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Application of Finite Absorbent Markov Chains to Sib Mating Populations with Selection

Jose A. Bosso, Oscar M. Sorarrain and Ewald E. A. Favret
Biometrics
Vol. 25, No. 1 (Mar., 1969), pp. 17-26
DOI: 10.2307/2528674
Stable URL: http://www.jstor.org/stable/2528674
Page Count: 10
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Application of Finite Absorbent Markov Chains to Sib Mating Populations with Selection
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Abstract

The general theory of Markov chains has been described by several authors: Kemeny and Snell [1960], Bharucha Reid [1960], Feller [1959], Takacs [1960], among others. Although the treatment given by Bharucha Reid is undoubtedly the most complete among those mentioned, Kemeny and Snell's approach is quite adequate for discrete chains in space and time when the number of possible states is finite, as is the case for several genetic models. Examples of application of the formalism developed by Kemeny and Snell to sib mating populations with selection are presented here. Kemeny and Snell give expressions for moments up to the second order in finite absorbing chains. New expressions for moments of the third and the fourth orders have been derived for these chains and are included in this paper as an appendix.

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