NOTE Toole and Nielsen: Microprobe precision associated with Sr:Ca ratios 



425 



Widths of 95% confidence intervals associated with 

 Sr/Ca ratios were determined with linear and nonlinear 

 regressions for each counting time. The ratios and 

 widths of confidence intervals were then converted to 

 temperatures using the four previously published Sr/Ca 

 vs. temperature regressions in Table 1. 



The effect of exposure time on Sr/Ca constancy was 

 analyzed with a multiple regression containing ex- 

 posure time and each location (coded as O's and I's) as 

 independent variables. Locations were included to re- 

 move possible effects of initial Sr/Ca concentrations, 

 which varied between sites. After determining that in- 

 teractions and nonlinear terms did not improve a model 

 with parallel straight lines, the common slope was com- 

 pared with a slope of using a <-test. 



Whenever the null hypothesis could not be rejected 

 at a = 0.05, statistical power (1-/3) of the test was 

 calculated as in (Neter et al. 1989:74-75). The power 

 of a test was considered acceptable if (l-/3)>0.80 

 (Peter man 1990). 



Results 



The twelve transects made under different beam con- 

 ditions on the otolith of a 65.7 mm SL juvenile Dover 

 sole exhibited consistent patterns of strontium and 

 calcium concentrations. Sr concentrations were highest 

 at the two innermost positions and lowest at the two 

 outermost positions in all transects. Sr/Ca ratios mir- 

 rored the pattern of Sr. Ca concentrations were ap- 

 proximately 100-500 times higher than Sr concentra- 

 tions. An example of one of the 12 transects (7/im beam 

 at 20-sec counting time) is presented in Figure 2. 



Relative error of Sr measurements decreased as 

 counting time and elemental concentrations increased, 

 and this was best described by an exponential regres- 

 sion model (Fig. 3, Table 2). The coefficient of varia- 

 tion was 1.4-4.2% for Sr concentrations of 0.2-1.2%. 

 When the effect of elemental concentration was re- 

 moved, Sr CV's increased with decreasing beam-power 

 density (Table 3); however, this effect was small com- 

 pared with those of elemental concentration and count- 

 ing time. Differences in Sr CV's attributable to beam- 

 power density was 0.012-0.076%. 



The coefficient of variation associated with Ca mea- 

 surements was 0.5% for 10- and 20-sec counts and 0.4% 

 for 30- and 40-sec counts, regardless of Ca concentra- 

 tion and beam-power density. 



Regressions of the widths of 95% confidence inter- 

 vals for Sr/Ca determinations against measured Sr/Ca 

 ratios are presented in Figure 4 and Table 4. These 

 regressions include only the effects of elemental con- 

 centration and counting time; the effect of beam-power 

 density is omitted. Although relative error decreases 



Table 3 



Relationship between Sr coefficient of variation (CV) and 

 beam power density, holding Sr concentration as a nonlinear 

 covariate, based upon microprobe transects along the saggital 

 plane of a Dover sole otolith. Each regression represents three 

 transects with 12 points each (A^ 36). Equations are in the 

 form; CV = A; -i- AoZj + AjZ, + B,* (Sr mole fraction) + B,« (Sr 

 mole fraction)^ where A is the intercept for the 10 ^m beam 

 (0.255 nAJiim density), A + AoZ, is the intercept for the T^m 

 beam (0.520 nA/jim density), and A + A3Z2 is the intercept for 

 the 5^im beam (1.019 nAJ^im density); Zj and Z, are dummy 

 variables for the 7 and 5fjm beams; and B, and B, are fitted 

 slope parameters. Partial-F tests indicate the significance of 

 beam power density effects in the model. Standard errors in 

 parentheses. 



Counts 



Parameter 



10-sec 



20-sec 



30-sec 



40-sec 



A, 



' (adj.) 



(0 05.2,31) 



4.990 



(0.101) 



-0.013 



(0.027) 



-0.076 



(0.027) 



-389.80 



(40.88) 



17940.3 



(3996.70) 



0.954 



4.479 



0.020 



3.394 



(0.043) 



-0.019 



(0.018) 



-0.055 



(0.018) 



-219.41 



(13.49) 



7746.5 



(921.47) 



0.969 



4.833 



0.015 



2.767 

 (0.051) 

 -0.027 

 (0.017) 

 -0.052 

 (0.017) 

 -169.07 

 (15.73) 

 5386.3 

 (959.47) 

 0.959 

 4.531 

 0.019 



2.420 



(0.041) 



-0.039 



(0.014) 



-0.053 



(0.014) 



-151.79 



(12.81) 



5229.6 



(796.05) 



0.962 



8.443 



0.001 



