The spread of genes in random mating control populations

Abstract

1. The effect of genetic sampling, when this sampling is without replacement, on variation in gene frequency is studied, and equations describing the genetic drift are derived. The effective size turns out to be about one greater than under sampling with replacement.2. The relation between ‘spread of genes’ and genetic drift is worked out.3. The University of Queensland control poultry flock is analysed by these methods.4. The design of control populations is discussed with particular reference to the relative importance of genetic drift and phenotypic sampling.

Abnormal segregation of a haemagglutinating gene in a control flock

“…Given this ideal situation, assuming an initial frequency of 0-23 in the parents of Gi, the drift in frequency of the Ka + gene between the parents of Gi and G2 would have an expected standard deviation (V8q) equal to 0-024. This is very close to 0-026, the value obtained by applying the formula of James (1962) to the representations of the parents of Gi which were observed in the pedigrees of the parents of G2. Thus with the selections and matings undertaken to reproduce the flock, the control over genetic change should have approached the maximum possible in a flock of this size under the pedigree system.…”

Interrelations between effective population size and other pedigree tools for the management of conserved populations

“…The jth column of this matrix gives the proportion of genes (genetic contributions, c i ; James, 1962) contributed by all previous ancestors (i) to individual j (including itself). For example, if i is a parent of j, z ij l 0n5; if i is a grandparent of j, z ij l 0n25 ; etc.…”

Developments in the prediction of effective population size

“…This dispersal of genes is that analysed in retrospect from pedigree data by James & McBride (1958), using the 'percentage of genes' technique (see James, 1962).…”