Heritability of heterozygosity offers a new way of understanding why dominant gene action contributes to additive genetic variance

Whenever allele frequencies are unequal, nonadditive gene action contributes to additive genetic variance and therefore the resemblance between parents and offspring. The reason for this has not been easy to understand. Here, we present a new single‐locus decomposition of additive genetic variance that may give greater intuition about this important result. We show that the contribution of dominant gene action to parent–offspring resemblance only depends on the degree to which the heterozygosity of parents and offspring covary. Thus, dominant gene action only contributes to additive genetic variance when heterozygosity is heritable. Under most circumstances this is the case because individuals with rare alleles are more likely to be heterozygous, and because they pass rare alleles to their offspring they also tend to have heterozygous offspring. When segregating alleles are at equal frequency there are no rare alleles, the heterozygosities of parents and offspring are uncorrelated and dominant gene action does not contribute to additive genetic variance.     

Association studies of QTL for multi-allele markers by mixed models

In this paper, we extend association study methods of both Fan et al. [Hum Hered 2002;53:130-145], in which a quantitative trait locus (QTL) and a multi-allele marker are considered for trio families, and Fan and Xiong [Biostatistics 2003, in press], in which a QTL and a bi-allelic marker are considered for nuclear families. The objective is to build mixed models for association study between a QTL and a multi-allelic marker for nuclear families with any number of offspring. Two types of nuclear family data are considered: the first is genetic data of offspring from at least one heterozygous parents, and the second is genetic data of offspring of nuclear family. (1) For the data of offspring from at least one heterozygous parents, we assume that at least one parent is heterozygous at the marker locus, and we may infer clearly the transmission of parental marker alleles to the offspring. We show that it can be used in association study in the presence of linkage. The theoretical basis is the difference between the conditional mean of trait value given an allele is transmitted and the conditional mean of trait value given the allele is not transmitted from a heterozygous parent. To build valid models, we calculate the variance covariance structure of trait values of offspring. Besides, the reduction of the number of parameters is discussed under an assumption of tight linkage between the trait locus and the marker. (2) For the data of offspring of nuclear family, we show that it can be used in general association study. In this case, the theoretical basis is the difference between the conditional mean of trait values given an allele is transmitted from a parent and the population mean. Then, we calculate variance-covariance structure of trait values of offspring. (3) Based on the theoretical analysis, mixed models are built for each type of the data, and related test statistics are proposed for association study. By power calculation and comparison, we show that, in some instances, the proposed test statistics have higher power than that by collapsing alleles to be new ones. The proposed models are used to analyze chromosomes 4 and chromosome 16 data of the Oxford asthma data, Genetic Analysis Workshop 12.     

Difficulties in parentage analysis: the probability that an offspring and parent have the same heterozygous genotype.

Parentage studies often estimate the number of parents contributing to half-sib progeny arrays by counting the number of alleles attributed to unshared parents. This approach is compromised when an offspring has the same heterozygous genotype as the shared parent, for then the contribution of the unshared parent cannot be unambiguously deduced. To determine how often such cases occur, formulae for co-dominant markers with n alleles are derived here for Ph, the probability that a given heterozygous parent has an offspring with the same heterozygous genotype, and Pa, the probability that a randomly chosen offspring has the same heterozygous genotype as the shared parent. These formulae have been derived assuming Mendelian segregation with either (1) an arbitrary mating system, (2) random mating or (3) mixed mating. The maximum value of Pa under random mating is 0.25 and occurs with any two alleles each at a frequency of 0.5. The behaviour with partial selfing (where reproduction is by selfing with probability s, and random mating otherwise) is more complex. For n < or = 3 alleles, the maximum value of Pa occurs with any two alleles each at a frequency of 0.5 if s < 0.25, and with three equally frequent alleles otherwise. Numerically, the maximum value of Pa for n > or = 4 alleles occurs with n* < or = n alleles at equal frequencies, where the maximizing number of alleles n* is an increasing function of the selfing rate. Analytically, the maximum occurs with all n alleles present and equally frequent if s > or = 2/3. In addition, the potential applicability of these formulae for evolutionary studies is briefly discussed.     

