Fish Population Dynamic and Stock Assessment (2+1)

Problem

Estimate the growth parameters using Bagenal’s least square method using the following data.

Age (years)	Length (Lt)
1	44.13
2	60.89
3	76.87
4	90.31
5	100.11
6	105.72
7	114.24

Estimate K and $$L_\infty$$

t	t-tₒ	$$e^{-k(t-t_0}$$	$$1-e^{-k(t-t_0)}$$	$$L^\infty (1 - e^{-k(t-t_0)})$$	$$Lt = L_\infty (1-e^{-t(t-t_0)})$$

Reasonable values of $$L_\infty$$ can generally be obtained from the empirical relation

$${Lmax \over 0.95} = L_\infty$$

Where Lmax is length of the largest fish reported form a well sampled stock.

A length estimation of tₒ can also be calculated from the empirical relationship(Pauly, 1983)

$$\log_{10}(-t_0)=-0.3922-0.2752 \log_{10} L_\infty = -1.038 \log_{10} K$$