A hidden Markov model approach to multilocus linkage analysis in a full-sib family

Statistical packages for constructing genetic linkage maps in inbred lines are well developed and applied extensively, while linkage analysis in outcrossing species faces some statistical challenges because of their complicated genetic structures. In this article, we present a multilocus linkage analysis via hidden Markov models for a linkage group of markers in a full-sib family. The advantage of this method is the simultaneous estimation of the recombination fractions between adjacent markers that possibly segregate in different ratios, and the calculation of likelihood for a certain order of the markers. When the number of markers decreases to two or three, the multilocus linkage analysis becomes traditional two-point or three-point linkage analysis, respectively. Monte Carlo simulations are performed to show that the recombination fraction estimates of multilocus linkage analysis are more accurate than those just using two-point linkage analysis and that the likelihood as an objective function for ordering maker loci is the most powerful method compared with other methods. By incorporating this multilocus linkage analysis, we have developed a Windows software, FsLinkageMap, for constructing genetic maps in a full-sib family. A real example is presented for illustrating linkage maps constructed by using mixed segregation markers. Our multilocus linkage analysis provides a powerful method for constructing high-density genetic linkage maps in some outcrossing plant species, especially in forest trees.     

Modeling Interference in Genetic Recombination

In analyzing genetic linkage data it is common to assume that the locations of crossovers along a chromosome follow a Poisson process, whereas it has long been known that this assumption does not fit the data. In many organisms it appears that the presence of a crossover inhibits the formation of another nearby, a phenomenon known as ``interference.' We discuss several point process models for recombination that incorporate position interference but assume no chromatid interference. Using stochastic simulation, we are able to fit the models to a multilocus Drosophila dataset by the method of maximum likelihood. We find that some biologically inspired point process models incorporating one or two additional parameters provide a dramatically better fit to the data than the usual ``no-interference' Poisson model.     

Multilocus linkage analysis in humans: detection of linkage and estimation of recombination.

Multilocus linkage analysis is investigated from the viewpoint of the efficiency of recombination estimates under different strategies for detecting linkage and determining gene order within a linkage group. We consider the appropriateness of assuming no interference with data available in human genetic studies. Examples are given to show the significance of multilocus analysis in humans. A computer program package, LINKAGE, for multilocus linkage analysis is described.     

Models of multilocus recombination: nonrandomness in chiasma number and crossover positions.

Cytological evidence indicates that genetic interference can be partitioned into two empirical components: nonrandomness in the number of chiasmata that occur and nonrandomness in the locations of multiple chiasmata. Previous studies have incorporated the first effect into genetic models for analyzing multipoint data. An extension to this approach is presented which allows for the second component of interference by modeling the probability density function of the locations of multiple crossovers. Results of reanalyses of multilocus data for the Drosophila X chromosome show that models that incorporate only the first effect give a better fit to these data than do standard mapping functions and that the extended model significantly improved the fit by decreasing the predicted frequency of multiple crossovers in nearby regions. Our results demonstrate that chiasma-based models of multilocus recombination, which are unique in incorporating direct estimates of the frequency of multiple crossovers for a chromosome region, can provide a powerful and realistic means of accounting for genetic interference when applied to the problems of gene localization, locus ordering, and exclusion mapping.     

Multilocus genomics of outcrossing plant populations

The structure and organization of natural plant populations can be understood by estimating the genetic parameters related to mating behavior, recombination frequency, and gene associations with DNA-based markers typed throughout the genome. We developed a statistical and computational model for estimating and testing these parameters from multilocus data collected in a natural population. This model, constructed by a maximum likelihood approach and implemented within the EM algorithm, is shown to be robust for simultaneously estimating the outcrossing rate, recombination frequencies and linkage disequilibria. The algorithm built with three or more markers allows the characterization of crossover interference in meiosis and high-order disequilibria among different genes, thus providing a powerful tool for illustrating a detailed picture of genetic diversity and organization in natural populations. Computer simulations demonstrate the statistical properties of the proposed model. This multilocus model will be useful for studying the pattern and amount of genetic variation within and among populations to further infer the evolutionary history of a plant species.     

