Kastelle et al.: Anoplopoma fimbria age validation 



295 



Eq. 1) in a Lucas cell (Lucas, 1957). The samples 

 were stored in a Rn-222 de-emanation flask for a 

 minimum of three weeks prior to counting. During 

 storage, Rn-222 reached secular equilibrium with 

 Ra-226. Reagent blanks were processed with each 

 sample. Lucas cell (Rn-222) counting times were 

 4,000 minutes for each sample or reagent blank. 

 Lucas cell and electronic backgrounds (counting 

 time 1,000 minutes) were measured multiple times 

 before and after any sample or reagent blank. The 

 counting efficiency (i.e. the percentage of decays that 

 was detected) of the de-emanation technique, Lucas 

 cells, and associated electronics was determined to 

 be 53.75% with the use of a Ra-226 standard solu- 

 tion supplied by the U.S. Environmental Protection 

 Agency. Activities of Ra-226 and associated errors 

 were calculated by using the methods of Sarmiento 

 et al. (1976). Details concerning incorporation of 

 blank and background measurements into the activ- 

 ity calculation for Po-210 and Ra-226 are given in 

 Kastelle (1991). All sources of error were propagated 

 through the calculations to estimate errors (stan- 

 dard deviation or SD) for the Ra-226 and Pb-210 

 measurements. 



Data analysis 



ANOVA with contrasts was used to test whether 

 break-and-burn otolith ages from the different age 

 readers were significantly different within each age 

 category. Statistical analyses of activity measure- 

 ments from samples, backgrounds, and reagent 

 blanks were conducted by using Z, t, and a likeli- 

 hood ratio x 2 test as described below. To test if the 

 Ra-226 (or Pb-210) activity from each age category 

 was statistically different, the likelihood ratio test 

 was employed. Assuming X ; is distributed 

 as Ni/u^crf), where the &f are known, the like- 

 lihood ratio x 2 test for H :/J l = ... =/J„. is 



I>, 



(if/of 



which is distributed as y 2 , . HereX, is the measured 

 Ra-226 (or Pb-210) activity for age category /, 



/} = £(X,/<T 2 )/£(1/CT, 2 >, 



and of is the variance for age category i. If of's are 

 underestimated, then the % 2 would be inflated. Z 

 tests were carried out between the reagent blanks 

 plus background, and background alone, for Po-209 

 and Po-210 measurements; a i-test was performed 

 between the mean Rn-222 reagent blank plus back- 

 ground and the background alone. 



Two sets of estimated Pb-210/Ra-226 ratios were 

 calculated: one by using the mean Ra-226 activity 



from the four categories and the second by using the 

 Ra-226 activity measured for each category. The 

 delta method was used to determine the variance of 

 the ratios (Seber, 1982). 



The measured ratio of Pb-210/Ra-226 in the 

 otoliths can be used to predict a radiometric age 

 from the curve: 





(2) 



where Aj is the activity for Ra-226, A 2 and X 2 are 

 the activity and decay constant respectively (^.=ln 

 (2)/half-life, for Pb-210, t is time (i.e. age), and R* is 

 the initial ratio of Pb-210/Ra-226 (Fig. 1, see also 

 Kastelle [1991]). The initial ratio was estimated by 

 solving Equation 2 for R* and applying the activity 

 ratio from age category 1 (R*=-0.034). The negative 

 value for R* is due to measurement error. Therefore, 

 we assume R* - in Figure 1. The actual fish ages 

 were predicted from the radiometric ages by sub- 

 tracting the time between collection and analysis 

 (4.5 yr) from the radiometric ages in Figure 1. Al- 

 ternatively, it is possible to calculate the radiomet- 

 ric ages by correcting the Pb-210 activity estimates 

 to the time of otolith collection. These adjusted ra- 

 diometric ages were then compared with ages read 

 from the burnt otolith cross-section by the three 

 readers. For each of the readers, a linear regression 

 line was fit through the origin and compared with 

 the 45° line of agreement by using a £-test. 



0.7 n 



(0 



£ 



<M 

 CM 



CO 



CM 



c! 



.o 

 O 



7 — f~ 



<■*.* '9.7 



0.0 L ** '•■7 20 i 27 2 '22 3 



Predicted Radiometric Age (yr) 



40 



Figure 1 



Predicted radiometric age of samples from 

 observed activity ratios and curve of ex- 

 pected activity ratio (Eq. 2). Predicted radio- 

 metric age includes the 4.5 years between 

 collection and analysis. 



