NEW CORRECTION METHODS FOR ELECTRON SPIN RESONANCE (ESR) DOSE RATES: EXAMPLES FROM STERKFONTEIN AND SWARTKRANS, SOUTH AFRICA by Bonnie Blackwell Windsor University Geology Department; Windsor, Ontario Ca. Author's Note: Because this paper contains several equations and many mathematical symbols, it was necessary to email it in a form that was ascii compatible, yet could be easily reformated into the proper format for people who wanted to get a copy of it. Wordperfect, Word, and other word processing system output are not emailable without expensive encoding and decoding protocols not yet available at most sites. Therefore, you will find the following paper and its accompanying tables have been entirely formatted an the ascii compatible format ready for processing with LaTeX. Most universities have some form of LaTeX available either as a PC or a mainframe version. Most mathematics, physics, and some economics departments have this software. More importantly, they are usually willing to let outsiders print files using this software, if you ask nicely. To print this file simply remove this note and everything that preceeds the line reading: \documentstyle[twoside]{article} Copy the file onto a suitable device (discette, tape, etc.). This document was formatted to be < 80 characters wide for the text portion. For the tables, however, some lines exceed 80 characters. You may have to remove extraneous line feeds that arise in copying the file from your email to whatever device you choose. You can test this using any screen editor. Except for blank lines between paragraphs, there should be almost no blank lines in this file. If you have them, you can remove them with a Wordperfect macro, provided you save the file afterward using the unformatted text option of wordperfect. Then take the file to your local LaTeX site and following their printing protocols. It take about 5-10 minutes to print if they are using a 386 or 486. Except for the mathematical symbols, the text reads as normal. If you wish to try to read the raw LaTeX version, here are some symbols to help you decipher the formatting commands: "\" starts any LaTeX command line \section{...} enclosed text is section heading \subsection{...} enclosed text is subsection heading {\em ...} = put enclosed text into italics {\bf ...} = put enclosed text into bold face {\rm ...} = put enclosed text into ordinary font $ ... $ encloses a mathematical symbol \begin{enumerate} | produces an itemized list \item | starts each new item \end{enumerate} | ends listing \begin{equation} | produces a mathematical equation ... | coding for equation \end{equation} | ends equation \begin{tabular} | sets a tabular environment & | defines new cell on table \\ | ends line for table \end{tabular} | ends table If you wish more information on LaTeX, see Lamport, L., 1986. {\em The LaTeX User's Guide and Reference Manual}. Addison-Wesley, Reading, 242 pp. PC versions of LaTeX are available through share-ware and from some software companies. Four figures accompany this text. If you wish copies, please write me. Bonnie Blackwell ----------------------------------------------------------------- \documentstyle[twoside]{article} \pagestyle{headings} \pagenumbering{arabic} \setcounter{secnumdepth}{0} \setcounter{tocdepth}{4} \setlength{\parskip}{1ex} \setlength{\itemsep}{3ex} %\setlength{\parindent}{0em} \setlength{\evensidemargin}{+0.6cm} \setlength{\oddsidemargin}{+0.1cm} \setlength{\textwidth}{6.0in} %\setlength{\marginparwidth}{0.5in} \setlength{\topmargin}{-0.25in} \setlength{\textheight}{9.0in} \raggedbottom \nofiles %\setlength{\baselinestretch}{2} %\renewcommand{\baselinestretch}{2} \hyphenation {Swart-krans Sterk-fon-tein aus-tra-lo-pi-the-cine iso-chron} \begin{document} \newcommand{\hs}[1]{\hspace{#1em}} \newcommand{\spp}[1]{\rule{0.0em}{#1cm}} \newcommand{\ru}[1]{\rule[-0.2ex]{#1in}{0.1ex}} \begin{titlepage} \Large \begin{center} {\bf NEW CORRECTION METHODS FOR} \\ \vspace{2ex} {\bf ELECTRON SPIN RESONANCE (ESR) DOSE RATES:}\\ \vspace{2ex} {\bf EXAMPLES FROM STERKFONTEIN AND} \\ \vspace{2ex} {\bf SWARTKRANS, SOUTH AFRICA} \\ \end{center} \vspace{4ex} \normalsize \begin{flushleft} Bonnie A. BLACKWELL, \\ Dept. of Geology, \\ University of Windsor, \\ Windsor, ON, N9B 3P4 Canada \\ \vspace{2ex} 9403.08 \\ \end{flushleft} \normalsize %\pagebreak %\renewcommand{\baselinestretch}{2} \section*{Abstract} A radiation-sensitive ESR signal at $g$ = 2.0018 occurs in well crystallized fossil tooth enamel, but not in modern teeth. In dating fossil teeth, the accumulated radiation dose (${\cal A}_{\Sigma}$) needed to produce the observed ESR signal is the time-integrated natural, environmental dose rate experienced by the tooth since its deposition. Regardless of the uranium (U) uptake history assumed, a reliable age estimate requires an accurate estimate for the external dose rate during the tooth's history. If an extraneous tooth (i.e. reworked from an older unit or younger post-depositional intrusion) occur in a stratigraphic unit, the external dose rates measured {\em in situ} will not accurately reflect those experienced by that tooth. For teeth from a single unit, significant variations and multimodal distributions in the calculated ages, ${\cal A}_{\Sigma}$ values, enamel or dentine U concentrations may all indicate mixed sample collections. In large ungulate teeth, isochron analyses can eliminate the need for a separate external dose measurement, because they provide both the sample age and the external dose rate experienced by the tooth. Otherwise, modelling the sedimentary dose rates using time-averaged total external dose calculations becomes necessary. Tooth assemblages from both the australopithecine sites Sterkfontein and Swartkrans, South Africa, contain extraneous teeth. \noindent {\bf Key words:} Electron spin resonance (ESR) dating - tooth enamel, tooth dentine; isochron ESR dating; external dose rate calculation; reworked and extraneous teeth; Swartkrans, South Africa; Sterkfontein, South Africa. \end{titlepage} \pagebreak \section{ESR Dating Extraneous Teeth} At many controversial sites, electron spin resonance (ESR) dates on tooth enamel, are now being accepted as the true age, because they have compared well with absolute dates determined by other methods or with expected geological estimates (i.e.