Evolution of Zygotic Linkage Disequilibrium in a Finite Local Population

One crucial feature of zygotic linkage disequilibrium (LD) analysis is its direct use of diploid genotyping data, irrespective of the type of mating system. Previous theories from an evolutionary perspective mainly focus on gametic LD, but the equivalent development for zygotic LD is not available. Here I study the evolution of zygotic LD and the covariances between gametic and zygotic LDs or between distinct zygotic LDs in a finite local population under constant immigration from a continent population. I derive the analytical theory under genetic hitchhiking effects or in a neutral process. Results indicate that zygotic LDs (diploid level) are more informative than gametic LD (haploid level) in indicating the effects of different evolutionary forces. Zygotic LDs may be greater than or comparable to gametic LD under the epistatic selection process, but smaller than gametic LD under the non epistatic selection process. The covariances between gametic and zygotic LDs are strongly affected by the mating system, linkage distance, and genetic drift effects, but weakly affected by seed and pollen flow and natural selection. The covariances between different zygotic LDs are generally robust to the effects of gene flow, selection, and linkage distance, but sensitive to the effects of genetic drift and mating system. Consistent patterns exist for the covariances between the zygotic LDs for the two-locus genotypes with one common genotype at one locus or without any common genotype at each locus. The results highlight that zygotic LDs can be applied to detecting natural population history.     

Maximum-likelihood models for mapping genetic markers showing segregation distortion. 2. F2 populations

In F₂ populations, gametic and zygotic selection may affect the analysis of linkage in different ways. Therefore, specific likelihood equations have to be developed for each case, including dominant and codominant markers. The asymptotic bias of the classical estimates are derived for each case, in order to compare them with the standard errors of the suggested estimates. We discuss the utility and the efficiency of a previous model developed for dominant markers. We show that dominant markers provide very poor information in the case of segregation distortion and, therefore, should be used with circumspection. On the other hand, the estimation of recombination fractions between codominant markers is less affected by selection than is that for dominant markers. We also discuss the analysis of linkage between dominant and codominant markers.     

Selection component analysis of natural polymorphisms using population samples including mother-offspring combinations, II

Population samples including mother-offspring combinations provide information on the selection components: zygotic selection, sexual selection, gametic seletion and fecundity selection, on the mating pattern, and on the deviation from linkage equilibrium among the loci studied. The theory for the analysis of a sample consisting of adult individuals including combinations of a mother and one randomly chosen offspring in the case of n polymorphic autosomal loci with m_a alleles at the ath locus, a = 1, 2,…, n, is developed for an organism with discrete non-overlapping generations. In this general analysis complete determination of the genotypes is assumed. The modifications in the analysis for the case n = 2 and m₁ = m₂ = 2 when the two double heterozygotes cannot be separated are discussed, and the analysis is illustrated by data from a population of Zoarces viviparus (a marine teleost).     

Prevalence of segregation distortion in diploid alfalfa and its implications for genetics and breeding applications

Segregation distortion (SD) is often observed in plant populations; its presence can affect mapping and breeding applications. To investigate the prevalence of SD in diploid alfalfa (Medicago sativa L.), we developed two unrelated segregating F₁ populations and one F₂ population. We genotyped all populations with SSR markers and assessed SD at each locus in each population. The three maps were syntenic and largely colinear with the Medicago truncatula genome sequence. We found genotypic SD for 24 and 34% of markers in the F₁ populations and 68% of markers in the F₂ population; distorted markers were identified on every linkage group. The smaller percentage of genotypic SD in the F₁ populations could be because they were non-inbred and/or due to non-fully informative markers. For the F₂ population, 60 of 90 mapped markers were distorted, and they clustered into eight segregation distortion regions (SDR). Most SDR identified in the F₁ populations were also identified in the F₂ population. Genotypic SD was primarily due to zygotic rather than allelic distortion, suggesting zygotic not gametic selection is the main cause of SD. On the F₂ linkage map, distorted markers in all SDR except two showed heterozygote excess. The severe SD in the F₂ population likely biased genetic distances among markers and possibly also marker ordering and could affect QTL mapping of agronomic traits. To reduce the effects of SD and non-fully informative markers, we suggest constructing linkage maps and conducting QTL mapping in advanced generation populations.     

