SUPPLEMENTARY INFORMATION

Transcription

1 SUPPLEMENTARY INFORMATION DOI: /NGEO1253 Sea-level oscillations during the last interglacial highstand recorded by Bahamas corals Supplementary notes Stratigraphic constraints Two primary stratigraphic units are observed at the sample sites, Reefs I and II. The in situ corals of are truncated by a wave-cut bench, and the in situ corals of I grew on that erosional surface. There are two additional sub-units of I. Samples of IIb are branching coral rubble, with occasional in situ specimens, stratigraphically younger than I; lying on, and filling in around, the in situ corals of I. This unit is not derived from stratigraphically older material, which is a distinctly different facies. Corals of IIc are of I age, but may be stratigraphically out of sequence within I on SS. At Site they are directly superposed on unit IIb, and at Site they are lower in elevation than nearby corals of I, suggesting some reworking of deposits within the I sequence on SS. In situ corals with distinctly younger ages (Top), representing a distinct late phase of reef growth, are found at the top of the stratigraphic sequence, and are directly overlain by regressive sands on SS. Stratigraphic units at each site were in direct superposition, and multiple corals were sampled from each unit over a lateral distance of a few meters. The development of a reef sequence can be complex, and no a priori assumptions are made regarding age-height relationships, particularly since these sites have a total relief of 3 m or less. However, no matter how complex the reef development is, it is indisputable that the erosional surface that cut during an interval of lowered sea level is younger than and that corals of I that grew directly on that erosional surface must be younger than the surface itself. Clearly, some geologically significant time interval has passed between the growth of Reefs I & II. Comparing corrected and conventional ages Comparing different geochronological approaches for reducing diagenetic age artifacts requires no a priori assumption that all the samples should be the same age, or any assumption at all about the distribution of true ages within any given suite of samples. For any suite of samples, the total age variance is the sum of the true age variance, analytical uncertainty, and the variance imposed by diagenesis. For two different methods of calculating the ages, A and B: VarA(total) = Var(true age) + Var(analytical) +VarA(diagenesis) VarB(total) = Var(true age) + Var(analytical) + VarB(diagenesis) For any given suite of data, Var(true age) and Var(analytical) are the same regardless of the method used to calculate the ages. Taking the difference between the two equations yeilds: VarA(total) VarB(total) = VarA(diagenesis) VarB(diagenesis) Thus, the difference in total variance between two methods of calculating the ages is equal to the difference in variance imposed by diagenesis. Therefore, the reduction of age differences in the corrected ages relative to the conventional ones is a direct measure of the success of the correction in overcoming diagenetic artifacts, regardless of what the true age distribution is. NATURE GEOSCIENCE 1

2 The potential for natural variability in the oceanic uranium isotope ratio The initial 234 U/ 238 U ratio of corals, which is calculated from the measured age and 234 U/ 238 U, is an important criterion for assessing conventional age quality. This is because corals incorporate the uranium isotopic composition of the seawater in which they grow, so that a suite of corals of a given age should yield consistent initial 234 U/ 238 U if there has been no disturbance of the U- series isotopes used for dating. The majority of LIG studies have used the modern oceanic 234 U/ 238 U value for screening, because first-order oceanic U budget considerations and data from the best preserved fossil corals indicate that the LIG seawater value must have be very similar to today 1-3. The water on the Bahamas banks is exchanging with the open Atlantic on a timescale of months and its 234 U/ 238 U is identical to open ocean values 4. Even faster exchange rates are expected for the Great Inagua and San Salvador coasts, which are within a few 100 m of water depths in excess of 1,000 m. Ocean U budget constraints clearly exclude gradients of 234 U/ 238 U where the ocean is well mixed, because the residence time of U ( kyr) is much longer than the mixing time of the ocean (~1 ka). For example, if U with an 800 difference is added to two ocean basins with a mixing time of 1,000 year and a residence time of 400,000 years the steady state difference between the two oceans would be less than 1 4. This expectation from U budget constraints is confirmed by measurements of open ocean 234 U/ 238 U, which are identical over the global ocean 5. Thus, to change the 234 U/ 238 U value at the study sites, one needs to change the 234 U/ 238 U of the open ocean. Again, oceanic U budget constraints suggest that changes in 234 U/ 238 U that exceed 10 over timescales of kyr would require unreasonably large changes in river inputs, driven by changes in river fluxes, weathering changes, or nonconservative behavior of U 1-4, 6. The expectation that shifts in oceanic 234 U/ 238 U should be small is confirmed by changes of ocean 234 U/ 238 U during the deglaciation, where the changes in factors that control the oceanic U budget (climate, weathering, river fluxes, and non-conservative behavior) are the most dramatic. Initial 234 U/ 238 U of pristine corals indicate a gradual shift of 6 over a period of 15 kyr, constraining the maximum possible rate of change to 0.4 /kyr (Supplementary Figure 1). It is particularly noteworthy that the oceanic 234 U/ 238 U value has not exceeded the modern value during the last 50,000 years, demonstrating conclusively that corals with initial 234 U/ 238 U greater than the modern oceanic value have experienced disturbance of the isotopes used for dating and that conventional age estimates from such corals should be treated with extreme caution 7. None of the factors affecting the oceanic U budget are changing substantially during an interglacial, suggesting that oceanic 234 U/ 238 U should be constant, and this expectation is confirmed by the initial 234 U/ 238 U of pristine corals, which show a constant value over the Holocene interglacial. Furthermore, factors controlling river fluxes should be very similar in different interglacials in comparison to dramatic glacial/interglacial differences. Thus, we fully expect that oceanic 234 U/ 238 U was constant during LIG, and had a value very close to the modern one. Nonetheless, we consider the sensitivity of our conclusions to the assumption of a constant oceanic 234 U/ 238 U. 2

