156 



Fishery Bulletin 103(1) 



Figure 1 



Transverse cross-section of a Pacific cod (Gadus macrocephalus) otolith with an unusually clear 

 annulus pattern. The otolith was taken from a 830-mm, 8-year-old fish that was recaptured 30 

 months after tagging. Annuli (black dots), checks, and edges (the space between the last annulus 

 and edge [white dot]) were traced and measurements of their areas (from the center of the oto- 

 lith to the outer margin of the translucent zone [dotted line]) and major axis lengths (from the 

 smallest rectangular box that will hold the translucent zone) were collected. T is the estimated 

 otolith size (length and area) at the time of tagging and was used to back-calculate fish length 

 at tagging. W corresponds to the annulus preceding T. 



the time of tagging. The second step was calculating the 

 area and length of that region, producing an estimated 

 otolith size at the time of tagging 



First, to approximate the location of the otolith that 

 corresponded to the time of tagging required the reader 

 to know how long (years) the fish had been at liberty, 

 after tagging. Using this knowledge and starting from 

 the last annulus before the edge, the reader counted 

 towards the center of the otolith, the number of years 

 (as represented by annuli) that the fish had been at 

 liberty. (In cases where the fish had been at liberty for 

 less than one year before being caught again, the reader 

 began at the edge rather than at the last annulus before 

 the edge). Assuming that all annuli are laid down by 

 late winter, the reader would end up on the annulus 

 that preceded the summer of tagging. This annulus 

 represents the size of the otolith just prior to tagging 

 and for sake of further explanation, its area and length 

 will be identified as W (Fig. 1). To complete the proce- 

 dure, the reader needed only to measure the summer 

 increment which followed W, divide it in half and add 

 it to W. These calculations were assumed to reflect the 

 size of the fish's otolith at time of tagging and were 

 used as O f values (the size of the otolith at tagging) to 

 back-calculate fish size at initial capture. 



Estimating fish length by using tagged fish and 

 back-calculations 



Annuli on tagged fish otoliths can be used to estimate 

 the length of each fish at an earlier age. Smedstad 



and Holm (1996) compared six different back-calcula- 

 tion formulae on tagged Atlantic cod (Gadus morhua) 

 and found that the age-independent, nonlinear, body 

 proportional (nbp) hypothesis worked the best. Pacific 

 cod is a gadid closely related to the Atlantic cod; there- 

 fore we also used the nonlinear, body proportional 

 formula 



L^iOJOJL, 



where L t = the predicted fish length at tagging or de- 

 sired age; 

 O, = the size (either radius or area) of otolith at 



tagging; 

 O r = the size of otolith at time of recapture; 

 v = the slope from the regression of Ln(L) on 

 Ln(O); and 

 L c = the fish length at recapture. 



This analysis was performed by using two different mea- 

 sures of otolith size, the cross-sectional area and major 

 axis (i.e., length) of otolith increments (Fig. 1). 



Estimating growth increments in fish length 

 from tagged fish 



We can use tagged fish otolith ages to estimate how 

 much each fish grew in length after tagging, in a manner 

 similar to Fabens' equation (Ricker, 1975), using the von 



