Our primary goal of confirming the accuracy of the growth zone counts was largely achieved, and some guidance in choosing the best interpretation also was provided. The sequential δ^{18}O measurements demonstrated clear seasonal signatures (Fig. 7) which made this validation possible. The percent agreement between the growth zone counts and the number of δ^{18}O maxima was 61.18%, the average coefficient of variation was 8.04%, and the average percent error was 5.69%. Considering specimens individually, specifically the locations of counted translucent growth zones with respect to δ^{18}O maxima, provided results in greater detail. For example, Figure 7 shows four images of thin-sections annotated with the counted growth zones and their respective δ^{18}O signatures. In three of these examples, the number of counted growth zones is equal to the number of δ^{18}O maxima. Further, the locations of the counted growth zones and the locations of the δ^{18}O maxima in the thin sections are generally similar (Fig. 7). Therefore, this adds confidence to our age validation. In approximately 39% of the specimens, where the counted growth zones were not equal to the number of δ^{18}O maxima, new guidance was provided for correct interpretation of problematic growth zone patterns. For example, we learned that a dark zone sometimes occurs inside the first true annual zone and should not be counted (Fig. 7). Also, a dark zone between the first and second true annual zones often occurs and should not be counted. This is clearly the case in panel 3 of Figure 7 where a dark zone was counted, but did not co-occur with a δ^{18}O maxima. These examples can now be applied to future age estimates in Pacific cod.

Figure 8. Probability of ageing bias, the difference between the growth zone-based age and true age, at each true age. A positive bias means an age older than the true age was assigned. A negative bias means an age less than the true age was assigned. Bars represent multinomial, solid line represents normal approximation.

Figure 9. Relationship between water temperature and δ^{18}O in Pacific cod otoliths.

Bias estimation considered the difference between true ages and ages derived from growth zones interpretation in the break-and-bake otolith. It was rare for an age reader to assign an age 2 years greater or less than the true age. Hence, there was a very small probability of bias by that degree (Fig. 8). In general, both the discrete-multinomial and continuous-normal approaches to estimating the probability of bias were similar (Fig. 8). Over all ages, there was a 64% probability that an age reader assigned the true age, with a 19% and 17% probability of assigning an age less or greater than the true age by 1 year, respectively (Fig. 8). The probability of bias at the ages of 2 and 3 years was also relatively symmetric about ±0 years, and the different estimation methods showed similar results. At these ages, there was approximately an 80% probability of assigning the true age, and about a 10% probability of assigning within 1 year of the true age (Fig. 8). At the ages of 4 and 5 years, age specific bias estimates were less symmetric about ±0 years and the different bias estimation methods had more discrepancies. At an age of 4 years with the discrete-multinomial approach, the probability of assigning an age equal to the true age was about 32%, to 1 year greater it was about 37%, and to 1 year less it was about 30%. In contrast, the continuous-normal approach showed a much greater probability (~62%) of assigning an age equal to the true age. Further, in this approach the probabilities of assigning an age 1 year greater or less than the true age were very unequal, about 36% and 8% respectively. At a true age of 5 years, the probabilities differed slightly between the two bias estimation methods. Both methods indicated a 50% to 60% probability of assigning an age equal to the true age. The probabilities in both methods were near 0% of assigning an age greater than the true age. However, the probabilities of assigning an age 1 year less than the true age were about 42% and 30% for the discrete-multinomial and continuous-normal approaches, respectively. Also, the discrete-multinomial approach indicated a small probability of under-ageing true age by 2 years (Fig. 8). While a comparison between the two estimation methods was instructive, we suggest that the discrete-multinomial approach was more faithful to the nature of age data.

The secondary goal of our research, to describe the relationship between otolith δ^{18}O and water temperature, was very successful. The instrumental temperatures we had, whether measured at time of capture or from recording archival tags, demonstrated the strength of the relationship between δ^{18}O in Pacific cod otoliths and water temperature (r^{2} = 0.74) (Fig. 9). In a related fish species, Atlantic cod (G. morhua), previous studies have also indicated that δ^{18}O is a function of temperature..

The δ^{18}O signatures indicated that the growth zone-based ages were usually correct, i.e. validated. When the number of δ^{18}O maxima was not the same as growth zone-based ages, valuable insights were provided to aid interpretation of the growth zones. The confirmed relationship between otolith δ^{18}O and water temperature lent credibility to this age validation study.

Craig R. Kastelle, Thomas E. Helser, Jennifer McKay, Delsa M. Anderl