The variability in Mg/Ca and Sr/Ca within individual tests and chambers of tests, and samples consisting of differing numbers of individuals, was determined for Globigerina bulloides and Globorotalia truncatulinoides in a North Atlantic core top sample (52.918°N 16.917°W′). The variability in Mg/Ca and Sr/Ca within individual tests and chambers was determined by electron microprobe, and samples consisting of variable sample size were measured using inductively coupled plasma optical emission spectrometer (ICP-OES). Large compositional heterogeneity was found within individual chambers, and within the test as a whole, of the two species and the presence of regions with up to ∼10 mmol/mol Mg/Ca, especially in G. bulloides. Mean Mg/Ca decreases in successive chambers of G. bulloides (especially the 300–355 μm fraction) and is accompanied by decreasing variance but is not statistical significant. Sr/Ca is much more homogeneously distributed, with a normal distribution, and shows no differences from chamber to chamber. The variability of Mg/Ca and Sr/Ca decreases with increasing sample size, from single to five to twenty tests per sample, approximately as for a normal distribution, with greater variability for G. bulloides than for G. truncatulinoides, equivalent to uncertainties in temperature (n = 20) of 1.1°C and 0.7°C for the two species within the whole of the sediment mixed layer.
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 One of the technical issues surrounding the application of Mg/Ca paleothermometry [e.g., Nuernberg et al., 1996; Rosenthal et al., 1997; Lea et al., 1999; Elderfield and Ganssen, 2000] relates to observations and inferences of chemical heterogeneity in the Mg contents of foraminiferal shells. This was highlighted from observations that dissolution of foraminifera leads to a lowering of Mg/Ca [Brown and Elderfield, 1996; Rosenthal et al., 2000], from analyses of individual shells using electron microprobe [Brown and Elderfield, 1996; Nuernberg et al., 1996] and studies based upon selective leaching [Barker et al., 2003; Benway et al., 2003] and laser ablation mass spectrometry [Eggins et al., 2003; Reichart et al., 2003] methods. In some cases, Sr/Ca was measured alongside Mg/Ca and also found to decrease with dissolution. Compositional heterogeneity at high spatial resolution is a common natural phenomenon. In paleoceanography it has been addressed through use of well-defined size fractions [e.g., Oppo and Fairbanks, 1989] and sample sizes [Boyle, 1984; Elderfield et al., 2000] to minimize variability. Apart from intrinsic natural variability within a single shell and between shells of the same age deposited in a sediment such as seasonality or variations in calcification depth, other factors may account for residual scatter in Mg/Ca data. These include, as well as dissolution, sample size and number, differences between cleaning procedures [see Rosenthal et al., 2004] and biological stirring of the sediment. There is little information on the effect of chemical heterogeneity on the reproducibility of foraminiferal Mg/Ca analyses. In this article we report on variability in Mg/Ca and Sr/Ca within and between individuals of Globigerina bulloides and Globorotalia truncatulinoides using samples from the mixed layer of a sediment core. Two approaches have been used: (1) analysis of variability within individual tests at high spatial resolution and (2) analysis of samples comprising different numbers of individuals.
 Tests of G. bulloides and G. truncatulinoides were picked from the surface and near surface of a “multicore” from Site A of the Benthic Boundary Layer programme (BENBO) at 52.918°N 16.917°W′ (3580 m water depth; CaCO3 content ∼76%). Oxygen penetration occurs to 8 cm [Tachikawa and Elderfield, 2002] and 210Pb and 14C analyses indicate that the sediment mixed layer extends to between 8.5 and 12.5 cm with a bioturbation mixing density of 0.045 cm2 yr−1 [Thomson et al., 2000]. Cd/Ca, δ18O and δ13C in a number of species of benthic foraminifera are constant over the top 10 cm [Tachikawa and Elderfield, 2002]. The carbonate lysocline is below 4000 m in the North Atlantic [Lewis and Wallace, 1998] such that the sample should be well preserved. The samples picked for analyses were visually well preserved but the effect of supra-lysoclinal dissolution cannot be ruled out.
