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Probability functions on complex pedigrees

Published online by Cambridge University Press:  01 July 2016

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

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.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 1978 

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