Fish Population Dynamic and Stock Assessment (2+1)

Problem: 1

Estimate the M and q using the following data.

L $$\infty$$= 29 cm, K=1.12/yr, $$L^'$$ =7.6 cm

Z is estimated for Beverton and Holt equation as Z= $$K\cdot{{{L\infty}-L}\over {L-L^'}}$$

Tabulate the readings

Sl.No.	Effort  in units of million of trawling hours (x)	Mean length $$\overline{L}$$	Z=$$K\cdot{{{L\infty}-L}\over {L-L^'}}$$(y)	xy	x2
1.	2.05	15.5
2.	2.10	16.0
3.	3.52	13.05
4.	3.60	13.10
5.	3.75	12.50
6.	7.23	12.20
7.	10.01	11.93
8.	5.85	12.58
Total

From the equation, Z = M + qf; where ‘q’ is the catchability coefficient or proportionality coefficient.

The slope of the straight line gives the values of ‘q’ that is b=q and ‘y’ intercept (a) gives the values of M. ie a = 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 cases, one makes an estimate of M and then forces the regression line to have an intercept equal to M.

Using Pauly’s empirical formula, M could be estimated if L$$\infty$$ , K and T the annual mean temperature (in ^oC) of the water in which the stock in question lives is known.

Problem: 2

Estimate M - in given stock using L$$\infty$$ = 30.1, K = 0.7 and T = 30ºC using Pauly’s empirical formula.

Problem: 3 (Rikter & Efanov’s formula)

Estimate ‘M’ in a fish stock living in water mass with temperature of 28.5ºC and another population living in the water mass with a temperature of 31ºC. The W $$\infty$$ =1300 gm and K = 0.632.

Rikhter and Efanov’s formula

Rikhter and Efanov (1975) showed a close association between M and Tm 50% the age when 50% of the population is mature (also called the age of massive maturation)

M = 1.521 / (Tm 50%^0.720 ) – 0.155 per year

Tm 50% is equal to the optimum age defined as the age at which the biomass of a cohort is maximal.

Problem: 4

When 50% of the population of a given fish stock mature at age group of 3, estimate ‘M’ using the above formula.

Fishing Mortality

When Z and M values are obtained ‘F’ could be estimated by

F = Z - M

In a fully exploited stock, Z = F as M is negligible and in unexploited stock, estimate of Z is an estimate of M.