The appropriate threshold for declaring linkage when allowing sex-specific recombination rates.

In human genetics, two loci are declared to be linked when the lod score at the maximum likelihood recombination fraction theta exceeds the threshold of 3.0. Since recombination rates differ between the sexes, one can alternatively detect linkage by estimating separate recombination rates, theta m and theta f, for male and female meiosis and examining the corresponding sex-specific lod scores. The question arises: In order to maintain the same chance of falsely declaring linkage, what is the correct threshold for declaring linkage when sex-specific lod scores are used? We show here that the appropriate threshold is about 3.5. If the restriction that theta f greater than theta m is added, the appropriate threshold falls to about 3.25. We also discuss the relative efficiency of detecting linkage by using sex-specific and sex-averaged lod scores.     

Estimating the contribution of mutation, recombination and gene conversion in the generation of haplotypic diversity

Recombination occurs through both homologous crossing over and homologous gene conversion during meiosis. The contribution of recombination relative to mutation is expected to be dramatically reduced in inbreeding organisms. We report coalescent-based estimates of the recombination parameter (rho) relative to estimates of the mutation parameter (theta) for 18 genes from the highly self-fertilizing grass, wild barley, Hordeum vulgare ssp. spontaneum. Estimates of rho/theta are much greater than expected, with a mean rho/theta approximately 1.5, similar to estimates from outcrossing species. We also estimate rho with and without the contribution of gene conversion. Genotyping errors can mimic the effect of gene conversion, upwardly biasing estimates of the role of conversion. Thus we report a novel method for identifying genotyping errors in nucleotide sequence data sets. We show that there is evidence for gene conversion in many large nucleotide sequence data sets including our data that have been purged of all detectable sequencing errors and in data sets from Drosophila melanogaster, D. simulans, and Zea mays. In total, 13 of 27 loci show evidence of gene conversion. For these loci, gene conversion is estimated to contribute an average of twice as much as crossing over to total recombination.     

Centromere mapping functions for aneuploid meiotic products: Analysis of rec8, rec10 and rec11 mutants of the fission yeast Schizosaccharomyces pombe.

Recent evidence suggests that the position of reciprocal recombination events (crossovers) is important for the segregation of homologous chromosomes during meiosis I and sister chromatids during meiosis II. We developed genetic mapping functions that permit the simultaneous analysis of centromere-proximal crossover recombination and the type of segregation error leading to aneuploidy. The mapping functions were tested in a study of the rec8, rec10, and rec11 mutants of fission yeast. In each mutant we monitored each of the three chromosome pairs. Between 38 and 100% of the chromosome segregation errors in the rec8 mutants were due to meiosis I nondisjunction of homologous chromosomes. The remaining segregation errors were likely the result of precocious separation of sister chromatids, a previously described defect in the rec8 mutants. Between 47 and 100% of segregation errors in the rec10 and rec11 mutants were due to nondisjunction of sister chromatids during meiosis II. In addition, centromere-proximal recombination was reduced as much as 14-fold or more on chromosomes that had experienced nondisjunction. These results demonstrate the utility of the new mapping functions and support models in which sister chromatid cohesion and crossover position are important determinants for proper chromosome segregation in each meiotic division.     

Sex-specific recombination rates in zebrafish (Danio rerio)

In many organisms, the rate of genetic recombination is not uniform along the length of chromosomes or between sexes. To compare the relative recombination rates during meiosis in male and female zebrafish, we constructed a genetic map based on male meiosis. We developed a meiotic mapping panel of 94 androgenetic haploid embryos that were scored for genetic polymorphisms. The resulting male map was compared to female and sex-average maps. We found that the recombination rate in male meiosis is dramatically suppressed relative to that of female meiosis, especially near the centromere. These findings have practical applications for experimental design. The use of exclusively female meiosis in a positional cloning project maximizes the ratio of genetic map distance to physical distance. Alternatively, the use of exclusively male meiosis to localize a mutation initially to a linkage group or to maintain relationships of linked alleles minimizes recombination, thereby facilitating some types of analysis.     