Population dynamics of a gametophytic factor controlling selective fertilization

The population behavior of a gametophytic factor (Ga) which involves gametic selection due to failure ofga pollen onGa Ga orGa ga styles in competition withGa pollen, was investigated by computer simulation. A constant versus randomly varying gametic selection parameter (k) and four different schemes of zygotic selection were introduced in this model for analyzing conditions favorable for the maintenance of locusGa polymorphic in a large, mixed selfing and random mating population. Stable polymorphism was obtained only with rather substantial heterozygote advantage at locusGa whereas the opposing pressures of gametic and zygotic selection yielded fixation of alleleGa orga around a critical value of k instead of a range of k-values allowing nontrivial equilibria. With weak selection and stochastic k, however, very slow rates of change in the genotypic proportions allowed transient polymorphism. In these cases, the rate of outcrossing (t) and the initial frequency ofGa were critical in determining the rate of allelic substitution. Moreover, low values of t allowed the replacement of alleleGa byga even with rather weak zygotic selection. These findings on the balance between gametic and zygotic selection and a markedly frequency-dependent process are briefly discussed in relation to the dynamics of similar factors involving the mating system.     

EVIDENCE FOR SELECTION AGAINST HYBRIDS IN THE FAMILY CYPRINIDAE (GENUS NOTROPIS)

Notropis cornutus and N. chrysocephalus are two cyprinid fishes which hybridize extensively in the midwest. In this paper, statistical analysis was used to determine if the deficiency of Notropis cornutus × N. chrysocephalus hybrids can be attributed partly to selection against hybrids. Principal component analysis was used to construct a folded hybrid index (FHI) using morphological and electrophoretic characters which distinguish N. cornutus, N. chrysocephalus, and their hybrids. A Wilcoxon signed-rank test comparing mean FHI between successive age classes within cohorts and regression analysis of FHI on age supported the conclusion that hybrids are less fit than parentals in nature; however, this analysis did not include a test of selection at zygotic and larval life history stages or partial infertility of hybrids. Selection eliminated hybrids at a rate of 9.2% per year. Considering the intensity of selection and the age of hybridization, it is surprising that premating reproductive isolating mechanisms have not been perfected by selection against gametic wastage as predicted by classical speciation theory. It appears that the reinforcement of premating isolating mechanisms is an extremely slow process, if it occurs at all, despite apparently intense selection against hybrids.     

Genomic Scans of Zygotic Disequilibrium and Epistatic SNPs in HapMap Phase III Populations

Previous theory indicates that zygotic linkage disequilibrium (LD) is more informative than gametic or composite digenic LD in revealing natural population history. Further, the difference between the composite digenic and maximum zygotic LDs can be used to detect epistatic selection for fitness. Here we corroborate the theory by investigating genome-wide zygotic LDs in HapMap phase III human populations. Results show that non-Africa populations have much more significant zygotic LDs than do Africa populations. Africa populations (ASW, LWK, MKK, and YRI) possess more significant zygotic LDs for the double-homozygotes (D_AABB) than any other significant zygotic LDs (D_AABb, D_AaBB, and D_AaBb), while non-Africa populations generally have more significant D_AaBb’s than any other significant zygotic LDs (D_AABB, D_AABb, and D_AaBB). Average r-squares for any significant zygotic LDs increase generally in an order of populations YRI, MKK, CEU, CHB, LWK, JPT, CHD, TSI, GIH, ASW, and MEX. Average r-squares are greater for D_AABB and D_AaBb than for D_AaBB and D_AABb in each population. YRI and MKK can be separated from LWK and ASW in terms of the pattern of average r-squares. All population divergences in zygotic LDs can be interpreted with the model of Out of Africa for modern human origins. We have also detected 19735-95921 SNP pairs exhibiting strong signals of epistatic selection in different populations. Gene-gene interactions for some epistatic SNP pairs are evident from empirical findings, but many more epistatic SNP pairs await evidence. Common epistatic SNP pairs rarely exist among all populations, but exist in distinct regions (Africa, Europe, and East Asia), which helps to understand geographical genomic medicine.     