3 data moving average ,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 45,000 50,000 Age (y) Supplementary Figure 1: Oceanic 234 U/ 238 U for the last 50,000 years. (Data from 4, 8-17 ). The data is consistent with a 6 per mil shift between the glacial and interglacial values. The modern seawater value is ± 1.7 ( and 1SD), identical to the average for the Holocene (0 to 10 ka) of ± 2.8. Glacial values (20 to 50 ka) average 141 ± 2.8. The uranium isotope ratio of the ocean begins to rise from its glacial low at 26 ka and reaches its interglacial value by 10 ka at the latest, leading changes in sea level by 4 to 6 thousand years. Grey error envelope is 1 SE. The impact a different oceanic 234 U/ 238 U for the LIG on results and conclusions To test the sensitivity of the results shown in Figures 2 & 3 (main text) to changes in oceanic 234 U/ 238 U, we plotted the results that would be obtained if it was suddenly discovered that Last Interglacial oceanic 234 U/ 238 U was 5 different than today. This would be equivalent to nearly the entire observed shift between glacial and interglacial states. In the hypothetical case that seawater 234 U/ 238 U during the Last Interglacial was 5 higher, a value that was chosen to minimize the age discrepancy between corrected and conventional ages, corrected ages are shifted ~ 2 ka older. The best estimate of the conventional screened ages is shifted by and identical amount (Supplementary Figure 2), and therefore the corrected ages still agree with the best conventional ages. 3

4 ka I 118 I ka Initial δ 234 U ( ) Supplementary Figure 2: The best conventional age estimates for Reefs I and II. If LIG seawater was 5 higher than modern (δ 234 U = 152), the best age estimates come from corals that have exactly this value. These ages can be calculated from the regression lines in the figure and are ka () and ka (I). For the corrected and conventional age comparison shown in Figure 2 (main text), the conventional ages don t change (panel a), but the results of the screened ages do (panels b & c). Because the screening criteria are now centered at a seawater δ 234 U value of 152, most of the conventional ages are accepted at both the 8 and 4 screening level. The result is that the conventional ages for and II overlap, regardless of screening criteria. If an even stricter criterion of 2 is applied, the screened ages agree with the corrected ones, and resolve the age difference between Reefs I and II. (Supplementary Figure 3). Therefore, in the case that LIG seawater δ 234 U was 5 higher, the primary conclusions drawn from Figure 2 (main text) are still valid: 1) Taking the of a suite of samples helps to reduce the age variability caused by small amounts of U gain or loss. 2) Mean corrected ages have better reproducibility than the conventional ages. 3) The conventional ages agree with the corrected ones, if a strict enough screening criteria is applied, validating the corrected ages and resolving the age difference between the 2 fossil reefs. Increasing the assumed LIG seawater δ 234 U value by 5 has a similar effect on Figure 3 (main text). Again, a majority of the conventional age data is accepted at the 8 and 4 screening level and there is overlap in the conventional ages between Reefs I and II (Supplementary Figure 4). It is necessary to reduce the δ 234 U screening criteria to within error of 152 (i.e., ± 0 ) to fully resolve the age difference with conventional ages, and in this case the screened conventional ages give similar results to the corrected ones. Therefore, the primary conclusions from Figure 3 (main text) are still valid: 1) Mean corrected ages have better reproducibility than the conventional ages. 2) The conventional ages agree with the corrected ones, if a strict enough screening criteria is applied, validating the corrected ages and resolving the age difference between the 2 fossil reefs. 4

