Abstract
Linkage disequilibrium (LD) is of great interest for gene mapping and the study of population history. We propose a multilocus model for LD, based on the decay of haplotype sharing (DHS). The DHS model is most appropriate when the LD in which one is interested is due to the introduction of a variant on an ancestral haplotype, with recombinations in succeeding generations resulting in preservation of only a small region of the ancestral haplotype around the variant. This is generally the scenario of interest for gene mapping by LD. The DHS parameter is a measure of LD that can be interpreted as the expected genetic distance to which the ancestral haplotype is preserved, or, equivalently, 1/(time in generations to the ancestral haplotype). The method allows for multiple origins of alleles and for mutations, and it takes into account missing observations and ambiguities in haplotype determination, via a hidden Markov model. Whereas most commonly used measures of LD apply to pairs of loci, the DHS measure is designed for application to the densely mapped haplotype data that are increasingly available. The DHS method explicitly models the dependence among multiple tightly linked loci on a chromosome. When the assumptions about population structure are sufficiently tractable, the estimate of LD is obtained by maximum likelihood. For more-complicated models of population history, we find means and covariances based on the model and solve a quasi-score estimating equation. Simulations show that this approach works extremely well both for estimation of LD and for fine mapping. We apply the DHS method to published data sets for cystic fibrosis and progressive myoclonus epilepsy.
Full Text
The Full Text of this article is available as a PDF (340.9 KB).
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- BENNETT J. H. On the theory of random mating. Ann Eugen. 1954 Mar;18(4):311–317. doi: 10.1111/j.1469-1809.1952.tb02522.x. [DOI] [PubMed] [Google Scholar]
- Devlin B., Risch N., Roeder K. Disequilibrium mapping: composite likelihood for pairwise disequilibrium. Genomics. 1996 Aug 15;36(1):1–16. doi: 10.1006/geno.1996.0419. [DOI] [PubMed] [Google Scholar]
- Foss E., Lande R., Stahl F. W., Steinberg C. M. Chiasma interference as a function of genetic distance. Genetics. 1993 Mar;133(3):681–691. doi: 10.1093/genetics/133.3.681. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Graham J., Thompson E. A. Disequilibrium likelihoods for fine-scale mapping of a rare allele. Am J Hum Genet. 1998 Nov;63(5):1517–1530. doi: 10.1086/302102. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Kaplan N. L., Hill W. G., Weir B. S. Likelihood methods for locating disease genes in nonequilibrium populations. Am J Hum Genet. 1995 Jan;56(1):18–32. [PMC free article] [PubMed] [Google Scholar]
- Kerem B., Rommens J. M., Buchanan J. A., Markiewicz D., Cox T. K., Chakravarti A., Buchwald M., Tsui L. C. Identification of the cystic fibrosis gene: genetic analysis. Science. 1989 Sep 8;245(4922):1073–1080. doi: 10.1126/science.2570460. [DOI] [PubMed] [Google Scholar]
- Kong A., Cox N. J. Allele-sharing models: LOD scores and accurate linkage tests. Am J Hum Genet. 1997 Nov;61(5):1179–1188. doi: 10.1086/301592. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Lazzeroni L. C. Linkage disequilibrium and gene mapping: an empirical least-squares approach. Am J Hum Genet. 1998 Jan;62(1):159–170. doi: 10.1086/301678. [DOI] [PMC free article] [PubMed] [Google Scholar]
- McPeek M. S., Speed T. P. Modeling interference in genetic recombination. Genetics. 1995 Feb;139(2):1031–1044. doi: 10.1093/genetics/139.2.1031. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Nevanlinna H. R. The Finnish population structure. A genetic and genealogical study. Hereditas. 1972;71(2):195–236. doi: 10.1111/j.1601-5223.1972.tb01021.x. [DOI] [PubMed] [Google Scholar]
- Pennacchio L. A., Lehesjoki A. E., Stone N. E., Willour V. L., Virtaneva K., Miao J., D'Amato E., Ramirez L., Faham M., Koskiniemi M. Mutations in the gene encoding cystatin B in progressive myoclonus epilepsy (EPM1) Science. 1996 Mar 22;271(5256):1731–1734. doi: 10.1126/science.271.5256.1731. [DOI] [PubMed] [Google Scholar]
- Rannala B., Slatkin M. Likelihood analysis of disequilibrium mapping, and related problems. Am J Hum Genet. 1998 Feb;62(2):459–473. doi: 10.1086/301709. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Slatkin M. On treating the chromosome as the unit of selection. Genetics. 1972 Sep;72(1):157–168. doi: 10.1093/genetics/72.1.157. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Terwilliger J. D. A powerful likelihood method for the analysis of linkage disequilibrium between trait loci and one or more polymorphic marker loci. Am J Hum Genet. 1995 Mar;56(3):777–787. [PMC free article] [PubMed] [Google Scholar]
- Virtaneva K., Miao J., Träskelin A. L., Stone N., Warrington J. A., Weissenbach J., Myers R. M., Cox D. R., Sistonen P., de la Chapelle A. Progressive myoclonus epilepsy EPM1 locus maps to a 175-kb interval in distal 21q. Am J Hum Genet. 1996 Jun;58(6):1247–1253. [PMC free article] [PubMed] [Google Scholar]
- Whittemore A. S. Genome scanning for linkage: an overview. Am J Hum Genet. 1996 Sep;59(3):704–716. [PMC free article] [PubMed] [Google Scholar]
- Xiong M., Guo S. W. Fine-scale genetic mapping based on linkage disequilibrium: theory and applications. Am J Hum Genet. 1997 Jun;60(6):1513–1531. doi: 10.1086/515475. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Zhao H., Speed T. P., McPeek M. S. Statistical analysis of crossover interference using the chi-square model. Genetics. 1995 Feb;139(2):1045–1056. doi: 10.1093/genetics/139.2.1045. [DOI] [PMC free article] [PubMed] [Google Scholar]