遗传标记作图的通用最大似然模型

作者在构建连锁图谱时,发现Newton-Raphson迭代求解似然方程组,即便纳入合子和配子选择因子,各基因型的估计值仍不能很好的接近实测值,本文提出了一种偏分离遗传标记作图的通用最大似然模型。     

Investigating Incipient Speciation in Arabidopsis lyrata from Patterns of Transmission Ratio Distortion

Our understanding of the development of intrinsic reproductive isolation is still largely based on theoretical models and thorough empirical studies on a small number of species. Theory suggests that reproductive isolation develops through accumulation of epistatic genic incompatibilities, also known as Bateson–Dobzhansky–Muller (BDM) incompatibilities. We can detect these from marker transmission ratio distortion (TRD) in hybrid progenies of crosses between species or populations, where TRD is expected to result from selection against heterospecific allele combinations in hybrids. TRD may also manifest itself because of intragenomic conflicts or competition between gametes or zygotes. We studied early stage speciation in Arabidopsis lyrata by investigating patterns of TRD across the genome in F₂ progenies of three reciprocal crosses between four natural populations. We found that the degree of TRD increases with genetic distance between crossed populations, but also that reciprocal progenies may differ substantially in their degree of TRD. Chromosomes AL6 and especially AL1 appear to be involved in many single- and two-locus distortions, but the location and source of TRD vary between crosses and between reciprocal progenies. We also found that the majority of single- and two-locus TRD appears to have a gametic, as opposed to zygotic, origin. Thus, while theory on BDM incompatibilities is typically illustrated with derived nuclear alleles proving incompatible in hybrid zygotes, our results suggest a prominent role for distortions emerging before zygote formation.     

The evolution of intrinsic reproductive isolation in the genus Cakile (Brassicaceae)

In theory, adaptive divergence can increase intrinsic post‐zygotic reproductive isolation (RI), either directly via selection on loci associated with RI, or indirectly via linkage of incompatibility loci with loci under selection. To test this hypothesis, we measured RI at five intrinsic post‐zygotic reproductive barriers between 18 taxa from the genera Cakile and Erucaria (Brassicaceae). Using a comparative framework, we tested whether the magnitude of RI was associated with genetic distance, geographic distance, ecological divergence and parental mating system. Early stages of post‐zygotic RI related to F₁ viability (i.e. initial seed set) tended to be stronger than later stages related to F₁ fecundity (i.e. flower number, fruit number). Mating system significantly influenced early stages of RI, such that RI was lowest when the mother was selfing and father was outcrossing, consistent with an imbalance between sink strength and resistance to provisioning. We found little evidence that adaptive divergence accelerates the evolution of intrinsic post‐zygotic RI, consistent with a nonecological model of evolution that predicts the nonlinear accumulation of RI and RI asymmetry with time (i.e. genetic distance), irrespective of adaptive divergence. Thus, although certain aspects of ecological divergence do not appear to have contributed strongly to the evolution of RI in this system, divergence in mating system actually reduced RI, suggesting that mating system evolution may play a significant role in speciation dynamics.     

