| In this paper, it is pointed out that von Bertalanffy’s assumptions that the increase of the fish weight is proportional to 2/3 power of the body weight and the decrease is proportional to the weight have certain limitation and deficencies in the grounds. Meanwhile, it is groudless that the variable “l” in the equation (2) is taken as the body length of fish in solying the equation (2). For this reason, it is put forward that the increase of the body weight of fish is proportional to p power of the weight and its decrease to q power. Their differences induce the growth of fish and the equation (5) is derived:
dw/dt=awp-bwq (5)
In the assumption that the growth curve of the weight against the age is type “S”, another more concrete and more realistic assumptions are made in this study. In the basis of strictly mathematical derivation, the parameters a, b, p, q in equation (5) have the relations: a > b; p < q. When a > b > 0, p < q, 0 < p< 1, the solution of the equation (5) is as following:
Integral sign dz/{a(1-p)-b(1-p)z[(q-p)/(1-p)]}= Integral sign dt (15)
Especially, when q = 1, the solution of the equation (5) is
w=winfinity [1-e-k (t-t0)]r (16)
In the formula (16), r = 3 when p = 2/3, this means that the von Bertalanffly’s supportions are only one special case of the equation (16). So the equation (16) is of universal significance and wide utilization. On the basis of the equation (16), if the parameters are estimated reasonably, the growth law of fish is able to be understanded much better. |
