Fish Population Dynamic and Stock Assessment

4.1.4.4.2. Estimation of Z by growth and selection parameters (Beverton and Holt equation)

In this method, Z is estimated from the mean length of the fish in the catch and from von Bertalanffy’s parameters ie., L$$\infty$$ and K. Input data for the estimation in this method is less compared to length based linearised catch curve methods.

The equation Z = K* $${L\infty-L}\over{L-L'}$$…………………………………… (1)

$$\overline{L}$$is the mean length of fish of length L’ and longer. While L’ is some length for which all fish of that length and longer are under full exploitation (According to Beverton and Holt, L’ is the smallest length of animals that are fully represented in catch samples). K and L$$\infty$$are von Bertalanffy’s parameters.

The equation is also be used based on length at first capture. This equation could also be written with the following notion. Here, L_C < L’

Hence, Z = K* $${L\infty-\overline{Lc}}\over{\overline{Lc}-L'}$$……………………… (2)

Lc is the length at which 50% of the fish entering the gear are retained and$$\overline{Lc}$$ is the average length of entire catch. When$$\overline{L}$$ and L' are not available, the above equation could be used for estimation of Z (when Lc and$$\overline{Lc}$$ are known). (For calculation of Z, by this method, refer to the Practical Section.