Estimating exotic gene flow into native pine stands: zygotic vs. gametic components

Monitoring contemporary gene flow from widespread exotic plantations is becoming an important problem in forest conservation genetics. In plants, where both seed and pollen disperse, three components of exotic gene flow with potentially unequal consequences should be, but have not been, explicitly distinguished: zygotic, male gametic and female gametic. Building on a previous model for estimating contemporary rates of zygotic and male gametic gene flow among plant populations, we present here an approach that additionally estimates the third (female gametic) gene flow component, based on a combination of uni‐ and biparentally inherited markers. Using this method and a combined set of chloroplast and nuclear microsatellites, we estimate gene flow rates from exotic plantations into two Iberian relict stands of maritime pine (Pinus pinaster) and Scots pine (Pinus sylvestris). Results show neither zygotic nor female gametic gene flow but moderate (6–8%) male gametic introgression for both species, implying significant dispersal of pollen, but not of seeds, from exotic plantations into native stands shortly after introduced trees reached reproductive maturity. Numerical simulation results suggest that the model yields reasonably accurate estimates for our empirical data sets, especially for larger samples. We discuss conservation management implications of observed levels of exposure to nonlocal genes and identify research needs to determine potentially associated hazards. Our approach should be useful for plant ecologists and ecosystem managers interested in the vectors of contemporary genetic connectivity among discrete plant populations.     

THE ROLE OF DEME SIZE,REPRODUCTIVE PATTERNS,AND DISPERSAL IN THE DYNAMICS OF t-LETHAL HAPLOTYPES

The t-lethal haplotypes (t) found in house mouse (Mus musculus) populations are recessive lethals favored by gametic selection whereby male heterozygotes exhibit a non-Mendelian transmission ratio of about 95% t. The expected equilibrium frequency is 0.385; however, empirical values are lower, averaging close to 0.13. We examined the hypothesis that interdemic selection is the cause of the low empirical values by using a deme-structured simulation model that included overlapping generations, a realistic breeding system, differential deme productivity, and a large total population. We found that under some conditions interdemic selection could lower t frequency below 0.13 in the face of immigration rates up to 5%. Low frequencies were correlated with effective deme size (n_e), regardless of whether n_e was changed through changing deme size (n) or through changing the proportion of breeding adults. Earlier workers showed how the first two phases of interdemic selection (random genetic differentiation and mass selection) interacted to reduce the haplotype frequency, but here we show the importance of the third phase (differential productivity of demes) once demes are linked by dispersal. The effect of this phase is not due to the (negative) covariation between deme productivity and haplotype frequency, but occurs when differential deme productivity generates a difference in t frequency between the population of juveniles recruited into their natal deme and the population of juvenile dispersers. This difference was maximized when the average productivity of demes was low, either because few adult females bred at any one time and/or because fecundity was low. Contrary to an earlier prediction, male-biased dispersal also reduced haplotype frequency, and this probably stems from the relative excess of wild-type genotypes among dispersers compared to the deme residents. Another unexpected finding was that the randomly generated excess of heterozygotes (F_IS < 0) found in small demes favored t haplotypes; however, the effect was only seen when the more powerful influence of the third phase of interdemic selection was removed. Simulations of neutral polymorphisms showed that a deme structure giving F_ST ≤ 0.6 is inconsistent with a haplotype frequency below 0.13. Based on current empirical estimates of F_ST (about 0.2), we concluded that immigration rates in the field are too high for interdemic selection alone to cause the observed deficit of lethal haplotypes. One factor that could combine with population structure effects is the observation that the transmission ratio is lowered to around 0.6 in litters produced from postpartum estrus (PPE). Incorporating this factor, we showed that interdemic selection could be effective in lowering the frequency of t below 0.13 when F_ST was above 0.43 even when migration rates were up to 10%. These results suggest that if empirical haplotype and F_ST estimates are accurate, then additional factors such as a lowered fitness of heterozygotes may be involved.     

A linkage map of sugar beet (Beta vulgaris L.)

Summary We have established a first linkage map for beets based on RFLP, isozyme and morphological markers. The population studied consisted of 96 F₂ individuals derived from an intraspecific cross. As was expected for outbreeding species, a relatively high degree of polymorphism was found within sugar beet; 47% of the DNA markers were polymorphic for the chosen population. The map consists of 115 independent chromosomal loci designated by 108 genomic DNA probes, 6 isozyme and one morphological marker. The loci cover 789 cM with an average spacing of 6.9 cM. They are dispersed over nine linkage groups corresponding to the haploid chromosome number of Beta species. Eighteen markers (15.4%) showed distorted segregation which, in most instances, can be explained by gametic selection of linked lethal loci. The application of the linkage map in sugar beet breeding is discussed.     

