Fish Population Dynamic and Stock Assessment

6.1.3.2. Fox model

This model gives a curved line when ‘Y/f’ is plotted directly on ‘f’. But a straight line is obtained when the logarithms of ‘y/f’ are plotted on effort.

Ln [y(i)/f(i)] = c+ d *f(i) .......................................................... (2)

The above equation could also be written as

Y(i)/f(i) = exp. (c+d *f (i))

Schaefer model plot on ‘Y/f’ on ‘f’ gives a straight line and in Fox model plotting of ‘Y/f’ on ‘f’ gives a curved line which approaches zero only at very high levels of effort without ever reaching it.

The figure depicts another basic feature of the two models. When effort (f) is close to zero, ‘Y/f’ takes the maximum value and also the biomass, because Y/f = q. B and ‘q’ is constant. The biomass corresponding to f = 0 is called virgin biomass or the unexploited biomass. This is denoted by ‘Bv’. In the equation of Schaefer and Fox, the ‘Y/f’ can be replaced by ‘q’. ‘Bv’. as follows:

q * Bv = a or Bv = a/q (Schaefer)

q * Bv = exp. (c) or Bv = exp.(c) / q. (Fox)

In both models, the unexploited biomass (Bv) is the same. When the effort (f) is increased to level of A (see above Fig.), the two curves (Schaefer and Fox curves) are approximately equal. But increasing the effort to the right of A, the differences become larger. Thus, one can use any one model and it becomes important only when relatively large values of ‘f’ are reached.