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.     

Efficient computations in multilocus linkage analysis.

This paper describes efficient methods for likelihood calculations and maximum-likelihood estimation in multilocus linkage analysis of reference families and general disease pedigrees, and it documents their performance as implemented in the LINKAGE programs. This information should be of considerable value in determining computing needs for linkage investigations, and in evaluating the merits of alternative algorithms.     

Maximum likelihood vs. minimum chi-square--a general comparison with applications to the estimation of recombination fractions in two-point linkage analysis.

Some relationships between the estimates of recombination fraction in two-point linkage analysis obtained by maximum likelihood, minimum chi-square, and general least squares are derived. These theoretical results are based on an approximation for the multinomial distribution. Applications (theoretical and experimental) with RFLP (restriction fragment length polymorphism) markers for a segregating F2 population are given. The minimum chi-square estimate is slightly larger than the maximum likelihood estimate. For applications, however, both estimates must be considered to be approximately equal. The least squares estimates are slightly different (larger or smaller) from these estimates.     

Statistical analysis of multilocus recombination

A general formula for the frequency of different recombinant gamete types, in terms of the underlying distribution of crossovers, is derived. This formula may be applied to any theoretical model of recombination in which it is assumed that there is no chromatid interference. Multiple-locus recombination data may be evaluated by using this formula in conjunction with a maximum likelihood procedure. The validity of any model of recombination may be tested in such a fashion. The possibilities are demonstrated through application to a generalized noninterference model of crossing over described in a previous paper (Risch and Lange, 1979, Annals of Human Genetics 43, 61-70).     

Age trends in human chiasma frequencies and recombination fractions. II. Method for analyzing recombination fractions and applications to the ABO:Nail-Patella linkage

A new method is presented for studying the relationship between human recombination fractions and parental age at the time of conception. Assuming the sex specific recombination fraction to be a linear function of age, a feasible computer algorithm is described whereby the likelihood of multigenerational families can be calculated. Using this method and the likelihood ratio test, it is found that for the ABO:nail-patella linkage age (P= .17)is more significant than sex (p= .23) in its effect on the recombination fraction. The age effect, if it is real, appears to be limited to males: the paternal recombination fraction decreases by .0062(+/- .0036) per year.     

A multilocus extension of the affected-pedigree-member method of linkage analysis.

The affected-pedigree-member (APM) method of linkage analysis is designed to detect departures from independent segregation of disease and marker phenotypes. The underlying statistic of the APM method operates on the identity-by-state relations implied by the marker phenotypes of the affected within a pedigree. Here we generalize the APM statistic to multiple linked markers. This generalization relies on recursive computation of two-locus kinship coefficients by an algorithm of Thompson. The distributional properties of the extended APM statistic are investigated theoretically and by simulation in the context of one real and one artificial data set. In both examples, the multilocus statistic tends to reject, more strongly than the single-locus statistics do, the null hypothesis of independent segregation between the disease locus and the marker loci.     

Maximum likelihood estimation of linkage and interference from tetrad data

Maximum likelihood equations have been derived for estimation of map distance and interference from two-point and ranked tetrad data. The estimators have been applied to data from Saccharomyces cerevisiae and Schizosaccharomyces pombe. S. cerevisiae consistently shows quite strong interference over the mapped genome. In striking contrast, S. pombe consistently shows much weaker interference and many crosses exhibit negative interference. In neither species was there a conspicuous tendency for intervals spanning a centromere to show less interference than those that did not. Since the amount of recombination per microgram of DNA in the two species is similar, the difference in interference characteristics seems to be a reflection of some fundamental difference in the recombination process of the two species.     

Mapping of human X-linked hypophosphataemic rickets by multilocus linkage analysis

Summary Eleven families with X-linked dominant hypophosphataemic rickets (HPDR) have been typed for a series of X chromosome markers. Linkage with probe 99.6 (DXS41) was demonstrated with a peak lod score of 4.82 at 10% recombination. Multilocus linkage analysis showed that HPDR maps distal to 99.6; this probe has previously been located at Xp22.31-p21.3 by in situ hybridisation. In the mouse hypophosphataemia (Hyp) maps to the distal part of the X chromosome; our location in man is consistent with a scheme which relates the mouse and human X chromosomes by two rearrangements. No marker has yet been found which shows no recombination with HPDR.     

