Abstract:
Theoretical Study on Optimal Flock Structure for Poultry Improvement J. A. M ORRIS * AND F. E. B INET * . Lush, in his early papers, (Lush, 1947a, 19473) established formulae for the weights to be given to the performance of an individual and to, the mean performance of its sibs. The weighted sum is then used as a ` selection-index. The weights are such as to maximise the correlation of the index with breeding value of the individual. Lerner (1952, p. 122) points out that Lush' formulae s are equally applicable ` full sibs and half sibs, the genetic relafor tionship, r, being respectively 3 and $. Thus these weights are optimal, when each animal has only full or only half-sibs. When the animal has both, the formulae are still applicable, but for r one must put some value between & and 2, the exact value being determined by the proportion of full sibs to half sibs. Osborne (1957a, 1957b) obtained new formulae from which an index based on the weighted sums of (i) individual performance, (ii) mean of performance of full sibs, (iii) mean of performance of half sibs, can be calculated. Weighted sums calculated by Osborne' formulae are s better indices than those which ignore performance of individuals in previous generations. Inspection of Figure 1 reveals, however, that maximising selection-accuracy is not equivalent to maximising genetic progress per generation. It. is known that the following formula expresses genetic progress per generation, with respeet to a measurable character: fi (1) *Division of Animal Health and Production, Research Centre, Werribee, Victoria. C. S.I.R.O., Poultry 110 In this expression is the additive genetic variability in the flock concerned; c Lo is the selection-pressure (expressed in phenotypic standard measure) exercised bY selecting sires ; is the correlation of the selection index for sires with breeding value ; are analogous quantities for dams. and m obtain a cumbersome, but straightforward mathematical expression, determining A, as a function of the number of sires in the flock, of average number of dams mated per sire, and average number of mature daughters required per dam. This function contains certain constants, which are independent of flock structure: the reproduction rate of females, the additive genetic variance of the breed on hand, the heritability of the character aimed at and the minimum number of sire-families required to avoid inbreeding depression. It can be sh,own that the flock-structure, which maximises selection accuracy, might diminish the two other factors (see Figure 1). Where a flock is kept for purely scientific investigations only, this circumstance can well be ignored; indices maximising selection-accuracy lead towards minimising the variances of the estimates of genetic parameters which might possibly be all the pure scientist is interested in. But, when it is desired to carry out flock-improvement (perhaps with an eye on appZ&~~tions of science) then a compromise is required. The requirements of the three factors (which jointly determine genetic progress in the given situation of constants depending on facts of biology and management only) for possible different flock structures must all be considered to establish the compromise. The mathematical proofs, on which th.e statements contained in this communication are based, are on file with the authors who intend to publish them elsewhere, in the near future. It is intended to seek the co-operation of mathematicians who have access to an electronic computer and thus tabulate values of the required number of sires, dams and offspring for ideal flock structure, for those values of the above mentioned constants, which occur in practice. Thanks are due to Mr. R. T. Leslie, University of Melbourne, for very helpful advice on the mathematical details, in particular R EF ERE NC E S Fisher, R. A. and Yates, F. (1953) .-' Statistical Tables for Biological, Agricultural and Medical Research' 4th Ed. p. 39. . ( Oliver and Boyd : Edinburgh.) Population Genetics and Animal ImproveLerner, I. M. (1950) .-' ment '. (Cambridge University Press.) Lush, J. L. (194% and b ) .-Amer. Nat. 81: 241 and 362. Osborne, R. (1957a) .-Heredity, 11 (1) : 93. Osborne, R. (19573) .-Proc. Roy. Sot. Ed&b. B66: (19) : 374 . 111