 Foraminifera for electron microprobe measurements were picked from the 212–250 μm and 300–355 μm size fractions in the 2–2.5 cm section of the core, cleaned by ultrasonification in ultrapure water, mounted whole in araldite (Resin MY753, Hardener HY951) and polished to reveal the desired cross sections. Analysis was performed using a Cameca Sx-50 electron microprobe (wavelength dispersive) at 15 kV and 25 nA with a beam size of ∼1 μm for quantitative analyses. Internal laboratory standards periclase (Mg), strontianite (Sr) and wollastonite (Ca) were used giving a precision of approximately 10% (Mg/Ca) and 6%, (Sr/Ca). Precision could not be assessed from samples because of sample heterogeneity and therefore we defined precision using the internal standards relative to bulk analyses. Backscattered electron (BSE) images of foraminiferal sections were taken to locate the exact position of transects on the sample analyzed and to aid the location of points within the chamber selected for analysis (Figure 1). Four or five chambers could be easily identified and were used for analysis. Points were selected along a transect running from the inside (wall) to the outside (surface) of the test, a distance of 2–3 μm depending upon shell thickness, but kept constant throughout the analysis for a particular species. Surfaces showing any pores, cracks, relief, inclusions and edges of the calcite were avoided. Occasionally, analyses yielded less than 35wt% of Ca and were discarded because they indicated that the beam was not entirely centered on the calcite or that non-calcitic material was present. Two to three single tests were analyzed for each species in the two size fractions.
 Foraminifera for “bulk” analysis were picked from the 300–355 μm size fraction. Sub-samples for two of the sample sizes tested (50 sub-samples each of one test and 20 sub-samples each of 5 tests) were picked from the 2–2.5 cm section of the core. Specimens for 12 sub-samples each of 20 tests were picked from depths within the top 10 cm of the core. Data were obtained using a slightly revised cleaning method [Barker et al., 2003], which consisted of three water washes and two methanol wash followed by oxidation step for 20 min (with ∼1% buffered H2O2) and a weak acid leach (0.001M HNO3) before dissolving the foraminiferal calcite into 0.075M HNO3. The analytical procedures for “bulk” foraminiferal tests measurements were employed [de Villiers et al., 2002] with an estimated precision of less than 1%.
 To compare bulk measurements for sub-samples of different sizes, the frequency of Mg/Ca and Sr/Ca within fixed bin size intervals was calculated. Results were compared with frequencies for a Gaussian curve fit in order to determine whether the distribution of values was normally distributed about the mean.
 Results are summarized in Figure 2, and all data are listed in auxiliary material Tables A1a–A1c. Figures showing transects analyzed within a chamber for each specimen for two species in two size fractions and Gaussian curve fits with statistical information are shown in auxiliary material Figures A1 and A2. Examples of the transect figures for Mg/Ca and Sr/Ca from one specimen are shown in Figures 5a5b5c–5d for both species in two size fractions. Electron microprobe data of all locations analyzed within individual tests shows a large internal variability in Mg/Ca (Figures 3a and 3b) for G. bulloides (45–47%) and G. truncatulinoides (44–63%). Given the variability, there are no significant differences in average Mg/Ca between the two size fractions. Fits of the data to a normal distribution gives Gaussian averages smaller than the arithmetic means, reflecting, as illustrated in the histograms, a number of samples with high Mg/Ca, up to nearly 10 mmol/mol. The samples described by a normal distribution have the same Mg/Ca in the two size fractions of G. bulloides but ∼30% lower Mg/Ca in the larger size fraction of G. truncatulinoides (t-test: G. bulloides, p = 0.19; G. truncatulinoides, p = 0.001). The variability of Sr/Ca within a test is smaller than for Mg/Ca, 11–14% in G. truncatulinoides and 9% in G. bulloides (Figures 3c and 3d) close to the electron-microprobe measurement precision of ∼6%. Given the variability, there are no significant differences in average Sr/Ca between the two size fractions of both species. The Gaussian and arithmetic averages are similar and show little difference between the two size fractions. Mg/Ca in G. bulloides is similar in the earliest chambers analyzed for each size fraction and decreases to the final chamber with lower ratios in the larger size fraction (Figures 4a(i), 4a(ii), 5a, and 6). This trend is accompanied by decreasing variance in the data, which is especially high in the earliest chambers (Figure 6). Mg/Ca in G. truncatulinoides is also similar in the earliest chambers analyzed for each size fraction but decreases before increasing to the final chamber (Figures 4a(iii), 4a(iv), 5c, 6). Variance also decreases but less so than in G. bulloides. In contrast, Sr/Ca ratios variance difference between chambers are minor (Figures 4b(i), 4b(ii), 5b, 5d, and 6). Analysis of “bulk” samples each comprising a single test showed significant variability in Mg/Ca of 35% of the mean value for G. bulloides and 25% of the mean value for G. truncatulinoides (Figures 7a and 7b). When the numbers of individuals per sample was increased to five and twenty, the variance in Mg/Ca decreased as expected, more for G. bulloides, than for G. truncatulinoides. The variability of Sr/Ca in between samples composed of a single test is very small compared to Mg/Ca, 3% for G. bulloides and 4% for G. truncatulinoides (Figures 7c and 7d) and shows little decrease in variance with increasing numbers of individuals per sample.
