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Probability functions on complex pedigrees

Published online by Cambridge University Press:  01 July 2016

C. Cannings ,
E. A. Thompson  and
M. H. Skolnick
C. Cannings
Affiliation:
University of Sheffield
E. A. Thompson
Affiliation:
University of Cambridge
M. H. Skolnick
Affiliation:
University of Utah
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Abstract

The calculation of probabilities on pedigrees of arbitrary complexity is discussed for a basic model of transmission and penetrance (encompassing Mendelian inheritance, and certain environmental influences).

The structure of pedigrees, and the types of loops occurring, is discussed. Some results in graph theory are obtained and, using these, a recurrence relation derived for certain probabilities. The recursive procedure enables the successive peeling off of certain members of the pedigree, and the condensation of the information on those individuals into a function on a subset of those remaining. The underlying theory is set out, and examples given of the utilization of the resulting algorithm.

Keywords

PEDIGREEPROBABILITYLOOPSPEELINGGRAPHOUSIOTYPEGENETICS

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 10 , Issue 1 , March 1978 , pp. 26 - 61
Copyright
Copyright © Applied Probability Trust 1978 

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Footnotes

The authors acknowledge partial support from NIH Research Grant CA-16573.

References

Berge, C. (1962) The Theory of Graphs. Methuen, London.Google Scholar
Cannings, C., Skolnick, M. H., De Nevers, K. and Sridharan, R. (1976a) Calculation of risk factors and likelihoods for familial diseases. Computers Biomed. Res. 9, 393–406.Google Scholar
Cannings, C., Thompson, E. A. and Skolnick, M. H. (1976b) The recursive derivation of likelihoods on complex pedigrees. Adv. Appl. Prob. 8, 622–625.Google Scholar
Cavalli-Sforza, L. L. and Feldman, M. W. (1973) Cultural versus biological inheritance. Phenotypic transmission from parents to children (a theory of the effect of parental phenotypes on children's phenotypes). Amer. J. Hum. Genet. 25, 618–637.Google Scholar
Cavalli-Sforza, L. L. and Bodmer, W. F. (1971) The Genetics of Human Populations. W. H. Freeman, San Francisco.Google Scholar
Cotterman, W. J. (1940) A Calculus for Statistical Genetics. , Ohio State University. Published in (1974) Genetics and Social Structure, ed. Ballonoff, P. Benchmark Papers in Genetics, Dowden, Hutchinson and Ross, New York.Google Scholar
De Nevers, K., Skolnick, M. H., Cannings, C. and Sridharan, R. (1975) A computer algorithm for calculation of risk factors and likelihoods for familial diseases. Department of Medical Biophysics and Computing, University of Utah, Technical Report No. 1.Google Scholar
Edwards, A. W. F. (1967) Automatic construction of genealogies from phenotypic information (Autokin). Bull. European Soc. Hum. Genet. 1, 42–43.Google Scholar
Elston, R. C. and Stewart, J. (1971) A general model for the genetic analysis of pedigree data. Hum. Hered. 21, 523–542.Google Scholar
Feller, W. (1968) An Introduction to Probability Theory and its Applications, Vol. 1, 3rd edn. Wiley, New York.Google Scholar
Harary, F. (1969) Graph Theory. Addison-Wesley, Reading, Mass.Google Scholar
Heuch, I. and Li, F. H. F. (1972) pedig—A computer program for calculation of genotype probabilities using phenotype information. Clin. Genet. 3, 501–504.Google Scholar
Hilden, J. (1970) genex—An algebraic approach to pedigree probability calculus. Clin. Genet. 1, 319–348.Google Scholar
Hogben, L. (1946) An Introduction to Mathematical Genetics. Norton, New York.Google Scholar
Lange, K. and Elston, R. C. (1975) Extensions to pedigree analysis. I. Likelihood calculations for simple and complex pedigrees. Hum. Hered. 25, 95–105.Google Scholar
Morton, N. E. (1958) Segregation analysis in human genetics. Science 127, 79–80.Google Scholar
Ott, J. (1974) Estimation of the recombination fraction in human pedigrees; efficient computation of the likelihood for human linkage studies. Amer. J. Hum. Genet. 26, 588–597.Google Scholar
Smith, C. A. B. (1976) The use of matrices in calculating Mendelian probabilities. Ann. Hum. Genet. (London) 40, 37–54.Google Scholar
Thompson, E. A. (1974) Gene identities and multiple relationships. Biometrics 20, 667–680.Google Scholar
Thompson, E. A. (1975) Estimation of pairwise relationships. Ann. Hum. Genet. 39, 173–187.Google Scholar
Thompson, E. A. (1976) Inference of genealogical structure. Soc. Sci. Inform. 15, 477–526.Google Scholar
Thompson, E. A. Ancestral inference II. The founders of Tristan da Cunha. To appear.Google Scholar
Thompson, E. A. and Skolnick, M. H. (1977) Likelihoods on complex pedigrees for quantitative traits. Proceedings of the International Conference on Quantitative Genetics, Ames. Iowa.Google Scholar
Thompson, E. A., Cannings, C. and Skolnick, M. H. Ancestral inference I. The problem and the method. To appear.Google Scholar