Combined linkage disequilibrium and linkage mapping: Bayesian multilocus approach

Quantitative trait loci (QTL) affecting the phenotype of interest can be detected using linkage analysis (LA), linkage disequilibrium (LD) mapping or a combination of both (LDLA). The LA approach uses information from recombination events within the observed pedigree and LD mapping from the historical recombinations within the unobserved pedigree. We propose the Bayesian variable selection approach for combined LDLA analysis for single-nucleotide polymorphism (SNP) data. The novel approach uses both sources of information simultaneously as is commonly done in plant and animal genetics, but it makes fewer assumptions about population demography than previous LDLA methods. This differs from approaches in human genetics, where LDLA methods use LA information conditional on LD information or the other way round. We argue that the multilocus LDLA model is more powerful for the detection of phenotype–genotype associations than single-locus LDLA analysis. To illustrate the performance of the Bayesian multilocus LDLA method, we analyzed simulation replicates based on real SNP genotype data from small three-generational CEPH families and compared the results with commonly used quantitative transmission disequilibrium test (QTDT). This paper is intended to be conceptual in the sense that it is not meant to be a practical method for analyzing high-density SNP data, which is more common. Our aim was to test whether this approach can function in principle.     

Cost-benefit analysis of recombination and its application for understanding of chiasma interference.

A cost-benefit analysis of recombination was undertaken. The beneficial effects of crossing-over are proportional to the frequency of recombinant offspring, while its harmful effects (errors of crossing-over leading to mutations) are proportional to the number of crossover exchanges. An equilibrium point should exist where the beneficial effects of crossing-over are balanced by its harmful effects. It is suggested that natural selection sustains a number of crossover exchanges per meiosis at the level that provides highest benefit-cost difference. Chiasma interference prevents the arising of closely located exchanges which are less effective in the production of recombinants than exchanges separated by some "interference distance". Computer simulation shows that chiasma interference increases the recombination effectiveness of the multiple crossover exchanges as compared to the case without interference.     

Linkage analysis using sex-specific recombination fractions with GENEHUNTER-MODSCORE

MOTIVATION: Sex-specific marker maps have become increasingly available. We have implemented the usage of sex-specific recombination frequencies in the GENEHUNTER-MODSCORE program that performs multipoint linkage analysis. Furthermore, we have devised a consistent method to choose the combinations of male and female genetic positions at which linkage scores should be calculated. Marker coordinates can be read automatically from publicly available genetic maps. RESULTS: In a MOD-score analysis of the COGA dataset provided for Genetic Analysis Workshop 14, the highest linkage peak on chromosome 1 further increases when using sex-specific maps, while some smaller peaks are decreased. Simulations confirm that the MOD score can be biased when a sex-averaged instead of the correct sex-specific map is employed. This shows that an adequate modeling of the female:male ratio of genetic distances is important, especially for complex traits. AVAILABILITY: The new version of GENEHUNTER-MODSCORE can be downloaded from the following website: http://www.staff.uni-marburg.de/~strauchk/software.html     

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.     

Immunofluorescent analysis of meiotic recombination and interference in the domestic cat

The aim of this work was an analysis of frequency, density and distribution of recombination sites in male meiosis of the domestic cat. The study was carried out using immunofluorescent staining of synaptonemal complex (SC) proteins, centromeric proteins and mismatch repair protein MLH1, a reliable marker of the sites of crossing over. We mapped 2633 sites of crossing over at 1098 individual autosomes. On the basis of these data the total length of the domestic cat genetic map was estimated as 2176 centimorgans. We found a typical for all mammals studied positive correlation between the length of SC and the number of recombination sites. The domestic cat demonstrated the highest among mammals density of recombination and the lowest interference.     

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.     

