Fassett et al. (2011) claim to have accomplished the “first successful direct dating of fossil vertebrate bone,” providing “a new methodology with the potential to directly obtain accurate dates for any vertebrate fossil” (p. 159). There are shortcomings, however, with the method used to extract U/Pb ages from the U/Pb isotopic analyses.
CORRECTION FOR COMMON Pb
The Pb in the analyzed samples is mostly “common” (that is, Pb unrelated to the radioactive decay of uranium in the samples), having a typical 206Pb/204Pb of ∼24. How the very large correction for common Pb was made is not mentioned in Fassett et al., and most readers will assume that the usual method of using 204Pb as the index isotope was followed (an isochron approach is seemingly ruled out, as only individual sample ages and errors are presented). However, examination of Fassett et al.’s data reveals that the common Pb index isotope was 207Pb, requiring an estimate for the common 207Pb/206Pb ratio, and solving for the age that forces the 206Pb/238U and 207Pb/235U ages into concordance. But two questions are left unanswered by Fassett et al., each of which is essential to evaluation of the accuracy and precision of their ages:
1) Why use the 207Pb correction method (generally reserved for analyses with very imprecise or missing 204Pb measurements) when the precisions of both the 206Pb/204Pb ratios and associated 204Pb-corrected ages are, if anything, somewhat better than that of the 207Pb/206Pb ratios and associated 207Pb-corrected ages? Note that Fassett et al. nowhere indicate that their 206Pb/204Pb measurements and precisions are any less valid than those of 207Pb/206Pb.
2) Given that any 207Pb-corrected ages calculated from the Fassett et al. data are very sensitive to the choice of common 207Pb/206Pb values, what values were actually used, and how they were selected? Without such information, the objectivity and reliability of the claimed ages is impossible for any but the most dedicated and specialized reader to evaluate.
However, back calculation of the data in Fassett et al.’s table DR1 shows that, for the control bone, three values for the common 207Pb/206Pb ratios were selected—0.794, 0.821, and 0.836 (give or take 0.001). There is every indication that, rather than being assigned on the basis of some (unmentioned) objective criterion such as 238U/204Pb ratios, sample location, chemistry, or mineralogy, the three common 207Pb/206Pb values were obtained by extracting arbitrary subgroups of the control analyses that clustered along different linear regressions (isochrons) on the 238U/207Pb-207Pb/206Pb diagram. The Y-intercepts of these regressions were then recycled for calculation of the individual ages reported in the Fassett et al. tables. The same type of approach seems to have also been used for sample BB-1, though in this case all analyses were used to determine the common 207Pb/206Pb intercept.
Such a procedure, however, is mathematically circular. If the common-Pb ratios used for calculation of individual ages are derived from an isochron fit to the data suite as a whole, complex sample-to-sample error correlations are forced on the individual ages. In fact, no amount of recycling of the isochron results into individual sample ages followed by simple weighted-mean calculations can improve upon the precision or accuracy of the isochron age.
EXTREME DATA CULLING
Out of 127 U-Pb analyses for the control bone (Fig. 1), 55 were rejected for falling outside an arbitrary 70–80 Ma age window (not 60–80 Ma as stated in Fassett et al.), and 47 rejected for having 238U/204Pb >500. The remaining 25 analyses are referred to as “unaltered parts of bone” (p. 160), implying that the other 102 samples are altered—in most cases based solely on the failure of their ages to fall within their entirely arbitrary 70–80 Ma acceptance window.
It is not surprising that exclusion of all ages falling outside a window whose midpoint is close to the desired age target of 73 Ma, and whose half width is similar to the individual age errors, yields a mean close to the target age, and a mean square of weighted deviates near 1. However, to regard the resulting age and uncertainty as meaningful, and a validation of their technique on any other such sample, cannot be justified.
DATA FOR SAMPLE BB-1
Concerns regarding common-Pb correction also affect sample BB-1. In common with analyses on the control bone, the BB-1 206Pb/204Pb-238U/204Pb ratio pairs give very different results than the 238U/206Pb-207Pb/206Pb system used for Fassett et al.’s calculations. For example, the 206Pb/204Pb-238U/204Pb isochron age for the BB-1 longitudinal samples is 55 ± 3 Ma, compared to Fassett et al.’s 64.8 ± 0.9 Ma (which is essentially a 238U/207Pb-207Pb/206Pb isochron age). This discrepancy (which must arise either from unrecognized analytical problems, a history of open-system behavior, or highly variable common Pb) is neither acknowledged nor discussed in Fassett et al.