Fish Population Dynamic and Stock Assessment

4.2.3.1. Pauly’s empirical formula

Natural mortality in fishes can also be correlated to mean environment temperature. The interrelationships can be expressed for length growth data by the multiple regressions as below:

For length-growth data

log₁₀^M =$$ -0.0066 - 0.279$$ log₁₀ L$$\infty$$+ 0.6543 log₁₀K + 0.4634 log₁₀^T

For weight – growth data

log₁₀^M = - 0.2107 - 0.0824 log₁₀ w$$\infty$$ + 0.6757 log₁₀K+ 0.4687 log₁₀^T

‘M’ is the natural mortality in a given stock, ‘L$$\infty$$ ’ (total length in cm) and ‘W$$\infty$$ ’ (live weight in g) being the asymptotic size of the fishes of that stock and ‘K’ the growth co-efficient. The value of ‘T’, is the annual mean temperature in ºC of the water in which the stock is found.

The above two equations give reasonable estimate of ‘M’ for about any set of growth parameters and temperature value. However for certain schooling pelagic fishes particularly for clupeoid fishes, the ‘M’ is generally overestimated by the above two equations. In such cases, it might be appropriate to reduce the estimate of ‘M’ by multiplying K by 0.8 (Pauly, 1983).

The equation should be avoided for crustaceans and molluscs or any other invertebrates. Pauly’s formula does not cover these groups.