\ Schwarcz {\em et al}., 1988; Schwarcz \& Gr\"{u}n, 1988; Stringer {\em et al}., 1989). Since the radiation sensitive peak in fossil enamel at $g$ = 2.0018 is absent in modern enamel, ESR dating can directly date teeth as old as 5 Ma, using the relation: \begin{equation} %1 {\cal A}_{\Sigma} = {\cal A}_{\rm int} + {\cal A}_{\rm ext} = \int^{t}_{0} \left( D_{\rm int}(t)+ D_{\rm ext}(t) \right) \; dt \end{equation} \begin{tabular}{lrcl} where & ${\cal A}_{i}$ & = & the radiation dose accumulated due to component $i$ since enamel formation, \\ & $D_{i}(t)$ & = & the radiation dose rate, as a function of time, from component $i$, \\ & $t$ & = & the sample age, \\ \end{tabular} \begin{tabular}{llll} and if & $i$ & = & ${\Sigma}$, the total radiation component, \\ & $i$ & = & ${\rm ext}$, the external radiation component, i.e.\ the adjacent sediment, \\ & $i$ & = & ${\rm int}$, the internal radiation sources, i.e.\ the enamel and adjacent dentine \\ \end{tabular} \noindent (Blackwell \& Schwarcz, 1993). The total accumulated dose (AD), ${\cal A}_{\Sigma}$, is extrapolated from experimental irradiation, while the dose rates are estimated by analyzing the natural radioactivity in the tooth's immediate environment, $D_{\rm ext}$, and in the enamel and dentine, $D_{\rm int}$, given an appropriate U uptake model. Linear uptake (LU) ages, assuming the tooth continuously absorbed U at a constant rate since its deposition, provide a median age, while early uptake (EU) ages, calculated assuming all the U was absorbed soon after deposition, represent the minimum possible ESR age inferable from a given ${\cal A}_{\Sigma}$ value, and recent uptake (RU) ages, assuming most uptake occurs very late in the tooth's history, represent the maximum. Although the best uptake model to predict the true sample age remains controversial ({\em cf}.\ Gr\"{u}n {\em et al}., 1990; McDermott {\em et al}., 1993; Blackwell {\em et al}., 1992), $D_{\rm ext}$ must be calculated precisely and accurately, because its error is often the most significant factor in the age uncertainty (Blackwell, 1989). When dating stratigraphic units or the hominids that they contain, extraneous teeth can cause considerable problems. Without several dates from a given unit, recognizing that some may have be extraneous is impossible (e.g.\ Zymela {\em et al}., 1988). To calculate an ESR age for a reworked tooth requires that the $D_{\rm ext}$ reflect both the time and dose accumulated in the unit where the tooth was collected and those in the unit where it was originally deposited. While the former is easily obtained, the latter can be challenging to determine. Herein, I discuss strategies to calculate ESR ages for extraneous teeth, using examples from karsted deposits in Swartkrans and Sterkfontein caves, South Africa. For simplicity, this discussion will only use LU model ages, although the models described herein apply to all models. \section{Recognizing Extraneous Teeth} Suppose that several teeth collected from the same unit have been analyzed. If all the teeth were {\em in situ}, then a frequency distribution for a parameter $x$ (i.e. dose, age, etc.) should be normally distributed about a mean $\mu_{x}$ with a standard deviation $\sigma_{x}$. If $x_{i}$ for any single analysis varies from $\mu_{x}$ by more than 3 to 4 $\sigma_{x}$, a significant difference statistically, it may not have been {\em in situ}. Which of some 15-20 variables, however, will prove best in recognizing extraneous teeth? Significant differences in the calculated ages should be an obvious criterion. For most ESR ages, the major variation derives from those in the ${\cal A}_{\Sigma}$, $D_{\rm ext}$, and U concentrations in enamel ($U_{\rm en}$), dentine ($U_{\rm den}$), and cement ($U_{\rm cem}$) (Blackwell, 1989). Two different teeth, however, may yield similar ages, using very different values for ${\cal A}_{\Sigma}$, $D_{\rm ext}$, $U_{\rm en}$, $U_{\rm den}$, and $U_{\rm cem}$. Therefore, these other important variables should also be inspected for homogeneity. Such tests, however, depend on there having been sufficient analyses to allow statistical inferences: For every extra extraneous source suspected, the number of analyses must double. Hence, three source units would normally require 16 analyses. Extraneous teeth, however, can be {\em either younger or older} than the unit containing them. If a tooth has been eroded from a much older unit and redeposited, the older tooth might have: \begin{enumerate} \item a significantly larger ${\cal A}_{\Sigma}$, \item possibly higher $U_{\rm en}$, \item higher $U_{\rm den}$ and $U_{\rm cem}$, \item a different $D_{\rm ext}$, if an isochron can be calculated, \item significantly older calculated EU, LU, and RU ages, \end{enumerate} compared to their respective means for {\em in situ} teeth. Conversely, if a unit that has been badly fissured, later sedimentary infilling can add a much younger tooth, that probably will have: \begin{enumerate} \item a significantly smaller ${\cal A}_{\Sigma}$, \item possibly lower $U_{\rm en}$, \item lower $U_{\rm den}$ and $U_{\rm cem}$, \item a different $D_{\rm ext}$, if an isochron can be calculated, \item significantly younger calculated EU, LU, and RU ages, \end{enumerate} compared to the those means for {\em in situ} teeth. These lists, however, assume that both units generally have roughly equal conditions, such as sedimentary dose rates and U available for uptake. If, however, the two contributing units differ significantly in mineralogy, porosity, permeability, radioactive trace element concentrations, etc., the effect on differences in the parameters listed above may not be so obvious. In some circumstances, such differences actually may offset each other to produce similar calculated ages for teeth with very different geological histories. For example, if an older tooth had originally been deposited into an impermeable travertine floor, with low U and little or no Th or K, when eroded out, the tooth would have a low ${\cal A}_{\Sigma}$, as well as low $U_{\rm en}$, $U_{\rm den}$, and $U_{\rm cem}$. If the younger unit contained a high clay concentrations, and, hence, high associated Th, K, and $D_{\rm ext}$, the subsequent radiation dose from the younger unit might well cause the older tooth have ${\cal A}_{\Sigma}$, ages, and possibly other parameters, almost indistinguishable from the younger teeth. In a single tooth, the expected variation in ${\cal A}_{\Sigma}$ should not exceed $\sim$ 10-20\% about the mean (i.e. if ${\cal A}_{\Sigma}$ = 1000 Gray, $\sigma$(${\cal A}_{\Sigma}$) $_{\sim}^{<}$ 200 Gray), but this may exceed the differences in ${\cal A}_{\Sigma}$ between an extraneous tooth and the {\em in situ} teeth. In single teeth, $U_{\rm en}$, $U_{\rm den}$, and $U_{\rm cem}$ can vary substantially, which provides the basis for the isochron method (Blackwell \& Schwarcz, 1993). Typical variation can approach $\pm$ 2 ppm for $U_{\rm en}$ or $\pm$ 5 ppm for $U_{\rm den}$ in large teeth. Therefore, such variation within a mixed group of extraneous and {\em in situ} teeth may not significantly exceed the variation seen within one tooth, especially if only a few samples have been analyzed, making it more difficult to recognize extraneous teeth. To now, this discussion has assumed that a reasonably homogeneous sediment surrounds the teeth. If not, (i.e. it contains large numbers of {\em \'{e}boullis} collapsed from the cavern ceiling or large bone concentrations as is common in archaeological sites; ``lumpy" sites {\em cf}.\ Rink \& Schwarcz, 1993), however, the expected $D_{\rm ext}$ variation can reach 100\%. Since both U for uptake and $D_{\rm ext}$ derive from the sediment, its inhomogeneity produces variation in ${\cal A}_{\Sigma}$, as well as in $U_{\rm en}$, $U_{\rm den}$, and $U_{\rm cem}$. In many situations, using a ``sphere of influence" calculation ($r$ = 30 cm for $\gamma$ dose; $r$ = 2 mm for $\beta$ dose) will compensate for the presence of such inhomogeneity (e.g.\ Blackwell {\em et al}., 1992). In curated samples or those not collected specifically for ESR dating, this is obviously not possible. Even a sphere calculation, however, will not completely compensate for the effects from ``lumpiness". In inhomogenous sediment, ages will tend to be skewed toward younger values if the ESR calculation has used only the $D_{\rm ext}$ calculated for the clastic sediment component. The greater the inhomogeneity, the more platykurtotic the distribution will appear. A multimodal distribution, however, signals extraneous teeth. Establishing a single criterion to prove a tooth extraneous, therefore, becomes very difficult. If other data can constrain the expected age range for the unit, those approximate limits can help filter the extraneous teeth from those {\em in situ}, but must be used cautiously to avoid tautological reasoning and suspect dates. Only multivariate statistics can effectively demonstrate that a tooth is extraneous. Certain geological settings are more prone to contamination by extraneous teeth. Fluvial and glacial sediment frequently contain reworked teeth, often deriving from several different older units (e.g.\ Zymela {\em et al}., 1988). In regions with permafrost or active tectonism, fissuring and subsequent infilling can introduce younger teeth into a unit. In karst systems, dissolution of cavern floors or upward stoping of ceilings can lead to sediment being reworked and redeposited into younger units. Partial dissolution of cemented units also occurs commonly producing well fissured beds infilled by secondary deposits. While not as common in young cave systems, units with multiple generations of sedimentary clasts, including teeth, either from reworking or secondary fissure filling, can be the norm in older or reactivated karst systems. \section{Extraneous Teeth in the Transvaal Australopithecine Sites} The australopithecine cave sites in South Africa occupy caves in a karst system which dates back at least 5 Ma developed in Precambrian dolomite, providing an ideal opportunity to find extraneous teeth. Both caves contain one or more stratigraphic units that have been repeatedly eroded, filled, and cemented, causing complex, brecciated stratigraphies (Partridge, 1978; Wilkinson, 1983; Brain, 1988). At Swartkrans, Member 3 is estimated to date between 1.0 and 0.7-0.5 Ma (Vrba, 1982, 1985; Vogel, 1985), and Member 3 to the Late Pleistocene. Only five teeth (8 separate analyses) have been dated (Blackwell {\em et al}., in prep.\ a). With few analyses and no teeth large enough to allow isochron analysis, recognizing reworked samples theoretically becomes more difficult. For the Member 5 teeth, T108's calculated ages, $U_{\rm en}$, and $U_{\rm den}$ differ significantly from those for T109, while their ${\cal A}_{\Sigma}$'s differ by almost an order of magnitude. Similarly among the Member 3 teeth, T127 differs from T125 and T126, its ages and ${\cal A}_{\Sigma}$ roughly double those for T125 and T126 (Table 1). Given that T109 and T127 are both extraneous, perhaps their other parameters offer useful criteria can be developed. In T109, $U_{\rm en}$ and $U_{\rm den}$ differ from the those for T108 by 21 and 480 $\sigma$ respectively. Plotting $U_{\rm en}$ or $U_{\rm den}$ {\em vs}.\ ${\cal A}_{\Sigma}$ for all five teeth clearly differentiates three or four significantly distinct subpopulations (Figure 1). Although this plot resembles that used in isochron analyses, the variation between these subgroups exceeds typical intratooth variations for a single variable by factors ranging from 2.5 to 6.8 (cf.\ Figure 4). At Sterkfontein, Member 4, estimated at 2.3-2.8 Ma (Partridge, 1982, 1986; Vrba, 1982; Jones {\em et al}., 1986), yielded 14 teeth (43 separate subsamples) that have been analyzed (Schwarcz {\em et al}., in press; Blackwell {\em et al}., in prep.