5 GI-6 GI-6 GI-7 GI-7 GI-12 GI-12 GI-13 GI-2 GI-3 GI-4 a Coral 1 Coral 2 Sample Coral 3 I Coral 4 I Sample GI-6 GI-6 GI-7 GI-7 GI-12 GI-12 GI-13 GI-2 GI-3 GI-4 b Coral 1 Coral Coral 3 I Coral 4 I Sample GI-6 GI-6 GI-7 GI-7 GI-12 GI-12 GI-13 GI-2 GI-3 GI-4 c Coral 1 Coral Coral 3 I Coral 4 I Sample GI-6 GI-6 GI-7 GI-7 GI-12 GI-12 GI-13 GI-2 GI-3 GI-4 d Coral 1 Coral Coral 3 I Coral 4 I Supplementary Figure 3: Changes to Figure 2 (main text) if LIG seawater δ 234 U is assumed to be 152. Diamonds are corrected ages and squares are conventional ages. Filled symbols are ages for each coral. Error bars are 2 SE. a) Corrected and conventional ages. b) Corrected ages and conventional ages passing a δ 234 U i screening criterion of ± 8. c) Corrected ages and conventional age screened to ± 4. d) Corrected ages and conventional ages screened to ± 2. 5

6 Site 110 a I IIc IIb top Site 110 b I IIc IIb top Site 110 c I IIc IIb top Site GI-J GI-B GI-H GI-F GI-I GI-E GI-D GI-D SS- GI-G GI-J GI-B GI-H GI-F GI-I GI-E GI-D GI-D SS- GI-G GI-J GI-B GI-H GI-F GI-I GI-E GI-D GI-D SS- GI-G GI-J GI-B GI-H GI-F GI-I GI-E GI-D GI-D SS- GI-G 110 d I IIc IIb top Supplementary Figure 4: Changes to Figure 3 (main text) if LIG seawater δ 234 U is assumed to be 152. Filled diamonds are corrected ages and open squares are conventional ages. Error bars are 2 SE. a) Corrected and conventional ages. b) Corrected ages, and conventional ages that pass an initial 234 U/ 238 U screening criterion of ± 8. c) Corrected ages, and conventional ages that pass an initial 234 U/ 238 U screening criterion of ± 4. d) Corrected ages, and conventional ages that have an initial δ 234 U within error of

7 In the equally unlikely alternative scenario that seawater 234 U/ 238 U during the Last Interglacial was 5 lower, corrected ages become ~ 2 ka younger. In this case, there are no conventional ages with initial δ 234 U exactly matching the criterion of 142. However, a best conventional age can still be calculated from the observed relationship between conventional age and initial δ 234 U (Supplementary Figure 5). The best conventional age is also shifted 2 ka younger, and the corrected ages agree with the best conventional age ka I ka I Initial δ 234 U ( ) Supplementary Figure 5: The best conventional age estimates for Reefs I and II. If LIG seawater was 5 lower than modern (δ 234 U = 142), the best age estimates come from corals that have exactly this value. These ages can be calculated from the regression lines in the figure and are ka () and ka (I). For the corrected and conventional age comparison shown in Figure 2 (main text), the conventional ages don t change (panel a), but the results of the screened ages do (panels b & c). Because the screening criteria are now centered at a seawater δ 234 U value of 142, very few of the conventional ages are accepted at the 8 screening level and none are accepted at the 4 screening level (Supplementary Figure 6). Because all of corals have an initial δ 234 U value significantly higher than the criteria of 142, all of the screened ages are still too old. However, applying screening criteria still improves the resolution of the conventional ages and their agreement with the corrected ages. Therefore, in the case that LIG seawater δ 234 U was 5 lower, the primary conclusions drawn from Figure 2 (main text) are still valid: 1) Taking the of a suite of samples helps to reduce the age variability caused by small amounts of U gain or loss. 2) In is not possible to assess the reproducibility of the conventional ages because not enough ages survive even the 8 screening. However, corrected ages still show good reproducibility. 3) Although none of the conventional ages survive a strict screening, the corrected ages still agree with a best estimate of the conventional age (Supplementary Figure 5). Decreasing the assumed LIG seawater δ 234 U value by 5 has a similar effect on Figure 3 (main text). Again, a majority of the conventional age data is rejected at the 8 and none passes the 4 screening level (Supplementary Figure 7). Because all of corals have an initial δ 234 U value significantly higher than the criteria of 142, all of the screened ages are still too old. However, 7