在雌不发生交换的鳞翅目类昆虫中使用F2群体作图显隐性分子标记连锁图谱的极大似然(ML)法

在鳞坡目昆虫中,雌性个体的减数分裂细胞不发生遗传重组。这类物种的杂效Ｆ２群体中杂合子基因型的与一般物种中雌雄个体的减数分裂细胞都发生遗传重组的Ｆ２群体杂合子表型不同,由于这个原因,作用这类物种的遗传连锁图谱通常中使用回交群体。但是,用回效群体傻所得的图谱是不完整的,因为图谱上所有的标记都是百轮回亲本提供的,因此 不会超过杂交Ｆ２各体的一半。另外,目前还没有任何方法和软件可以用杂效Ｆ２群体来作图鳞翅     

Mapping disease genes: family-based association studies.

With recent rapid advances in mapping of the human genome, including highly polymorphic and closely linked markers, studies of marker associations with disease are increasingly relevant for mapping disease genes. The use of nuclear-family data in association studies was initially developed to avoid possible ethnic mismatching between patients and randomly ascertained controls. The parental marker alleles not transmitted to an affected child or never transmitted to an affected sib pair form the so-called AFBAC (affected family-based controls) population. In this paper, the theoretical foundation of the AFBAC method is proved for any single-locus model of disease and for any nuclear family-based ascertainment scheme. In a random-mating population, when there is a marker association with disease, the AFBAC population provides an unbiased estimate of the overall population (control) marker alleles when the recombination fraction (theta) between the marker and disease genes is sufficiently small that it can be taken as zero (theta = 0). With population stratification, only marker associations present in the subpopulations will be detected with family-based analyses. Of more importance, however, is the fact that, when theta not equal to 0, differences between transmitted parental (patient) marker allele frequencies and non- or never-transmitted parental marker allele frequencies (implying a marker association with disease) can only be observed for marker genes linked to a disease gene (theta < 1/2). Thus, associations of unlinked marker loci with disease at the population level, caused by population stratification, migration, or admixture, are eliminated. This validates the use of family-based association tests as an appropriate strategy for mapping disease genes.     

Effect of recombination on the accuracy of the likelihood method for detecting positive selection at amino acid sites

Maximum-likelihood methods based on models of codon substitution accounting for heterogeneous selective pressures across sites have proved to be powerful in detecting positive selection in protein-coding DNA sequences. Those methods are phylogeny based and do not account for the effects of recombination. When recombination occurs, such as in population data, no unique tree topology can describe the evolutionary history of the whole sequence. This violation of assumptions raises serious concerns about the likelihood method for detecting positive selection. Here we use computer simulation to evaluate the reliability of the likelihood-ratio test (LRT) for positive selection in the presence of recombination. We examine three tests based on different models of variable selective pressures among sites. Sequences are simulated using a coalescent model with recombination and analyzed using codon-based likelihood models ignoring recombination. We find that the LRT is robust to low levels of recombination (with fewer than three recombination events in the history of a sample of 10 sequences). However, at higher levels of recombination, the type I error rate can be as high as 90%, especially when the null model in the LRT is unrealistic, and the test often mistakes recombination as evidence for positive selection. The test that compares the more realistic models M7 (beta) against M8 (beta and omega) is more robust to recombination, where the null model M7 allows the positive selection pressure to vary between 0 and 1 (and so does not account for positive selection), and the alternative model M8 allows an additional discrete class with omega = d(N)/d(S) that could be estimated to be >1 (and thus accounts for positive selection). Identification of sites under positive selection by the empirical Bayes method appears to be less affected than the LRT by recombination.     

