Relation between the Sardine and the Food Plankton-III

YOSHIDA Yoichi

doi:10.2331/suisan.21.1007

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イワシとその食餌プランクトンとの関係-III
イワシトソノショクジプランクトントノカンケイ 3
On the Growth Curve of Sardinops melanosticta
マイワシの生長曲線について

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Previous investigations have shown that the quantity of the plankton fed by the sardine is nearly proportional to the square of body length and that the straining velocity for plankton is proportional to the surface of the gill-rakers of the sardine. In this paper, using these results and assuming that the sardine follows the proportional growth, I tried to obtain the growth curve of the sardine. Since the energy e₁ taken by the sardine is proportional to surface, if the energy consumed by Maintenance Metabolism (e₂), Work Metabolism (e₃) and Reproduction Metabolism (e₄), except Growth Metabolism (e₅), is proportional to weight, or is divided into two parts, viz. one is proportional to surface and the other to weight, the change of the body weight w of the sardine is given by: dw/dt=e₅/δ=1/δ(e₁-e₂-e₃-e₄)=1/δ(βw^2/3-γw). In words : e is the taken or consumed quantity per unit time of the free energy which is used by the sardine; δ is the energy per unit weight used for construction of the increased portion of body, and δ=e₅/w', when w' is the increased weight per unit time of body; δ, β and γ are constants. Therefore, I could obtain “Exponential-type Curve” as the linear growth curve and “Sigmoid Curve” as the weight growth curve. Although these formulae have been proposed by B_ERTALANFFY trying to establish relations between growth and total metabolism, there are some differences in the interpretation. For instance, I have used the free energy as indicator, by introduction of the conception of δ, as mentioned above.

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