Quantitative genetic variance associated with chromosomal markers in segregating populations

Summary Use of chromosomal markers can accelerate genetic progress for quantitative traits in pedigree selection programs by providing early information on Mendelian segregation effects for individual progeny. Potential effectiveness of selection using markers is determined by the amount of additive genetic variance traced from parents to progeny by the markers. Theoretical equations for the amount of additive genetic variance associated with a marker were derived at the individual level and for a segregating population in joint linkage equilibrium. Factors considered were the number of quantitative trait loci linked to the marker, their individual effects, and recombination rates with the marker. Subsequently, the expected amount of genetic variance associated with a marker in a segregating population was derived. In pedigree selection programs in segregating populations, a considerable fraction of the genetic variance on a chromosome is expected to be associated with a marker located on that chromosome. For an average chromosome in the bovine, this fraction is approximately 40% of the Mendelian segregation variance contributed by the chromosome. The effects of interference and position of the marker on this expectation are relative small. Length of the chromosome has a large effect on the expected variance. Effectiveness of MAS is, however, greatly reduced by lack of polymorphism at the marker and inaccuracy of estimation of chromosome substitution effects. The size of the expected amount of genetic variance associated with a chromosomal marker indicates that, even when the marker is not the active locus, large chromosome substitution effects are not uncommon in segregating populations.     

Assessing parent numbers from offspring genotypes: the importance of marker polymorphism

Methods to infer parent numbers from offspring genotypes either determine the minimum number of parents required to explain alleles and multilocus genotypes detected in the offspring or use models to incorporate information on population allele frequencies and allele segregation. Disparate results by different approaches suggest that one or perhaps all methods are subject to bias. Here, we investigate the performance of minimum parent number estimates, maximum likelihood, and Bayesian analyses (programs COLONY and PARENTAGE) with respect to marker information content in simulated data sets without knowledge of parental genotypes. Offspring families of different sizes were assumed to share one parent and to be sired by 1 or 5 additional parents. All methods committed large errors in terms of underestimation (minimum value) and overestimation (COLONY), or both (PARENTAGE) of parent numbers, unless the data were highly informative, and their relative performances depended on full-sib group sizes and sire numbers. Increasing the number of markers with low gene diversity (H(e) < or = 0.68) yielded only slow improvement of the results, but all 3 methods performed well with 5-7 markers of H(e) = 0.84. We emphasize the importance of high marker polymorphism for inferring parent numbers and individual parent contributions, as well as for the detection of monogamous reproduction.     

Models and tests of linkage and association studies of quantitative trait locus for multi-allele marker Loci

In this paper, we explore models and tests for association and linkage studies of a quantitative trait locus (QTL) linked to a multi-allele marker locus. Based on the difference between an offspring's conditional trait means of receiving and not receiving an allele from a parent at marker locus, we propose three statistics T(m), T(m,row) and T(m,col) to test association or linkage disequilibrium between the marker locus and the QTL. These tests are composite tests, and use the offspring marginal sample means including offspring data of both homozygous and heterozygous parents. For the linkage study, we calculate the offspring's conditional trait mean given the allele transmission status of a heterozygous parent at the marker locus. Based on the difference between the conditional means of a transmitted and a nontransmitted allele from a heterozygous parent, we propose statistics T(parsi), T(satur), T(gen) and T(m,het) to perform composite tests of linkage between the marker locus and the quantitative trait locus in the presence of association. These tests only use the offspring data that are related to the heterozygous parents at the marker locus. T(parsi) is a parsimonious or allele-wise statistic, T(satur) and T(gen )are satured or genotype-wise statistics, and T(m,het) compares the row and column sample means for offspring data of heterozygous parents. After comparing the powers and the sample sizes, we conclude that T(parsi) has higher power than those of the bi-allele tests, T(satur), T(gen), and T(m,het). If there is tight linkage between the marker and the trait locus, T(parsi) is powerful in detecting linkage between the marker and the trait locus in the presence of association. By investigating the goodness-of-fit of T(parsi), we find that T(satur) does not gain much power compared to that of T(parsi). Moreover, T(parsi) takes into account the pattern of the data that is consistent with linkage and linkage disequilibrium. As the number of alleles at the marker locus increases, T(parsi) is very conservative, and can be useful even for sparse data. To illustrate the usefulness and the power of the methods proposed in this paper, we analyze the chromosome 6 data of the Oxford asthma data, Genetic Analysis Workshop 12.     