\ b). Their calculated ages, ${\cal A}_{\Sigma}$'s, $U_{\rm en}$'s, and $U_{\rm den}$'s (Table 2), however, all have multimodal frequency distributions (Figure 2), suggesting that not all these teeth are the same age. The total variation in ${\cal A}_{\Sigma}$ approaches 3000 Gray, about a total population mean near 1350 Gray ($\sim$ 225\%), 10-20 times the typical 150-300 Gray variation. For $U_{\rm en}$ and $U_{\rm den}$, variation in the whole Sterkfontein population approaches 2-5 times that typically seen in a single tooth (Table 2). The age distribution has three modes, suggesting that at least three distinct groups are present. Considering only LU ages, the group with T128, RG246, and RG247 averages 1420 $\pm$ 120 ka, while the group containing T123, T124, RG306, T37, and T41, would average 1810 $\pm$ 90 ka (LU). Using ${\cal A}_{\Sigma}$, $U_{\rm en}$, and $U_{\rm den}$, however, defines more subgroups. For example, T128's ${\cal A}_{\Sigma}$ value differs significantly from those of RG246 and RG247, while $U_{\rm en}$ for T39 and RG308 differ significantly from those for RG248 and RG309. Plotting $U_{\rm en}$ or $U_{\rm den}$ {\em vs}.\ ${\cal A}_{\Sigma}$ shows significant scatter (Figure 3), much beyond what might be expected within a single unit. While the enamel plot distinguishes the subgroups more effectively for the Sterkfontein data, both plots do indicate enough non-random scatter to suggest some teeth are extraneous. As many as eight distinct groups may exist. Although some groups are not statistically supportable without more analyses, the data do strongly suggest significant inhomogeneity in the tooth ages, and hence, in Member 4 itself: \begin{enumerate} \item Member 4 may contain several teeth reworked from older units in the cave. \item Several younger teeth may have been added post-depositionally along with karst fissure filling. \item All the teeth may be the same age, but Member 4 may be the ultimate in ``lumpy" units. \item Some combination of those above may apply. \end{enumerate} Member 4 being an extremely ``lumpy" site does not preclude extraneous teeth being present. \section{Calculating a Time-Averaged $D_{\rm ext}$ for Reworked Teeth} When reworked teeth are suspected, isochron analysis represents the most reliable determination for $D_{\rm ext}$, since the tooth becomes its own dosimeter, independent of sedimentary conditions. Isochron analyses, however, require at least five subsamples, and hence, large teeth. Without isochrons, $D_{\rm ext}$ must be modelled using time-integration in order to calculate an ESR age. \subsection{$\overline{D}_{\rm ext}$ from Isochron Analysis} Because isochron analysis assumes that the sedimentary U and Th series isotopes are equilibrated closed systems, multiple enamel subsamples collected from the same tooth should have accumulated the same ${\cal A}_{\rm ext}$. When ${\cal A}_{\Sigma}$ for each subsample is plotted against its $D_{\rm int}$, small differences in their $U_{\rm en}$ and $U_{\rm den}$ will cause the points to plot on a straight line, an isochron, whose intercept at $D_{\rm int}$ = 0 will equal ${\cal A}_{\rm ext}$ and whose slope gives the age (Figure 4). Moreover, the LU and EU isochrons will converge on the same point, which will be independent of U uptake model. $\overline{D}_{\rm ext}$, which is model dependent, is ${\cal A}_{\rm ext}$ divided by the model age (Blackwell \& Schwarcz, 1993). Isochron analyses confirm that some Sterkfontein teeth have indeed acquired different ${\cal A}_{\rm ext}$'s and are different ages (Figure 4). Although the regression coefficient for T123 is low, T123 acquired an ${\cal A}_{\rm ext}$ of approximately 145 $\pm$ 86 Gray during 4.45 $\pm$ 2.64 My (LU), at an average $\overline{D}_{\rm ext}$ near 0.033 $\pm$ 0.038 mGray/y (LU). This age here overlaps the predicted age for Member 4. T128, however, gained an ${\cal A}_{\rm ext}$ near 123 $\pm$ 40 Gray over 1.33 $\pm$ 0.33 My (LU) at $\overline{D}_{\rm ext}$ = 0.087 $\pm$ 0.041 mGray/y (LU). Assuming any uptake model, both T123 and T129 experienced a different $\overline{D}_{\rm ext}$ than those suggested by dosimetry for Member 4 sediment, where $D_{\rm ext}$'s currently range from 0.300 to 0.700 mGray/y (Blackwell {\em et al}., in prep.\ b; Schwarcz {\em et al}., in press). The very low $D_{\rm ext}$ for both T123 and T128 may have resulted from their having been encased in impermeable travertine for some considerable time. Using these $\overline{D}_{\rm ext}$'s to recalculate other Sterkfontein ages, significantly increases them (see details in Blackwell {\em et al}., in prep.\ b). If the isochrons are reliable, T123 and T128 experienced radically different depositional histories. Then, one or both are extraneous to Member 4. \subsection{$\overline{D}_{\rm ext}$ without Isochrons} Without isochron analyses, dates for a reworked tooth must employ a time-averaged $D_{\rm ext}$ calculated to reflect their multistage depositional history: \pagebreak \begin{equation} \overline{D}_{\rm ext} \; = \; \frac{\int_{0}^{t_{\Sigma}} D_{\rm ext}(t) \; dt}{t_{\Sigma}} \; \cong \; \frac{\sum_{i=1}^{n} {D}_{{\rm ext},i} * t_{i}} {\sum_{i=1}^{n} t_{i}} \end{equation} \begin{tabular}{crcl} where & $\overline{D}_{\rm ext}$ & = & the time-averaged external dose rate,\\ & $t_{\Sigma}$ & = & the age of the tooth,\\ & $D_{{\rm ext},i}$ & = & the external radiation dose rate in unit $i$,\\ & $t_{i}$ & = & the time the tooth spent in unit $i$,\\ & $n$ & = & the number of units in which the tooth spent time.\\ \end{tabular} \noindent In this calculation, however, $\overline{D}_{\rm ext}$ and $t_{\Sigma}$ covary and depend upon the U uptake model. Using Equation 2 with T109 and T127 illustrates this method. Despite differences in ${\cal A}_{\Sigma}$, $D_{\rm ext}$, and $U_{\rm en}$, T109 and T127 may have similar dates. Recalculating their ages with the two extreme $D_{\rm ext}$'s, 0.271 $\pm$ 0.023 mGray/y (Table 3a) and 0.820 $\pm$ 0.098 mGray/y (Table 3b), the new ages are not significantly different at the 2$\sigma$ level for any uptake model, but both still differ from those for all the other teeth. Therefore, T109 and T127 probably derived originally from the same unit, Member X, which must predate both Members 3 and 5. Although this rough calculation using single stage histories demonstrates they are extraneous and similar in age, these new ages are still incorrect, because neither extreme $D_{\rm ext}$ above likely equals the average $D_{\rm ext}$ experienced by either tooth. These rough ages do, however, constrain $t_{\Sigma}$ between approximately 870 and 1270 $\pm$ 