Bertalanffy Curve Research Articles

The growth pattern of the African tortoise Geochelone pardalis and other chelonians

Growth rings were measured in dead African leopard tortoises, Geochelone pardalis, collected in the seasonal tropics of Zimbabwe over an 11-year period. A series of Ford-Walford plots using growth measured from annuli showed that growth fitted a logistic by mass curve best, logistic by length and Gompertz curves less well, and a Bertalanffy curve least well. The Bertalanffy curve, often fitted to growth of chelonians, is characterised by particularly high growth rates of juveniles compared with larger individuals. It is suggested that this growth pattern is likely to be found in species showing a marked decrease in diet quality with size. This hypothesis is supported by a review of growth patterns in chelonians: Bertalanffy curves are associated with an omnivorous (and thus potentially variable) diet and other growth patterns with an obligate carnivorous or herbivorous diet. Geochelone pardalis in Zimbabwe showed significant sexual size dimorphism, the mean asymptotic mass of females being 1.7 times that of males, unlike populations with larger body sizes to the north and south. Annual survival estimated from age-frequency distributions was significantly higher in males (0.80) than in females (0.72), the difference being sufficient to account for the male-biased sex ratio of live animals.

Do Bertalanffy's growth curves result from optimal resource allocation?

Bertalanffy's equation is commonly used to model indeterminate growth. Bertalanffy claimed that this growth pattern results from growth potential decreasing with age. An alternative approach provided by life history theory predicts that indeterminate growth is optimal for organisms in a seasonal environment and results not from decreasing growth potential but from allocating increasingly less energy with age into growth, and more into reproduction. Bertalanffy's curves are the result of evolutionary optimization and should not be used in optimization models as an assumption, but they can be used as a tool to describe the indeterminate growth pattern phenomenologically.