Study of half-sib correlations and parent-off spring correlations under half-sib mating system

Abstract

A purely theoretical investigation entitled ’ a study of half-sib correlations and parent-off spring correlationsi under half-sib mating system was carried out with the following objectives. i) to derive the joint distribution - correlation table as well as the correlation of half-sib pairs under different generations of half-sib mating, in the case of autosomal genes, assuming single locus with two alleles. ii) to derive the joint distribution - correlation table as well as the correlation of parent-off spring pairs under different generations of half-sib mating, in the case of autosomal genes, assuming single locus with two alleles. iii ) to derive the joint distribution - correlation table and the correlation between both the parents and several offspring as well as the correlation between one parent and several offspring under different generations of half-sib mating, in the case of autosomal genes, assuming .single locus with two alleles. iv) to derive the joint distribution - correlation table as well as the correlation of the different ’ half-sib pairs, viz ., brother-sister, brother-brother and sister-sister and also the correlations of different parent-off spring pairs, viz ., mother-daughter, mother-son and father-daughter, in the sex-linked gene case. As the generation matrix of half-sib pairs is too tedious to derive, the Joint distribution of half-sib pairs, both in the autosomal gene case and sex-linked gene case, was derived from fir s t principles and the correlation was calculated from the correlation table, assuming additive genic effects and by using the product-moment correlation coefficient formula. The correlations were worked out for the first ten generations of half-sib mating. The Joint distribution of parent-offspring pairs under half-sib mating system, both in the autosomal gene case and sex-linked gene case was derived by using the generation matrix approach. Here also, the correlations were worked out for the fir s t ten generations of half-sib mating. A comparative study of the half-sib correlations and parent-offspring correlations, conducted both numerically and graphically, revealed that even though the half-sib correlations are of lower order than parent-off spring correlations, the rate of Increase in the former is much higher than the rate of increase in the latter.