FISHERY BULLETIN: VOL 86. NO 1 



ticularly field data), but they may be nearly valid 

 for many sets of data (Harris 1975). No direct test 

 of normality in a trivariate, joint probability dis- 

 tribution is available (Bernard 1981), but bias 

 arising from nonnormal, multivariate, joint dis- 

 tributions is minimized with large sample sizes 

 (Bernard 19811. While methods are available to 

 test the hypothesis of equal variance-covariance 

 matrices (e.g.. Box's modification of Bartlett's 

 test), these methods are very sensitive and even 

 minor differences between group dispersions will 

 likely be discovered (Pimentel 1979). In any 

 event, the use of MANOVA in this paper relies on 

 variance-covariance matrices estimated from 

 nonlinear regressions, and these are not 

 amenable to testing. However, both MANOVA 

 and Hotel ling's tests are extremely robust even 

 under violation of the assumptions of homo- 

 scedasticity and multivariate normality (Harris 

 1975). 



RESULTS 



Increment Formation 



The age of gulf menhaden at formation of the 

 first otolith growth increment was estimated 

 from laboratory-reared larvae. The intercept (2.6 



days) of the regression of the number of growth 

 increments on known posthatch age of 36 larval 

 gulf menhaden (Fig. 3) was used to estimate 

 posthatch age at formation of the first increment. 

 This value was added to the time from spawning 

 to hatching which at 20°C is 2 days (Powell'M. 

 This sum (4.6 days) is the estimated time from 

 spawning to formation of the first increment. 

 Hence, it was necessary to add 5 days to each 

 increment count to estimate the age of larval gulf 

 menhaden from spawning. 



The periodicity of increment formation was as- 

 certained from the regression of the number of 

 growth increments on the known age (Fig. 3). The 

 slope did not differ significantly (/-test, P < 0.05) 

 from 1.0, and thus, on the average, one otolith 

 growth increment was formed per day in 

 laboratory-reared larvae up to 31 days after 

 hatching. Results of a second experiment (Table 

 1 ) confirmed this periodicity. The age of gulf men- 

 haden larvae estimated from otolith increment 

 counts ( + 5) closely approximated the known ages 

 of 51 laboratory-reared larvae. Mean estimated 

 age of larvae differed by < 1 day from the known 



3A. B. Powell, Southeast Fisheries Center Beaufort Labora- 

 tory, National Marine Fisheries Service, NOAA, Beaufort, NC 

 28516-9722, pers. commun. February 1986. 



CO 



H 

 Z 

 111 



liJ 

 DC 

 O 



z 



O 



o 



o 



tr 



LU 



m 



Z 



35 



30 



25 



20 



15 



10 



No. increments=-2.617+ 0.921(known age) 

 r= 0.928 

 n= 36 



5- 



10 15 20 25 



KNOWN AGE (days) 



30 



35 



Figure 3. — Regression of the number of 

 growth increments on the known 

 posthatch age of 36 laboratory-reared 

 gulf menhaden. Standard error of the 

 slope IS 0.108. 



80 



