## Growth of Individuals

Growth is of interest both as the mechanism by which fish add weight (thus increasing the stock's biomass) and because growth is the link between size and age. The most common growth model is the von Bertalanffy model of length at age (henceforth, VBGF):

where La is length at age a; model parameters are LK (asymptotic length), k (growth rate), and a0 (theoretical age at length zero). This model fits most observed data on fish growth reasonably well, especially when the youngest ages are excluded.

The relationship between fish weight (W) and length (L) is commonly modeled with the allometric function

where g and b are constants. Weight would be expected to be proportional to body volume, and indeed in most data sets, it is found that b « 3. (We use the notation x throughout to refer to an estimate of quantity x.)

Equations [2] and [3] can be combined to form a model of weight at age:

Here, Wm = g(L1)b is the asymptotic weight of a fish; other parameters are as in eqns [2] and [3].

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