196 THE RATE "OF GROWTH [ch. 



an epoch in the fish's life; it is about the size when sexual maturity 

 begins, or at least near enough to suggest a connection between the 

 two phenomena*. 



A step towards further investigation would be to determine k for the two 

 sexes separately, and to see whether or no the point of inflection occurs, as 

 maturity is known to be reached, at a smaller size in the male. This d'Ancona 

 has done, not for the plaice but for the shad {Alosa finta). He finds that the 

 males are the first to reach maturity, first to shew a retardation of the rate 

 of growth, first to reach a maximal value of th^ ponderal index, and in all 

 probability the first to diet • 



Again we may enquire whether, or how, k varies with the time 

 of year; and this torrelation leads to a striking result J. For the 

 ponderal index fluctuates periodically with the seasons, falling 

 steeply to a minimum in March or April, and rising slowly to an 

 annual maximum in December (Fig. 51) §. The main and obvious 

 explanation hes in the process of spawning, the rapid loss of weight 

 thereby, and the slow subsequent rebuilding* of the reproductive 

 tissues; whence it follows that, without ever seeing the fish spawn, 

 and without ever dissecting one to see the state of its reproductive 

 system, we may by this statistical method ascertain its spawning 

 season, and determine the beginning and end thereof with con- 

 siderable accuracy. But all the while a similar fluctuation, of 

 much less amphtude, is to be found in voung plaice before the 

 spawning age; whence we learn that the* fluctuation is not only 

 due to shedding and replacement of spawn, but in part also to 

 seasonal changes in appetite and general condition. 



Returning to our former instance, we now see that the March 

 and December samples of plaice, which shewed such discrepant 

 variations of the ponderal index with increasing size, happen to 



♦ The carp shews still more striking changes than does the plaice in the weight - 

 length coefl&cient: in other words, still greater changes in bodily shape with 

 advancing age and increasing size; cf. P. H. Stnithers, The Champlain Watershed, 

 Albany, New York, 1930. 



■j- U. d'Ancona, II problema dell' accrescimento dei pesci, etc., Mem. R. Acad, 

 dei Lincei (6), n, pp. 497-540, 1928. 



J Cf. Lammel, Ueber periodische Variationen in Organismen, Biol. Centralbl. 

 xxn, pp. 368-376, 1903. 



§ When we restrict ourselves, for simphcity'a sake, to fish of one particular 

 size, we need not determine the values of k, for changes in weight are obvious 

 enough; but when we have small numbers and various sizes to deal with, the 

 determination of k helps very much. 