On the determination of recombination rates in intermated recombinant inbred populations

The recurrent intermating of F(2) individuals for some number of generations followed by several generations of inbreeding produces an intermated recombinant inbred (IRI) population. Such populations are currently being developed in the plant-breeding community because linkage associations present in an F(2) population are broken down and a population of fixed inbred lines is also created. The increased levels of recombination enable higher-resolution mapping in IRI populations relative to F(2) populations. Herein we derive relationships, under several limiting assumptions, for determining the expected recombination fraction in IRI populations from the crossover rate per meiosis. These relationships are applicable to situations where the inbreeding component of IRI population development is by either self-fertilization or full-sib mating. Additionally, we show that the derived equations can be solved for the crossover rate per meiosis if the recombination fraction is known for the IRI population. Thus, the observed recombination fraction in any IRI population can be expressed on an F(2) basis. The implications of this work on the expansion of genetic maps in IRI populations and limits for detecting linkage between markers are also considered.     

Disequilibrium likelihoods for fine-scale mapping of a rare allele.

Genetic linkage studies based on pedigree data have limited resolution, because of the relatively small number of segregations. Disequilibrium mapping, which uses population associations to infer the location of a disease mutation, provides one possible strategy for narrowing the candidate region. The coalescent process provides a model for the ancestry of a sample of disease alleles, and recombination events between disease locus and marker may be placed on this ancestral phylogeny. These events define the recombinant classes, the sets of sampled disease copies descending from the meiosis at which a given recombination occurred. We show how Monte Carlo generation of the recombinant classes leads to a linkage likelihood for fine-scale mapping from disease haplotypes. We compare single-marker disequilibrium mapping with interval-disequilibrium mapping and discuss how the approach may be extended to multipoint-disequilibrium mapping. The method and its properties are illustrated with an example of simulated data, constructed to be typical of fine-scale mapping of a rare disease in the Japanese population. The method can take into account known features of population history, such as changing patterns of population growth.     

On Genetic Map Functions

Various genetic map functions have been proposed to infer the unobservable genetic distance between two loci from the observable recombination fraction between them. Some map functions were found to fit data better than others. When there are more than three markers, multilocus recombination probabilities cannot be uniquely determined by the defining property of map functions, and different methods have been proposed to permit the use of map functions to analyze multilocus data. If for a given map function, there is a probability model for recombination that can give rise to it, then joint recombination probabilities can be deduced from this model. This provides another way to use map functions in multilocus analysis. In this paper we show that stationary renewal processes give rise to most of the map functions in the literature. Furthermore, we show that the interevent distributions of these renewal processes can all be approximated quite well by gamma distributions.     

Genetic similarities within and between human populations

The proportion of human genetic variation due to differences between populations is modest, and individuals from different populations can be genetically more similar than individuals from the same population. Yet sufficient genetic data can permit accurate classification of individuals into populations. Both findings can be obtained from the same data set, using the same number of polymorphic loci. This article explains why. Our analysis focuses on the frequency, omega, with which a pair of random individuals from two different populations is genetically more similar than a pair of individuals randomly selected from any single population. We compare omega to the error rates of several classification methods, using data sets that vary in number of loci, average allele frequency, populations sampled, and polymorphism ascertainment strategy. We demonstrate that classification methods achieve higher discriminatory power than omega because of their use of aggregate properties of populations. The number of loci analyzed is the most critical variable: with 100 polymorphisms, accurate classification is possible, but omega remains sizable, even when using populations as distinct as sub-Saharan Africans and Europeans. Phenotypes controlled by a dozen or fewer loci can therefore be expected to show substantial overlap between human populations. This provides empirical justification for caution when using population labels in biomedical settings, with broad implications for personalized medicine, pharmacogenetics, and the meaning of race.     

Two- and three-locus tests for linkage analysis using recombinant inbred lines

We consider fixed recombinant inbred lines (RILs) derived either by selfing or by full-sib mating; when applicable, we also consider intermated recombinant inbreds (IRIs). First, we show that the usual estimate of recombination fraction based on RIL data is biased, and we provide an estimate where the major part of that bias is removed. Second, we derive simple formulas to compute the frequencies of genotypes at three loci in RILs. We describe the nonindependence of multiple recombinations arising in RIL recombination data even though there may be no interference in each meiosis. Finally, we give formulas for interference tests, gene mapping, or QTL detection in RIL populations.     

