Cappo et al : A new approach to validation of periodicity and timing of opaque zone formation 



481 



our second working approximation that outer cycles 

 had equal widths on the marked otoHths. The plots 

 were fitted best by exponential curves: W = 0.38 + 

 4 92e-08ir, fo,. species pooled; W = 0.70 + 11.44e-i68o 

 for L. erythroptems; W=0.30 + 3.21e-"5« for L. johnii; 

 and W = 0.75 + 9,12e~'-'^" for L. sebae. On average, 

 there was a small decrease in cycle width from the 

 third to the fourth cycle and then successive cycles were 

 similar; however captivity or tagging may have caused 

 anomalous growth of some otoliths. TwoL. sebae showed 

 no (sl976), or insignificant (sl980), growth along the 

 ventral axis (Fig. 4) but their otoliths did continue 

 to thicken. The largest L. sebae and L. erythropterus 

 showed substantial growth along the ventral axis in 

 relation to other individuals ( Figs. 4 and 5 ), contributing 

 to the high coefficients of variation shown in Table 2. 

 For some captives this phenomenon led to a progressive 

 or irregular increase in cycle width, most notable for L. 

 erythropterus marked in August 1993 (eg. sl937, sl943. 

 sl954, and sl958 in Fig. 5), that violated the second 

 approximation of our model. 



Periodicity of zone formation 



Using the informal validation approach, and assuming 

 a springtime completion date of 1 October, we estimated 

 the frequency distributions shown in Table 3 that 

 indicated an annual periodicity of deposition of opaque 

 zones in the majority of otolith sections. However, there 

 was a small minority of fish with more or less zones 

 than expected, and information about the opaque zones 

 counted for these individuals was available by applying 

 the "direct method" developed in our study by rewriting 

 Equation 3 as 



V={1F + FF)/L + N/L. 



(8) 



L. johnii 



,1 mm. 



13-Feb-94 



Date fish l<illed 



2-IVlar-95 



S6666 



S2001 

 S2003 



23-IVlar-95 



5-IVtar-94 

 3-Feb-93Ll7-Mar-93 

 ZI'IZIJ 3-Apr-94 



17-r^ar-93, 

 ^'' ^ ~J" ] 28-Dec-94 



6-Mar-94, 



27-IVIar-95 



26-tVlar-95 

 J 12-Feb-94 



30-Sep-94 

 17-Dec-95 



12-tVlay-93, 



I 2-Apr-94 



Figure 6 



Measurements of the position of opaque zones and the OTC 

 marks on the ventral LI axis for L. johnii. All conventions are 

 the same as those in Figures 4 and 5. 



