The role of finite population size and linkage in response to continued truncation selection : I. Additive gene action.
In an attempt to analyse long-term response in finite dioecious populations, selection processes are simulated on a computer with situations of parental population size, linkages between loci, selection intensity, and heritability, specified in a 3(4) factorial design. A diploid polygenic system of 40 loci on 4 chromosomes is considered for additive genes. Linkage levels are specified as free recombinations, adjacent loci 5 map units apart, and as clusters on chromosomes with a distance of only .5 units between adjacent loci. Parental populations of 8, 16, and 64, truncation selection of 1/2, 1/4, and 1/8 of the progeny each generation, and initial heritability of 1, 1/3, and 1/9 are simulated for various populations.For these populations, which are initially samples from a theoreticalHARDY-WEINBERG situation, it is shown that an initial linear phase of response, which may last for only 2 or 3 generations in some cases, depends on the intensity of selection alone. The effects and interactions of all the above factors on the curvilinearity of response in later generations are analysed. It appears that linkages between loci have a strong influence in reducing the rate of response and the total response. In the extreme cases of gene clusters in a parental population size of 8 with low heritability, truncation selection is relatively almost completely ineffective in causing change in the mean over generations. The effect of tight linkage is also exhibited in causing more reduction in genotypic variance than can be accounted for by corresponding response.The depressing effect of finiteness of population size on the rate of response and the total response appears to increase in geometric proportion with linkages between loci. The number of generations to fixation appears to be reduced in a similar manner. A strong interaction between population size and linkage is thereby found in various analyses. With parental populations as large as 64, linkage effects on response are negligible when recombinations between adjacent loci are .05 or more. In such situations there is a slower rate of response in later generations with linkage but the total response attained and the rate of fixation of inferior genes is about the same as for free recombinations. Increase in the intensity of selection appears to augment the effects of linkage in reducing the rate of response in later generations. This type of interaction is attributed to the accumulation of gametic disequilibria due to selection which are retained in the population over generations with linkage.
Iowa State University, Ames, Iowa.
A W
AW
Qureshi
O
O
Kempthorne
L N
LN
Hazel