A stochastic model of animal growth

The plasticity of growth of animals in time, due to the resilience of their response to the ways they can be fed, suggests the difficulty of describing growth by a stochastic model in the time domain. A model is presented which avoids this difficulty by describing growth as a Markov process in the food-consumed domain, assuming that, at conception, (1) the maximum mature weight as a number α of biomass units of mass μ, and (2) the probability B of production of a biomass unit per unit of food consumed, are specified. Constancy of α, μ and B, as the animal feeds, is the basis of the proposed Markov process. The mean growth from infancy to maturity in the food-consumed domain is then the old law of diminishing returns empirically formulated first by Spillman (1924) for cattle and swine, and confirmed by Titus, Jull &; Hendricks (1934) for fowl, and by Parks (1972) across species from mice to steers. The solution also leads to the possibility that the distribution of weights in a population of growing animals of the same species, is related to the distribution of mature weights among the individuals. An experiment by Lister &; McCance (1967) with well-fed and severely undernourished pigs, shows the stability of growth in the foodconsumed domain compared to the plasticity in the time domain. Other implications of the model are discussed.