150 ky (Table 3). For the older units in Swartkrans, $D_{\rm ext}$ are not known. This situation is not atypical in many dating studies, where the older units may have not yet been excavated, they may have been completely eroded, or they may not have been collected because they were not recognized as important for studying the younger units. Lacking $D_{\rm ext}$ estimates for the older units, we can still estimate ranges for $\overline{D}_{\rm ext}$ and $t_{\Sigma}$ by calculating their extreme boundary conditions. Let's assume that Member X's $D_{\rm ext}$ will likely fall within or close to the extremes established for the other sedimentary units, which are typical values seen in archaeological sites. The maximum age limit for T109 and T127 then will arise from calculating $\overline{D}_{\rm ext}$ using $D_{\rm ext, \; Member \; X}$ = 0.271 $\pm$ 0.023 mGray/y, and the minimum age limit from $D_{\rm ext, \; Member \; X}$ = 0.820 $\pm$ 0.09 8 mGray/y. Having determined that both T109 and T127 are roughly contemporaneous, we can also assume that T109 spent as much time in Member 5 as did T108, i.e. $t_{\rm Member \; 5}$ = 150 ky. If T108 were also reworked, that would only lessen the time that T109 spent in Member 5, thereby reducing the differences between the ages calculated by assuming a one or two phase depositional history. If we assume that T109 was eroded out and redeposited within a short time geologically, then, \begin{equation} t_{\rm Member \; X} = t_{\Sigma} - t_{\rm Member \; 5} \end{equation} Therefore, T109 spent between 620 and 1120 ky in Member X (Table 4). In the first iteration of the maximum limit calculation, T109 experienced $\overline{D}_{\rm ext}$ = 0.306 mGray/y over roughly 1270 ky (Table 4a). T109's recalculated LU age, 1240 $\pm$ 180 ky, is not significantly different from the single phase age for T109 or that for T127 using either a one or two phase calculation (Table 3a). After several iterations for T127 to converge on $D_{\rm ext}$ = 0.465 mGray/y (Table 5), the LU ages, 870 $\pm$ 140 ky for T109 and 1110 $\pm$ 180 ky for T127, from minimum limit calculation yields agree within their errors (Tables 4b, 3b). If T109 and T127 were both reworked from Member X at the same time and deposited first into Member 3, following which T109 was reworked into Member 5, we should consider a three stage depositional history for T109. While we still assume that $t_{\rm Member \; 5}$ = 150 ky, now its time in Member X would equal the time that T127 spent there, i.e.\$t_{\rm Member \; X}$ = 380 ky for the minimum, or $t_{\rm Member \; X}$ = 530 ky for the maximum. The results change little from those for the two phase model calculation (Tables 5, 3), although the minimum age, 980 $\pm$ 180 ka, more closely matches T127's two phase age. Given the assumptions noted, the true date for Member X probably falls between 1050 $\pm$ 180 and 1230 $\pm$ 120 ka (LU). While such speculations become more tenuous without good evidence for the actual times that the teeth spent in each unit and the $D_{\rm ext}$ experienced therein, they do roughly estimate the dates. \section{Conclusions} Provided the number of analyses allow statistical comparisons, extraneous teeth can be recognized from dissimilarities in calculated ages ${\cal A}_{\Sigma}$, $U_{\rm en}$, or $U_{\rm den}$ values. Plotting $U_{\rm en}$ or $U_{\rm den}$ {\em vs}.\ ${\cal A}_{\Sigma}$ can highlight such differences. Although reworked teeth in the Swartkrans samples were recognized here using very few analyses per unit due to their extreme differences in the ${\cal A}_{\Sigma}$'s and ages, such a small statistical base would not likely have elucidated more subtle differences. A reliable estimate for a unit requires at least 8-10 analyses for at least 4-5 teeth, and where possible, isochron analyses employing a minimum of 5-7 subsamples per isochron. For each suspected extraneous source, the number of teeth must double. For an extraneous tooth, an isochron analysis best estimates the ${\cal A}_{\rm ext}$ and ages, and hence, the $\overline{D}_{\rm ext}$'s, since their calculation does not require any knowledge of the units in which the tooth resided. Otherwise, the various model ESR ages require individually calculated time-averaged $\overline{D}_{\rm ext}$'s that model the total time spent within each stratigraphic unit and the $D_{\rm ext}$ experienced therein. \small \section{Acknowledgements} I thank A.\ Skinner, H.P.\ Schwarcz, J.F.\ Thackeray, and P.V.\ Tobias for their comments on the manuscript, and H.P.\ Schwarcz for access to his Sterkfontein data. Grants to H.P.\ Schwarcz from the Natural Sciences and Engineering Research Council (NSERC), Canada, and the National Science Foundation, USA (NSF grant BNS 8801699 to F.C.\ Howell, University of California, Berkeley) supported some analyses discussed herein. Purdue, Nipissing, McMaster, and Windsor Universities provided logistical support. \section{References} \footnotesize \setlength{\leftmargin}{+2em} \setlength{\listparindent}{-3em} \begin{list}{}{}%{\setlength{\rightmargin}{\leftmargin}} \item \hspace{-2em} BLACKWELL, B., 1989. ESR dating of tooth enamel. {\em McMaster University Dept of Geology Technical Memo} {\bf 89.2}, 234 pp. \item \hspace{-2em} BLACKWELL, B., H.P.\ SCHWARCZ, 1993. ESR isochron dating for teeth: A brief demonstration in solving the external dose calculation problem. {\em Applied Radiation \& Isotopes} {\bf 44}: 243-252. \item \hspace{-2em} BLACKWELL, B., H.P.\ SCHWARCZ, J.F.\ THACKERAY, in prep., 1993a. Electron spin resonance dating of tooth enamel from the Australopithecine site, Swartkrans, South Africa. \item \hspace{-2em} BLACKWELL, B., H.P.\ SCHWARCZ, P.V. TOBIAS, in prep., 1993b. Electron spin resonance dating of tooth enamel from the Australopithecine site, Sterkfontein, South Africa. %{\em Journal of Human Evolution}. \item \hspace{-2em} BLACKWELL, B., N.\ PORAT, H.P.\ SCHWARCZ, A.\ DEB\'{E}NATH, 1992. ESR dating of tooth enamel: Comparison with $^{230}$Th/$^{234}$U speleothem dates at La Chaise-de-Vouthon (Charente), France. {\em Quaternary Science Reviews} {\bf 11}: 231-244. \item \hs{-2} BRAIN, C.K., 1988. New information from the Swartkrans cave of relevance to ``robust" australopithecines. {\em In} F.E.