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Application of Parker-Larkin equation to growth of fishes and other aquatic organisms Kilambi, Varadaraja Ayyangar

Abstract

Any mathematical formulation for depicting the growth of organisms must yield an empirical fit that is reasonably good. Its validity is enhanced if the equation yields information of biological interest. This investigation is aimed at applying the Parker-Larkin (1959) growth equation to a number of aquatic organisms to describe the problems encountered in making use of this technique. The data are also analysed by the Von Bertalanffy growth equation to bring out the similarities of the constants of both the equations. The data pertaining to three species of marine fish, brill, halibut and herring, four species of freshwater fish, rainbow trout, cutthroat trout and sturgeon and to a lamelli-branch species scallops, have been analysed. It is pointed out that the exponent of the length-weight relationship should not be taken as 3. It is shown that the length-weight relationship of rainbow trout varies depending on sex, maturity and size. In many species the Parker-Larkin growth equation predicted the lengths at various ages accurately. Von Bertalanffy’s equation progressively overestimated the sizes. In white sturgeon the growth increments decrease at first and then become equal. In such a situation it is suggested that the data be split into two stanzas for analysis since the analysis without splitting underestimates the sizes in the early years and overestimates in the older ages. The anterior radius of the scale grows relatively slower than the length of the fish in herring. The regression equation of the body-scale relationship is used only to obtain the value of the intercept. The back calculation of lengths is made by keeping the intercept constant with variable slopes for the individual fish. The Parker-Larkin equation gave an excellent fit for the data on halibut. This is because the observed values of halibut are actually calculated values from a linear logarithmic regression of weight on age - an algebraic equivalent of the Parker-Larkin equation in which the slope is the reciprocal of (l-x). The range of values of z between 1.0 and 1.5, when the line of best fit on a Walford plot approaches the 45° diagonal, is true for salmonids only and in similar situations for other species a value as high as 3.6 for z is obtained. The variability of z depending on the density of the population and/or availability or non-availability of food material is shown for rainbow trout. This dependence of z on the food available is similar to that of L₀₀ or W₀₀. There is an inverse relationship between L₀₀ and z as that of L₀₀ and Κ. It is tentatively suggested that z might be a parameter of physiological importance in the Parker-Larkin equation. Further work of an experimental nature is suggested to establish the physiological significance of the parameters of the Parker-Larkin equation.

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