Modelling the ontogeny of ectotherms exhibiting indeterminate growth

Numerous growth functions exist to describe the ontogeny of animals. Such functions (e.g., von Bertalanffyʹs equation, thermal-unit growth coefficient) are currently applied to ectotherms even though they fail to provide analytical expressions that adapt to a wide range of fluctuating temperatures. The underlying mechanisms responsible for the ontogeny of ectotherms exhibiting indeterminate growth have not yet been summarised in terms of a simple but meaningful mathematical equation. Here, a growth function is developed, with parameters having physical or biological interpretation that accommodates indeterminate growth under fluctuating temperatures assuming the latter vary seasonally. The equation is derived as a special case of von Bertalanffyʹs equation providing realistic growth trajectories throughout the ontogeny of several groups of ectotherms (R2>0.90). The results suggest that the effect of temperature on growth trajectory supersedes that of reproduction in an environment with fluctuating temperature. Furthermore, values of the allometric weight exponent (0<b<0.75) indicate that the rules of body surface and body weight do not apply under certain circumstances. Finally, the growth function circumvents problems associated with models based on thermodynamic and chemical kinetic principles (e.g., inability to predict growth of organisms in which ontogeny exceeds 3 months) and on rule of thermal summation (e.g., reliable only in a certain range of temperature). The growth function can handle a wide range of temperature fluctuations, encompass life stages and apply to key organisms in ecology, fisheries and agriculture.