\ Grine, ed. {\em The Evolutionary History of the Robust Australopithecines}. de Gruyter, New York, p.\ 311-316. \item \hspace{-2em} GR\"{U}N, R., P. BEAUMONT, C.B. STRINGER, 1990. ESR dating evidence for early modern humans at Border Cave in South Africa. {\em Nature} {\bf 344}: 537-539. \item \hspace{-2em} JONES, D.L., A.\ BROCK, P.L. McFADDEN, 1986. Paleomagnetic results from the Kromdraai and Sterkfontein hominid sites. {\em South African Journal of Physical Anthropology} {\em 82}: 160-163. \item \hs{-2} McDERMOTT, F., R.\ GR\"{U}N, C.B.\ STRINGER, C.J.\ HAWKESWORTH, 1993. Mass-spectrometric U-series dates for Israeli Neanderthal/early modern hominid sites. {\em Nature} {\bf 363}: 252-255. \item \hspace{-2em} PARTRIDGE, T.C., 1986. Paleoecology of the Pliocene and Lower Pleistocene hominids of southern Africa: How good is the chronological and palaeoenvironmental evidence? {\em South African Journal of Science} {\bf 82}: 80-83. \item \hspace{-2em} PARTRIDGE, T.C., 1982. The chronological positions of fossil hominids of southern Africa. {\em In} M.A.\ de Lumley, ed. {\em L'{\rm Homo erectus} et la Place de l'Homme de Tautavel parmi les Hominid\'{e}s fossiles}. 1er Congr\`{e}s International de Pal\'{e}ontologie Humaine, Nice, p.\ 617-675. \item \hspace{-2em} PARTRIDGE, T.C., 1978. Reappraisal of lithostratigraphy of Sterkfontein hominid site. {\em Nature} {\bf 275}: 282-287. \item \hs{-2} RINK, W.J., H.P.\ SCHWARCZ, 1993. ESR dating of fossil tooth enamel: How it's done in archeological sites. {\em Geological Society of America Abstracts} {\bf 25}: A187. \item \hspace{-2em} SCHWARCZ, H.P., R.\ GR\"{U}N, P.V.\ TOBIAS, in press, 1993. ESR dating studies of the Australopithecine site of Sterkfontein, Sough Africa. {\em Journal of Human Evolution}. \item \hspace{-2em} SCHWARCZ, H.P., R.\ GR\"{U}N, 1988. ESR dating of level L 2/3 at La Micoque (Dordogne), France: Excavations of Deb\'{e}nath and Rigaud. {\em Geoarchaeology} {\bf 3}: 293-296. \item \hspace{-2em} SCHWARCZ, H.P., R.\ GR\"{U}N, A.G.\ LATHAM, D.\ MANIA, K. BRUNNACKER, 1988. New evidence for the age of the Bilzingsleben archaeological site. {\em Archaeometry} {\bf 30}: 5-17. \item \hspace{-2em} STRINGER, C.B., R.\ GR\"{U}N, H.P.\ SCHWARCZ, P.\ GOLDBERG, 1989. ESR dates for the hominid burial site of Es Skhul in Israel. {\em Nature} {\bf 338}: 756-758. \item \hs{-2} VOGEL, J.C., 1985. Further attempts at dating the Taung tufas. {\em In} P.V.\ Tobias, ed. {\em Hominid Evolution: Past, Present, and Future}. Liss, New York, p.\ 189-194. \item \hs{-2} VRBA, E.S., 1985. Early hominids in southern Africa: Updated observations on chronological and ecological background. {\em In} P.V.\ Tobias, ed. {\em Hominid Evolution: Past, Present, and Future}. Liss, New York, p.\ 195-200. \item \hs{-2} VRBA, E.S., 1982. Biostratigraphy and chronology, based particularly on Bovidae, of Southern hominid-associated assemblages: Makapansgat, Sterkfontein, Taung, Kromdraai, Swartkrans; also Elansfontein (Saldanha), Broken Hill (now Kabwe), and Cave of Hearths. {\em In} M.A.\ de Lumley, ed. {\em L'} {\cal Homo erectus} {\em et la Place de l'Homme de Tautavel parmi les Hominid\'{e}s fossiles}. 1er Congr\`{e}s International de Pal\'{e}ontologie Humaine, Nice, p.\ 707-752. \item \hspace{-2em} WILKINSON, M.J., 1983. Geomorphic perspectives on the Sterkfontein australopithecine breccias. {\em Journal of Archaeological Science} {\bf 10}: 515-529. \item \hs{-2} ZYMELA, S., H.P.\ SCHWARCZ, R.\ GR\"{U}N, A.M\ STALKER, C.S.\ CHURCHER, 1988. ESR dating of Pleistocene fossil teeth from Alberta and Saskatchewan. {\em Canadian Journal of Earth Sciences} {\bf 25}: 235-245. \end{list} \pagebreak \setlength{\leftmargin}{0em} \normalsize \section{Figure Captions} \begin{enumerate} \item Inhomogeneities in Swartkrans teeth.\\ Plotting the U concentration in the Swartkrans teeth against accumulated dose, ${\cal A}_{\Sigma}$, demonstrates that at least three different depositional histories are represented by the analyses shown: \begin{enumerate} \item Enamel \item Dentine \end{enumerate} \noindent (data from Blackwell {\em et al}., in prep., a). \item Frequency Distributions for the Sterkfontein data.\\ Simple frequency distributions for the Sterkfontein data indicate that there may be multiple generations of teeth in Member 4: \begin{enumerate} \item Accumulated Dose, ${\cal A}_{\Sigma}$ \item U concentrations in the enamel \item U concentrations in the dentine \end{enumerate} \item Inhomogeneities in Sterkfontein teeth.\\ Plotting the U concentration in the Sterkfontein teeth against accumulated dose, ${\cal A}_{\Sigma}$, clearly shows that several different depositional histories are represented in the analyses shown: \begin{enumerate} \item Enamel \item Dentine \end{enumerate} \noindent (data from Schwarcz {\em et al}., in press, 1993; Blackwell {\em et al}., in prep., b). \item Isochron plots for Sterkfontein teeth. \\ On isochron plots, the slope of the line gives the sample's age, while the convergence point at $D_{\rm int}$ = 0 gives the total absorbed dose due to the external dose component, ${\cal A}_{\rm ext}$. Dividing ${\cal A}_{\rm ext}$ by the age gives the uptake-model-dependent, time-averaged dose rate, $\overline{D}_{\rm ext}$. \begin{enumerate} \item T123, third iteration. \item T128a, third iteration. \end{enumerate} (Data from Blackwell {\em et al}., in prep., b). These two teeth have different ages. Regardless of the model, both analyses indicate that the $\overline{D}_{\rm ext}$ experienced by the teeth are much lower than those suggested by NAA or $\gamma$ spectroscopy for the sediment at the collection site (see Blackwell {\em et al}., in prep.