Document Type



Virginia Institute of Marine Science

Publication Date



Journal Of Shellfish Research





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Condition indexes are commonly derived from bivalve species. Usable meat yields (UMY, in l/bu) from 181 daily landings of Atlantic surfclams, Spisula solidissima (Dellwyn, 1817), at a Virginia processing plant in 1974 and 160 landings in 1975 were used as an index in our analysis. The data were fitted to a basic sinusoidal model and a two-compartment sinusoidal model to demonstrate the utility of these models for quantifying cyclic events. The basic model, x = x(0) + A cos2 pi t + B sin2 pi t, is linear in its independent variables and fitted by multiple regression, with x = UMY, 1 = time in years, where x(0), A, and B are constants determined by the regression procedure (x(0) = mean UMY). Its alternate form is x = x(0) + r cos2 pi(t - t(0)), with x, x(0), and t as before, r = amplitude of the sinusoidal variation, and t, = time when the maximal UMY occurs; r and t, are related to A and B as r = root A(2) + B-2, and t(0) = (1/2 pi)tan(-1) (B/A). The sinusoidal fit to the 1974 data was highly significant (p < 0.0005); therefore, the null hypothesis that the data are not a function of time was rejected. The annual mean yield, x(0), was 5.93 l/bu, t(0) was 0.45 (i.e., the maximal UMY occurred about mid-June), and the amplitude r was 0.730; thus, the difference between the lowest and highest yields, 2r, was almost 1.5 l/bu. Similar estimates were determined from the 1975 data and the combined data. The fit was recalculated for both data sets after excluding apparent outliers. As expected, the root-mean-square residual (RMS,,,) decreased, whereas the coefficient of determination (R(2)) increased with the removal of the apparent outliers, but the fitted parameters were inconsequentially affected. A fit of the data to a two-component sinusoidal model, x = x(0) + A(1) cos2 pi t + B-1 sin2 pi t + A(2) cos4 pi t + B-2 sin4 pi t, modeled an annual variation with an asymmetric rise and fall. As a demonstration, the data were also fitted to a parabolic model, x = a, + a(1)t + a(2)t(2). Although this model produced fits comparably as close as the sinusoidal models, the coefficients are not interpretable in a simple manner, as is the case with the sinusoidal fits, and it does not allow asymmetric behavior.


Spisula Solidissima; Condition Index; Usable Meat Yields; Seasonal Variation; Maximum; Minimum; Sinusoidal; Parabolic

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This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.