Inference of population structure using multilocus genotype data: linked loci and correlated allele frequencies

We describe extensions to the method of Pritchard et al. for inferring population structure from multilocus genotype data. Most importantly, we develop methods that allow for linkage between loci. The new model accounts for the correlations between linked loci that arise in admixed populations ("admixture linkage disequilibium"). This modification has several advantages, allowing (1) detection of admixture events farther back into the past, (2) inference of the population of origin of chromosomal regions, and (3) more accurate estimates of statistical uncertainty when linked loci are used. It is also of potential use for admixture mapping. In addition, we describe a new prior model for the allele frequencies within each population, which allows identification of subtle population subdivisions that were not detectable using the existing method. We present results applying the new methods to study admixture in African-Americans, recombination in Helicobacter pylori, and drift in populations of Drosophila melanogaster. The methods are implemented in a program, structure, version 2.0, which is available at http://pritch.bsd.uchicago.edu.     

The effects of Hill-Robertson interference between weakly selected mutations on patterns of molecular evolution and variation

Associations between selected alleles and the genetic backgrounds on which they are found can reduce the efficacy of selection. We consider the extent to which such interference, known as the Hill-Robertson effect, acting between weakly selected alleles, can restrict molecular adaptation and affect patterns of polymorphism and divergence. In particular, we focus on synonymous-site mutations, considering the fate of novel variants in a two-locus model and the equilibrium effects of interference with multiple loci and reversible mutation. We find that weak selection Hill-Robertson (wsHR) interference can considerably reduce adaptation, e.g., codon bias, and, to a lesser extent, levels of polymorphism, particularly in regions of low recombination. Interference causes the frequency distribution of segregating sites to resemble that expected from more weakly selected mutations and also generates specific patterns of linkage disequilibrium. While the selection coefficients involved are small, the fitness consequences of wsHR interference across the genome can be considerable. We suggest that wsHR interference is an important force in the evolution of nonrecombining genomes and may explain the unexpected constancy of codon bias across species of very different census population sizes, as well as several unusual features of codon usage in Drosophila.     

Multipoint Genetic Mapping with Trisomy Data

Trisomy is the most common genetic abnormality in humans and is the leading cause of mental retardation. Although molecular studies that use a large number of highly polymorphic markers have been undertaken to understand the recombination patterns for chromosome abnormalities, there is a lack of multilocus approaches to incorporating crossover interference in the analysis of human trisomy data. In the present article, we develop two statistical methods that simultaneously use all genetic information in trisomy data. The first approach relies on a general relationship between multilocus trisomy probabilities and multilocus ordered-tetrad probabilities. Under the assumption that no more than one chiasma exists in each marker interval, we describe how to use the expectation-maximization algorithm to examine the probability distribution of the recombination events underlying meioses that lead to trisomy. One limitation of the first approach is that the amount of computation increases exponentially with the number of markers. The second approach models the crossover process as a chi(2) model. We describe how to use hidden Markov models to evaluate multilocus trisomy probabilities. Our methods are applicable when both parents are available or when only the nondisjoining parent is available. For both methods, genetic distances among a set of markers can be estimated and the pattern of overall chiasma distribution can be inspected for differences in recombination between meioses exhibiting trisomy and normal meioses. We illustrate the proposed approaches through their application to a set of trisomy 21 data.     

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.     

Estimating the minimum rate of genetic transformation in bacteria

Extensive data from multilocus electrophoresis are available for many bacterial populations. In some cases, for example Neisseria gonorrhoeae, these data are consistent with the population being in linkage equilibrium. This raises the following question. What frequency of transformation, or other means of genetic recombination, is needed, relative to mutation, to produce apparent panmixis? Simulation of a finite-population model suggests that, if transformation is at least twenty times as frequent as mutation, the population structure will be indistinguishable from a panmictic one, using the best available data sets. That is, relatively infrequent transformation is sufficient to produce approximate linkage equilibrium.     