\ b). \end{enumerate} \pagebreak %\setcounter{table}{0} \begin{table}[h] \centering \caption{ESR Dating Summary, Swartkrans$^{\ddag}$} \begin{tabular}{lrccrrrrr} \hline \hline & \multicolumn{1}{c}{Accumulated\spp{0.41}} & \multicolumn{1}{c}{External} & \multicolumn{3}{c}{U Concentrations} & \multicolumn{3}{c}{Ages} \\ \cline{4-9} \multicolumn{1}{l}{Sample\spp{0.41}} & \multicolumn{1}{c}{Dose} & \multicolumn{1}{c}{Dose Rate} & \multicolumn{1}{c}{Enamel} & \multicolumn{1}{c}{Dentine} & \multicolumn{1}{c}{Cement} & \multicolumn{1}{c}{EU} & \multicolumn{1}{c}{LU} & \multicolumn{1}{c}{RU} \\ & \multicolumn{1}{c}{(Gray)} & \multicolumn{1}{c}{(mGray/y)} & \multicolumn{1}{c}{(ppm)} & \multicolumn{1}{c}{(ppm)} & \multicolumn{1}{c}{(ppm)} & \multicolumn{1}{c}{(ka)} & \multicolumn{1}{c}{(ka)} & \multicolumn{1}{c}{(ka)} \\ \hline \multicolumn{6}{l}{A. Member 5\spp{0.36}} \\ T108e1b \spp{0.41} & 175 \hs{1.5} & 0.820 & 0.67 & 8.59 \hs{0.5} & - \hs{1.0} & 120 & 160 & 210 \\ \hs{4} $\pm$ & 10 \hs{1.5} & 0.098 & 0.02 & 0.02 \hs{0.5} & - \hs{1.0} & 10 & 10 & 20 \\ T108e2b \spp{0.41} & 164 \hs{1.5} & 0.820 & 0.61 & - \hs{1.0} & - \hs{1.0} & 120 & 150 & 200 \\ \hs{4} $\pm$ & 13 \hs{1.5} & 0.098 & 0.02 & - \hs{1.0} & - \hs{1.0} & 10 & 10 & 20 \\ \cline{2-9} \hs{2} Mean \spp{0.41} & 169 \hs{1.5} & 0.820 & 0.64 & 8.59 \hs{0.5} & - \hs{1.0} & 120 & 150 & 210 \\ \hs{4} $\pm$ & 12 \hs{1.5} & 0.098 & 0.03 & 0.02 \hs{0.5} & - \hs{1.0} & 10 & 10 & 20 \\ T109e1b\spp{0.41} & 1160 \hs{1.5} & 0.567 & 1.28 & 18.19 \hs{0.5} & - \hs{1.0} & 640 & 980 & 2030 \\ \hs{4} $\pm$ & 160 \hs{1.5} & 0.034 & 0.02 & 0.02 \hs{0.5} & - \hs{1.0} & 90 & 140 & 260 \\ \hline \multicolumn{6}{l}{B. Member 3\spp{0.36}} \\ T125e1 \spp{0.41} & 1140 \hs{1.5} & 0.271 & 1.49 & 25.94 \hs{0.5} & 17.72 \hs{0.5} & 390 & 710 & 4120 \\ \hs{4} $\pm$ & 130 \hs{1.5} & 0.023 & 0.02 & 0.02 \hs{0.5} & 0.02 \hs{0.5} & 50 & 90 & 570 \\ T125e2 \spp{0.41} & 1220 \hs{1.5} & 0.271 & 3.41 & 20.83 \hs{0.5} & - \hs{1.0} & 440 & 800 & 4380 \\ \hs{4} $\pm$ & 220 \hs{1.5} & 0.023 & 0.02 & 0.02 \hs{0.5} & - \hs{1.0} & 80 & 150 & 850 \\ T126e1 \spp{0.41} & 880 \hs{1.5} & 0.271 & 2.65 & 22.36 \hs{0.5} & 13.73 \hs{0.5} & 360 & 650 & 3170 \\ \hs{4} $\pm$ & 200 \hs{1.5} & 0.023 & 0.02 & 0.02 \hs{0.5} & 0.02 \hs{0.5} & 80 & 150 & 750 \\ T126e2 \spp{0.41} & 1090 \hs{1.5} & 0.271 & 4.07 & 16.15 \hs{0.5} & - \hs{1.0} & 390 & 700 & 3940 \\ \hs{4} $\pm$ & 160 \hs{1.5} & 0.023 & 0.02 & 0.02 \hs{0.5} & - \hs{1.0} & 60 & 110 & 640 \\ \cline{2-9} \hs{2} Mean \spp{0.41} & 1080 \hs{1.5} & 0.271 & 2.91 & 21.32 \hs{0.5} & 15.73 \hs{0.5} & 390 & 720 & 3900 \\ \hs{4} $\pm$ & 180 \hs{1.5} & 0.023 & 0.96 & 3.71 \hs{0.5} & 2.00 \hs{0.5} & 70 & 130 & 700 \\ \cline{2-9} T127e1 \spp{0.41} & 1820 \hs{1.5} & 0.271 & 3.99 & 18.05 \hs{0.5} & - \hs{1.0} & 690 & 1250 & 6560 \\ \hs{4} $\pm$ & 80 \hs{1.5} & 0.023 & 0.02 & 0.02 \hs{0.5} & - \hs{1.0} & 60 & 90 & 550 \\ \hline \hline \multicolumn{9}{l}{$^{\ddag}$ Data from Blackwell {\em et al}., in prep. a} \\ \end{tabular} \end{table} \pagebreak \begin{table}[h] \centering \caption{ESR Dating Summary, Sterkfontein} \begin{tabular}{lrcrrrrr} \hline \hline & \multicolumn{1}{c}{Accumulated\spp{0.41}} & \multicolumn{3}{c}{U Concentrations} & \multicolumn{3}{c}{Ages} \\ \cline{3-8} \multicolumn{1}{l}{Sample$^{{\dag}{\ddag}}$} & \multicolumn{1}{c}{Dose} & \multicolumn{1}{c}{Enamel} & \multicolumn{1}{c}{Dentine} & \multicolumn{1}{c}{Cement} & \multicolumn{1}{c}{EU} & \multicolumn{1}{c}{LU} & \multicolumn{1}{c}{RU\spp{0.41}} \\ & \multicolumn{1}{c}{(Gray)} & \multicolumn{1}{c}{(ppm)} & \multicolumn{1}{c}{(ppm)} & \multicolumn{1}{c}{(ppm)} & \multicolumn{1}{c}{(ka)} & \multicolumn{1}{c}{(ka)} & \multicolumn{1}{c}{(ka)} \\ \hline T128 \spp{0.41} & 660 \hs{1.5} & 1.18 & 7.21 \hs{0.5} & - \hs{1.0} & 660 & 1300 & 1900 \\ (5) \hs{3} $\pm$ & 80 \hs{1.5} & 0.27 & 0.77 \hs{0.5} & - \hs{1.0} & 160 & 300 & 200 \\ \hline RG247 \spp{0.41} & 2100 \hs{1.5} & 2.98 & 9.84 \hs{0.5} & - \hs{1.0} & 810 & 1500 & \\ (3) \hs{3} $\pm$ & 250 \hs{1.5} & 0.16 & 0.02 \hs{0.5} & - \hs{1.0} & 90 & 200 & \\ RG246 \spp{0.41} & 1850 \hs{1.5} & 2.69 & 8.03 \hs{0.5} & - \hs{1.0} & 930 & 1600 & \\ (2) \hs{3} $\pm$ & 150 \hs{1.5} & 0.04 & 0.02 \hs{0.5} & - \hs{1.0} & 70 & 100 & \\ \cline{2-8} \hs{2} Mean \spp{0.41} & 2000 \hs{1.5} & 2.86 & 9.12 \hs{0.5} & - \hs{1.0} & 860 & 1500 & \\ \hs{4.5} $\pm$ & 130 \hs{1.5} & 0.14 & 0.89 \hs{0.5} & - \hs{1.0} & 70 & 100 & \\ \hline T124 \spp{0.41} & 850 \hs{1.5} & 0.20 & 4.32 \hs{0.5} & - \hs{1.0} & 1200 & 1700 & 2500 \\ (2) \hs{3} $\pm$ & 120 \hs{1.5} & 0.05 & 0.12 \hs{0.5} & - \hs{1.0} & 300 & 300 & 400 \\ T123 \spp{0.41} & 870 \hs{1.5} & 0.11 & 4.37 \hs{0.5} & 4.40 \hs{0.5} & 1300 & 1800 & 2500 \\ (6) \hs{3} $\pm$ & 140 \hs{1.5} & 0.07 & 0.29 \hs{0.5} & 0.05 \hs{0.5} & 300 & 300 & 400 \\ RG306 \spp{0.41} & 820 \hs{1.5} & 0.29 & 3.39 \hs{0.5} & - \hs{1.0} & 1400 & 1800 & \\ (2) \hs{3} $\pm$ & 10 \hs{1.5} & 0.16 & 0.03 \hs{0.5} & - \hs{1.0} & 200 & 200 & \\ \cline{2-8} \hs{2} Mean \spp{0.41} & 860 \hs{1.5} & 0.16 & 4.16 \hs{0.5} & 4.40 \hs{0.5} & 1300 & 1800 & 2500 \\ \hs{4.5} $\pm$ & 90 \hs{1.5} & 0.10 & 0.39 \hs{0.5} & 0.05 \hs{0.5} & 200 & 200 & 300 \\ \hline T37 \spp{0.41} & 1430 \hs{1.5} & 0.24 & 4.48 \hs{0.5} & 10.25 \hs{0.5} & 1400 & 1800 & 2400 \\ (3) \hs{3} $\pm$ & 200 \hs{1.5} & 0.23 & 3.31 \hs{0.5} & 2.05 \hs{0.5} & 900 & 800 & 700 \\ T41 \spp{0.41} & 1370 \hs{1.5} & 0.09 & - \hs{1.0} & 11.40 \hs{0.5} & 1400 & 2100 & 2500 \\ (1) \hs{3} $\pm$ & 150 \hs{1.5} & 0.02 & - \hs{1.0} & 1.00 \hs{0.5} & 200 & 200 & 300 \\ RG307\spp{0.41} & 1360 \hs{1.5} & 0.95 & 4.08 \hs{0.5} & - \hs{1.0} & 1500 & 2400 & \\ (3) \hs{3} $\pm$ & 430 \hs{1.5} & 0.35 & 0.76 \hs{0.5} & - \hs{1.0} & 300 & 400 & \\ \cline{2-8} \hs{2} Mean \spp{0.41} & 1390 \hs{1.5} & 0.52 & 4.28 \hs{0.5} & 10.54 \hs{0.5} & 1400 & 2100 & 2400 \\ \hs{4.5} $\pm$ & 120 \hs{1.5} & 0.34 & 1.53 \hs{0.5} & 0.49 \hs{0.5} & 300 & 300 & 300 \\ \hline T39 \spp{0.41} & 1630 \hs{1.5} & 0.31 & 7.03 \hs{0.5} & 37.00 \hs{0.5} & 2000 & 2800 & 3900 \\ (5) \hs{3} $\pm$ & 150 \hs{1.5} & 0.34 & 2.77 \hs{0.5} & 0.02 \hs{0.5} & 300 & 300 & 300 \\ RG308\spp{0.41} & 1760 \hs{1.5} & 0.45 & 10.18 \hs{0.5} & - \hs{1.0} & 1800 & 2500 & \\ (2) \hs{3} $\pm$ & 70 \hs{1.5} & 0.05 & 0.95 \hs{0.5} & - \hs{1.0} & 400 & 500 & \\ \cline{2-8} \hs{2} Mean \spp{0.41} & 1670 \hs{1.5} & 0.35 & 7.93 \hs{0.5} & 37.00 \hs{0.5} & 1900 & 2700 & 3900 \\ \hs{4.5} $\pm$ & 120 \hs{1.5} & 0.07 & 1.42 \hs{0.5} & 0.02 \hs{0.5} & 400 & 400 & 300 \\ \hline RG309\spp{0.41} & 2230 \hs{1.5} & 1.77 & 12.48 \hs{0.5} & - \hs{1.0} & 1400 & 2300 & \\ (2) \hs{3} $\pm$ & 440 \hs{1.5} & 0.92 & 0.02 \hs{0.5} & - \hs{1.0} & 400 & 500 & \\ RG248 \spp{0.41} & 2080 \hs{1.5} & 1.33 & 5.37 \hs{0.5} & - \hs{1.0} & 1700 & 2800 & \\ (3) \hs{3} $\pm$ & 250 \hs{1.5} & 0.05 & 0.28 \hs{0.5} & - \hs{1.0} & 200 & 200 & \\ \cline{2-8} \hs{2} Mean \spp{0.41} & 2140 \hs{1.5} & 1.51 & 8.21 \hs{0.5} & - \hs{1.0} & 1600 & 2600 & \\ \hs{4.5} $\pm$ & 280 \hs{1.5} & 0.22 & 3.48 \hs{0.5} & - \hs{1.0} & 200 & 300 & \\ \hline RG305 \spp{0.41} & 3550 \hs{1.5} & 2.71 & 9.64 \hs{0.5} & - \hs{1.0} & 1700 & 3100 & \\ (3) \hs{3} $\pm$ & 520 \hs{1.5} & 0.25 & 1.73 \hs{0.5} & - \hs{1.0} & 200 & 400 & \\ \hline T123I$^{\S}$\spp{0.41} & 870 \hs{1.5} & 0.13 & 4.35 \hs{0.5} & 4.40 \hs{0.5} & 2500 & 4500 & \\ (8) \hs{3} $\pm$ & 140 \hs{1.5} & 0.08 & 0.26 \hs{0.5} & 0.05 \hs{0.5} & 1400 & 2600 & \\ \hline \hline \multicolumn{8}{l}{$^{\dag}$ All RG$x$ ages recalculated from data in Schwarcz {\em et al}., in press.