Fish Population Dynamic and Stock Assessment

3.2.5. Estimation of growth parameters for Elasmobranches

The growth parameters of Elasmobranches

Lt = L $$\infty$$ [1 – e ^{-K (t - to)}] ............................................... (1)

This equation can be modified as

Lt + T - Lt = (L$$\infty$$ - Lt)(1 - e ^{- KT}) ................................. (2)

(i.e. Lt + T/L $$\infty$$ = 1 - e ^{- KT}) ........................................... (3)

Where

Lt = Length at conception = 0 at zero time;

Lt +T = length at birth;

T = length of gestation or hatchery period (the elasmobranches being viviparous,

ovoviviparous or oviparous, with the egg taking a long time to hatch).

L $$\infty$$ = maximum observed length, i.e., Lmax.

Since there is evidence that ‘T’ is exactly the value of t₀ in Eq.(1) or its modification, Eq.(2) could also be expressed in the form,

Lo = L $$\infty$$ (1- e ^{- K/(o – t}₀⁾) ................................................ (4)

Where, Lo = length at birth, (Lt + T) corresponding to O age, and t₀ = gestation or hatching period in years. Since Lo, t₀ and Lmax (= L $$\infty$$ ) in the above equation can be empirically recorded, the only parameter to be computed is K.

Once this is made, age for any given length can be estimated by incorporating K, t₀ and Lmax values in the equation (1)