8 applying screening criteria still improves the resolution of the conventional ages and their agreement with the corrected ages. Therefore, in the case that LIG seawater δ 234 U was 5 lower, the primary conclusions drawn from Figure 3 (main text) are still valid: 1) Mean corrected ages have better reproducibility than the conventional ages. 2) Although none of the conventional ages survive a strict screening, the corrected ages still agree with a best estimate of the conventional age (Supplementary Figure 5) Sample GI-6 GI-6 GI-7 GI-7 GI-12 GI-12 GI-13 GI-2 GI-3 GI-4 a Coral 1 Coral Coral 3 I Coral 4 I Sample GI-6 GI-6 GI-7 GI-7 GI-12 GI-12 GI-13 GI-2 GI-3 GI-4 b Coral 1 Coral Coral 3 I Coral 4 I Supplementary Figure 6: Changes to Figure 2 (main text) if LIG seawater δ 234 U is assumed to be 142. Diamonds are corrected ages and squares are conventional ages. Filled symbols are ages for each coral. Error bars are 2 SE. a) Corrected and conventional ages. b) Corrected ages and conventional ages passing a δ 234 U i screening criterion of ± 8. No conventional ages survive a screening criterion of ±4. 8

9 Site 110 a I IIc IIb top Site GI-J GI-B GI-H GI-F GI-I GI-E GI-D GI-D SS- GI-G GI-J GI-B GI-H GI-F GI-I GI-E GI-D GI-D SS- GI-G 110 b I IIc IIb top Supplementary Figure 7: Changes to Figure 3 (main text) if LIG seawater δ 234 U is assumed to be 142. Filled diamonds are corrected ages and open squares are conventional ages. Error bars are 2 SE. a) Corrected and conventional ages. b) Corrected ages, and conventional ages that pass an initial 234 U/ 238 U screening criterion of ± 8. No conventional ages pass an initial δ 234 U screening criterion of ± 4. The impact of a changing oceanic 234 U/ 238 U during the LIG on results and conclusions We fully expect that the oceanic 234 U/ 238 U during the course of the LIG is constant, because the climate, weathering rates, and river fluxes during an interglacial are quite stable when compared to the dramatic changes between glacial and interglacial states, which result in a relatively small shift in oceanic 234 U/ 238 U. Nonetheless, we consider the potential impact of such shifts on our estimate of sea level change rates. Using the observed rate of change in oceanic 234 U/ 238 U during the deglaciation of 0.4 /kyr, and the sensitivity of the corrected ages to oceanic 234 U/ 238 U of 0.4 ka/, we arrive at a maximum shift of 0.16 kyr/kyr in the corrected ages assuming the dramatic oceanic U-budget shifts that occurred during the deglacial. This would be a total maximum shift in the corrected ages of 0.6 ka over the 4 ka interval elapsed between the sea level highstands represented by Reefs I & II. This has a negligible impact on our estimated the rate of change. Age calculation Conventional ages were calculated iteratively using the standard U-Th age equations 18. Opensystem ages were calculated iteratively using the open-system age equations of Thompson 19. A brief description of the rationale and practice of open-system corrections is given here. It has long been known that corals suffer from diagenetic addition of excess daughter isotopes 230 Th 9

