Theoretical analysis of the weight-length relationship in fish juveniles

The weight-length relationship in fish juveniles was investigated theoretically, to assess the significance of the allometric factor and the validity of the condition factor; these biological factors often remain undetermined, because most fishery studies have been conducted for commercial-sized and/or adult populations. The exponent b (allometric factor) seemed to be the main parameter, performing a key role in the equation W=aL ^b , where W=weight, a is a constant and L=length. The parameters a (condition factor) and K (ponderal index; K=10³ W/L ³) were judged to be less important in comparative studies, since these parameters were closely correlated with b. It is recommended that the assumed theoretical value of b=3 not be used in applied ichthyological surveys, since this value was rarely obtained in the studies, and since a much wider range is usually seen. These analyses led to a new working hypothesis — not yet verified — which opens a new approach to understanding the biological significance of the allometric factor. This approach involves the fractal theory (where b may be considered as a fractal dimension equivalent) linked to the theory of saltatory ontogeny where b is a threshold characteristic in the (early) life history of fishes].