FISHERY BULLETIN: VOL. 80, NO. 2 



in Figure 7 also can be expressed by a simple lin- 

 ear relationship. The long axis of the otolith 

 shows a positive allometry with respect to head 

 length for recently hatched larvae to a size of 

 about 35 mm SL. Hempel (1959) reported nearly 

 isometric growth between head and otolith 

 length after metamorphosis for German Bight 

 herring. 



Figure 7. — Otolith length (anterior + posterior radii)-head 

 length relation for herring larvae collected from the three 

 areas: western Gulf of Maine, Georges Bank, and Nantucket 

 Shoals, with composite regression line and correlation coeffi- 

 cient (r). 



function of age where r, the number of incre- 

 ments, represents age plus some unknown con- 

 stant (see Pennington 1979 for details of the 

 model fit). 

 The fitted equation was found to be 



L = 12.70 exp[0.89(l - exp[-0.03(r - 7)])] 



for r>7, (1) 



where 12.70 = Li, the mean length of a 7-incre- 

 ment larvae. 

 Equation (1) may be rewritten as 



L = 30.90 exp[-1.07 exp(-0.03 r)], r>l, (2) 



where 30.90 = L x , the asymptotic limit of mean 

 growth during the October-March period. As- 

 suming: 1) for at least r>7, increments are de- 

 posited daily and 2) a curve in the form of Equa- 

 tion (2) approximates growth from hatch, then 

 denoting age by x, 



x = r + c, r>7, 



from 1), where c is an unknown constant, or 



r = x — c, x>c + 7. 



Thus 



Larval Growth 



A composite plot of larval length versus num- 

 ber of otolith increments is presented in Figure 

 8. A Gompertz growth curve was fitted to the 

 field data to produce a description of the mean 

 growth of larval herring based on the 311 speci- 

 mens with otolith growth increments ranging 

 from 7 to 160. The Gompertz-type curve (Laird 

 1969) has been used to describe growth of a wide 

 variety of organisms that often grow exponen- 

 tially at a rate which is decaying exponentially. 

 Previous use of the Gompertz model to more 

 accurately describe the growth of young fish has 

 been made by Kramer and Zweifel (1970), Saka- 

 gawa and Kimura (1976), Zweifel and Lasker 

 (1976), and Methot and Kramer (1979). Using the 

 field data as a starting point, it was assumed that 

 increments were deposited daily at least after 

 the 7th increment so that the equation 



L = L 7 exp[fc(l - exp[-«(r - 7)])], r>7, 



was taken to represent mean larval length as a 

 194 



L = 30.90 exp(-1.07 exp[-0.03(x - c)]), 



x>c + 7, (3) 



fio 



7 



70 90 



OTOLITH INCREMENTS 



80 100 120 



ESTIMATED AGE ( DAYS I 



Figure 8.— Composite standard length-otolith increment plot 

 for field-collected herring larvae in the Gulf of Maine-Georges 

 Bank region, October 1976-March 1977. A Gompertz curve is 

 fitted to larval length at estimated age, x, over their first 6 mo 

 of life from a mean hatch length of 5.7 mm to an asymptotic 

 limit of mean growth of 30.9 mm. A larva with 7 otolith incre- 

 ments is estimated to be on average 24.8 d old. See text for de- 

 tails. 



