Basic Growth Models

Fish growth models can be divided into two categories. The first category includes statistically based models for fish growth. The models of this type often assume that growth is a function of the current body size of the individual, and they ignore or have only a loose connection to the biology behind the actual growth processes. A handful of different statistical models are available that fit empirical data quite well: for example, the Logistic, Gompertz, Monomolecular, and Richards growth models (Table 1). As discussed later, most uses of the von Bertalanffy growth model should also be classified as statistically based. In some applications, correlations with quantifiable physical or biological variables, such as temperature or food availability, may be built into parameters of the statistically based models.

The second category is mechanistically based growth models, derived from the biological processes that govern growth. Most often they include considerations about bioenergetics (the acquisition of energy and its use for all the processes that are underway in an organism) and how these scale with body size. These models may refer explicitly to processes that rely on temperature, body size, or food availability, and can thus be predictive and more nuanced than the statistical growth models. Mechanistically based models also have the advantage that as we learn more about the physiological and ecological processes, in general or for a particular species, this

Table 1 Statistically based models for fish growth

Growth model

Growth function f(W)

How is growth rate related to weight?

Logistic

K(1 - W/W1)

Growth rate linear function of W

Gompertz

K{lnW^- lnW)

Growth rate linear function of ln W

Monomolecular

K[(W1/W) -1]

Growth rate rectangular hyperbolic function of W

Richards

[1 - (W/ Wi)"]k/n

Growth rate linear function of Wn

Growth is a function of body weight (W); k, n, and are constants.

From Wootton RJ (ed.) (1998) Ecology of Teleost Fishes, 2nd edn., table 6.2, p. 132. Dordrecht: Kluwer Academic Publishers.

Growth is a function of body weight (W); k, n, and are constants.

From Wootton RJ (ed.) (1998) Ecology of Teleost Fishes, 2nd edn., table 6.2, p. 132. Dordrecht: Kluwer Academic Publishers.

knowledge can be built into the model to improve it. Although mechanistically based models are better for understanding and predicting growth, their use has been limited because they require more biological understanding and parameters that can be difficult to quantify. When the processes or parameters are uncertain, there may be good reasons to prefer a statistically based model.

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