A simple and precise method for fitting a von Bertalanffy growth curve

Abstract

The parameter K of the von Bertalanffy equation, as developed by Beverton and Holt (1957), is first estimated by the relation

$$\log _e \left( {dL_t /dt} \right) = A - Kt$$

where dLt/dt denotes growth increments per a unit of age, t denotes age, and A is a constant. The K estimate is used to evaluate L∞;

$$L_\infty = \left( {e^K \sum\limits_2^n {L_t - \sum\limits_1^{n - 1} {L_t } } } \right)/\left( {n - 1} \right)\left( {e^K - 1} \right)$$

The L∞ estimate is used to estimate t _o, and to obtain a better estimate for K;

$$\log _e \left( {1 - L_t /L_\infty } \right) = - Kt + Kt_0 $$

The K estimate may be used to obtain another estimate for L∞. Solved examples show that a single iteration is sufficient to obtain fitted equations which are, on the average, as precise as equations fitted by the least squares method shown by Tomlinson and Abramson (1961). This new method can be used, with a slight modification, for the second equation given above, if growth data have unequal age intervals. The variance of K, t _o and log _e L∞ can be estimated by applying the simple methods used in the case of straight-line relationships.