# Mathematical Junctions of growth in elephants

There are several mathematical expressions that can represent the growth in body size of an animal. A polynomial function, for instance, can provide a purely empirical fit to growth data, but lacks analytical capability. Two sets of functions, the Gompertz functions and the von Bertalanffy functions, have been extensively used to study growth in vertebrates. The von Bertalanffy functions, in particular, are considered particularly suitable for representing growth in elephants.

The general form of the von Bertalanffy function is

where St is the size at time t, S« is the asymptotic size (the maximum an animal can attain), K is the coefficient of catabolism (a fitted constant representing the catabolism of body materials per unit weight and time), t is the age of the animal, t0 is the theoretical age at which the animal would have zero size (this constant is usually an artificial one), and M is the power of the function.

For growth in body length or height, the equation used is

Lt = L. (1 - exp-K(t-t0)) The cubic form of the function best represents growth in body weight:

The von Bertalanffy functions have been applied to aspects of growth in several African savanna elephant populations and in one Asian elephant population. I provide the growth parameters from each of these populations, along with supplemental information on allometric relationships for variables such as height-weight, height-foot dimensions, tusk growth, and so on.