Recombination hotspots as a point process

The variation of the recombination rate along chromosomal DNA is one of the important determinants of the patterns of linkage disequilibrium. A number of inferential methods have been developed which estimate the recombination rate and its variation from population genetic data. The majority of these methods are based on modelling the genealogical process underlying a sample of DNA sequences and thus explicitly include a model of the demographic process. Here we propose a different inferential procedure based on a previously introduced framework where recombination is modelled as a point process along a DNA sequence. The approach infers regions containing putative hotspots based on the inferred minimum number of recombination events; it thus depends only indirectly on the underlying population demography. A Poisson point process model with local rates is then used to infer patterns of recombination rate estimation in a fully Bayesian framework. We illustrate this new approach by applying it to several population genetic datasets, including a region with an experimentally confirmed recombination hotspot.     

Genomics of natural populations: Evolutionary forces that establish and maintain gene arrangements in Drosophila pseudoobscura

The evolution of complex traits in heterogeneous environments may shape the order of genes within chromosomes. Drosophila pseudoobscura has a rich gene arrangement polymorphism that allows one to test evolutionary genetic hypotheses about how chromosomal inversions are established in populations. D. pseudoobscura has >30 gene arrangements on a single chromosome that were generated through a series of overlapping inversion mutations with >10 inversions with appreciable frequencies and wide geographic distributions. This study analyses the genomic sequences of 54 strains of Drosophila pseudoobscura that carry one of six different chromosomal arrangements to test whether (i) genetic drift, (ii) hitchhiking with an adaptive allele, (iii) direct effects of inversions to create gene disruptions caused by breakpoints, or (iv) indirect effects of inversions in limiting the formation of recombinant gametes are responsible for the establishment of new gene arrangements. We found that the inversion events do not disrupt the structure of protein coding genes at the breakpoints. Population genetic analyses of 2,669 protein coding genes identified 277 outlier loci harbouring elevated frequencies of arrangement‐specific derived alleles. Significant linkage disequilibrium occurs among distant loci interspersed between regions with low levels of association indicating that distant allelic combinations are held together despite shared polymorphism among arrangements. Outlier genes showing evidence of genetic differentiation between arrangements are enriched for sensory perception and detoxification genes. The data presented here support the indirect effect of inversion hypothesis where chromosomal inversions are favoured because they maintain linked associations among multilocus allelic combinations among different arrangements.     

Linkage mapping from pair-wise recombination data.

The problem of obtaining a genetic map of a linkage group from pair-wise recombination data is considered. A non-parametric approach is proposed, that does not require the definition of a mapping function, computation of coefficients of coincidence, nor knowledge of map length or sex differences in recombination. An application to Bridges and Morgan's (1923) data on chromosome 3 of Drosophila melanogaster is presented.     

Population genetic analysis of Helicobacter pylori by multilocus enzyme electrophoresis: extensive allelic diversity and recombinational population structure.

Genetic diversity and relationships in 74 Helicobacter pylori isolates recovered from patients assigned to distinct clinical categories were estimated by examination of allelic variation in six genes encoding metabolic housekeeping enzymes by multilocus enzyme electrophoresis. Seventy-three distinct allele profiles, representing multilocus chromosomal genotypes, were identified. All six loci were highly polymorphic, with an average of 11.2 alleles per locus. The mean genetic diversity in the sample was 0.735, a value that exceeds the level of diversity recorded in virtually all bacterial species studied by multilocus enzyme electrophoresis. A high frequency of occurrence of null alleles (lack of enzyme activity) was identified and warrants further investigation at the molecular level. Lack of linkage disequilibrium (nonrandom association (of alleles over loci) indicates that horizontal transfer and recombination of metabolic enzyme genes have contributed to the generation of chromosomal diversity in H. pylori. In this sample of isolates, there was no statistically significant association of multilocus enzyme electrophoretic types or cluster of related chromosomal types and disease category.     

A new strategy for estimating two-locus recombination fractions under some natural inequality restrictions

Linkage analysis is now being widely used to map markers on each chromosome in the human genome, to map genetic diseases, and to identify genetic forms of common diseases. Two-locus linkage analysis and multi-locus analysis have been investigated comprehensively, and many computer programs have been developed to perform linkage analysis. Yet there exists a shortcoming in traditional methods, i.e., the parameter space of two-locus recombination fractions has not been emphasized sufficiently in the usual analyses. In this paper, we propose a new strategy for estimating the two-locus recombination fractions based on data of backcross family in the framework of some natural and necessary parameter restrictions. The new strategy is based on a restricted projection algorithm, which can provide fast reasonable estimates of recombination fraction, and can therefore serve as a superior alternative algorithm. Results obtained from both real and simulated data indicate that the new algorithm performs well in the estimation of recombination fractions and outperforms current methods.     

