaneously stable. Therefore, the result of evolution may be highly sensitive to perturbations in the initial conditions or in the underlying genetic parameters. For the special case of equal effects, global stability results are proved. In the general case, we rely in part on numerical computations. The results are compared with previous analyses of the special case of extremely strong selection, of an approximate model that assumes linkage equilibrium, and of the much simpler quadratic optimum model.     

Geographic components of linkage disequilibrium in natural populations of Escherichia coli

Geographic variation in the genetic structure of natural enteric populations of Escherichia coli was assessed at both the single-locus and dilocus levels from allozyme genotypes at 12 enzyme loci in 178 cell lines isolated from human hosts in Sweden, Iowa, and Tonga. Although there was significant heterogeneity in allele frequencies at six of the 12 loci, geographic variation accounted for only 2.0% of the total genetic diversity (HT = 0.518). Ohta's D-statistics were used to partition the total variance of dilocus linkage disequilibrium into within-population and between-population components. The observed total variance in disequilibrium (0.0339), averaged over 66 locus-pairs, was significantly greater than would be expected (0.0103) if alleles were randomly associated in an unstructured total population; and both within-locality and between-locality components made substantial contributions to the total variance. Half the locus-pairs exhibited the specific dual relationship among components expected when random factors are generating disequilibrium, but 20% of the locus-pairs showed the opposite relationship, reflecting systematic allele associations. The magnitude of dilocus disequilibrium apparently is unrelated to the chromosomal distance between loci. This and other evidence indicates that substitutive recombination rates in natural populations are sufficiently low to permit indirect periodic selection to play a prominent role in generating multilocus genetic structure.      

Evolution of recombination due to random drift

In finite populations subject to selection, genetic drift generates negative linkage disequilibrium, on average, even if selection acts independently (i.e., multiplicatively) upon all loci. Negative disequilibrium reduces the variance in fitness and hence, by Fisher's (1930) fundamental theorem, slows the rate of increase in mean fitness. Modifiers that increase recombination eliminate the negative disequilibria that impede selection and consequently increase in frequency by "hitchhiking." Thus, stochastic fluctuations in linkage disequilibrium in finite populations favor the evolution of increased rates of recombination, even in the absence of epistatic interactions among loci and even when disequilibrium is initially absent. The method developed within this article allows us to quantify the strength of selection acting on a modifier allele that increases recombination in a finite population. The analysis indicates that stochastically generated linkage disequilibria do select for increased recombination, a result that is confirmed by Monte Carlo simulations. Selection for a modifier that increases recombination is highest when linkage among loci is tight, when beneficial alleles rise from low to high frequency, and when the population size is small.     

Tracking changes in chromosomal arrangements and their genetic content during adaptation

There is considerable evidence for an adaptive role of inversions, but how their genetic content evolves and affects the subsequent evolution of chromosomal polymorphism remains controversial. Here, we track how life‐history traits, chromosomal arrangements and 22 microsatellites, within and outside inversions, change in three replicated populations of Drosophila subobscura for 30 generations of laboratory evolution since founding from the wild. The dynamics of fitness‐related traits indicated adaptation to the new environment concomitant with directional evolution of chromosomal polymorphism. Evidence of selective changes in frequency of inversions was obtained for seven of 23 chromosomal arrangements, corroborating a role for inversions in adaptation. The evolution of linkage disequilibrium between some microsatellites and chromosomes suggested that adaptive changes in arrangements involved changes in their genetic content. Several microsatellite alleles increased in frequency more than expected by drift in targeted inversions in all replicate populations. In particular, there were signs of selection in the O₃₊₄ arrangement favouring a combination of alleles in two loci linked to the inversion and changing along with it, although the lack of linkage disequilibrium between these loci precludes epistatic selection. Seven other alleles increased in frequency within inversions more than expected by drift, but were not in linkage disequilibrium with them. Possibly these alleles were hitchhiking along with alleles under selection that were not specific to those inversions. Overall, the selection detected on the genetic content of inversions, despite limited coverage of the genome, suggests that genetic changes within inversions play an important role in adaptation.     

Demarcation of informative chromosomes in tropical sweet corn inbred lines using microsatellite DNA markers

A study of genetic variation among 10 pairs of chromosomes extracted from 13 tropical sweet corn inbred lines, using 99 microsatellite markers, revealed a wide range of genetic diversity. Allelic richness and the number of effective alleles per chromosome ranged from 2.78 to 4.33 and 1.96 to 3.47, respectively, with respective mean values of 3.62 and 2.73. According to the Shannon’s information index (I) and Nei’s gene diversity coefficient (Nei), Chromosome 10 was the most informative chromosome (I = 1.311 and Nei = 0.703), while Chromosome 2 possessed the least (I = 0.762 and Nei = 0.456). Based on linkage disequilibrium (LD) measurements for loci less than 50 cM apart on the same chromosome, all loci on Chromosomes 1, 6 and 7 were in equilibrium. Even so, there was a high proportion of genetic variation in Chromosomes 4, 5, 8, 9 and 10, thereby revealing their appropriateness for use in the genetic diversity investigations among tropical sweet corn lines. Chromosome 4, with the highest number of loci in linkage disequilibrium, was considered the best for marker-phenotype association and QTL mapping, followed by Chromosomes 5, 8, 9 and 10.     