4.1. Mg/Ca and Sr/Ca Variability Within Tests and Chambers
 The most striking observations for Mg/Ca from the electron probe investigation are (1) the large compositional heterogeneity within individual chambers, and within the test as a whole, of the two species and the presence of regions with high Mg/Ca, especially in G. bulloides; (2) the decrease in mean Mg/Ca in successive chambers of G. bulloides (especially the 300–355 μm fraction) accompanied by decreasing variance although not statistically significant; and (3) the small statistically insignificant increase in Mg/Ca of the final chambers of G. truncatulinoides. In contrast, Sr/Ca is much more homogeneously distributed, with a normal distribution, and shows no differences from chamber to chamber. These results (large compositionally variability for Mg/Ca and not for Sr/Ca) are similar to those observed for G. tumida and G. sacculifer [Brown and Elderfield, 1996].
 The wide range in Mg/Ca within tests of G. bulloides and G. truncatulinoides cannot be translated to calcification temperatures because calibrations are based on analysis of whole shells. However, it is interesting to consider differences between chambers, as has been done for δ18O [Bemis et al., 1998]. It must be remembered that differences between median values, derived from the multiple individual electron probe analyses, are not statistically significant but if we consider the average value for each chamber as an individual analysis with its analytical uncertainty then the exercise is instructive. The calcification process in planktonic foraminifera occurs by the growth of new calcite over previous chambers as new chambers form [see Hemleben et al., 1989]. Hence the earlier chamber will contain calcite produced during calcification of the later chambers and therefore presents an integrated Mg/Ca ratio of their growth and subsequent chamber formation. For example, the differences in Mg/Ca associated with the initial growth of each chamber of G. bulloides will be much greater than shown in Figure 6. (J. Erez, personal communication, 2002) has shown that the initial precipitation process produces high-Mg calcite). We would also expect, as observed, that the variance in Mg/Ca is greater in the earlier chambers than subsequent ones. We have found that the high-Mg calcite is associated with the earlier chambers (especially in the inside of the chamber) compared to the final chamber of G. bulloides (300–355 μm) (see Figures 5a and A2) [Erez, 2003]. But we have not found different and possibly high Mg/Ca ratios associated with the gametogenic calcite in G. bulloides (Figures 5a, 5b, and A2) as previously observed in G. sacculifer [Nuernberg et al., 1996]. Instead we observe, in general, low Mg/Ca at the surface of the chamber calcite which is possibly due to the calcite precipitated during the formation of the final chamber. Additionally, we found low Mg-calcite outside (surface) of all the chambers (except in the final chamber and few points in earlier chambers of one specimen) in G. truncatulinoides which is due to the presence of secondary crust calcite formed at deeper water depths in this species (Figures 5c, 5d, and A2). Similar low Mg-calcite was observed in G. tumida [Brown and Elderfield, 1996].
 It should also be noted that we were unable to identify for analysis more than five of the fourteen chambers of G. bulloides. If a common temperature equation (from Mashiotta et al.  for G. bulloides and Anand et al.  for G. truncatulinoides) is applied to each chamber of a species, the inferred temperature range from the “warmest” to the “coldest” chamber is 6°C (G. bulloides, final 5 chambers, 300–355 μm), 3°C (G. bulloides, final 4 chambers, 212–250 μm), 4°C (G. truncatulinoides, final 5 chambers, 300–355 μm) and 3°C (G. truncatulinoides, final 5 chambers, 212–250 μm). The seasonal variation in the North Atlantic sea surface temperatures (53°N) is ∼4°C [Levitus and Boyer, 1994] and the range between 0 and 100 m at the core site is about 4°C. The mean temporal variation (45° to 65°N, 15° to 55°W) over 100 years is ∼1°C [Kaplan et al., 1998]. Given that chamber Mg/Ca, except for the final chamber, is an integrated signal it is unlikely that the estimated G. bulloides temperature ranges derived from the individual chambers are accurate. Given the observations of Erez , it is likely, in particular for early chambers, that “biomineralization effects” will be pronounced. Although the inferred temperature range for G. truncatulinoides may seem realistic (its depth habitat is large, and the temperature at Site A between 0 and 900 m is ∼15–9°C) it would require the final chamber to calcified at warmer temperatures than previous ones; and demonstrates also for this species that calibrations obtained using whole tests cannot be applied at the level of a single chamber.
