THE ALLOMETRIC HYPOTHESIS WHEN THE SIZE VARIABLE IS UNCERTAIN - ISSUES IN THE STUDY OF CARCASS COMPOSITION BY SERIAL SLAUGHTER

The allometric hypothesis which relates the shape (y) of biological or gans to the size of the plant or animal (x), as a function of the rela tive growth rates, is ubiquitous in biology. This concept has been esp ecially useful in studies of carcass composition of farm animals, and is the basis for the definition of maintenance requirements in animal nutrition. When the size variable is random the differential equation describing the relative growth rates of organs becomes a stochastic di fferential equation, with a solution different from that of the determ inistic equation normally used to describe allometry. This is importan t in studies of carcass composition where animals are slaughtered in d ifferent sizes and ages, introducing variance between animals into the size variable. This paper derives an equation that relates values of the shape variable to the expected values of the size variable at any point. This is the most easily interpreted relationship in many applic ations of the allometric hypothesis such as the study of the developme nt of carcass composition in domestic animals by serial slaughter. The change in the estimates of the coefficients of the allometric equatio n found through the usual deterministc equation is demonstrated under additive and multiplicative errors. The inclusion of a factor based on the reciprocal of the size variable to the usual log - log regession equation is shown to produce unbiased estimates of the parameters when the errors can be assumed to be multiplicative. The consequences of s tochastic size variables in the study of carcass composition are discu ssed.