10 and 234 U 20. This has been most often observed as a linear trend between the conventionally calculated ages and initial 234 U/ 238 U values 7, 21-25, and it is clear that corals with high initial 234 U yield artificially older ages (Figure 4 (main text)). Because of this, previous workers have used an initial 234 U/ 238 U screening criteria to identify corals that have behaved as closed systems. This criteria for acceptable or reliable or strictly reliable ages is typically expressed as a range around the modern seawater value: e.g ±.008 for reliable, and ±.004 for strictly reliable 25. Although this puts an upper limit on the impact of excess daughters on the calculated age, it may not completely remove the bias towards older ages (Figure 5 (main text)). Equations that correct for the effects of daughter addition use the observation that the source of the excess daughters is likely the adsorption of 234 Th and 230 Th that is produced by radioactive decay in the carbonate matrix surrounding the corals. This leads to a set of decay equations that take the added daughters into account in calculating the ages 19. In numerous instances, these equations have been shown to produce robust and reliable ages 2, 3, 26-29, although U gain or loss is not accounted for by these equations and can cause problems for both conventional and corrected ages 30, and it is critical to screen rigorously for 232 Th 31. Both screening of conventional ages and age correction equations rely on an assumed seawater 234 U/ 238 U value during the period under consideration. The fact that the lowest initial 234 U/ 238 U values in our dataset overlap with the modern range of ± 3 ( and 2 SD) Supplementary Figure 1), strongly suggests that Last Interglacial ocean 234 U/ 238 U was indistinguishable from the modern value, and other studies have reached similar conclusions 1, 3, 6, 7, 25, 32. Furthermore, using the modern seawater ratio ensures that our corrected age results are comparable to conventional results in previous studies, which have used the modern seawater value as a screening criterion. Mass Spectrometry Sample preparation, including cutting, cleaning, drying, and chemistry to isolate U and Th were carried out under clean-room conditions in a lab dedicated to carbonate sample processing for geochronology. Chemical extraction of U and Th from its carbonate matrix was done with standard chromatography protocols using ultra pure reagents and Teflon labware in a redundantly HEPA filtered laminar flow fume hood. U-series isotope ratios were measured on a Thermo Scientific Neptune high-resolution large-format multi-collector inductively-coupled mass spectrometer, using standard measurement protocols adapted from Robinson 18. Abundance sensitivity was typically 2 ppm or better as measured by the 237/ 238 U ratio. 234 U/ 238 U ratios were determined on un-spiked aliquots by standard bracketing with NIST standard SRM 4321C, which corrects for the tailing of the large 238 U beam under the minor 234 U peak, and any small drifts in the multiplier/faraday gain. Ions were collected statically with 234 U in the multiplier. Sample and standard multiplier intensities were carefully matched, with typical count rates of 30,000 to 50,000 cps on the multiplier and typical 238 beams of volts. Each analysis consisted of 35 measurements of 16 seconds each. Mass bias is monitored and corrected for using a value of for the 235 U/ 238 U ratio of the sample. Recently, this value has been determined to be slightly different for different materials at the sub-per mil level 19, 20. These differences have a negligible impact on the measurements reported here as they are an order of magnitude less that the measurement precision 21, particularly since all our measurements are referenced either directly or indirectly to HU-1. We retain the nominal value of to make the results directly comparable to previously published work. Washout between samples is monitored until the baseline levels fall below 1 ppm of the measurement intensities. Several standards were used to assess the accuracy and reproducibility of the 234 U/ 238 U measurements 10

11 over the course of the analysis of the samples measured for this work. The secular equilibrium standard HU-1 gave an activity ratio of ± ( and 2SD, n=41). The activity ratio is the product of the atomic ratio and the ratio of the decay constants, and here we use the decay constants from Cheng 22. Seawater from Vineyard Sound, Massachusetts gave an activity ratio of ± ( and 2SD, n=11). Our in-house coral standard gave an activity ratio of ± ( and 2SD, n=27). Thorium isotopes were measured with a multidynamic routine, alternating 229 Th and 230 Th on the multiplier, while measuring 235 U, 236 U, and 238 U on the Faraday cups. Mass fractionation was normalized to the 238 U/ 235 U ratio assuming a value of Samples were spiked so that the 229 Th/ 230 Th ratio was approximately 1 to avoid any artifacts from potential intensity biases. 232 Th was measured either on the multiplier or a Faraday cup, depending on beam intensity. The 229 Th- 236 U mixed spike was calibrated against the secular equilibrium standard HU-1, assuming secular equilibrium. Two independent assessments of the HU Th/ 238 U ratio with gravimetric U-Th solutions gave values within error of secular equilibrium. Accuracy and reproducibility of the 230 Th/ 238 U measurement was assessed using HU-1 and an in-house coral standard. Over the course of the analysis of the samples measured for this work, HU-1 gave an activity ratio of ± ( and 2SD, n=25), and the coral standard ±.001 ( and 2SD, n=9). 11

