## BIOLOGICAL GROWTH LAWS

BIOLOGICAL GROWTH LAWS

-APPLICATION TO PRAWNS

SAHIL PERSHAD1and RAJENDRA DHOBAL2

The growth laws of bacteria, populations, and many biological species have been the center of the bio-mathematical studies in the past. Various attempts were made to find a growth/decay law of these living beings and in the history of this kind of studies many derivations have come through. But some of those laws which fit the observations have been put here for computation of the growth of the prawn in aquaculture.

The logistic curve primarily describes the fundamental law of biological growth and supports a great number of such observations. If the length of prawn at a time‘t’ is denoted by Y (t), then law is

(α, β>0)

Where α, β, m are characteristic for a particular species.Thorton (1922) had applied this law for the studies of bacterial colony of B.DENDROIDES. But later other probabilistic models were put forward by Feller and Lotka- kostitzin and they are as follows:

Where all a, b, α, β, m, c, are characteristic constants.

These laws have been applied to the growth of plants also and the height growth with time has been found very satisfactory. Questions which can be studied now are the effect of temperature, turbidity, colour of water, soil and various other parameters on characteristics constants.

(I)

Lotka & Kostitzin law of Growth

For t = 0

For t = 1 unit

For t = 2 unit

For t= 3 unit

For t = 4 unit

For t = 5 unit

(II)

Feller Growth Law

(III)

(IV)

Logistic Growth Law

Aquaculture

Growth of a Prawn

- Age Observed I II III IV

0 0.24 0.25 0.07 0.57 0.37

1 2.78 2.03 1.86 2.82 2.51

2 13.53 13.08 13.82 13.86 13.62

3 36.30 37.05 36.06 36.60 36.30

4 47.50 47.39 47.70 47.14 47.42

5 49.40 49.02 49.40 49.40 49.55