230 



Fishery Bulletin 97(2), 1999 



racycline hydrochloride (OTC), and released at the 

 Poor Knights Islands (Fig. 2). Two OTC brands and 

 dosage rates were used: 27 fish were injected with 

 terramycin at a dosage rate of 80 mg/kg; and 12 were 

 injected with engemycin at 35 mg/kg. Five OTC-in- 

 jected fish were recaptured and their otoliths re- 

 moved. One otolith from each pair was sectioned as 

 described above and viewed under transmitted white 

 light and reflected UV light. The composition of the 

 otolith (number of opaque or hyaline bands) outside 

 the OTC mark was determined, and the amount of 

 new otolith material laid down along the dorso- 

 nuclear axis was measured. 



Growth curves were fitted to the length-at-age data 

 bu using the von Bertalanffy growth model: 



L Jl- 



-KU-tJ 



). 



where L, = the expected length at age t years; 



L^^= the asymptotic maximum length; 



K = the von Bertalanffy growth constant; and 



t,. = the theoretical age at zero length. 



Length-frequency distributions 



Hapuku length-frequency distributions were ob- 

 tained from a series of four bottom trawl surveys 

 conducted from the research vessel Tangaroa (tow- 

 ing a 60-mm mesh codend) off Southland (the south- 

 ern coast of South Island and the Stewart Island shelf 

 between latitudes 46-49''S). The surveys were car- 

 ried out annually in February and March, 1993-96, 

 and covered a depth range of 30-600 m. Further de- 

 tails of the surveys are provided in the studies of 

 Hurst and Bagley ( 1994) and Bagley and Hurst ( 1995, 

 1996a, 1996b). 



Von Bertalanffy growth curves were fitted to the 

 four length-frequency distributions by using the 

 MULTIFAN model (Fournieretal., 1990). This model 

 analyses multiple length-frequency distributions si- 

 multaneously and uses a maximum likelihood 

 method to estimate the number of age classes repre- 

 sented by the data, the proportions of fish in each 

 age class, and the von Bertalanffy growth param- 

 eters L^ and K. The main assumptions of the 

 MULTIFAN model are the following: 1 ) the lengths 

 of the fish in each age class are normally distributed 

 around their mean length; 2) the mean lengths-at- 

 age lie on or near a von Bertalanffy growth curve; 

 and 3) the standard deviations of the actual lengths 

 about the mean length-at-age are a simple function 

 of the mean length-at-age (Fournier et al., 1990). 



The growth parameters were estimated by conduct- 

 ing a systematic search across a parameter space of 

 plausible K values (0.005-0.30) and age classes (6- 



15). It is possible to constrain the MULTIFAN search 

 further by specifying initial estimates for the mean 

 length-at-age, and the range of the mean length, for 

 one or more age classes (Fournier et al., 1990). How- 

 ever, this is not necessary when the length distribu- 

 tions contain adequate modal structure; therefore 

 such constraints were not used in this study. 



For each of the identified age classes, MULTIFAN 

 also estimates the ratio of the last to first length 

 standard deviations (S^j and the geometric mean of 

 the first and last standard deviations (S^). The 

 MULTIFAN model was fitted for two different growth 

 hypotheses: 1) constant length standard deviation 

 for all age classes (fitted by setting S^^=l and esti- 

 mating S^); and 2) variable length standard devia- 

 tion across age classes (fitted by estimating both S^ 

 and Sjj). Because all four trawl surveys were con- 

 ducted at the same time of year, the data contain no 

 information on seasonal variability of growth, and 

 no seasonal parameters were fitted. 



Each combination of K and the number of age 

 classes constituted a model fit. The constant stan- 

 dard deviation hvpothesis was fitted to the data first, 

 followed by the addition of the parameter for variable 

 standard deviation. For each combination of K, num- 

 ber of age classes, and gi'owth hypothesis, the maxi- 

 mum log-likelihood (A) was calculated. Likelihood ra- 

 tio tests were used to test for significant improvement 

 in model fit. Twice the increase in A is distributed as a 

 X~ distribution with degrees of freedom equal to the 

 number of additional parameters. Following Fournier 

 et al. (1990), a significance level of 0.10 was used for 

 testing whether there was any gain in introducing an 

 additional age class in the length-frequency analyses. 

 The test for improvement resulting from the addition 

 of the parameter for variable standard deviation was 

 carried out with a significance level of 0.05. 



The von Bertalanffy growth parameter t^^ was es- 

 timated from the equation 



tn 



t. 



where a^ = the age estimated by MULTIFAN (in 

 years since zero length) of the youngest 

 age class at the time it first appeared in 

 the length-frequency samples; and 

 t^ - the time elapsed in years between the 

 theoretical birthday and the first ap- 

 pearance of the youngest year class in 

 the samples. 



The theoretical birthday was defined as 1 Septem- 

 ber based on observations of prespawning fish in 

 June-August and postspawning fish in October- 

 December (Johnston, 1983; Roberts, 1986). 



