Application of hierarchical biphasic growth models to long-term data for snapping turtles

Somatic growth rates are critical to the population dynamics of long-lived ectotherms. While the von Bertalanffy (VB) growth curve has been used extensively to model growth of such animals, the conventional form of the model fails to account for individual variation or for changes in resource allocation after sexual maturation. Bayesian modelling has recently been used in fisheries research to fit a modification of the VB model that is both hierarchical (allowing individual variation in growth parameters) and biphasic (allowing an age-specific change in growth rate). We extend this approach by developing a range of hierarchical biphasic models allowing a size- rather than age-dependent change of one or more growth parameters in one or both sexes. We applied the approach to a long-term data set of growth measurements for snapping turtles (Chelydra serpentina), as data on nesting status show females begin nesting predictably at about 24cm carapace length. The data consisted of 1996 carapace-length measurements taken from 1972 to 2005 in Algonquin Park, Canada, from 317 individual turtles. These included 24 turtles of known age, most of which were juveniles of unknown sex, and 293 turtles of unknown age, most of which were adults of known sex. The modelling revealed substantial individual variation in both the asymptotic size (a) and growth rate (k) parameter, and clear evidence of biphasic growth. The model that best explained the data (based on DIC) was that males and females grow similarly until they reach 24cm, after which females shift trajectory towards a reduced asymptotic size target. The number of years taken to reach 24cm was estimated to range from 11 to 44 years in 95% of individuals, with asymptotic size ranging from 38.2 to 40.9 in males and 31.0 to 33.6 in females. Our approach is applicable to a range of long-lived ectotherms likely to have size-dependent biphasic growth, and provides essential information for modelling the long-term dynamics of populations under threat.