Allometry and multivariate growth revisited

Turner (1978) introduced a class of deterministic models to describe multivariate growth processes along with a least squares fitting procedure. Turner's fitting procedure is shown to be ill founded and the methods of inference associated with it dangerously misleading. An alternative class of stochastic models is introduced; this is largely based on Turner's generalization of allometry and the Lotka-Volterra equations. The associated fitting procedure is the method of maximum likelihood which allows valid inferences to be made. As an example of the superiority of this new class of models in describing multivariate growth processes one of the data sets analysed by Turner is reconsidered here. Some general comments are made on Turner's analysis of the famous lynx and hare data.