Estimation of Effects of Quantitative Trait Loci in Large Complex Pedigrees

A method was derived to estimate effects of quantitative trait loci (QTL) using incomplete genotype information in large outbreeding populations with complex pedigrees. The method accounts for background genes by estimating polygenic effects. The basic equations used are very similar to the usual linear mixed model equations for polygenic models, and segregation analysis was used to estimate the probabilities of the QTL genotypes for each animal. Method R was used to estimate the polygenic heritability simultaneously with the QTL effects. Also, initial allele frequencies were estimated. The method was tested in a simulated data set of 10,000 animals evenly distributed over 10 generations, where 0, 400 or 10,000 animals were genotyped for a candidate gene. In the absence of selection, the bias of the QTL estimates was <2%. Selection biased the estimate of the Aa genotype slightly, when zero animals were genotyped. Estimates of the polygenic heritability were 0.251 and 0.257, in absence and presence of selection, respectively, while the simulated value was 0.25. Although not tested in this study, marker information could be accommodated by adjusting the transmission probabilities of the genotypes from parent to offspring according to the marker information. This renders a QTL mapping study in large multi-generation pedigrees possible.     

Prediction of X and Y chromosome content in bovine sperm by using DNA pools through capillary electrophoresis

Livestock resource management through gender offspring preselection is an efficient tool in terms of genetic improvement and farm management and additionally provides the opportunity to adjust offspring to market demands. In this study bull ejaculates were tested using PCR amplification of a segment of the X-Y homologous amelogenin gene in order to estimate the X and Y chromosome frequencies by capillary electrophoresis. Results were quantified against a regression function constructed with pools prepared with DNA from bulls and cows with known X and Y ratios. An average of 50.02 +/- 2.79% X chromosome content was found with normal distribution ranging from 38.7 to 58.2%. Bull effect was significant in the analysis of variance representing 8.5% of the total variance. This simple analysis provides a low-cost and quick method of evaluating an X-Y ratio in a high number of ejaculates, particularly when external factors can be manipulated to alter it.     

Sex Differences in Polymorphism and Expression of AAT-1 in the Hiroshima Population of Buergeria buergeri (Anura, Rhacophoridae)

Buergeria buergeri is female heterozygous in sex determination; chromosome pair No. 7 in this species is a pair of sex chromosomes of the ZZ/ZW type. Genetic analysis of AAT-1 variants was carried out to elucidate the mode of inheritance of this locus by starch-gel electrophoresis using field-caught females and males and their offspring produced by artificial crossings. The results showed that the AAT-1 locus is sex-linked and that alleles are expressed on the Z chromosome, but not the W chromosome. It is evident that the AAT-1 gene of female offspring is hemizygous and that the allele present is on the Z chromosome, which is derived from the male parent.     

Biochemical evidence of haplodiploidy in the whiteflyBemisia tabaci

Polymorphic esterase and acetylcholinesterase alleles in the whiteflyBemisia tabaci were studied using electrophoretic and colorimetric assays. The segregation of these alleles between parental and F₁ generations provided unequivocal evidence of haplodiploidy in this pest species. Unmated females, heterozygous at a polymorphic locus, produced a 1:1 ratio of haploid males expressing either of the maternal alleles. Although male offspring were produced by both virgin and mated females, the segregation of alleles showed they were always haploid (hemizygous) for the marker enzymes. Females only arose from fertilized eggs and invariably expressed paternal and maternal alleles.     

