J Austral Math Soc Ser B 38 pp477--488, 1997.
(Received 21 February 1995; revised 17 July 1995)
The allometric hypothesis which relates the shape (y) of biological organs to the size of the plant or animal (x), as a function of the relative
growth rates, is ubiquitous in biology. This concept has been especially 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 differential
equation, with a solution different from that of the deterministic equation normally used to describe allometry. This is important in studies of
carcass composition where animals are slaughtered in different 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 applications of the allometric hypothesis such as the study of the development of carcass composition
in domestic animals by serial slaughter. The change in the estimates of the coefficients of the allometric equation found through the usual
deterministic 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 regression equation is shown to produce unbiased estimates of the parameters when the errors can be assumed to be
multiplicative.
The consequences of stochastic size variables in the study of carcass composition are discussed.
Last Modified: Mon Dec 10 17:04:52 2001