618 



Fishery Bulletin 101(3) 



10 



15 



20 



25 30 



15 



20 



25 



10 



20 



25 



Figure 2 



Annual fjrowth as a function of jaw size for six models: lopislic dose- 

 response, Gaussian, Tanaka, Ricker, Richards, and von Birtalanffy 

 models. J=jaw length (mm); 4J = change in jaw length (mm). 



tion of one model. Nevertheless, it is clear that 

 the von Bertalanffy model does not represent 

 the data well over the full range of urchin 

 sizes iJf). To investigate this point further, we 

 divided our data set into three groups over the 

 range of of J, . The groups are 



1 Juveniles (J, < 8 mm) that do not fall on the 

 linear descent of 4 J versus J, characteristic 

 of von Bertalanffy growth. 



2 Sublegal, actively growing adults (8 mm< 

 J,<16 mm) that do follow von Bertalanffy 

 kinetics. 



3 Adults ( 16 mm< J, < 24 mm) that appear to 

 grow to large J^ but only very slowly, and do 

 not conform to the von Bertalanffy model. 



If the data were fitted to the von Bertalanffy 

 equation, all three groups should give the same 

 slope AJ IJf because three segments of the same 

 straight line all have the same slope. Instead, 

 group 1 gives a small positive slope, group 2 

 gives a negative slope that leads to unrealistic 

 conclusions for early growth rate and time-to- 

 fishery estimates shown in (Fig. lA), and group 

 3, excluding growth information from sublegal 

 urchins, yields a plausible mean final jaw size 

 of 22.6 mm but gives a growth rate constant 

 that indicates very slow growth for adults and 

 many decades for time-to-fishery. 



In the present study we fitted a decreasing, 

 linear von Bertalanffy function only to the 

 sublegal (group 2) urchins (Fig. lA) which did 

 conform to von Bertalanffy growth. The von 

 Bertalanffy function for the partial data set of 

 actively growing urchins in (Fig. 1) has a slope 

 of -0.504/yr, a AJ intercept of 8.7 mm/yr, and 

 a Jf intercept of 17.3 mm. These results lead 

 one to predict that final grow to 90'7f of their 

 final size in 3.5 years and that mean final size 

 will be less than the legal size (89 mm test 

 diameter), which is obviously false. We also 

 show the same function superimposed on the 

 entire data set (Fig. IB) where discrepancies 

 between the von Bertalanffy function and data 

 groups 1 and 3 above are evident. For our data 

 set (Fig. 1) and, we suggest, for urchin growth 

 in general, the von Bertalanffy curve does not 

 represent early growth, and a transition curve 

 or a peaked function reflects actual growth 

 better For our data set, the von Bertalanffy 

 model gives an overestimate of the rate of ur- 

 chin growth and an underestimate of the time 

 to enter the fishery. 



The slopes of these three line segments give 

 an indication how the von Bertalanffy model, 

 despite its implausible fit to the complete data 

 set, can give plausible growth parameters. Er- 

 rors in fitting a von Bertalanffy curve to a data 

 set resembling ours lie in opposite directions 