Epistatic Control of Non-Mendelian Inheritance in Mouse Interspecific Crosses

Strong deviation of allele frequencies from Mendelian inheritance favoring Mus spretus-derived alleles has been described previously for X-linked loci in four mouse interspecific crosses. We reanalyzed data for three of these crosses focusing on the location of the gene(s) controlling deviation on the X chromosome and the genetic basis for incomplete deviation. At least two loci control deviation on the X chromosome, one near Xist (the candidate gene controlling X inactivation) and the other more centromerically located. In all three crosses, strong epistasis was found between loci near Xist and marker loci on the central portion of chromosome 2. The mechanism for this deviation from Mendelian expectations is not yet known but it is probably based on lethality of embryos carrying particular combinations of alleles rather than true segregation distortion during oogenesis in F(1) hybrid females.     

Assignment of the gene for porcine insulin-like growth factor 1 (IGF1) to chromosome 5 by linkage mapping

Investigation of published sequence data from the porcine insulin-like growth factor 1 (IGF1) gene, resulted in the detection of a microsatellite in the first intron of the gene. Polymerase chain reaction (PCR) primers flanking the (CA)₁₉ repeat were constructed. Polymorphism and Mendelian segregation were documented in a three-generation pedigree and allele frequencies were determined in 74 unrelated animals from four different breeds. Seven alleles were encountered. Linkage analysis was performed in a large pedigree established for gene mapping. Linkage between the IGF1 microsatellite and an anonymous microsatellite marker, S0005, was detected. Furthermore, IGF1 and S0005 was found to be linked to the porcine submaxillary gland mucin (MUC) gene, previously assigned to chromosome 5. The results presented here extend the linkage group on pig chromosome 5 and are in accordance with conserved synteny between human chromosome 12, cattle chromosome 5, mouse chromosome 10 and pig chromosome 5.     

Experimental verification of microsatellite null alleles in Norway spruce (Picea abies [L.] Karst.): Implications for population genetic studies

Three stands ofPicea abies [L.] Karst. with different density in the Harz Mountains (Lower Saxony, Germany) were characterized at 4 microsatellite loci. An excess of homozygotes was observed in all 3 stands at 1 simple sequence repeat (SSR) locus, suggesting the presence of null alleles. To test for the segregation of a null allele, 24 openpollinated seeds (haploid megagametophytes and embryos) from apparently homozygous mother trees were analyzed. For 1 of 3 trees that could be identified as heterozygous for a null allele, no significant deviation from the expected 1∶1 segregation into marker absence (null allele) and marker presence of the second maternal allele could be observed in the haploid megagametophyte. Concordantly, the numbers of embryos heterozygous for the null allele and for the other maternal allele were not significantly different from each other. Inheritance analyses in seedlings and corresponding megagametophytes of gymnosperms were used as a direct experimental verification of microsatellite null alleles in single-tree progeny. Microsatellites with an abundance of null alleles should be discarded from further analysis because inclusion of these loci results in incorrect estimation of allele frequencies.     

Gamete-competition models

The gamete-competition model is an application of the Bradley-Terry model for ranking of sports teams. If allele i of a marker locus is assigned parameter taui>0, then the probability that a parent with heterozygous genotype i/j transmits allele i is Pr(i/j-->)=tau(i)/(tau(i) + tau(j). Mendelian segregation corresponds to the choice tau(i)=1 for all i. To test whether Mendelian segregation is true, one can estimate the tau(i) from pedigree data and perform a likelihood-ratio test under the constraint that one tau(i) equals 1. Although this procedure generates an interesting method for performance of segregation analysis with a marker locus, its real promise lies in generalization of the transmission/disequilibrium test. Quantitative as well as qualitative outcomes can be considered. The gamete-competition model uses full pedigree data and gives an estimate of the strength of transmission distortion to affected children for each allele. Covariates are incorporated by rewriting of tau(i)=exp(beta(t)x(k)), where beta is a parameter vector and xk is a covariate vector for the kth transmitted gamete. Examples of covariates include disease-severity indicators for the child, sex of the child, or repeat number for tandem-repeat alleles.     

