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A Monte Carlo approach to calculating probabilities for continuous identity by descent data

Part of: Special processes Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  14 July 2016

Sharon Browning
Sharon Browning*
Affiliation:
North Carolina State University
*
∗Postal address: Department of Statistics, North Carolina State University, Raleigh, NC 27695-8203, USA. Email address: [email protected]
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Abstract

Two related individuals are identical by descent at a genetic locus if they share the same gene copy at that locus due to inheritance from a recent common ancestor. We consider idealized continuous identity by descent (IBD) data in which IBD status is known continuously along chromosomes. IBD data contains information about the relationship between the two individuals, and about the underlying crossover processes. We present a Monte Carlo method for calculating probabilities for IBD data. The method is not restricted to Haldane's Poisson process model of crossing-over but may be used with other models including the chi-square, Kosambi renewal and Sturt models. Results of a simulation study demonstrate that IBD data can be used to distinguish between alternative models for the crossover process.

Keywords

GeneticsMonte Carloidentity by descentchiasma interference

MSC classification

Primary: 92D10: Genetics 65C05: Monte Carlo methods
Secondary: 60K40: Other physical applications of random processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 3 , September 2000 , pp. 850 - 864
Copyright
Copyright © Applied Probability Trust 2000 

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References

Barnard, G. A. (1963). Discussion of paper by M. S. Bartlett. J. R. Statist. Soc. Ser. B 25, 294.Google Scholar
Boehnke, M., and Cox, N. J. (1997). Accurate inference of relationships in sib-pair linkage studies. Amer. J. Human Genet. 61, 423–429.Google Scholar
Broman, K. W., Murray, J. C., Sheffield, V. C., White, R. L., and Weber, J. L. (1998). Comprehensive human genetic maps: individual and sex-specific variation in recombination. Amer. J. Human Genet. 63, 861–869.CrossRefGoogle ScholarPubMed
Browning, S. (1998). Relationship information contained in gamete identity by descent data. J. Comput. Biol. 5, 323–334.Google Scholar
Browning, S. (1999). Monte Carlo likelihood calculation for identity by descent data. PhD thesis, University of Washington.% Available at http://statgen.ncsu.edu/sharon/thesis.pdf (822 kb).Google Scholar
Browning, S. (2000). The relationship between count-location and stationary renewal models for the chiasma process. Genetics 155, 1955–1960.CrossRefGoogle ScholarPubMed
Efron, B., and Tibshirani, R. (1986). Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy. Statist. Sci. 1, 54–75.Google Scholar
Geyer, C. J., Ryder, O. A., Chemnick, L. G., and Thompson, E. A. (1993). Analysis of relatedness in the California condors, from DNA fingerprints. Molec. Biol. Evolut. 10, 571–589.Google Scholar
Haldane, J. B. S. (1919). The combination of linkage values, and the calculation of distances between the loci of linked factors. J. Genetics 8, 299–309.Google Scholar
Hope, A. C. A. (1968). A simplified Monte Carlo significance test procedure. J. R. Statist. Soc. Ser. B, 30, 582–598.Google Scholar
Jöckel, K.-H. (1986). Finite sample properties and asymptotic efficiency of Monte Carlo tests. Ann. Statist. 14, 336–347.Google Scholar
Kosambi, D. D. (1944). The estimation of map distances from recombination values. Ann. Eugenics 12, 172–175.CrossRefGoogle Scholar
Lange, K. (1997). Mathematical and Statistical Methods for Genetic Analysis. Springer, New York, pp. 206–227.CrossRefGoogle Scholar
Sturt, E. (1976). A mapping function for human chromosomes. Ann. Human Genet. 40, 147–163.Google Scholar
Zhao, H., and Liang, F. (2000). On relationship inference using gamete identity by descent data. Unpublished manuscript.Google Scholar
Zhao, H., and Speed, T. P. (1996). On genetic map functions. Genetics 142, 1369–1377.Google Scholar
Zhao, H., McPeek, M. S., and Speed, T. P. (1995). Statistical analysis of chromatid interference. Genetics 139, 1057–1065.CrossRefGoogle Scholar
Zhao, H., Speed, T. P., and McPeek, M. S. (1995). Statistical analysis of crossover interference using the chi-square model. Genetics 139, 1045–1056.CrossRefGoogle Scholar