Isolation and characterization of microsatellite loci in the long-fingered bat Miniopterus fuliginosus

We isolated and characterized 10 microsatellite loci in the long-fingered bat Miniopterus fuliginosus. These loci were tested on 48 individuals from Anhui Province of China, and all loci were highly polymorphic. The mean number of observed alleles per locus was 13.6 (range from six to 27). Observed and expected heterozygosity values ranged from 0.364 to 0.957, and from 0.676 to 0.951, respectively. After Bonferroni correction, four loci deviated significantly from Hardy-Weinberg equilibrium. No pairs of loci were in linkage disequilibrium. These polymorphic markers will be used to examine population structure and genetic diversity in this species.     

Effect on linkage disequilibrium of selection for a quantitative character with epistasis

Summary Selection for a character controlled by additive genes induces linkage disequilibrium which reduces the additive genetic variance usable for further selective gains. Additive x additive epistasis contributes to selection response through development of linkage disequilibrium between interacting loci. To investigate the relative importance of the two effects of linkage disequilibrium, formulae are presented and results are reported of simulations using models involving additive, additive x additive and dominance components. The results suggest that so long as epistatic effects are not large relative to additive effects, and the proportion of pairs of loci which show epistasis is not very high, the predominant effect of linkage disequilibrium will be to reduce the rate of selection response.     

豌豆种质表型性状SSR标记关联分析

关联分析是以连锁不平衡原理为基础,鉴定某一群体内表型性状与遗传标记或候选基因间关系的遗传分析方法。本研究利用59个多态性SSR标记,对192份豌豆种质进行全基因组扫描,以分析SSR位点遗传多样性,寻找其连锁不平衡位点;采用TASSEL软件的一般线性模型,利用59个SSR标记对19个形态性状进行关联分析。结果显示SSR位点间有较高的多态性和一定程度的连锁不平衡,共检测出32个SSR标记位点与14个表形性状相关联,一些SSR标记与2个或多个形态性状相关联。     

Characterization of 30 new microsatellite markers,developed from enriched genomic DNA library of zoysiagrass Zoysia japonica Steud.

The present study reports the development of 30 polymorphic microsatellite markers for zoysiagrass Zoysia japonica Steud. The 30 markers produced a total of 125 alleles with an average of 4.2 alleles per locus. Values for observed and expected heterozygosities ranged from 0.10 to 0.95 and from 0.15 to 0.81, respectively. At significance threshold (P < 0.05), 11 loci deviated from Hardy–Weinberg equilibrium, whereas significant linkage disequilibrium values were observed between 16 pairs of loci. These markers may provide information needed to select genetically diverse parents for developing breeding and mapping populations of zoysiagrass.     

A cladistic analysis of phenotypic associations with haplotypes inferred from restriction endonuclease mapping. I. Basic theory and an analysis of alcohol dehydrogenase activity in Drosophila

Because some genes have been cloned that have a known biochemical or physiological function, genetic variation can be measured in a population at loci that may directly influence a phenotype of interest. With this measured genotype approach, specific alleles or haplotypes in the probed DNA region can be assigned phenotypic effects. In this paper we address several problems encountered in implementing the measured genotype approach with restriction site data. A number of analytical problems arise in part as a consequence of the linkage disequilibrium that is commonly encountered when dealing with small DNA regions: 1) different restriction site polymorphisms are not statistically independent, 2) the sites being measured are not likely to be the direct cause of the associated phenotypic effects, 3) haplotype classes may be phenotypically heterogeneous, and 4) the sites that are most strongly associated with phenotypic effects are not necessarily the most closely linked to the actual genetic cause of the effects. When recombination and gene conversion are rare, the primary cause of linkage disequilibrium is history (mutational origin, genetic drift, hitchhiking, etc.). We deal with historical association directly by producing a cladogram that partially reconstructs the evolutionary history of the present-day haplotype variability. The cladogram defines a nested analysis of variance that simultaneously detects phenotypic effects, localizes the effects within the cladogram, and identifies haplotypes that are potentially heterogeneous in their phenotypic associations. The power of this approach is illustrated by an analysis of the associations between alcohol dehydrogenase (ADH) activity and restriction site variability in a 13-kb fragment surrounding the ADH locus in Drosophila melanogaster.