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Probability Functions on Complex Pedigrees

C. Cannings, E. A. Thompson and M. H. Skolnick
Advances in Applied Probability
Vol. 10, No. 1 (Mar., 1978), pp. 26-61
DOI: 10.2307/1426718
Stable URL: http://www.jstor.org/stable/1426718
Page Count: 36
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Probability Functions on Complex Pedigrees
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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.

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