| 摘要: |
| 指出von Bertalanffy生长公式的局限性在于公式导出时所用假设“鱼的体重增加量同体重的2／3次方成比例，减少量同体重成比例”的根据不充分；其不足之处在于解方程时将变量l误为鱼的体长。本文作了更为一般的假设，即鱼的体重增加量同体重的p次方成比例；减少量同体重的q次方成比例。进而通过严格的数学推导，得出鱼的更为一般的生长方程w=winfinity [1-e-k (t-t0)]r，使von Bertalanffy生长公式是该方程的特殊情形。 |
| 关键词: 鱼 体重 生长方程 修正 |
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附件 |
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| STUDY ON THE FISH GROWTH EQUATIONI. A MENDMENT TO THE FISH GROWTH EQUATION |
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Zhao Weiqian
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Applied Methematics Department, Ocean Unirersity of Qingdao, Qingdao 266003
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| Abstract: |
| 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. |
| Key words: Fish, Body weight, Growth equation, Mendment |
