A Genetic Investigation of Allometric Growth in Hereford Cattle.

IOLOGISTS have long directed attention to problems relating to the B determination of quantitative measures of body conformation and the genetic factors responsible for variation in conformation. Such variation in conformation hetween individual aninials within a species is due to differences in the relative proportions of the various parts to each other and to the animal as a whole. D’ARCY p t k o M P s o N (1917) pointed out that all but the simplest organisms reach their adult form by differential growth in different directions. Variation in conformation is the result of differences in relative growth rates of the various dimensions. A study of relative growth, or allometry, offers an approach to the problems of conformation. liamifications arising from the simple expression relating the size of a part to that of another part or the whole have been studied by investigators in the fields of theoretical and applied 1)iology. Jn the present discussion reference will he made to a number of these investigations, most of which have heen critically reviewed by REEVE and HUXLEY (1945), MEDAWAR (1945), and RICHARDS and KAVANAGH (1945). The basic allometric relationship is that expressed by the equation y = bxa in which y represents a part, x another part or the whole, and b and a are constants. The equation is either a paralmla or hyperbola, depending on whether a is positive or negative. In logarithmic form the equation I)ecomes log y = 3 log x -Ilog 11, or Y = I< i-a S, where Y = logy x = log x K = log 1, Thus in logarithtnic forin the allometric eqciation is that of a straight line with slope n a n d Y intercept K. Altlwugh the allometric equation had been used previously to express I~raiti weight/body weight relations in nianinials ( SNELL 1891 and DUBOIS 1898, 1914) and birds (IAPICQUE 189s) as well as heart-body-weight rela-