age score is significantly lower (0.62). Out of every record with a PbPb concordance score, 77.9% (471 out of 605) are concordant (have a score of 1.00) and 9.3% (56) are discordant (have a score of 0.00). When compared with other methods, Pb-Pb shows the highest concordance with 235U-207Pb (concordance score 0.54). Its score with FT is 0.00, meaning the two methods are never concordant with each other. Pb-Pb yields consistently greater ages than every other method, ranging from Rb-Sr (where Pb-Pb ages are greater 54.4% of the time) to 232Th-208Pb (where Pb-Pb ages are greater 84.2% of the time). 2. Rubidium-strontium (Rb-Sr) For all Rb-Sr age determinations for the same record, Rb-Sr has a 0.80 average concordance score with itself (that is, compared with other Rb-Sr determinations for the same records). For “Three Method Comparisons,” the average score is much lower (0.61). Out of every record with a Rb-Sr concordance score, 73.0% (797 out of 1,092) are concordant (have a score of 1.00) and 12.6% (138) are discordant (have a score of 0.00). When compared with other methods, Rb-Sr shows the highest degree of concordance with K-Ar (concordance score of 0.51), with the others ranging from 0.40 concordance (235U-207Pb) to 0.21 concordance (FT). The percentage of Rb-Sr age determinations that are greater than those yielded by other methods ranges from 45.4% (Pb-Pb) to 70.8% (FT). Pb-Pb is the only method that gives consistently greater ages than Rb-Sr, suggesting that Rb-Sr most often overestimates ages in relation to other methods. 3. Uranium-lead (235U-207Pb) For all 235U-207Pb age determinations for the same record, 235U-207Pb has a 0.80 average concordance score with itself (that is, compared with other 235U-207Pb determinations for the same records). For “Three Methods Comparisons,” the average score is the same (0.80). Out of every record with a 235U-207Pb concordance score, 71.3% (347 out of 487) are concordant (have a score of 1.00) and 11.3% (55) are discordant (have a score of 0.00). When compared with other methods, 235U-207Pb shows the hightainty range was given. There are some noteworthy outliers within the database. Three K-Ar ages, one 235U-207Pb age, and eleven Pb-Pb ages are negative. One 235U-207Pb age and 647 Pb-Pb ages are given as zero. These zero ages make up 24.7% of the 2,621 Pb-Pb ages in the database. On the opposite end of the spectrum, there are nine K-Ar ages, four Rb-Sr ages, three 238U-206Pb ages, one Pb-Pb age, and three 232Th-208Pb ages that are greater than 4.5 billion years (Ga), the conventionally accepted age of the Earth. Two are over 10 Ga. Of the 18,575 records in the database, only 4,875, or 26.2%, included more than one calculated age. These were the ones that could be analyzed using our “Concordance Metric,” and thus relevant in our investigation of the frequency of concordance and discordance. Of these records, 1,135 (23.3%) had a concordance score of 0.00 (i.e. the reported ages were totally discordant) and 2,593 (53.2%) had a concordance score of 1.00. The average concordance score for the whole database is 0.64. Table 1 shows the concordance scores for all 4,875 records, along with a breakdown of the concordance scores for each radioisotope method. The distribution of concordance scores for all 4,875 records is shown as a histogram in Fig. 1. Appendix B provides pie charts representing all pairwise comparisons in our “Two Methods Comparison” dataset. A scatterplot showing the number of ages involved in the calculation of the concordance score for each record is shown in Fig. 2. There is a slight negative correlation between the number of ages and the concordance score but this correlation is not statistically significant (R2=0.0016). Table 2 shows the proportion of concordant ages between specified pairs of radioisotope methods for each of our “Two Methods Comparisons.” Table 3 shows how often the age calculated using one method was greater than the age calculated using another. A. Individual methods 1. Lead-lead (Pb-Pb) For all Pb-Pb age determinations for the same record, Pb-Pb has a 0.84 average concordance score with itself (that is, compared with other Pb-Pb determinations for the same records), which is the highest of all the methods. For “Three Methods Comparisons,” the aver- Pb-Pb Rb-Sr 235U- 207Pb 238U- 206Pb 232Th-208Pb K-Ar FT All Methods Score = 0 708 138 68 55 56 43 108 1135 0 < Score < 0.50 119 84 53 47 41 13 27 638 0.50 ≤ Score < 1 76 73 47 38 37 14 19 509 Score = 1 1228 797 330 347 471 80 150 2593 Total Count 2131 1092 498 487 605 150 304 4875 Average Score 0.62 0.80 0.76 0.80 0.84 0.62 0.56 0.64 % Concordant (Score = 1) 58% 73% 66% 71% 78% 53% 49% 53% Table 1. The distribution of concordance scores for each method, as well as for the whole database. Also includes the average score and the percentage of concordant records. BEACHY, KINARD AND GARNER How often do radioisotope ages agree? 2023 ICC 389
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