} \\ \multicolumn{8}{l}{$^{\ddag}$ All T$x$ ages from data in Blackwell {\em et al}., in prep. b} \\ \multicolumn{8}{l}{$^{\S}$ Isochron analysis} \\ \end{tabular} \end{table} \pagebreak %\setcounter{table}{0} \begin{table}[h] \centering \caption{ESR Ages for T109 and T127, Member ``X", Swartkrans} \begin{tabular}{lcrrr} \hline \hline & \multicolumn{1}{c}{External} & \multicolumn{3}{c}{Ages\spp{0.41}} \\ \cline{3-5} \multicolumn{1}{l}{Sample} & \multicolumn{1}{c}{Dose Rate} & \multicolumn{1}{c}{EU} & \multicolumn{1}{c}{LU} & \multicolumn{1}{c}{RU\spp{0.41}} \\ & \multicolumn{1}{c}{(mGray/y)} & \multicolumn{1}{c}{(ka)} & \multicolumn{1}{c}{(ka)} & \multicolumn{1}{c}{(ka)} \\ \hline \multicolumn{5}{l}{A. Maximum possible age speculation\spp{0.36}} \\ T109e1b \spp{0.41} & 0.271$^{1}$ & 750 & 1290 & 4190 \\ \hs{4} $\pm$ & 0.023$^{1}$ & 110 & 190 & 550 \\ T127e1 \spp{0.41} & 0.271$^{1}$ & 690 & 1250 & 6560 \\ \hs{4} $\pm$ & 0.023$^{1}$ & 50 & 90 & 550 \\ T109e1b \spp{0.41} & variable$^{2}$ & 730 & 1240 & 4020 \\ \hs{4} $\pm$ & & 110 & 180 & 520 \\ T127e1 \spp{0.41} & variable$^{3}$ & 690 & 1250 & 6560 \\ \hs{4} $\pm$ & & 50 & 90 & 550 \\ T109e1b \spp{0.41} & variable$^{4}$ & 710 & 1210 & 3880 \\ \hs{4} $\pm$ & & 100 & 180 & 510 \\ \hline \multicolumn{5}{l}{B. Minimum possible age speculation\spp{0.36}} \\ T109e1b \spp{0.41} & 0.820$^{5}$ & 560 & 820 & 1390 \\ \hs{4} $\pm$ & 0.098$^{5}$ & 130 & 150 & 200 \\ T127e1 \spp{0.41} & 0.820$^{5}$ & 580 & 920 & 2200 \\ \hs{4} $\pm$ & 0.098$^{5}$ & 80 & 150 & 270 \\ T109e1b \spp{0.41} & variable$^{6}$ & 580 & 870 & 1430 \\ \hs{4} $\pm$ & & 130 & 140 & 200 \\ T127e1 \spp{0.41} & variable$^{3}$ & 640 & 1110 & \\ \hs{4} $\pm$ & & 90 & 180 & \\ T109e1b \spp{0.41} & variable$^{4}$ & 630 & 980 & \\ \hs{4} $\pm$ & & 150 & 180 & \\ \hline \hline \end{tabular} \begin{tabular}{rl} \hs{-1} $^{1}$\spp{0.41} & Member 3 external dose rate \\ \hs{-1} $^{2}$\spp{0.36} & 2 phase time-averaged external dose rates (Table 4a, 5) \\ \hs{-1} $^{3}$\spp{0.36} & 2 phase time-averaged external dose rates (Table 5) \\ \hs{-1} $^{4}$\spp{0.36} & 3 phase time-averaged external dose rates (Table 5) \\ \hs{-1} $^{5}$\spp{0.36} & Member 5 external dose rate \\ \hs{-1} $^{6}$\spp{0.36} & 2 phase time-averaged external dose rates (Table 4b, 5) \\ \hs{-1} $^{2, 3, 4, 6}$\spp{0.36} & U uptake model dependent \\ \end{tabular} \end{table} \pagebreak %\setcounter{table}{0} \begin{table}[h] \centering \caption{Time Integrated External Dose Rates for T109} \begin{tabular}{ccrc} \hline \hline \multicolumn{1}{c}{U} & \multicolumn{1}{c}{Tooth} & \multicolumn{1}{c}{Time Spent} & \multicolumn{1}{c}{External\spp{0.41}} \\ \multicolumn{1}{c}{Uptake} & \multicolumn{1}{c}{Occupying} & \multicolumn{1}{c}{in Unit} & \multicolumn{1}{c}{Dose Rate$^{\dag}$} \\ \multicolumn{1}{c}{Model} & \multicolumn{1}{c}{Member} & \multicolumn{1}{c}{(ky)} & \multicolumn{1}{c}{(mGray/y)} \\ \hline \multicolumn{4}{l}{\spp{0.36}A. Maximum possible age speculation,} \\ \multicolumn{4}{l}{\hs{1} $D_{\rm ext}$ = 0.271 $\pm$ 0.023 mGray/y} \\ LU \spp{0.41} & X & 1120 \hs{1.25} & 0.271 \\ & 5 & 150 \hs{1.25} & 0.567 \\ \cline{3-4} \hs{2} $^{\Sigma}$\spp{0.41} & & 1270 \hs{1.25} & 0.306 \\ \hline \multicolumn{4}{l}{\spp{0.36}B. Minimum possible age speculation,} \\ \multicolumn{4}{l}{\hs{1} $D_{\rm ext}$ = 0.820 $\pm$ 0.098 mGray/y} \\ LU \spp{0.41} & X & 620 \hs{1.25} & 0.820 \\ & 5 & 150 \hs{1.25} & 0.567 \\ \cline{3-4} \hs{2} $^{\Sigma}$\spp{0.41} & & 870 \hs{1.25} & 0.725 \\ \hline \hline \end{tabular} \end{table} \begin{table}[h] \centering \caption{Time Integrated External Dose Rates for T109, T127} \begin{tabular}{lccccc} \hline \hline \multicolumn{2}{c}{Tooth} & & \multicolumn{3}{c}{External Dose Rates\spp{0.41}} \\ \cline{4-6} \multicolumn{2}{c}{Extreme} & \multicolumn{1}{c}{Phases\spp{0.36}} & \multicolumn{1}{c}{EU} & \multicolumn{1}{c}{LU} & \multicolumn{1}{c}{RU} \\ \multicolumn{2}{c}{Assumed} & & \multicolumn{1}{c}{(mGray/y)} & \multicolumn{1}{c}{(mGray/y)} & \multicolumn{1}{c}{(mGray/y)} \\ \hline T109 & Max & 2 & 0.320 & 0.306 & 0.283 \\ T109 & Min & 2 & 0.767 & 0.725 & 0.792 \\ T127 & Max & 2 & 0.271 & 0.271 & 0.271 \\ T127 & Min & 2 & 0.451 & 0.461 & \\ T109 & Max & 3 & 0.364 & 0.337 & 0.293 \\ T109 & Min & 3 & 0.589 & 0.568 & \\ \hline \hline \end{tabular} \end{table} \pagebreak %\setcounter{table}{0} \begin{table}[h] \centering \caption{ESR Dating Summary, Swartkrans} \begin{tabular}{lrrrr} \hline \hline & \multicolumn{1}{c}{Mean\spp{0.41}} & & & \\ & \multicolumn{1}{c}{Accumulated} & \multicolumn{3}{c}{Ages} \\ \cline{3-5} \multicolumn{1}{l}{Member} & \multicolumn{1}{c}{Dose} & \multicolumn{1}{c}{EU} & \multicolumn{1}{c}{LU} & \multicolumn{1}{c}{RU\spp{0.41}} \\ & \multicolumn{1}{c}{(Gray)} & \multicolumn{1}{c}{(ka)} & \multicolumn{1}{c}{(ka)} & \multicolumn{1}{c}{(ka)} \\ \hline 5$^{1}$ \spp{0.41} & 170\hs{1.5} & 120 & 150 & 210 \\ \hs{6} $\pm$ & 10\hs{1.5} & 10 & 10 & 10 \\ 3$^{1}$ \spp{0.41} & 1080\hs{1.5} & 390 & 720 & 3900 \\ \hs{6} $\pm$ & 180\hs{1.5} & 30 & 60 & 500 \\ ``X" minimum$^{1}$ \spp{0.41} & 1490\hs{1.5} & 630 & 1050 & 1820 \\ \hs{6} $\pm$ & 330\hs{1.5} & 120 & 180 & 400 \\ ``X" maximum$^{1}$ \spp{0.41} & 1490\hs{1.5} & 700 & 1230 & 5220 \\ \hs{6} $\pm$ & 330\hs{1.5} & 80 & 120 & 1300 \\ \hline \hline \multicolumn{5}{l}{$^{1}$ Data from Blackwell {\em et al}., in prep., a}\\ \end{tabular} \end{table} \end{document}