NOTE Davis and West: Growth and mortality of Lutjanus vittus 



397 



used to test for significant differences in this index with 

 time of year after arcsine square-root transformation. 



Growth analysis 



Two forms of length-at-age data were available: lengths 

 were back-calculated to the last annulus (Whitney and 

 Carlander 1956, Carlander 1981) to provide length-at- 

 age data unconfounded by differences in the time of 

 year of sampling. Absolute age-at-observed-length was 

 also assigned, using an artificial January 1 birthdate. 

 The von Bertalanffy growth curve parameters were 

 fitted to both sets of length-at-age data by direct non- 

 linear least-squares estimation. The null hypothesis that 

 there was no difference between males and females in 

 the three growth-curve parameters was tested using 

 the extra sum-of-squares principle (Draper and Smith 

 1981, Ratkowsky 1983). The mean lengths at the last 

 annulus of fish aged 1-6 years were also compared be- 

 tween sexes using analysis of variance. 



Population structure and mortality 



Sex-specific length-frequency distributions and sex- 

 specific age-length keys were obtained from the sub- 

 samples from each random station, pooled for each 

 sampling period. It was assumed that neither the sex 

 ratio nor the sex-specific growth rate varied in some 

 systematic way between the different strata. The log- 

 likelihood ratio X" was used to test for departures 

 from a 1:1 sex ratio. 



For each sampling period in 1983, the length fre- 

 quency of the total population was determined using 

 the following equation (K.J. Sainsbury, CSIRO Div. 

 Fish., pers. commun. 1991): 



j = 13 



Fi = I fi,A^/n„ 



(2) 



where F; is the relative frequency of size-class i in the 

 population, fjj is the frequency of size-class i in stra- 

 tum j, Aj is the area of stratum j, and nj is the number 

 of trawls in stratum j. These length frequencies were 

 then broken down by sex, using sex-specific length- 

 frequency distribution determined for each sampling 

 period in 1983. The sex-specific age structure at each 

 sampling period was then calculated using the sex- 

 specific age-length keys determined for each sampling 

 period (Kicker 1975, Kimura 1977). A catch curve for 

 each sex was then constructed (Gulland 1969) and total 

 instantaneous mortality estimated by least-squares 

 linear regression of the descending right-hand of the 

 catch curve. Equality of mortality rates between the 

 sexes was determined by analysis of covariance. 



Results 



Depth distribution 



Lutjanus vittus were caught in depths from 20 m (the 

 shallowest depth sampled) to 120 m, with the largest 

 catches being at 30-70 m (Fig. 3). There was a positive 

 correlation between individual fish lengths and depth 

 (r 0.337, t 24.7, df 4754, P<0.001). While almost the 

 full size-range was encountered at most depths, there 

 was a marked absence of fish < 200 mm at depths >90m 

 (Fig. 4). 



Length/weight relationship 



In the regression of log weight/log length, the test for 

 homogeneity of slopes between sexes was found to be 

 not significant (ANCOVA, F 0.318, df 1, 2604, P 0.57) 

 and, assuming a common slope, there was no signifi- 

 cant difference in the intercepts for the two sexes 

 (ANCOVA, F 1.76, df 1, 2605, P 0.19). Both sexes and 

 juveniles whose sex could not be determined were then 

 combined and a general relation between length (L in 

 mm) and weight (W in g) for L. vittus was determined: 



W = 9.99x10-6 L3086 



{F 367248, df 1, 2797, P<0.001). 