Use of DNA fingerprints for the detection of major genes for quantitative traits in domestic species

The detection of marker loci linked to major genes or quantitative trait loci (QTL) of large effect in farm animal populations is of great potential value, both because it allows the easy manipulation of the major genes and because it provides a possible route to their ultimate isolation. At present the number of markers available is limited in farm animals. DNA fingerprints provide a promising source of informative marker loci and have the advantage that several loci can be detected on a single Southern hybridization. The disadvantage of DNA fingerprints is the difficulty in determining allelism of DNA fingerprint bands in different pedigrees and the fact that not all potentially resolvable loci can be resolved in a single pedigree. With probes capable of detecting 50 randomly distributed loci, about 50% of the genome of a typical domestic mammal might be expected to be closely linked to a marker (at a distance of 0.2 Morgans or less). If a proportion of DNA fingerprint loci prove to be clustered near chromosomal telomeres or elsewhere in the genome, coverage will be less. In order to detect linkage to a major gene, sires known or suspected to be heterozygous are used to produce large half-sibships, all animals in the pedigree are DNA fingerprinted and the phenotypes of the offspring are recorded. Where several heterozygous sires are available, sires can be selected in an attempt to maximize the number of marker loci resolved. The optimum number of sires needed to produce pedigrees will depend upon the size of the major gene, the number of DNA fingerprint probes available and the characteristics of the DNA fingerprints produced, but often one or two pedigrees will be optimum. Monte Carlo simulation was used to explore the power of detection of linkage between a major gene and a marker locus in a backcross. Maximum likelihood and analysis of variance of mean differences between marker genotypes were of similar power, but maximum likelihood provided reasonable estimates of the major gene effect and its linkage to the marker under some circumstances. One hundred offspring informative for the segregation of a marker would provide reasonable power for the detection of a gene causing a difference between the heterozygote and the homozygote of at least one within-sire, within-genotype standard deviation when linkage was very close (0.05 or less).(ABSTRACT TRUNCATED AT 400 WORDS)     

Linkage analysis for mapping genes of sex-influenced traits

Abstract Statistical methods are developed to estimate gender-specific and gender-average recombination frequencies between a biallelic or multiallelic marker and a sex-influenced gene. Iterative solutions are developed for intercross (or F-2 design). For biallelic markers, two iterative solutions are required, one for coupling and repulsion parental linkage phases and one for mixed parental linkage phases. For multiallelic markers, one set of iterative equations applies to all possible parental linkage phases. The resulting formulae for estimating recombination frequency use the full data set and yield estimates that are exactly the same as the true parameters if the observed and expected phenotypic distributions are equal. When one parent is homozygous for the sex-influenced gene as is expected with the backcross design, simple solutions exist for estimating recombination frequencies. However, offspring of one gender (male or female) do not have linkage information depending on whether the homozygous parent has two male-dominant or male-recessive alleles. Consequently, an F-2 design is more efficient than a backcross design for mapping a sex-influenced gene. Knowing each parental linkage phase is important to apply the methods developed in this article. It is shown that an individual's linkage phase of the sex-influenced locus can be determined based on allele transmission from the parents for all crosses except under the mating between an expressed male and an unexpressed female.     

Detection of linkage between marker loci and loci affecting quantitative traits in crosses between segregating populations

