A COMPONENT OF VARIANCE DUE TO COMPETITION1

Abstract

Abstract and SummaryThe existence of a component of variance for competition among sampling units or among individuals in a group was discussed by Yates and Zacopany in 1935. No procedure was suggested for estimating this component of variance. It is the purpose of this paper to give a procedure for estimating the component of variance due to competition and to apply the procedure to a set of data on weaning weights of pigs with 116 litters of various sizes and for Yorkshire, Chester‐White, and Berkshire breeds. The first problem was to define litter size. Within this definition then, litters sizes of 3 to 14 pigs per litter were obtained. The variation among pigs within a litter of size h was considered to have an expected value equal to Vs+ Vch where Vs is the sampling variance component and Vch is the competition variance component for a litter of size h. In order to obtain an estimate of Vch, a polynomial relation between h and Vch was postulated. In particular, it was postulated that where E(.) denotes expected value. This form states that Vch goes to zero for one pig per litter; it may be appropriate as long as small litter sizes (say 1 and 2 at least) are omitted from the analysis as was done in the present instance.Using an iterative procedure of reestimating the weights at each stage, a form of weighted least squares analysis was performed. The procedure appears to converge after three to four steps of iteration. Solutions for some or all of the parameters Vp, Vs, β1 and β2 for h even, h odd, and all h = 3, 4, …, 14, were obtained using among litter mean squares, Ah, only, using within litter mean squares, Wh, only, and using both Ah, and Wh values. The Ah values for h = 3, 4, and 5 appeared to form a different group than for the other values of h. Both the Ah and Wh mean squares were from 56 day weights adjusted for birth weight.The maximum value of Vch for odd h, was nine whereas it was six for even h. Using all h the maximum value for Vch occurred when h was equal to nine. It appeared that expressing Vch as a quadratic function of litter size was satisfactory for these litter sizes and mean squares.