• Korean Journal of Fisheries and Aquatic Sciences
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• v.8 no.2
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• pp.47-60
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• 1975

For the calculation of population parameter and estimation of recruitment of a fish population, an application of multiple regression method was used with some statistical inferences. Then, the differences between the calculated values and the true parameters were discussed. In addition, this method criticized by applying it to the statistical data of a population of bigeye tuna, Thunnus obesus of the Indian Ocean. The method was also applied to the available data of a population of Pacific saury, Cololabis saira, to estimate its recuitments. A stock at t year and t+1 year is, $N_{0,\;t+1}=N_{0,\;t}(1-m_t)-C_t+R_{t+1}$ where $N_0$ is the initial number of fish in a given year; C, number o: fish caught; R, number of recruitment; and M, rate of natural mortality. The foregoing equation is $$\phi_{t+1}=\frac{(1-\varrho^{-z}{t+1})Z_t}{(1-\varrho^{-z}t)Z_{t+1}}-\frac{1-\varrho^{-z}t+1}{Z_{t+1}}\phi_t-a'\frac{1-\varrho^{-z}t+1}{Z_{t+1}}C_t+a'\frac{1-\varrho^{-z}t+1}{Z_{t+1}}R_{t+1}......(1)$$ where $\phi$ is CPUE; a', CPUE $(\phi)$ to average stock $(\bar{N})$ in number; Z, total mortality coefficient; and M, natural mortality coefficient. In the equation (1) , the term $(1-\varrho^{-z}t+1)/Z_{t+1}$s almost constant to the variation of effort (X) there fore coefficients $\phi$ and $C_t$, can be calculated, when R is a constant, by applying the method of multiple regression, where $\phi_{t+1}$ is a dependent variable; $\phi_t$ and $C_t$ are independent variables. The values of Mand a' are calculated from the coefficients of $\phi_t$ and $C_t$; and total mortality coefficient (Z), where Z is a'X+M. By substituting M, a', $Z_t$, and $Z_{t+1}$ to the equation (1) recruitment $(R_{t+1})$ can be calculated. In this precess $\phi$ can be substituted by index of stock in number (N'). This operational procedures of the method of multiple regression can be applicable to the data which satisfy the above assumptions, even though the data were collected from any chosen year with similar recruitments, though it were not collected from the consecutive years. Under the condition of varying effort the data with such variation can be treated effectively by this method. The calculated values of M and a' include some deviation from the population parameters. Therefore, the estimated recruitment (R) is a relative value instead of all absolute one. This method of multiple regression is also applicable to the stock density and yield in weight instead of in number. For the data of the bigeye tuna of the Indian Ocean, the values of estimated recruitment (R) calculated from the parameter which is obtained by the present multiple regression method is proportional with an identical fluctuation pattern to the values of those derived from the parameters M and a', which were calculated by Suda (1970) for the same data. Estimated recruitments of Pacific saury of the eastern coast of Korea were calculated by the present multiple regression method. Not only spring recruitment $(1965\~1974)$ but also fall recruitment $(1964\~1973)$ was found to fluctuate in accordance with the fluctuations of stock densities (CPUE) of the same spring and fall, respectively.