Gametic selection in anther culture of rice (Oryza sauva L.)

Summary The segregation and recombination of heterozygous isozyme markers have been monitored in anther culture derivatives (i.e., six nonmorphogenic microspore-derived callus [NMC] populations and two anther culture plant [ACP] populations) and F₂ plants generated from six F₁ hybrids of rice, including five japonica upland/improved indica tropical hybrids. The alleles in excess at some loci displaying skewed segregations in the F₂s were consistently overrepresented in the NMC populations. These alleles were also generally found to be overabundant in the two ACP populations except for certain loci that contrastingly segregated in a 11 ratio. Additional distortions were found to be specific to AC derivatives indicating the existence of in vitro gametic selection. Overall, however, the gametic selection in the ACP materials was neutral with regard to the indica and japonica differentiation. Estimates of linkages between markers borne by chromosome 6 using AC-derivative data were consistent with those noted in the F₂s and with current knowledge of the isozyme locus linkage map. Given the average neutrality of gametic selection and the consistency of linkage relationships in the ACPs, their further use as rice molecular mapping and gene tagging populations can be investigated with confidence.Joint contribution with Research Institute for Tropical Food Crops, Department of the International Centre of Agronomical Research for Development (IRAT-CIRAD), 45bis avenue de la Belle Gabrielle, F-94736 Nogent s/Marne Cédex, France and International Rice Research Institute (IRRI), P.O.Box 933, Manila, Philippines     

Conditions for the Maintenance of Prezygotic and Zygotic Isolation in a Continent-Island Model

A continent-island model is studied in which differences are initially present at a gene locus with assortative mating (which causes prezygotic reproductive isolation) and at one or two unlinked selected loci, (which cause zygotic reproductive isolation). This model simulates secondary contact between two populations which have diverged allopatrically at loci which control isolating mechanisms. Two different models of prezygotic isolation and three different models of zygotic isolation are studied. The analysis is focused on those conditions under which differentiation is not lost through the swamping effect of gene now. In each case the critical migration rate (m_c) below which differences can be maintained is found. Results depend on the degree of assortative mating, on the level of selection on the genes involved, and on the particular models of reproductive isolation considered. However, in all the models, for high values of such parameters the two isolating mechanisms interact strongly, and consequently the stability of the difference at each locus (as measured by m_c) is noticeably influenced by the presence of the difference at the other locus (or loci). The nature and strength of the effects of this interaction differ according to whether or not there is selection on the assortative mating locus and whether selection against hybrids or directional selection is hypothesized.     

Stable Heliconius butterfly hybrid zones are correlated with a local rainfall peak at the edge of the Amazon basin

Multilocus clines between Müllerian mimetic races of Heliconius butterflies provide a classic example of the maintenance of hybrid zones and their importance in speciation. Concordant hybrid zones in the mimics Heliconius erato and H. melpomene in northern Peru were carefully documented in the 1980s, and this prior work now permits a historical analysis of the movement or stasis of the zones. Previous work predicted that these zones might be moving toward the Andes due to selective asymmetry. Extensive deforestation and climate change might also be expected to affect the positions and widths of the hybrid zones. We show that the positions and shapes of these hybrid zones have instead remained remarkably stable between 1985 and 2012. The stability of this interaction strongly implicates continued selection, rather than neutral mixing following secondary contact. The stability of cline widths and strong linkage disequilibria (gametic correlation coefficients R_max = 0.35–0.56 among unlinked loci) over 25 years suggest that mimetic selection pressures on each color pattern locus have remained approximately constant (s ≈ 0.13–0.40 per locus in both species). Exceptionally high levels of precipitation at the edge of the easternmost Andes may act as a population density trough for butterflies, trapping the hybrid zones at the foot of the mountains, and preventing movement. As such, our results falsify one prediction of the Pleistocene Refugium theory: That the ranges of divergent species or subspecies should be centered on regions characterized by maxima of rainfall, with hybrid zones falling in more arid regions between them.     