The use of map functions in multipoint mapping.

The analysis of multipoint data in humans involves detection of linkage, inferences about order, and estimation of map lengths. In order to calculate likelihoods, it is necessary to have predictive formulas for multiple recombination frequencies. In the present study the Markovian assumption of Morton and MacLean is generalized to give predictive formulas for multiple-region recombination using realistic map functions. The best-fitting map functions have been determined by fitting the nine-locus data of Morgan et al. and the seven-locus data of Weinstein on the Drosophila X chromosome. Two map functions fit the data better than other published functions: that of Rao et al. with a map parameter of P = .33 and a new function suggested in the present paper. The close agreement of the estimate of the mapping parameter with a previous estimate inferred from human male meiosis suggests that the map function is robust. A further improvement in the fit to the data can be obtained by the addition of a second parameter to reduce the expected number of multiple recombinants. By comparison with the map functions recommended in the present paper, the assumption of no interference gives a poor fit to the data.     

Recombination, mutation, or constitutive expression at a Gm locus and familial hypergammaglobulinemia.

In a hypercholesterolemic Lebanese family, an uncommon Gm haplotype carrying an unexpected C gamma 1 gene was inherited by only one of 10 siblings. A new recombination during the maternal or paternal meiosis could explain its formation. According to this hypothesis, our data would be informative for the linkage relationship between the gamma-cistrons and the alpha 2-cistron. The latter might be located near the N-terminal side of the gamma-cistron linkage group, and the sequence of genes would be alpha 2, gamma 4, gamma 3, and gamma 1. A mutation could also effect the change from G1m(17) (codons AAA and AAG) TO G1m(3) (codons AGA and AGG). Another alternative is to postulate a constitutive expression of a C gamma 1 structural gene which, normally, would not be expressed. The uncommon derepression could be the consequence of uncommon cellular response to environmental, pathological or metabolic perturbation of a regulatory mechanism.     

Mitochondrial Genetics VII. Allelism and Mapping Studies of Ribosomal Mutants Resistant to Chloramphenicol, Erythromycin and Spiramycin in S. CEREVISIAE

We have isolated 15 spontaneous mutants resistant to one or several antibiotics like chloramphenicol, erythromycin and spiramycin. We have shown by several criteria that all of them result from mutations localized in the mitochondrial DNA. The mutations have been mapped by allelism tests and by two- and three-factor crosses involving various configurations of resistant and sensitive alleles associated in cis or in trans with the mitochondrial locus omega which governs the polarity of genetic recombination. A general mapping procedure based on results of heterosexual (omega(+)x omega(-)) crosses and applicable to mutations localized in the polar segment is described and shown to be more resolving than that based on results of homosexual crosses. Mutations fall into three loci which are all linked and map in the following order: omega-R(I)-R(II)-R(III). The first locus is very tightly linked with omega while the second is less linked to the first. Mutations of similar resistance phenotype can belong to different loci and different phenotypes to the same locus. Mutations confer antibiotic resistance on isolated mitochondrial ribosomes and delineate a ribosomal segment of the mitochondrial DNA. Homo- and hetero-sexual crosses between mutants of the ribosomal segment and those belonging to the genetically unlinked ATPase locus, O(I), have been performed in various allele configurations. The polarity of recombination between R(I), R(II), R(III) and O(I) decreases as a function of the distance of the R locus from the omega locus rather than as a function of the distance of the R locus from the O(I) locus.     

Likelihood of a particular order of genetic markers and the construction of genetic maps

We model the recombination process of fungal systems via chromatid exchange in meiosis, which accounts for any type of bivalent configuration in a genetic interval in any specified order of genetic markers, for both random spore and tetrad data. First, a probability model framework is developed for two genes and then generalized for an arbitrary number of genes. Maximum likelihood estimators (MLEs) for both random and tetrad data are developed. It is shown that the MLE of recombination for tetrad data is uniformly more efficient over that from random spore data by a factor of at least 4 usually. The MLE for the generalized probability framework is computed using the expectation-maximization (EM) algorithm. Pearson's chi-squared statistic is computed as a measure of goodness of fit using a product-multinomial setup. We implement our model with genetic marker data on the whole genome of Neurospora crassa. Simulated annealing is used to search for the best order of genetic markers for each chromosome, and the goodness of fit value is evaluated for model assumptions. Inferred map orders are corroborated by genomic sequence, with the exception of linkage groups I, II, and V.     

