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As to theoretical models of prey-predator relationships among fishes, VOLTERRA's differential equations are well-known. Nevertheless, there are a great deal of criticism that those equations cannot stand for real circumstances of community of fishes or animals. But as the equations are convenient to examine the community problems of fishes, discussions about the equations are now often presented. This report is a trial to prove whether VOLTERRA's equations are applicable to the predatory relationships between bluefin tuna, a predator, and coastal fishes in the southern waters of Japan. An electronic analogue computer was employed in solving the equation which is a kind of non-linear differential equations. The following are the results obtained. First, relationships between bluefin tuna and common squid in the waters for the years 1951 to 1955 have been examined. In Fig. 2 the broken line, generated by a function fitter of the analogue computer, represents the actual variations in the stock of common squid for the years 1951 to 1955, and the other curves stand for the theoretical variations in the bluefin tuna computed by the analogue computer for various values of a parameter of VOLTERRA's equation. The graphical form in the middle of theoretical curves is similar to an actual variation of bluefin tuna. Therefore, as far as those years are concerned, it seems that these two fishes are in prey-predator relationships fitted to VOLTERRA's equation. In the second place, for the years 1951 to 1956 instead of to 1955, it was found impossible to make a theoretical graphical form similar to actual variations of bluefin tuna. But when total catch of coastal fishes is considered instead of common squid alone, it is possible to find out the predatory relationships between bluefin tuna and the sum of coastal fishes for the year 1951 to 1956, as shown in Fig. 4. From these results it is concluded that bluefin tuna and coastal fishes including common squid are in predatory relationships in the southern waters of Japan.

ON THE PREDATORY RELATIONSHIPS AMONG BLUEFIN TUNA AND COASTAL FISHES IN THE SOUTHERN WATERS OF JAPAN