The Von Bertalanffy Growth Curve and Its Application to Capture -- Recapture Data in Fisheries Biology

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Abstract
Other commonly used approaches involve the graphical estimation of growth parameters by plotting the length at recapture, Li, against the length at release, Li–1, from the same individual. For the time interval di between recaptures, a straight line with slope exp [−kdi] results. However when di is varying, a non-linear function is obtained and an iterative solution isrequired. When the time interval di is small compared with the total life of the animal the plot of ength against time may be assumed linear within these intervals. The length of the animal at some fixed time interval tf can be estimated by linear interpolation. The resulting plot of estimated length at time tf after release against length at release gives a straight line with slope exp [−ktf]. Alternatively, differentiation of the Von Bertalanffy growth equation shows that the derivative of the length with respect to time is a linear function of the length at release. For small time intervals between recaptures this derivative is given by the increase in length from release to recapture divided by the corresponding time interval. The regression of this derivative on the length at release gives a straight line with slope −k. These methods give similar results to those obtained from the direct fitting of non-linear models to data in capture-recapture form.

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