Hill-Robertson interference in Drosophila melanogaster: reply to Marais,Mouchiroud and Duret

The usage of preferred codons in Drosophila melanogaster is reduced in regions of lower recombination. This is consistent with population genetics theory, whereby the effectiveness of selection on multiple targets is limited by stochastic effects caused by linkage. However, because the selectively preferred codons in D. melanogaster end in C or G, it has been argued that base-composition-biasing effects of recombination can account for the observed relationship between preferred codon usage and recombination rate (Marais et al., 2003). Here, we show that the correlation between base composition (of protein-coding and intron regions) and recombination rate holds only for lower values of the latter. This is consistent with a Hill-Robertson interference model and does not support a model whereby the entire effect of recombination on codon usage can be attributed to its potential role in generating compositional bias.     

A test of the chromosomal rearrangement model of speciation in Drosophila pseudoobscura

Recent studies suggest that chromosomal rearrangements play a significant role in speciation by preventing recombination and maintaining species persistence despite interspecies gene flow. Factors conferring adaptation or reproductive isolation are maintained in rearranged regions in the face of hybridization, while such factors are eliminated from collinear regions. As a direct test of this rearrangement model, we evaluated the genetic basis of hybrid male sterility in a sympatric species pair, Drosophila pseudoobscura pseudoobscura and D. persimilis, and an allopatric species pair, D. pseudoobscura bogotana and D. persimilis. Our results are consistent with the proposed model: virtually all of the sterility factors in the former pair are associated with three inverted regions, whereas sterility factors are present in the collinear regions in the latter pair. These findings indicate recombination and selection may have eliminated sterility factors outside the inverted regions between D. p. pseudoobscura and D. persimilis, suggesting chromosomal rearrangements may facilitate species persistence despite hybridization.     

A Polymerization Model of Chiasma Interference and Corresponding Computer Simulation

A model of chiasma interference is proposed and simulated on a computer. The model uses random events and a polymerization reaction to regulate meiotic recombination between and along chromosomes. A computer simulation of the model generates distributions of crossovers per chromosome arm, position of events along the chromosome arm, distance between crossovers in two-event tetrads, and coincidence as a function of distance. Outputs from the simulation are compared to data from Saccharomyces cerevisiae and the X chromosome of Drosophila melanogaster. The simulation demonstrates that the proposed model can produce the regulation of recombination observed in both genetic and cytological experiments. While the model was quantitatively compared to data from only Drosophila and Saccharomyces, the regulation observed in these species is qualitatively similar to the regulation of recombination observed in other organisms.     

Hill-Robertson interference is a minor determinant of variations in codon bias across Drosophila melanogaster and Caenorhabditis elegans genomes

According to population genetics models, genomic regions with lower crossing-over rates are expected to experience less effective selection because of Hill-Robertson interference (HRi). The effect of genetic linkage is thought to be particularly important for a selection of weak intensity such as selection affecting codon usage. Consistent with this model, codon bias correlates positively with recombination rate in Drosophila melanogaster and Caenorhabditis elegans. However, in these species, the G+C content of both noncoding DNA and synonymous sites correlates positively with recombination, which suggests that mutation patterns and recombination are associated. To remove this effect of mutation patterns on codon bias, we used the synonymous sites of lowly expressed genes that are expected to be effectively neutral sites. We measured the differences between codon biases of highly expressed genes and their lowly expressed neighbors. In D. melanogaster we find that HRi weakly reduces selection on codon usage of genes located in regions of very low recombination; but these genes only comprise 4% of the total. In C. elegans we do not find any evidence for the effect of recombination on selection for codon bias. Computer simulations indicate that HRi poorly enhances codon bias if the local recombination rate is greater than the mutation rate. This prediction of the model is consistent with our data and with the current estimate of the mutation rate in D. melanogaster. The case of C. elegans, which is highly self-fertilizing, is discussed. Our results suggest that HRi is a minor determinant of variations in codon bias across the genome.     

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.