Relative efficiencies of chi 2 models of recombination for exclusion mapping and gene ordering

Pedigree data analysis with crossover interference

We propose a new method for calculating probabilities for pedigree genetic data that incorporates crossover interference using the chi-square models. Applications include relationship inference, genetic map construction, and linkage analysis. The method is based on importance sampling of unobserved inheritance patterns conditional on the observed genotype data and takes advantage of fast algorithms for no-interference models while using reweighting to allow for interference. We show that the method is effective for arbitrarily many markers with small pedigrees.

Crossover interference in humans

Crossing-over between homologous chromosomes facilitates proper disjunction of chromosomes during meiosis I. In many organisms, gene functions that are essential to crossing-over also facilitate the intimate chromosome pairing called "synapsis." Many organisms--including budding yeast, humans, zebrafish, Drosophila, and Arabidopsis--regulate the distribution of crossovers, so that, most of the time, each chromosome bundle gets at least one crossover while the mean number of crossovers per chromosome remains modest. This regulation is obtained through crossover interference. Recent evidence suggests that the organisms that use recombination functions to achieve synapsis have two classes of crossovers, only one of which is subject to interference. We statistically test this two-pathway hypothesis in the CEPH data and find evidence to support the two-pathway hypothesis in humans.

A reaction-diffusion model for interference in meiotic crossing over

One crossover point between a pair of homologous chromosomes in meiosis appears to interfere with occurrence of another in the neighborhood. It has been revealed that Drosophila and Neurospora, in spite of their large difference in the frequency of crossover points, show very similar plots of coincidence-a measure of the interference-against the genetic distance of the interval, defined as one-half the average number of crossover points within the interval. We here propose a simple reaction-diffusion model, where a "randomly walking" precursor becomes immobilized and matures into a crossover point. The interference is caused by pair-annihilation of the random walkers due to their collision and by annihilation of a random walker due to its collision with an immobilized point. This model has two parameters-the initial density of the random walkers and the rate of its processing into a crossover point. We show numerically that, as the former increases and/or the latter decreases, plotted curves of the coincidence vs. the genetic distance converge on a unique curve. Thus, our model explains the similarity between Drosophila and Neurospora without parameter values adjusted finely, although it is not a "genetic model" but is a "physical model," specifying explicitly what happens physically.

Characterization of human crossover interference

We present an analysis of crossover interference over the entire human genome, on the basis of genotype data from more than 8,000 polymorphisms in eight CEPH families. Overwhelming evidence was found for strong positive crossover interference, with average strength lying between the levels of interference implied by the Kosambi and Carter-Falconer map functions. Five mathematical models of interference were evaluated: the gamma model and four versions of the count-location model. The gamma model fit the data far better than did any of the other four models. Analysis of intercrossover distances was greatly superior to the analysis of crossover counts, in both demonstrating interference and distinguishing between the five models. In contrast to earlier suggestions, interference was found to continue uninterrupted across the centromeres. No convincing differences in the levels of interference were found between the sexes or among chromosomes; however, we did detect possible individual variation in interference among the eight mothers. Finally, we present an equation that provides the probability of the occurrence of a double crossover between two nonrecombinant, informative polymorphisms.

An efficient, robust, and unified method for mapping complex traits (II): multipoint linkage analysis

Extending the method for two-point linkage analysis [Zhao et al., 1998: Am J Med Genet 77:366-383], this paper introduces a semiparametric method for multipoint linkage analysis, expected to gain efficiency by using multiple markers simultaneously. Overcoming the longstanding statistical and computational challenge to the parametric approaches (or lod score methods) for multipoint linkage analysis, this semiparametric approach, based on the estimating equation technique, yields statistically efficient and yet robust estimates and enjoys the computational efficiency in processing multiple markers from large pedigrees. Its computational burden increases linearly with the sizes of pedigrees and with the number of marker loci. To illustrate this semiparametric method, we apply it to marker data gathered for the Breast Cancer Consortium. The result supports the earlier finding of the positive linkage with BRCA1 and has also shown that the multipoint linkage analysis has an improved power. In addition, we have applied this method to analyze genome scanning data that have been used to localize genes responsible for type 1 diabetes. In support of the earlier findings, the genome scanning detects the linkage signals on chromosome 6 but does not support the earlier suggestions of two major genes in that genome segment. Through sensitivity analysis, it appears that the results are robust to misspecification of penetrance and allele frequency.