A STUDY ON THE RELATIONSHIP BETWEEN BODY WEIGHT AND BODY DIMENSIONS IN FISH

The formula W=a lb (or W=a Lb), though widely recognized to be reflecting the relationship between body weight and body dimensions in growth studies of fish, does have its limitation. Proceeding from setting a boundary curve equation for a model fish and making use of the method for determining the volume of a rotating object, the authors established a multivariate formula for body weight, length, and height: W= a lb1 Hb2 (or W=a Lb1 Hb2), and from which two other formulae have been derived, i. e., W=a lb1 Sb3 (or aLb1Sb3 and W=alb1Hb2Sb3 (or W=aLb1Hb2Sb3), in which W stands for body weight, L for total length, 1 for standard length, H for body depth, S for girth of fish, and b1, b2, b3 for partial indices.When checked with actual measurement of the population of Hypophthalmichthys molitrix, Erythroculter ilishaeformis and Parabramis pekinensis, including their various stages of growth, the multivariate formula gives better agreement with the data of actual measurement than does the unary form.That the multivariate formulae can give better results is due to the fact that they reflect more comprehensively the effect of various dimensions on the weight of fish.For fishes of divergent body forms, the extent to which the various dimensions affect the body weight is different, hence there should be some choice from among these dimensions when applied.Since the body depth of a fish is easier to measure than is the girth, the binary formula involving body length and body depth is of more practical interest.To sum up, the authors recommend the use of the formulae W=alb1Hb2 (or W=aLb1Hb2) and W=alb1Sb3 (or W=a L b1Sb2) in describing the relationship between dody weight and body dimensions in theoretical or applied studies of fish growth.