The Rate of Overlapping of Fish Scales as an ' Index of Their Relative Growth Rate I. A Preliminary Examination on Goldfish Scales

Investigation into the relation of the length of the fish to the size of its scales plays an important part in population studies of fishes. Since such the relationship seems to show a straight line regression, it has generally been ac-cepted that the scale increases in size proportionally with the increase in length of the fish. Strictly speaking, however, it should follow an exponential equation, S=aLb (S: scale length; L: body length; a,b: constant), when the growth of scales is considered from an allometric viewpoint. In fact, it has frequently been sug-gested that in many fishes the "scale size-body length " relationship shows a curvilinear character when traced throughout their lives (reviews by Kubo and Yoshihara, 1957, and by Nikolsky, 1963). Furthermore, one might expect that the relative growth rate of scales would vary according to seasons even within a year. The scale sizes plotted against a certain length of fish usually cover so wide a range that it is fairly difficult to discuss minute changes of the relative growth rate by scale size-body length analysis. The growth of a fish is naturally accompanied by an extension in area o