LOUGH ET AL: AGE AND GROWTH OF LARVAL ATLANTIC HERRING 



which, if assumption 2) is reasonable, Equation 

 (3) holds for ,r>0. Letting L denote mean length 

 at hatch (x = 0), then solving Equation (3) for c 

 yields, 



Ln(3.431 - Ln U) - 0.065 



0.026 



Table 3 gives an estimate of the age of larvae 

 with 7 increments (24.8 d) derived from the mean 

 length of recently hatched larvae collected on the 

 Jeffreys Ledge spawning beds (Cooper et al. foot- 

 note 3). 



When the mean hatching size (L ) = 5.7 mm, 

 c — 17.8 d, and from Equation (3), length as a 

 function of age is given by 



L = 30.90 exp[-1.70 exp(-0.03 x)\ x>0. (4) 



From Equation (4) the mean length at age 

 along with 95% confidence limits, and growth 

 rate (millimeters/day) are estimated from the 

 time of hatch through 175 d in Table 4. Also, the 

 fitted growth curve is shown in Figure 8 with the 

 estimated larval age referenced to the lower 

 scale. The growth curve is based on data with 

 more than 6 increments and a mean length of 5.7 

 mm at hatch. Obviously, if the functional form 

 changes between age and the age correspond- 

 ing to 7 increments, then the predicted age of fish 

 with 7 or more increments is biased. 



This growth curve is based on larvae that sur- 

 vived to the age when caught. Therefore, the 

 back-casted curve represents the mean length of 

 larvae for a given age which survive and hence, 

 may be higher than the mean length of the total 

 population. 



The mean lengths at age of laboratory-reared 

 larvae having 1 and 2 increments from Table 2 

 fall reasonably close to the extrapolated curve 

 near the origin. The mean length of the labora- 

 tory-reared larvae at hatch was reported by 

 Beyer and Laurence (1981) to be 7.66 mm (SD 

 = 0.58 mm). After correcting for a 20-min net- 

 treatment and Formalin preservation shrinkage 

 factor to compare with the field data, their re- 

 ported mean hatching size is estimated to be 6.4 

 mm, which is not significantly different from the 

 Jeffreys Ledge diver-collected, Formalin-pre- 

 served yolk-sac lar vae of 5. 7 mm mean SL. 



An estimate of \/var(.r |r), the standard devia- 

 tion of age for a fixed number of increments, was 

 made from the field data by Pennington (1979), 

 and its value of 2.9 d compares closely with the 



Table 'i.— Age of larval herring with 7 otolith growth incre- 

 ments estimated from an initial mean hatching size of 5.7 mm 

 (0.54 mm SD) and 95% confidence intervals of the mean. Stan- 

 dard lengths of 100 newly hatched yolk-sac larvae (Formalin' 

 preserved) were measured from egg bed samples collected by 

 divers 2 on the Jeffreys Ledge study site (38 m depth), 8 October 

 1974. 



Hatch 95% confidence Estimated age of larva 95% confidence 

 length (L ) . lntervals with 7 increments mlervals 



(mm) 



lower upper 



(d) 



lower upper 



5.7 



5.6 



5.8 



248 



244 25.2 



'Reference to trade names does not imply endorsement by the National 

 Marine Fisheries Service, NOAA. 



2 Northeast Fisheries Center's Manned Undersea Research and Tech- 

 nology (MURT) Dive Team. 



Table 4.— Mean standard length at age, 95% confidence 

 limits, and growth rate (mm/d) of larval herring from 

 hatch through 175 d estimated from the Gompertz growth 

 model fit. 



rough estimate of 3.1 d obtained from the labora- 

 tory data (Lough et al. footnote 7). 



The first larva with 3 increments observed 

 during the laboratory-rearing occurred on day 

 16 after estimated hatch. The mean age of fish 

 with 3 increments cannot be estimated directly 

 because sampling stopped after 18 d. But assum- 

 ing a range of ages of 12 d (4 standard devia- 

 tions), the mean age of a 3-increment larva would 

 be approximately 22 d. Assuming daily incre- 

 ment deposition for the population after the third 

 increment, a 7-increment larva would have an 

 average age of 26 d, which compares well with 

 the field estimate of 25 d. 



Messieh and Moore (footnote 9), working 

 with autumn-spawned herring larvae in the 

 Gulf of St. Lawrence, recently estimated the 

 age of larvae at the time of the nuclear check 

 completion to be 15-17 d from hatching on 

 average. 



195 



