WARLEN; AGE AND GROWTH OF LARVAL GULF MENHADEN 



Figure 2. — Photomicrograph of a saggital otohth with 22 increments from a 17.4 mm SL 

 field collected larval gulf menhaden. Scale bar represents 10 pim. Growth increments 

 appear as pairs of wide incremental and narrow discontinuous bands. 



number of days from spawning to first increment 

 formation. Results of the laboratory experiments 

 established the periodicity of otolith increment 

 formation. 



A spawning date was assigned each ageable 

 larva by using the estimated age of the fish in 

 days to back-calculate from the date of capture. It 

 was assumed that there were no differences in 

 either the age at initial increment deposition or 

 the otolith increment deposition rate between lo- 

 cations and seasons and that the rate was not a 

 function of temperature, food, or photoperiod. 



Average growth of larvae was described by the 

 Laird version (Laird et al. 1965) of the Gompertz 

 growth equation (Zweifel and Lasker 1976) fitted 

 to estimated age and size at time of capture for 

 fish from all cruises and transects. To stabilize 

 the variance of length over the observed age in- 

 terval, length data were log-transformed and 

 model parameters were estimated from the log- 

 transformed version of the growth equation. The 

 model was fit to data for each transect within 

 each cruise and for pooled data from all cruises. 



Potential differences in the overall growth 

 curves among years and between seasons for lar- 

 vae caught off Louisiana and between years ( 1981 

 and 1982) for larvae caught off Louisiana and 



Texas were examined by treating the parameters 

 of the Gompertz equation as dependent variables 

 in two-way multivariate analysis of variance 

 (MANOVA) designs. A one-way MANOVA de- 

 sign was used to test for differences 

 among transects (LA, FL, TX) within one season 

 (February 1982). Following significant 

 MANOVA results, prespecified pairwise 

 Hotelling's T'^ test comparisons (Bernard 1981, as 

 modified by Hoenig and Hanumara 1983) were 

 made using the Bonferroni procedure (Harris 

 1975) to provide conservative tests of statistical 

 significance. Bonferroni critical values for these 

 individual tests were equal to the overall error 

 rate (significance level = 0.05) divided by the 

 number of possible comparisons in the particular 

 MANOVA design. The emphasis in the compari- 

 sons was to look for overall differences in the 

 growth of larvae using these statistics as a guide 

 and not to look for differences in individual 

 parameters of the growth models. 



Hotelling's T^ test and MANOVA both require 

 that the data fit a multivariate normal distribu- 

 tion and that the variance-covariance matrices of 

 the populations are not different (Harris 1975). 

 These assumptions are difficult to test and are 

 almost certainly not valid for real data sets (par- 



79 