ASSOCIATIONS BETWEEN MITOCHONDRIAL AND NUCLEAR GENOTYPES IN CUTTHROAT TROUT HYBRID SWARMS

We examined mtDNA and nuclear allozyme genotypes in hybrid populations formed from interbreeding of westslope cutthroat trout (Oncorhynchus clarki lewisi) and Yellowstone cutthroat trout (O. c. bouvieri). These subspecies show substantial genetic divergence (Nei's D = 0.30; mtDNA P = 0.02). Diagnostic alleles at multiple nuclear loci and two distinct mtDNA haplotypes segregate in the hybrids. Nuclear and mtDNA genotypes are largely randomly associated, although there is slight disequilibrium in both nuclear and cytonuclear measures in some samples. Consistent positive gametic disequilibria for three pairs of nuclear loci confirm one previously reported linkage, and indicate two more. Allele frequencies provide no evidence for selection on individual chromosome segments. However, westslope mtDNA haplotype frequencies exceed westslope nuclear allele frequencies in all samples. This may be explained by differences in the frequency of occurrence of reciprocal F₁ matings, by viability, fertility, or sex ratio differences in the progeny of reciprocal matings, or by weak selection on mtDNA haplotypes.     

Variable selection with P-splines in functional linear regression: Application in graft-versus-host disease

This paper focuses on the problems of estimation and variable selection in the functional linear regression model (FLM) with functional response and scalar covariates. To this end, two different types of regularization (L₁ and L₂) are considered in this paper. On the one hand, a sample approach for functional LASSO in terms of basis representation of the sample values of the response variable is proposed. On the other hand, we propose a penalized version of the FLM by introducing a P-spline penalty in the least squares fitting criterion. But our aim is to propose P-splines as a powerful tool simultaneously for variable selection and functional parameters estimation. In that sense, the importance of smoothing the response variable before fitting the model is also studied. In summary, penalized (L₁ and L₂) and nonpenalized regression are combined with a presmoothing of the response variable sample curves, based on regression splines or P-splines, providing a total of six approaches to be compared in two simulation schemes. Finally, the most competitive approach is applied to a real data set based on the graft-versus-host disease, which is one of the most frequent complications (30% –50%) in allogeneic hematopoietic stem-cell transplantation.     

Hitchhiking: A Comparison of Linkage and Partial Selfing

Genetic hitchhiking occurs when alleles at unselected loci are changed in frequency because of an association with alleles at a selected locus. This association may be mediated either by linkage or partial selfing (inbreeding) and can affect the gene frequency and gametic disequilibrium at the neutral loci. Hitchhiking from partial selfing (unlinked loci) occurs more quickly than linkage hitchhiking and generally has a greater effect. In addition, partial-selfing hitchhiking can cause increases or changes in sign in gametic disequilibrium between neutral loci. The effects of the two types of hitchhiking with different levels of dominance, zygotic frequencies and number of selected loci are also examined. The general conditions for linkage and partial-selfing hitchhiking are outlined and the implications of hitchhiking are discussed for marker or electrophoretic loci.     

Sample sizes required to detect linkage disequilibrium between two or three loci.

Estimates of the degree of nonrandom association among genes (linkage disequilibrium) can provide evidence of the role of natural selection in maintaining allozyme polymorphisms in natural populations. This paper outlines the maximum likelihood procedures for such estimates based on gametic or zygotic frequencies at the level of two loci. The analysis is extended to estimating disequilibrium between three loci. In particular, the question of the sampling requirements to detect different intensities of disequilibrium is considered. It is found that relatively large samples are required to detect nonrandom association, unless gene frequencies are intermediate and disequilibrium is relatively intense. This might be one reason why cases of linkage disequilibrium have so far proved to be the exception, rather than the rule, in population studies.