4.2. Mg/Ca and Sr/Ca Variability With Increasing Sample Size
 As expected, the variability of Mg/Ca and Sr/Ca decreases with increase in sample size from single test to five tests to twenty tests per sample (Figures 2 and 7). The large sample size averages the heterogeneity due to natural variability inherent within a species. The range of Mg/Ca in G. truncatulinoides is a close fit to a normal distribution but a poorer fit for G. bulloides. The variability for Sr/Ca is much less than for Mg/Ca. A factor affecting the distribution of Mg/Ca but not Sr/Ca in the analyses of the samples of twenty individuals is that they were drawn from different depths within the mixed layer (Figure 2). In the case of G. truncatulinoides, Mg/Ca decreases from 1.73 mmol/mol at the core surface to, on average, 1.37 ± 0.05 at and below 1.5–2.0 cm interval. The pattern for G. bulloides is, within the higher variance for this species, of similar Mg/Ca and δ18O in the core surface as at depth, except for an interval within the mixed layer where Mg/Ca is higher and δ18O lower than adjacent depths. In this case, the inferred temperature differences are similar on the basis of Mg/Ca (4°C) and δ18O (5°C), suggesting of injection of material by bioturbation at this depth.
 Using the methodology employed in our laboratory, Barker et al.  compared the precision of analysis of ten samples each of twenty individuals of G. ruber (300–355 μm) with those of ten aliquots taken from two hundred homogenized individuals. The natural variability attained for the ten unmixed sub-samples was ±3.7% (1σ) for Mg/Ca (equivalent to 28.3 ± 0.4°C) and ±1.2% (1σ) for Sr/Ca. Variability associated with the homogenized samples was less than half that of the non-mixed samples for both Mg/Ca (1.8%, 0.2°C) and Sr/Ca (0.5%). Determination of what precision is achievable for a particular species, and assessment of the sample size required to achieve the required accuracy of Mg/Ca temperature, or of Sr/Ca, may be made from a comparison of the precision of analyses based on different numbers of individual tests (Figure 8). Although the data are not described fully by normal distribution they approximate to the √n law. According to √n law if the distribution of a variable is described by a normal distribution then the precision of the mean for such variable improves with the square root of the sample size (SDn = SDn=1/√n; where sd = standard deviation; n = number of measurements), which implies that the population average is usually within sample average ±2σ/√n.
 Best fit values of standard deviations are G. bulloides Mg/Ca SDn=1 = 1.3, Sr/Ca SDn=1 = 0.04, G. truncatulinoides SDn=1 = 0.42, Sr/Ca SDn=1 = 0.06. High precision on Sr/Ca is easily achievable. High precision on Mg/Ca for G. bulloides requires more individuals than for G. truncatulinoides. For example, for a sample of twenty individuals, SDn=20 = 0.28 and 0.09, respectively for Mg/Ca, equivalent to uncertainties in temperature of 1.1°C and 0.7°C for the two species within the whole of the sediment mixed layer of this particular core. This difference is logical: in addition to the reasons for variability within tests of species, the variability is determined by differences between shells within the population comprising the analysis sample. G. truncatulinoides comprises a large proportion of secondary compared to the primary calcite [Bé, 1980; Hemleben et al., 1989] and its range of depth habitats reflects a narrow temperature range. In contrast, G. bulloides is opportunistic and can occupy a range of surface and near-surface temperatures as well as showing seasonality.
4.3. Implications for Mg/Ca Thermometry
 The analysis of variability within individual tests at high spatial resolution has shown differences in Mg/Ca between chambers of the two species analyzed. The differences in Mg/Ca between chambers do not appear to be solely controlled by temperature as described by a single thermometry equation. Analysis of samples at depths through the mixed layer of a carefully collected multicore revealed, in contrast to what has been recorded for Sr/Ca in the two species analyzed (and in δ18O, δ13C and Cd/Ca in benthic foraminifera), significant differences in Mg/Ca and δ18O of both G. bulloides and G. truncatulinoides that are not fully understood. There is a need for a wider collection of such high quality core top material in order to better understand how the incorporation of Mg/Ca by planktonic foraminifera is translated into the paleoceanographic record. Analysis of different numbers of individuals for “bulk” analysis shows a distribution in precision approximated by but not the same as that for a normal distribution. The precision of temperature estimate for G. bulloides is greater than for G. truncatulinoides in the core studied, probably because of its seasonality or variability in shallow depth habitat. The simple exercise of evaluating precision from replicate analyses using the √n law is a helpful initial step in determining the appropriate sample size for application of Mg/Ca thermometry to a particular species and sample location, and problem.
 We thank colleagues in Cambridge, especially Stephen J. Reed for assistance with electron microprobe analyses, and Linda Booth and Mervyn Greaves for help in the laboratory. P.A. is thankful to Stephanie de Villiers for help with ICP-OES and her useful comments. We thank Daniel McCorkle, Margaret Delaney, Greet-Jan Reichart, and Bill White for their useful comments, which helped us to improve the manuscript significantly. Research funded by a Cambridge Commonwealth Trust Studentship (to P.A.) and funding from the European Commission (EVRI-CT-40018; CESOPF) and the Natural Environment Research Council (GR3/Jif/05a). We thank CESOPF colleagues for discussions.