Allelic and Ectopic Interactions in Recombination-Defective Yeast Strains

Ectopic recombination in the yeast Saccharomyces cerevisiae has been investigated by examining the effects of mutations known to alter allelic recombination frequencies. A haploid yeast strain disomic for chromosome III was constructed in which allelic recombination can be monitored using leu2 heteroalleles on chromosome III and ectopic recombination can be monitored using ura3 heteroalleles on chromosomes V and II. This strain contains the spo13-1 mutation which permits haploid strains to successfully complete meiosis and which rescues many recombination-defective mutants from the associated meiotic lethality. Mutations in the genes RAD50, SPO11 and HOP1 were introduced individually into this disomic strain using transformation procedures. Mitotic and meiotic comparisons of each mutant strain with the wild-type parental strain has shown that the mutation in question has comparable effects on ectopic and allelic recombination. Similar results have been obtained using diploid strains constructed by mating MATa and MAT alpha haploid derivatives of each of the disomic strains. These data demonstrate that ectopic and allelic recombination are affected by the same gene products and suggest that the two types of recombination are mechanistically similar. In addition, the comparison of disomic and diploid strains indicates that the presence of a chromosome pairing partner during meiosis does not affect the frequency of ectopic recombination events involving nonhomologous chromosomes.     

The haplotype-relative-risk (HRR) method for analysis of association in nuclear families.

One major problem in studying an association between a marker locus and a disease is the selection of an appropriate group of controls. However, this problem of population stratification can be circumvented in a quite elegant manner by family-based methods. The haplotype-relative-risk (HRR) method, which samples nuclear families with a single affected child and uses the parental haplotypes not transmitted to that child as a control individual, represents such a method for estimating the relative risk of a marker phenotype. In the special case of a recessive disease, it was already known that the equivalence of the HRR method with the classical relative risk (RR) obtained from independent samples holds only if the probability theta of a recombination between marker and disease locus is zero. We extend this result to an arbitrary mode of inheritance. Furthermore, we compare the distribution of the estimators for HRR and RR and show that, in the case of a positive linkage disequilibrium between a marker and disease allele, the distribution of the estimator for HRR is (stochastically) smaller than that for RR, irrespective of the recombination fraction. The practical implication of this result is that, for the HRR method, there is no tendency to give unduly high risk estimators, even for theta > 0. Finally, we give an expression for the standard error of the estimator for HRR by taking into account the nonindependence of transmitted and nontransmitted parental marker alleles in the case of theta > 0.     

Genetic and physical mapping of two centromere-proximal regions of chromosome IV in Aspergillus nidulans

Chromosome IV is the smallest chromosome of Aspergillus nidulans. The centromere-proximal portion of the chromosome was mapped physically using overlapping clones of a cosmid genomic library. Two contiguous segments of a physical map, based on restriction mapping of cosmid clones, were generated, together covering more than 0.4 Mb DNA. A reverse genetic mapping approach was used to establish a correlation between physical and genetic maps; i.e., marker genes were integrated into physically mapped segments and subsequently mapped by mitotic and meiotic recombination. The resulting data, together with additional classical genetic mapping, lead to a substantial revision of the genetic map of the chromosome, including the position of the centromere. Comparison of physical and genetic maps indicates that meiotic recombination is low in subcentromeric DNA, its frequency being reduced from 1 crossover per 0.8 Mb to approximately 1 crossover per 5 Mb per meiosis. The portion of the chromosome containing the functional centromere was not mapped because repeat-rich regions hindered further chromosome walking. The size of the missing segment was estimated to be between 70 and 400 kb.