An Asymptotic Growth Model Allowing Seasonal Variation in Growth Rates, with Application to a Population of the Cascade Frog, Rana cascadae (Amphibia, Anura, Ranidae)

Abstract

An asymptotic growth model is applied to the individual growth of Rana cascade from the Oregon Cascade mountains. The model fits anniversary dates well but the growth is not uniform during the active period each year. The frogs grow slowly early and late in the season when food is more scarce and temperatures are lower. They grow more rapidly during the mid season. A regression model is developed to account for the growth variability and the combined model is used to estimate mean individual growth. Once yearly growth is estimated, age classes can be established and age distribution estimated in studies of population ecology. * * * are desirable (reviewed by Turner, 1960b) for then length can be used as an estimate of age. When animal populations can be broken down into age classes, life tables can be constructed and much can be learned about the structure and dynamics of the population (Deevey, 1947). The development of the present growth model arose from a field investigation of the cascade frog, Rana cascadae. A survey of the literature on frog growth shows that in all cases growth of younger frogs is much more rapid than that of older frogs. The plot of length against age is approximately asymptotal with variations in rate during different parts of the growing season (Turner, 1960a, b; Martof, 1955). This seasonal variation is probably due to the low temperatures and lack of food immediately before and after hibernation (Martof, 1955). The asymptotic regression curve has been used to describe growth in many different kinds of animals (Fabens, 1965; Riffenburgh, 1966; Stevens, 1951; Walford, 1946) and the difference equation presented by Walford was used to develop a growth model for R. cascadae. The model allows estimation of mean annual growth and mean seasonal variation for each age class by means of standard measure-remeasure data. A rough check can be made of the growth data to see if it represents an asymptotic curve by the method of Walford using a few selected data. This method can also be used to estimate the mean asymtotic length of the individuals in the population.