The growth cessation model: a growth model for species showing a near cessation in growth with application to bigeye tuna (Thunnus obesus)

Abstract

We present the growth cessation model, which is designed for species, such as some tropical tunas, that have an apparent linear relationship between length and age, followed by a marked reduction of growth after the onset of sexual maturity. The growth curve simply assumes linear growth for the youngest individuals and then uses a logistic function to model how the growth rate falls to zero at greater ages. One characteristic of the model is that, as t → 0, the model converges to a linear regression. The range of ages for which a linear regression adequately represents the mean length at age depends on when the logistic function becomes influential. A beneficial characteristic of this model is that, unlike other growth models, a preponderance of younger fish may not overwhelm the information from older fish, which biases the estimates of mean length at age for older fish. We apply the growth curve to bigeye tuna (Thunnus obesus) data from the eastern Pacific Ocean, obtained from otolith daily increment counts and tagging experiments, and compare the results with those from the von Bertalanffy and Richards growth curves. The growth cessation model fits the eastern Pacific Ocean bigeye tuna data better than do the von Bertalanffy and Richards growth curves. These results support the use of the growth cessation model for bigeye tuna in the eastern Pacific Ocean, and since many species have growth curves that flatten out to the point where growth is almost undetectable, this indicates that the growth cessation model may be widely applicable.