12 Supplementary Table 1: Coral geochemical and isotope ratio data Sample 1 Species 2 U ± Th ± ( 234 U/ 238 U) 3 ± ( 230 Th/ 238 U) 3 ± QC 4 (ppm) (ppb) GI-1 Ma Th GI-2 Ma GI-3 Ma GI-4 Ma GI-5 Ma U GI-5 Ma Th GI-6 Ma GI-6 Ma GI-7 Ma GI-7 Ma Ma Ma Ma Ma Ma Ma Ma Th Ma Ma Ma Ma Ma Th Ma Ma Ma GI-12 Ma GI-12 Ma GI-13 Ma GI-13 Ma Th GI-14 Ma GI-15 Ma Th GI-16 Ma GI-17 Ma S GI-18 Ma S GI-19 Ma GI-20 Ac GI-21 Dc GI-22 Ma Th GI-23 Ma Th GI-24 Ma GI-25 Dc

13 GI-26 Ds GI-27 Dc GI-28 Ap Th GI-29 Ap GI-30 Dc Th GI-31 Dc GI-32 Dc Th GI-33 Ss Th GI-34 Ma GI-35 Ma Th GI-36 Dc Th GI-37 Dc Th GI-38 Ds Th GI-39 Ds Th GI-40 Ma GI-41 Ap GI-42 Ap GI-43 Ap GI-44 Ma GI-45 Ma Th GI-46 Ap Th GI-47 Ap GI-48 Ma Th GI-49 Ap GI-50 Ap GI-51 Ma GI-52 Ma GI-53 Ds Th GI-54 Ma GI-55 Ma GI-56 Ma GI-57 Ac GI-58 Ac GI-59 Ma GI-60 Ma Th GI-61 Ma Th GI-62 Ma Th GI-63 Ma SS-1 Ap SS-2 Ap SS-3 Ap SS-4 Ap SS-5 Ap SS-6 Ap

14 SS-7 Ap SS-8 Ap SS-8 Ap SS-9 Ap SS-10 Ap SS-10 Ap SS-11 Ap SS-12 P Th SS-12 P Th SS-13 Ap SS-14 Ap SS-15 Ap SS-16 Ap SS-16 Ap SS-17 Ap SS-18 Ap SS-19 Ap SS-20 Ap SS-21 Ma SS-22 Ds SS-23B Ma SS24 Ac SS-25 Ac SS-26 Ma SS-27 Ma SS-28 Ma SS-28 Ma SS-29 Ap SS-30 Ap SS-31 Ap SS-32 Ds SS-33 Ap SS-34 Dc SS-35 Dc SS-36 Ap SS-37 Ap SS-38 Ap SS-39 Ma SS-40 Ds SS-41 Ap SS-42 Ap SS-43 Ap S SS-44 Ap U SS-44 Ap

15 SS-45 Ap SS-46 Ap SS-47 Ap SS-48 Ap SS-49 Ap Th SS-55 Ma Th SS-63 Ds S SS-63 Ds S SS-64 Dc Th SS-64 Dc Th SS-65 Dc Th SS-66 Dc Th SS-67 Dc SS-07-1 Ma SS-07-2 Ma SS-07-3 Ma SS-07-4 Ma (SS) San Salvador Island, Bahamas; (GI) Great Inagua Island, Bahamas. Identical sample numbers are results from discrete slabs of the same hand specimen. For the following sample numbers, each group are hand specimens from the same large individual coral: (GI-2, 3, 4), (GI- 5, 6, 7), (, 9, 10), (, 12, 13), (GI-14, 15, 16), (GI-19, 54, 55, 56), (GI-22, 23, 24), (GI- 25, 26), (GI-27, 30, 31), (GI-51, 52). 2 Species (Ap) Acropora palmata, (Ac) Acropora cervicornis, (Ma) Montastraea annularis, (Ds) Diploria strigosa, (Dc) Diploria clivosa, (Ss) Siderastrea siderea. 3 Isotope ratios are expressed as activity ratios, using the decay constants of Cheng QC (quality control) ages that were rejected as unreliable based on the following criteria: (Th) 232 Th concentration greater than 0.4 ppb. (U) 238 U concentration outside the range of living corals; Ac & Ap ppm; other species ppm. (S) Age significantly different from others in the same stratigraphic unit and out of stratigraphic sequence. All error estimates are 2 SE. 15