Summary By making use of pedigree information and information on marker-genotypes of the parent and F-1 individuals crossed to form an F-2 population, it is possible to carry out a linkage analysis between marker loci and loci affecting quantitative traits in a cross between segregating parent populations that are at fixation for alternative alleles at the QTL, but share the same alleles at the marker loci. For two-allele systems, depending on marker allele frequencies in the parent populations, 2–4 times as many F-2 offspring will have to be raised and scored for markers and quantitative traits in order to provide power equivalent to that obtained in a cross between fully inbred lines. Major savings in number of F-2 offspring raised can be achieved by scoring each parent pair for a large number of markers in each chromosomal region and scoring F-1 and F-2 offspring only for those markers for which the parents were homozygous for alternative alleles. For multiple allele systems, particularly when dealing with hypervariable loci, only 10%–20% additional F-2 offspring will have to be raised and scored to provide power equivalent to that obtained in a cross between inbred lines. When a resource population contains novel favorable alleles at quantitative trait loci that are not present (or rare) in a commercial population, analyses of this sort will enable the loci of interest to be identified, mapped and manipulated effectively in breeding programs.Contribution no. 2124-E, 1987 series from The Agricultural Research Organization, The Volcani Center, Bet Dagan, Israel     

Frequencies of Twelve Ascus-Types and Arrangement of Three Genes from Tetrad Data

Equations expressing the theoretical frequencies of twelve ascus-types in the tetrad analysis of a triply heterozygous diploid are described. Using these equations, a mapping procedure for a gene X, is proposed. The procedure requires that two genes, X and Y, of the same phenotype be heterozygous and that the map position of Y be known, and that another standard gene, Z, show an independent phenotype from X and Y. This procedure does not require the laborious allelism test of the segregants to determine the allelic 2:2 segregation in tetrads for the X and Y genes, which is indispensable for mapping by the conventional procedure. The exact placement of the X gene on a chromosome is possible by the chi2 minimization procedure in comparison with the expected frequencies of the six ascus-types or four spore-types deduced from the twelve expected ascus-types to give the optimal fit with the observed data.     

Meiotic Gene Conversion Mutants in SACCHAROMYCES CEREVISIAE . I. Isolation and Characterization of pms1-1 and pms1-2

The pms1 mutants, isolated on the basis of sharply elevated meiotic prototroph frequencies for two closely linked his4 alleles, display pleiotropic phenotypes in meiotic and mitotic cells. Two isolates carrying recessive mutations in PMS1 were characterized. They identify a function required to maintain low postmeiotic segregation (PMS) frequencies at many heterozygous sites. In addition, they are mitotic mutators. In mutant diploids, spore viability is reduced, and among survivors, gene conversion and postmeiotic segregation frequencies are increased, but reciprocal exchange frequencies are not affected. The conversion event pattern is also dramatically changed in multiply marked regions in pms1 homozygotes. The PMS1 locus maps near MET4 on chromosome XIV. The PMS1 gene may identify an excision-resynthesis long patch mismatch correction function or a function that facilitates correction tract elongation. The PMS1 gene product may also play an important role in spontaneous mitotic mutation avoidance and correction of mismatches in heteroduplex DNA formed during spontaneous and UV-induced mitotic recombination. Based on meiotic recombination models emphasizing mismatch correction in heteroduplex DNA intermediates, this interpretation is favored, but alternative interpretations involving longer recombination intermediates in the mutants are also considered.     

Segregation of Microsatellite Alleles in Gynogenetic Diploid Pacific Abalone (Haliotis discus hannai)

Inheritance of 9 microsatellite loci was examined in 3 families of gynogenetic Pacific abalone Haliotis discus hannai produced by fertilizing eggs with UV-irradiated sperm followed by inhibition of the second meiotic division. The proportion of heterozygous progeny was used to estimate marker-centromere (M-C) distances. All loci conformed to Mendelian segregation in the control crosses when null alleles were accounted for. The absence of paternal alleles confirmed the gynogenetic origin of the offspring and indicated 100% success for 3 families. Estimated recombinant frequencies ranged from 0.10 to 0.60, which is lower than those observed in other gynogenetic diploid animals. The mean recombination frequency was 0.22, corresponding to a fixation index of 0.78 in one generation. This is 3.12 times the increase in homozygosity expected after one generation of sib mating (0.25), suggesting meiotic gynogenesis may be an effective means of rapid inbreeding in the abalone. M-C map distances for the 9 loci varied between 5 and 30 cM under the assumption of complete interference. The information about M-C distances will be useful for future gene mapping in H. discus hannai.