Bulletin of Mathematical Biology Vol. 55, No. 3, pp. 609~35, 1993. Printed in Great Britain. 0092 8240/9356.00+0.00 Pergamon Press Ltd 9 1993 Society for Mathematical Biology COMPARATIVE KINETICS OF EMBRYO DEVELOPMENT C. ZONNEVELD and S. A. L. M. KOOIJMAN Department of Theoretical Biology, Vrije Universiteit, De Boeblaan 1087, 1081 HV Amsterdam, The Netherlands ( Email :cor@b io.vu.nl) A model of embryo energetics was fitted to data from the literature for species as different as snails and mammals. The model is based on assumptions about energy uptake, storage and utilization. It describes the animal by two state variables: volume and energy storage. Embryo weight is taken to be proportional to volume, yolk weight to energy storage, and respiration rate to storage utilization rate. The fits were good, with minor deviations occurring only in the early phases of development. For altricial birds, good model fits were obtained, but the parameter values markedly differed from those of other species. We hypothesized that, due to an increase in energy utilization towards hatching, the temperature of the embryo increases. As a result, metabolic processes are accelerated. When this was taken into account, parameter values were obtained that correspond better with those of other animals. 1. Introduction. The description of quantitative aspects of embryo development has long captured the scientific imagination. This can be easily understood. Embryos show a huge increase in size, relative to the initial condition. Moreover, there is no variability due to food intake, since they have to rely on stored energy and building materials. These characteristics make them particularly promising systems for the study of size-dependent processes such as growth and energy utilization. Data on embryonic growth and respiration are often described with simple mathematical expressions. Examples are the logistic equation (growth and respiration rate in turtles, e.g. Ackerman, 1981a,b; and also for birds, Pettit and Whittow, 1983), the Gompertz equation (growth in avian and mammalian embryos, Laird, 1966) and the allometric equation (growth in bird embryos, Ricklefs, 1987). Except for the explanation offered by Payne and Wheeler (1967) for mammalian growth, these formulae are descriptive only, and lack a biological justification. Kooijman (1986a,b; 1988) has developed a dynamic energy budget (DEB) model, based on assumptions about energy uptake, storage and utilization. The model aims to explain physiological processes such as growth and reproduction in feeding animals. It describes the animal by two state variables, namely volume 609