904 



Fishery Bulletin 101(4) 



1-0 



0123456789 101 1 12 13 14 15 1617 1£ 

 ONDJ FMAMJ J ASONDJFM 



12 3 4 5 6 7 

 ONDJ FMAM 



Month 



Figure 3 



Index of completion at time t , (c,, t), for L. vitta for growth-ring categories 2 ,3, 4, 5, 6, 7, 8, and 9-12 sampled 

 between the months 1 October 1993 (;=0) to 31 March 1995 (?=18). The solid circles (•) represent those (c,, 

 t) most likely represented by t-j and lying closest to the function Fj and the solid triangles (A) are those 

 most likely represented by c, and lying closest to the function F.,. The logistic function, P, , indicates the 

 probability that points (c,, I) are most likely represented by function F,. 



and 5. Because of the smaller numbers offish, the data was 

 pooled for L. vitta with 9-12 growth rings, for N. furcosus 

 with 7-9 growth rings, and for L. sebae with 13-14 and 

 15-19 growth rings. 



The estimates of the parameters b, d^, d, (the rate of in- 

 crease and phase shift of Fj and F^), R, the time of formation 

 of a new growth ring, with the range ±(S-R), and the stan- 

 dard deviation (cj) for the four species are listed in Table 1. 



The estimated time of formation of a new ring varied 

 between age classes and occurred for L. sp. 3 from mid 

 July to mid September, for L. vitta from early July to early 

 September, for N. furcosus from mid July to late September, 

 and for L. sebae from mid July to mid November. 



The confidence intervals are small for L. sp. 3 and L. vitta 

 and generally larger for A^. furcosus and L. sebae where read- 

 ing increments was more difficult. The confidence interval 

 was smaller for L. sebae with 12-19 growth rings because 

 the clarity of the rings generally improved for older fish. 



The difference between the phase shift for functions f j 

 and F^, that is d^-di, was between 11 to 13 months. This 

 difference indicated an annual cycle of growth-ring forma- 

 tion. The standard deviation, a, of the values of index of 

 completion was lowest for forL. vitta (0.1-0.14) and highest 

 fori, sebae (0.11-0.21) and L. sp. 3 (0.11-0.24). 



Discussion 



With different starting values for the parameters, the 

 method we described found that the time of detection of 

 growth-ring formation for the four species was consistent. 

 Although the timing varied considerably for different num- 

 bers of growth rings, the estimate was generally similar 

 for each species. 



Other marginal increment studies on these species pro- 

 duced estimates of the times for growth-ring formation 