Incorporating interference into linkage analysis for experimental crosses

The phenomenon of interference in genetic recombination is well-known and studied in a wide variety of organisms. Multilocus linkage analysis, which makes use of recombination patterns among all genetic markers simultaneously, is routinely used with data on humans and experimental organisms to build genetic maps. It is also used to try to determine the genes involved in traits of interest, such as common diseases. Most linkage analyses performed today ignore the occurrence of genetical interference. We present an extension to the Lander-Green algorithm for experimental crosses (backcross and intercross) to incorporate crossover interference according to the chi2 model. Simulation results show the impact of using this model on the accuracy of estimated genetic maps.     

A multilocus linkage map of mouse chromosome 8

We present a genetic linkage map of mouse chromosome 8 that spans 53 cM and includes eight cloned loci. This map was derived from analysis of 100 progeny of an interspecific backcross between Mus spretus and Mus musculus domesticus. Genes that were mapped in this analysis include L7, Plat, Lpl, Ucp, Es, Mt-1, Um, and Tat. This analysis positions a new extremely proximal marker on chromosome 8, which is discussed as a potential candidate gene for the nervous locus. These linkage data will be useful for the mapping of additional loci on chromosome 8.     

Joint linkage and linkage disequilibrium mapping in natural populations

A new strategy for studying the genome structure and organization of natural populations is proposed on the basis of a combined analysis of linkage and linkage disequilibrium using known polymorphic markers. This strategy exploits a random sample drawn from a panmictic natural population and the open-pollinated progeny of the sample. It is established on the principle of gene transmission from the parental to progeny generation during which the linkage between different markers is broken down due to meiotic recombination. The strategy has power to simultaneously capture the information about the linkage of the markers (as measured by recombination fraction) and the degree of their linkage disequilibrium created at a historic time. Simulation studies indicate that the statistical method implemented by the Fisher-scoring algorithm can provide accurate and precise estimates for the allele frequencies, recombination fractions, and linkage disequilibria between different markers. The strategy has great implications for constructing a dense linkage disequilibrium map that can facilitate the identification and positional cloning of the genes underlying both simple and complex traits.     

LIAN 3.0: detecting linkage disequilibrium in multilocus data. Linkage Analysis

SUMMARY: LIAN is a program to test the null hypothesis of linkage equilibrium for multilocus data. LIAN incorporates both a Monte Carlo method as well as a novel algebraic method to carry out the hypothesis test. The program further returns the genetic diversity of the sample and the pairwise distances between its members.     

Mutation and recombination with tight linkage

An exact solution of the mutation-recombination equation in continuous time is presented, with linear ordering of the sites and at most one mutation or crossover event taking place at every instant of time. The differential equation may be obtained from a mutation-recombination model with discrete generations, in the limit of short generations, or weak mutation and recombination. The solution relies on the multilinear structure of the dynamical system, and on the commuting properties of the mutation and recombination operators. It is obtained through diagonalization of the mutation term, followed by a transformation to certain measures of linkage disequilibrium that simultaneously linearize and diagonalize the recombination dynamics. The collection of linkage disequilibria, as well as their decay rates, are given in closed form. Received: 26 January 1999 / Revised version: 20 October 2000 / Published online: 10 April 2001     

On different approximations to multilocus identity-by-descent calculations and the resulting power of variance component-based linkage analysis

An empirical comparison between three different methods for estimation of pair-wise identity-by-descent (IBD) sharing at marker loci was conducted in order to quantify the resulting differences in power and localization precision in variance components-based linkage analysis. On the examined simulated, error-free data set, it was found that an increase in accuracy of allele sharing calculation resulted in an increase in power to detect linkage. Linkage analysis based on approximate multi-marker IBD matrices computed by a Markov chain Monte Carlo approach was much more powerful than linkage analysis based on exact single-marker IBD probabilities. A "multiple two-point" approximation to true "multipoint" IBD computation was found to be roughly intermediate in power. Both multi-marker approaches were similar to each other in accuracy of localization of the quantitative trait locus and far superior to the single-marker approach. The overall conclusions of this study with respect to power are expected to also hold for different data structures and situations, even though the degree of superiority of one approach over another depends on the specific circumstances. It should be kept in mind, however, that an increase in computational accuracy is expected to go hand in hand with a decrease in robustness to various sources of errors.