16 Supplementary Table 2: Coral stratigraphic and age data Raw Sample 1 Island 2 Site Unit 3 Age 4 ± age 5 ± δ U i ± (ka) (ka) GI-1 GI none? GI-2 GI A II GI-3 GI A II GI-4 GI A II GI-5 GI A I GI-5 GI A I GI-6 GI A I GI-6 GI A I GI-7 GI A I GI-7 GI A I GI A II GI A II GI A II GI A II GI A II GI A II GI A II GI A II GI A II GI A II GI A II GI A II GI A I GI A I GI A I GI-12 GI A I GI-12 GI A I GI-13 GI A I GI-13 GI A I GI-14 GI B I GI-15 GI B I GI-16 GI B I GI-17 GI C II GI-18 GI C I GI-19 GI D II GI-20 GI D IIb GI-21 GI E I GI-22 GI E I GI-23 GI E I GI-24 GI E I GI-25 GI E I

17 GI-26 GI E I GI-27 GI E I GI-28 GI E I GI-29 GI E I GI-30 GI E I GI-31 GI E I GI-32 GI E I GI-33 GI E I GI-34 GI E I GI-35 GI E I GI-36 GI E I GI-37 GI E I GI-38 GI E I GI-39 GI E I GI-40 GI E I GI-41 GI F I GI-42 GI F I GI-43 GI F I GI-44 GI F I GI-45 GI F I GI-46 GI G I GI-47 GI G top GI-48 GI G I GI-49 GI H I GI-50 GI H I GI-51 GI H I GI-52 GI H I GI-53 GI H I GI-54 GI D II GI-55 GI D II GI-56 GI D II GI-57 GI D IIb GI-58 GI D IIb GI-59 GI I I GI-60 GI I I GI-61 GI I I GI-62 GI J I GI-63 GI J I SS-1 SS D IIc SS-2 SS D IIb SS-3 SS D IIb SS-4 SS D IIb SS-5 SS D IIb SS-6 SS D IIb

18 SS-7 SS D IIb SS-8 SS D IIc SS-8 SS D IIc SS-9 SS D IIb SS-10 SS D IIb SS-10 SS D IIb SS-11 SS D IIb SS-12 SS D IIb SS-12 SS D IIb SS-13 SS D IIb SS-14 SS D IIb SS-15 SS D IIb SS-16 SS D IIc SS-16 SS D IIc SS-17 SS D IIc SS-18 SS D top SS-19 SS D IIc SS-20 SS D IIb SS-21 SS D IIc SS-22 SS D top SS-23B SS D I SS24 SS D IIb SS-25 SS D IIb SS-26 SS D I SS-27 SS D I SS-28 SS D II SS-28 SS D II SS-29 SS D IIb SS-30 SS C top SS-31 SS C II SS-32 SS C II SS-33 SS C II SS-34 SS C II SS-35 SS C II SS-36 SS C top SS-37 SS C I SS-38 SS C I SS-39 SS C I SS-40 SS C I SS-41 SS C II SS-42 SS C II SS-43 SS C II SS-44 SS C II SS-44 SS C IIc

