426 



Fishery Bulletin 90(2). 1992 



Table 4 



Relationship between Sr/Ca ratios and 95% confidence interval 

 of measurements at different counting times, based upon 

 microprobe transects along the saggital plane of a Dover sole 

 otohth. Each equation was derived from three transects of 

 12 points each (AT 36). Form of the relationship is: 95% 

 CI = A + (B* Sr/Ca ratio). Standard errors in parentheses. 



Seconds 



B 



R^ 



10 

 20 

 30 

 40 



with increasing Sr/Ca, the actual width of the confi- 

 dence interval increases. Conversion of Sr/Ca ratios 

 and 95% confidence limits to temperatures, using the 

 20-sec regression and previously published temperature 

 vs. Sr/Ca ratios, is presented in Figure 5. Confidence 

 limits associated with calculated temperatures were 

 0.6-4.7°C, depending upon species, study, and tem- 

 perature level. 



The model which best fit the six multiple exposures 

 is presented in Figure 6. The common slope of - 1.3* 

 10 '' was not different from a slope of (fo.05,29 = 

 0.176, P = 0.86). This experiment could have detected 

 a change as small as 1.86*10-'' Sr/Ca per sec in- 

 creased exposure (or 1.21*10''' for each 65-sec treat- 

 ment) at = 0.05 and (1 -/3) = 0.90, had such an effect 

 existed. 



Discussion 



Our results confirm that measurement error asso- 

 ciated with Sr/Ca determinations is nontrivial. At 

 the standard counting time of 20 sec, measurement 

 error associated with Sr/Ca determinations (expressed 

 as 95% confidence intervals) was equal to or greater 

 than the Sr/Ca increment representative of a 1°C tem- 

 perature change in three of the four previously-pub- 

 lished studies. Even in Townsend et al. (1989), at tem- 

 peratures <4°C, measurement error was >1°C. The 

 highest measurement error in the studies was repre- 

 sentative of a 4.7°C temperature change. Inferred 

 temperature differences between otolith regions or be- 

 tween fish should be considered in light of these values. 

 Statistical error in the Sr/Ca vs. temperature regres- 

 sions will add to the measurement error associated with 

 temperature calculations. 



< 

 > 



LU 



O 



LU 

 Q 



o 



LO 

 CD 



O 



I 

 I- 

 9 



5 



RADTKE (1989) 

 MUMMICHOG 



RADTKE (1984) 

 ATLANTIC COD 



RADTKE ETAL (1990) 

 ATLANTIC HERRING 



TOWNSEND ET AL (1989) 

 ATLANTIC HERRING 



TEMPERATURE (C) 



Figure 5 



Relationship between back-calculated temperature estimates 

 and 95% confidence intervals (for measurement error only) 

 surrounding those estimates. Temperature vs. Sr/Ca conver- 

 sions are from Table 1. Confidence intervals are converted 

 from Sr/Ca confidence intervals for 20-sec counts in Table 4 

 and Figure 4. 



400 



EXPOSURE TIME (SEC) 



Figure 6 



Relationship between Sr/Ca level and exposure time, based 

 upon microprobe samples at six sites on one Dover sole otolith. 

 Six sequential analyses were made at each site (N 36). The 

 six exposure times corresponded to counting times of 20, 40, 

 60, 80, 100, and 120 sec. The equation describing the rela- 

 tionship is: Sr/Ca level = 0.0023 -f (0.0054*Z, ) -^ (0.00026*2, ) 

 -^(0.0114•Z.^) + (6.6xl0-*•ZJ■^(0.012•Z5)-(1.30xl0-'• 

 exposure time), where Z,-Z5 are dummy variables for loca- 

 tions. Adjusted fi- = 0.991, P<0.0001. 



