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Fishery Bulletin 104(4) 



[1975] for importance of limiting bias by using data from 

 multiple sampling methods). Von Bertalanffy growth 

 equations were fitted to the fork lengths of the female 

 and male fish at their estimated ages at capture by 

 using nonlinear regression in the Statistical Package for 

 the Social Sciences software (SPSS 12.0.2 for Windows, 

 SPSS Inc., Chicago, IL). The lengths at age of small 

 fish whose sex could not be determined were allocated 

 randomly to both the male and female data sets used 

 for calculating the growth curves. The von Bertalanffy 

 growth equation is 



L (1 



exp" 



'o'). 



where L, = the estimated length at age t\ 

 L ^ = the asymptotic length; 

 k = the rate at which L, approaches L ,; and 

 ^1, = the hypothetical age at zero length. 



A likelihood-ratio test was used to compare the 

 growth curves of the females and males of P. uitta 

 (Cerrato, 1990). The hypothesis that a common growth 

 curve could be fitted for the two sexes was rejected at 

 the a= 0.05 level of significance if the test statistic, 

 calculated as twice the difference between the log-like- 

 lihoods obtained by fitting a common growth curve 

 for both sexes and by fitting separate growth curves 

 for each sex, exceeded X'jQ^- where q is the difference 

 between the numbers of parameters (i.e., 3) in the two 

 approaches. 



Reproductive biology 



The gonads of each fish that could be sexed macroscopi- 

 cally were removed and weighed to the nearest 0.01 g 

 and, in the case of ovaries, staged macroscopically by 

 using the scheme of Laevastu (1965) and the histological 

 characteristics of the ovaries. For histology, ovaries of a 

 random subsample of female P. vitta from each month of 

 the year were preserved in Bouin's fixative for 48 hours, 

 after which they were dehydrated in an ascending series 

 of alcohol concentrations, embedded in paraffin wax, 

 cut into 6-;(m thick sections, and stained with either 

 Ehrlich's haematoxylin and eosin or Mallory's trichrome 

 (Humanson, 1972). On each histological slide, the maxi- 

 mum and minimum diameters of 30 randomly selected 

 oocytes, which had been sectioned through their nuclei, 

 were recorded to the nearest 5 fim. The mean of these 

 two measurements for each oocyte was considered to 

 represent the diameter of that oocyte (see Foucher and 

 Beamish, 1980). 



The gonadosomatic indices (GSIs) of females and 

 males al year of age were determined from the 

 equation 



W1/W2 X 100, 



where Wl = weight of gonad; and 



W2 = weight of whole fish minus the weight of 

 gonad. 



Mortality 



Age-frequency distributions for female and male P. 

 vitta caught during extensive trawling in November 

 and December 1997 were used to estimate the instan- 

 taneous rate of total mortality (Z) for both females 

 and males. Age classes on the descending limb of the 

 age-frequency distribution for each sex (i.e., immedi- 

 ately after the peak in this distribution), were consid- 

 ered fully recruited to the fishery (Ricker, 1975). The 

 catch curve for each sex was analysed by using the 

 assumptions that Z and the levels of annual recruit- 

 ment are constant and that the age composition of 

 fully recruited fish represents a random sample from 

 a multinominal distribution with uniform selectivity 

 from the age of full recruitment (Hall et al., 2004). 

 The value of Z was estimated by maximizing the 

 log-likelihood by using the SOLVER routine in Micro- 

 soft™ Excel (vers. 2002, Microsoft Inc., Redmond, 

 WA). The data for P. vitta were randomly resampled 

 with replacement and analyzed to create 1000 sets 

 of bootstrap estimates. The point estimate for Z was 

 taken as the median of the 1000 bootstrap estimates. 

 The 95% confidence limits were calculated as the 2.5 

 and 97.5 percentiles of the corresponding estimated 

 values. The likelihood-ratio test used to compare 

 growth curves was also used to compare the catch 

 curves for the two sexes. 



Estimates of natural mortality, M, for female and 

 male P. vitta were calculated from the relationship 

 between natural mortality, growth, and water tem- 

 perature (Pauly, 1980). This relationship was refitted 

 to Pauly s data for 175 fish stocks by using SPSS 12.0.2 

 for Windows (SPSS Inc., Chicago, IL). The values of 

 /; (per year) and L, (cm TL). estimated from the as- 

 ymptotic FL in the growth curves derived for P. vitta, 

 and the water temperature, T, were then inserted into 

 SPSS to obtain point estimates and associated 95% 

 confidence limits for M. thereby taking into account 

 the uncertainty of the parameter estimates and the 

 variation of the data around the regression line. The 

 mean annual bottom water temperature in Shark Bay 

 is 23.1°C (data provided by Department of Fisheries 

 Western Australia). 



The values for mortality, derived for each sex by 

 using the above approaches, were combined with the 

 estimates of total mortality obtained from the maxi- 

 mum recorded ages of the two sexes with Hoenig's 

 (1983) regression model for fish and those obtained 

 with a simulation approach (Hall et al., 2004). This 

 method reconciles the inconsistencies among the in- 

 dividual estimates of mortality and, through combin- 

 ing the different values, improves the precision of the 

 resulting estimates of natural and total mortality. To 

 provide a more precise estimate, the simulation routine 

 was modified slightly from that described by Hall 

 et al. (2004) to use the number of males or females 

 within the sample that were older than a specified 

 age rather than the age associated with the oldest of 

 those fish. 



