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Prediction of rates of inbreeding in selected populations

Published online by Cambridge University Press:  14 April 2009

Naomi R. Wray  and
Robin Thompson
Naomi R. Wray
Affiliation:
Institute of Animal Genetics, University of Edinburgh, West Mains Road, Edinburgh EH9 3JN
Robin Thompson
Affiliation:
AFRC Institute of Animal Physiology and Genetics Research, Edinburgh Research Station, Roslin, Midlothian, EH25 9PS
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A method is presented for the prediction of rate of inbreeding for populations with discrete generations. The matrix of Wright's numerator relationships is partitioned into ‘contribution’ matrices which describe the contribution of the Mendelian sampling of genes of ancestors in a given generation to the relationship between individuals in later generations. These contributions stabilize with time and the value to which they stabilize is shown to be related to the asymptotic rate of inbreeding and therefore also the effective population size, where N is the number of individuals per generation and μr and are the mean and variance of long-term relationships or long-term contributions. These stabilized values are then predicted using a recursive equation via the concept of selective advantage for populations with hierarchical mating structures undergoing mass selection. Account is taken of the change in genetic parameters as a consequence of selection and also the increasing ‘competitiveness’ of contemporaries as selection proceeds. Examples are given and predicted rates of inbreeding are compared to those calculated in simulations. For populations of 20 males and 20, 40, 100 or 200 females the rate of inbreeding was found to increase by as much as 75% over the rate of inbreeding in an unselected population depending on mating ratio, selection intensity and heritability of the selected trait. The prediction presented here estimated the rate of inbreeding usually within 5% of that calculated from simulation.

Type
Research Article
Information
Genetics Research , Volume 55 , Issue 1 , February 1990 , pp. 41 - 54
Copyright
Copyright © Cambridge University Press 1990

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