390 



Fishery Bulletin 94(3). 1996 



respect to length for each of the seven field seasons 

 studied was best described by a Gompertz-type curve. 

 The methodology for fitting the curve is discussed in 

 Pennington (1979). Previous uses of the Gompertz 

 growth curve are presented in Al-hossaini et al. 

 ( 1989) and Jearld et al. ( 1993). The Gompertz curve 

 not only permits the calculation of growth rate but 

 also provides mean hatching size (length at age 0) 

 and predicted length at metamorphosis (the asymp- 

 totic limit of mean larval growth). 



Analysis of the seven field seasons resulted in the 

 following relationships, where L = standard length 

 in mm and Age = number of days (increments plus 

 19) from hatch: 



1976/77 L 

 1988/89 L 

 1989/90 L 

 1990/91 L 

 1991/92 L 

 1992/93 L 

 1993/94 L  



:33.5381<? 

 : 38.9217e 

 : 35.2189e 

 : 36.0859e 

 : 34.1978e 

 ; 34.1176e 

 37.4796e 



-i.i055c-° 0,9M * p 

 [ra=187, r 2 -- 



-1.5483e-°- 0213A «« 



[n = 139, r 2 -- 



1.6232?-° 027W *'' 



[n=379, r 2 = 



-1.6104*' D-0240A* 



[n=382, r 2 -- 



-1.9677e-° 03m4 «'' 



[n=313, r 2 -- 



-2.1559c """^v. 



[n=20A,r 2 -- 



1.8986c ""™<-. 



[n = 142, r 2 -. 



0.89651; 

 0.8951]; 

 0.8914]; 

 0.9161]; 

 0.8540]; 

 0.9085]; 

 0.94351. 



A summary of the growth parameters generated by 

 the above equations may be found in Table 2. Plots 

 of the Gompertz curves fitted to standard length vs. 

 age in days are presented in Figure 2. 



In order to compare the rate of growth for the seven 

 seasons, the Gompertz curves were linearized and 

 examined for homogeneity of slope with /-tests (Table 

 3; Fig. 3). With this method, three groupings were 

 discernible: 1) the 1976-77 season; 2) the 1988-89, 

 1989-90, and 1990-91 seasons; and 3) the 1991-92, 

 1992-93, and 1993-94 seasons. Larval growth for the 

 1976-77 season was the slowest (0.16 mm/d) of the 

 time series, and although larvae for this season had 

 the greatest hatch length, standard length at 120 

 days posthatch was 2.2 to 4.8 mm less than that in 

 the other six years. There was no significant differ- 

 ence at the 0.05 level between the 1988-89, 1989- 

 90, and 1990-91 seasons. Hatching length for these 

 three seasons differed by less than 1.5 mm, and over- 

 all rates of growth for the first 120 days were identi- 

 cal. The rate of growth during the overwintei'ing pe- 

 riod of 1988-89 was the greatest of the seven years 



and compensated for the relatively slow growth ear- 

 lier in the season. Larvae were on average 2.7 mm 

 smaller at hatching in the autumns of 1991, 1992, 

 and 1993 than in the preceding three years. The rate 

 of growth for the first 40 to 60 days was consider- 

 ably faster than that in previous years; however, this 

 initial rapid increase in length was followed in 1991- 

 92 and 1992-93 by a period of slower than average 

 growth. The overall higher rates of growth in these 

 two years were not enough to compensate for the 

 small size of larvae at hatching (4.0-4.8 mm), and 

 projected lengths at metamorphosis (34.1-34.2 mm) 

 were smaller than in all previous years except 1976- 

 77. Although hatching lengths in 1993-94 were small, 

 growth was good throughout the season, and the 

 average length at 120 days posthatch (35.0 mm) was 

 the largest of the time series. 



Predictability 



A generalized growth model for larval herring was 

 created by pooling data (/? = 1,559) from the six most 

 recent field seasons (1988-94) and by fitting them 

 with a Gompertz curve: 



L = 34.995ft?- 1 - 74 -- 1 '' 



[r 2 =0.88631. 



The model tracks growth for the first four months of 

 life from an estimated hatch length of 6.1 mm to a 

 predicted length at 120 days posthatch of 33.0 mm 

 (0.22 mm/d). Figure 4 shows the growth curve with 

 95% confidence intervals for predicting standard 

 length (mm) for a given age in days. This informa- 

 tion is also presented in Table 4 along with age-spe- 

 cific growth rates. 



Because it is desirable, especially during field sur- 

 veys when direct analysis of otoliths is impossible, 

 to be able to estimate the age of larvae based on their 

 length, inverse regression (Draper and Smith, 1966) 

 was performed on the Atlantic herring composite 

 growth curve to establish confidence intervals for 

 predicting age from a given standard length. In its 

 reduced form the equation obtained for herring was 



I 1-X ±0.0470/ 



I 

 X, 



In 



(X - 0.7523) 2 /26.5957J + ( 1 + II n ) 



! 2 



-0.0281 



where X v and X L = upper and lower confidence lim- 

 its; 

 X = l-e-° 02S1 ; and 

 n = sample size. 



