Welsford and Lyle: Estimates of growth of Notolabrus fuacola from length- and age-based models 



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multiple recaptures allowed, the initial length and pen- 

 ultimate length measurement and their corresponding 

 dates were used in length-based analyses at this site. 

 Individual length-at-age estimates were also adjusted 

 according to the date of any previous reliable length 

 record. 



Age-based growth modeling 



Data consisted of ages estimated from otoliths (T) and 

 lengths at final recapture (or last reliable length mea- 

 surement at Point Bailey) (L). Kolmogorov-Smirnov tests 

 were conducted between sites and between sexes within 

 sites to determine if there were differences between 

 the proportional frequency distributions of fish lengths 

 in length-at-age data sets. Growth was modeled by 

 using the standard von Bertalanffy growth function 

 (VBGF): 



L = ljl-e 



-k(T-t«h 



(1) 



The VBGF for the two sites and sexes within sites 

 were modeled separately (Table 1). Fish for which sex 

 could not be determined were not included in the sex- 

 specific models. 



A reparameterized version of the VBGF was also es- 

 timated from Equation 4 in Francis (1988b): 



L = L 



[l l .-l T ][l-r- 



'] 



1-r 2 



where r  





(2) 



(3) 



and where l x , l v and l m , are the mean lengths at ages t, 

 v, and co=(t+u)/2 — ages chosen from within the observed 

 range within the data set. The values chosen for all the 

 otolith-based models were t=4, oj=7 and o=10 years, 

 encompassing the range of ages represented in the data 

 sets for both sites. Estimates of these parameters have 

 a direct biological meaning and have more statistically 

 favorable properties than the standard VBGF para- 

 meters l v , k, and t (Francis, 1988b; Cerrato, 1991). 



Models were fitted by minimizing a likelihood func- 

 tion and assuming normally distributed residuals 

 (Eq. 4): 



-A = -X,ln 



^exp 



2a 1 



(4) 



The measured length of the ( th fish, L r has its corre- 

 sponding expected mean length at age ii,, as determined 

 from Equation 1 or 2 above, where ;<, is normally distrib- 

 uted and has a standard deviation a. The quality of the 

 fits was gauged visually in the first instance by the lack 

 of trends in plots of residuals against length-at-age. 



To further investigate each model, each data set was 

 bootstrapped 5000 times. The bootstrapping procedure 

 involved randomly resampling, with replacement, from 

 the original data set, and then fitting the VBGF to this 

 new data set, thereby generating new estimates of all 

 model parameters (Haddon, 2001). 



Based on the percentile distribution of bootstrap 

 parameter estimates, 95% confidence intervals (CIs) 

 around the original sample estimates were calculated for 

 each VBGF parameter. To account for any skew in the 

 distribution of bootstrap parameter estimates, a first-or- 

 der correction for bias of CIs was performed, where boot- 

 strap percentiles used to estimate the CIs were adjusted 

 on the basis of the proportion of bootstrap estimates less 

 than the original estimate (Haddon, 2001). 



To determine whether growth showed any site or sex- 

 within-site (referred to as "sex-") differences, we com- 

 pared the overlap of first-order corrected CIs and plots 

 of bootstrap estimates. Simple comparison of CI overlap 

 as a test for parameter difference has been shown to be 

 overly conservative (Schenker and Gentleman, 2001). 

 Hence the null hypothesis of no difference was accepted 

 in the first instance only in cases were the amount of 

 overlap was obviously large. In cases were the extent 

 of overlap was small, and the chance of incorrectly ac- 

 cepting the null hypothesis existed, a randomization 

 test was performed. This test involved constructing the 

 distribution of the difference between the estimates of 

 the parameter of interest. Parameter estimates were 

 randomly selected with replacement from each set of 

 bootstrap estimates for the two populations, and the dif- 

 ferences were determined for these 5000 random pairs. 

 Then a 95% first-order corrected CI was constructed as 

 above, and the null hypothesis was rejected only if the 

 CI did not include zero. Likelihood ratio tests were also 

 conducted on the VBGFs and individual parameters 

 (Kimura, 1980). 



Length-based growth modeling 



Growth trajectories consisted of the initial length (L,), 

 time at first capture (Tj), time at final recapture (or pen- 

 ultimate recapture at Point Bailey) (T., ), change in length 

 from the first to the final recapture (AL), and duration in 

 years between capture and last recapture (AT). T 1 and 

 T., were measured in years from an arbitrarily chosen 

 point, 1 January 1999 — the first day in the earliest 

 year in which tagging was conducted. For individuals 

 recaptured more than once, only information relating to 

 the initial and final captures was used in the analyses. 

 This approach maximized the time between recaptures 

 for any fish, increasing the chance of detecting growth, 

 and gave equal weight to each fish sampled. 



Because the two sites were sampled over different 

 time periods, only samples from Lord's Bluff that were 

 taken at the same time as samples at Point Bailey were 

 considered for the purposes of between-site growth com- 

 parisons (Table 1). The resulting data set, designated 

 LB res , reduced potentially confounding effects of longer 

 sampling durations at Lord's Bluff. 



