Fish Population Dynamic and Stock Assessment

4.2.3. Estimation of ‘M’

When values of ‘Z’ are available for several years pertaining to different annual values of effort (f), the value of ‘M’ can be calculated from

Z = M + qf

Where (q) is the ‘catchability coefficient’ or ‘proportionality coefficient’, which relates fishing effort (f) and fishing mortality (F). The fishing mortality (F) is almost always assumed to be proportional to effort and is mathematically expressed as,

F = q* f

The more efficient the gear is, the higher the value of ‘q’ because ‘q’ is the measure of the ability of the gear to catch the fish.

When series of ‘Z’ (mean annual) values are plotted against their corresponding values of ‘f’, a straight line can be fitted to the points by means of linear regression technique. This results in a regression line with the equation

y = a + bx

The slope of the line is an estimate of ‘q’ and the ‘y’ the intercept is an estimate of ‘M’. Sometimes, a regression line fitted to data of this type will give an estimate of ‘M’ which is negative. But ‘M’ cannot be negative. In such case, one makes an estimate of ‘M’ and then forces the regression line to have an intercept equal to ‘M’.

If only one value of ‘Z’ and ‘f’ are available, or when there are only few values of ‘Z’ and ‘f’ are available, reasonable values of ‘M’ and ‘q’ could be obtained. In such case, the ‘q’ is estimated through

q=$${\overline{z}-m} \over \overline{f}$$

Where ‘$$\overline{z}$$ ’ is the mean of the available values of ‘Z’ (or a single value of Z) and ‘$$\overline{f}$$ ’ is the mean of the values of ‘f’ (or a single value of f), ‘M’ being an independent estimate of Natural mortality.