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<br />7 <br /> <br />Relative growth was calculated from recaptured fish for comparison with increment <br />increase from back-calculated lengths. Average yearly growth was calculated for fish within 50 <br />mm length groups (e.g. 401-450 and 451 -500 mm TL). April through September were considered <br />potential growth months. Only days within this period were counted in the interval between <br />tagging and recapture. A fish tagged August I and recaptured the following May 1 would have <br />spent 270 days between captures; but the growth interval would have been only 90 days (i.e. 30 <br />days in August + 30 days in September + 30 days in April). Recaptured fish were classified into <br />those recaptured less than one year later, those recaptured approximately one year later, and those <br />recaptured more than one year later. Fish recaptured less than 30 days after tagging were not <br />included in the analysis because of the potential of small measurement error to increase <br />dramatically when converting to yearly growth. Negative growth of individual fish was <br />converted to zero growth prior to calculation of length group averages. Relative growth was <br />calculated by dividing the increment grown during 1 year by initial length at the start of the <br />year. <br /> <br />A verage lengths at age from the summary table were used to estimate three unknown <br />parameters (L(I)' K, and to) of the von Bertalanffy growth equation: <br /> <br />II = L(I) (l_e-K(I.IO)). (8) <br /> <br />where II is length at time t, L(I) is asymptotic length, e is the inverse of the natural log, K is a <br />growth coefficient, and to is the time when length would theoretically be zero. <br /> <br />Methods of estimating the unknown parameters follow those outlined by Everhart and <br />Youngs (1981). Mean length at age t + I year (II + I), was plotted as a function of mean length at <br />age t, (II)' on a Walford plot (Walford 1946). A linear regression was fitted by the least-squares <br />method. Asymptotic length was estimated as the point where (It + I) is equal to It" Solving the <br />linear regression equation of the Walford line for Y=X or (I, + 1) = It results in: <br /> <br />L =.JL....., <br />(I) l-b <br /> <br />(9) <br /> <br />where a is the y-intercept and b is the slope from the Walford plot regression. To obtain an <br />estimate of K, the von Bertalanffy growth curve (equationS) ,was transformed: <br /> <br />loge (Lw - II) = loge Lw + Klo - Kt. <br />This is similar to the linear equation: <br /> <br />(10) <br /> <br />y = a + bx, <br /> <br />(11 ) <br /> <br />where: <br /> <br />y = loge (Lw - It), <br /> <br />a = loge Lw + Klo, <br /> <br />b = -K. <br /> <br />By plotting the loge (L(I) - It) as a function of I and fitting a linear regression, an estimate of '0 <br />can be obtained from the equation: <br /> <br />1 :: a - loge~' <br />o K <br /> <br />(12) <br /> <br />where a is the intercept and K is the negative slope of equation 10. <br />