Fish Population Dynamic and Stock Assessment

3.2.4.1. Gulland and Holt Plot

The linear relationship could be derived from VBGF equation - cm/year

$${\triangle L \over \triangle t } = K^\ast [L_\infty - L(t)]$$...........................................(1)

This equation can be written as $${\triangle L \over \triangle t}= K^\ast L_\infty - K^\ast {\overline{L}}(t)$$ …………… (2)

(The length “L(t)” in the equation (2) represents the length range from Lt at age ‘t’ to $$L(t) \ + \triangle t \ at \ age \ t + \triangle t$$).

The mean length equation $${\overline Lt} = { L(t) + \triangle t + L(t) \over 2}$$ goes as an entry data in Gulland Holt plot.

Using $${\overline(L)}(t)$$ as the independent variable and $${ \triangle L \over \triangle t}$$dependent variable and above equation (equation 2) becomes linear function.

$${\triangle L \over \triangle t}= a+ b^\ast {\overline{L_t}}$$ .......................................................(3)

The growth parameters K and $$L_\infty$$ are calculated by using the formula

K = -b and $$L_\infty$$ = - a/b

In Gulland and Holt Plot, the input data are‘t’ and ‘L(t)’.

L(t) and $$\triangle L(t)$$ are calculated between the successive ‘t’ and ‘ $$\triangle t$$’ respectively.

$${\overline{L_t}} = { L (t+\triangle t) + L_t \over 2} \$$ is taken as ‘x’ variable

$${ \triangle L(t) \over \triangle t} \$$ is taken as ‘y’ variable.

Using the regression equation (y= a = bx), the K is determined by K=-b and $$L_\infty =-a/b$$.

A graph can be drawn by taking mean length as ‘x’ axis and $${\triangle L \over \triangle t}$$in ‘y’ axis. (Problem is given in practical section)

The Gulland and Holt equation is reasonable only for a small values of $$\triangle t$$