Ratios as criteria for selection in animal or plant breeding, with particular reference to efficiency of food conversion in sheep

Abstract

Ratios are frequently advocated as criteria for selection, in either animal or plant breeding; for example, production per unit of food eaten is currently receiving attention, particularly with Merino sheep. Clean wool weight per head (W) is already widely used as a selection criterion, but suggestions have been made that wool weight per pound of body weight (B) or per unit skin area (estimated as B^0.6, or measured) should be used instead, as estimates of the efficiency of conversion of food into wool. This paper develops formulae for writing the heritability of any ratio, as well as its genetic correlations with its numerator and its denominator, in terms of the relationships between the numerator and the denominator. From these formulae the likely result of selecting for the ratio can be predicted, for a given range of values of the genetic and phenotypic parameters of the numerator and denominator. The formulae can be used for any ratio, provided gene x environment interactions and epistasis can be neglected. In particular, it is shown that the genetic correlation between W and W/B or W/B^0.6 is consistently positive for a wide range of values of the parameters of W and B, so that selection for high wool weight will also increase efficiency, as measured by either ratio. The genetic correlation between B and W/B or W/B^0.6, on the other hand, is nearly always negative, sometimes very strongly so, and selection for high values of W/B or W/B^0.6 will decrease body weight. The theoretical predictions are confirmed by results from experimental selection groups, in which the observed correlated responses are all in the predicted direction, and in most cases agree well in magnitude. It is suggested that more information is required on the importance of body size itself, in relation to factors such as fertility and survival, before the value of selection on W/B or W/B^0.6 can be accurately assessed.