19 SS-45 SS C IIc SS-46 SS C IIc SS-47 SS C IIc SS-48 SS C IIc SS-49 SS C II SS-55 SS other? SS-63 SS other top SS-63 SS other top SS-64 SS other top SS-64 SS other top SS-65 SS other top SS-66 SS other top SS-67 SS other top SS-07-1 SS D II SS-07-2 SS D I SS-07-3 SS D II SS-07-4 SS D II Identical sample numbers are results from discrete slabs of the same hand specimen. For the following sample numbers, each group are hand specimens from the same large individual coral: (GI-2, 3, 4), (GI-5, 6, 7), (, 9, 10), (, 12, 13), (GI-14, 15, 16), (GI-19, 54, 55, 56), (GI- 22, 23, 24), (GI-25, 26), (GI-27, 30, 31), (GI-51, 52). 2 (SS) San Salvador Island, Bahamas; (GI) Great Inagua Island, Bahamas. 3 Stratigraphic units: I: ; lowest unit; in situ head coral, planed off by a wave-cut bench. II: I; in situ head coral growing on top of the wave-cut bench, except where mixed head and branching corals occur. IIb: I; rubble of branching corals with occasional in situ individuals, draping in situ corals of and II. IIc: I; rubble of branching corals, consistent I ages; may not be stratigraphically in place with respect to other I sub-units (reworked). Top: In situ corals at the top of the stratigraphic sequence, with significantly younger ages. 4 Ages calculated from the age-correction equations of Thompson & Goldstein Ages calculated from conventional U/Th age equations Initial 234 U/ 238 U activity ratio, calculated from the age and measured 234 U/ 238 U, expressed as the deviation in parts per thousand from the secular equilibrium value of 1. All error estimates are 2 SE. 19

20 Supplementary Table 3: Calculation of ages for stratigraphic units. Island 1 Site Unit 2 Sample Species or Age 4 ± Raw age 5 ± Type 3 (ka) (ka) GI A I GI-6 Ma GI A I GI-6 Ma GI A I GI-7 Ma GI A I GI-7 Ma GI A I i GI A I Ma GI A I Ma GI A I Ma GI A I GI-12 Ma GI A I GI-12 Ma GI A I GI-13 Ma GI A I i GI A II GI-2 Ma GI A II GI-3 Ma GI A II GI-4 Ma GI A II i GI A II Ma GI A II Ma GI A II Ma GI A II Ma GI A II Ma GI A II Ma GI A II Ma GI A II Ma GI A II Ma GI A II Ma GI A II i GI B I GI-14 Ma GI B I GI-16 Ma GI B I i GI D II GI-19 Ma GI D II GI-54 Ma GI D II GI-55 Ma GI D II GI-56 Ma GI D II i GI D IIb GI-20 Ac GI D IIb GI-57 Ac GI D IIb GI-58 Ac GI D IIb m

21 GI E I GI-21 Dc GI E I GI-24 Ma GI E I GI-25 Dc GI E I GI-26 Ds GI E I GI-27 Dc GI E I GI-29 Ap GI E I GI-31 Dc GI E I GI-34 Ma GI E I GI-40 Ma GI E I m GI F I GI-41 Ap GI F I GI-42 Ap GI F I GI-43 Ap GI F I GI-44 Ma GI F I m GI G top GI-47 Ap GI G top i GI H I GI-49 Ap GI H I GI-50 Ap GI H I GI-51 Ma GI H I GI-52 Ma GI H I m GI I I GI-59 Ma GI I I i GI J I GI-63 Ma GI J I i SS D I SS-23B Ma SS D I SS-26 Ma SS D I SS-27 Ma SS D I SS-07-2 Ma SS D I m SS D II SS-28 Ma SS D II SS-28 Ma SS D II SS-07-1 Ma SS D II SS-07-3 Ma SS D II SS-07-4 Ma SS D II m SS D IIb SS-2 Ap SS D IIb SS-3 Ap SS D IIb SS-4 Ap SS D IIb SS-5 Ap

22 SS D IIb SS-6 Ap SS D IIb SS-7 Ap SS D IIb SS-9 Ap SS D IIb SS-10 Ap SS D IIb SS-10 Ap SS D IIb SS-11 Ap SS D IIb SS-13 Ap SS D IIb SS-14 Ap SS D IIb SS-15 Ap SS D IIb SS-20 Ap SS D IIb SS24 Ac SS D IIb SS-25 Ac SS D IIb SS-29 Ap SS D IIb m SS D IIc SS-1 Ap SS D IIc SS-8 Ap SS D IIc SS-8 Ap SS D IIc SS-16 Ap SS D IIc SS-16 Ap SS D IIc SS-17 Ap SS D IIc SS-19 Ap SS D IIc SS-21 Ma SS D IIc m SS D top SS-18 Ap SS D top SS-22 Ds SS D top m SS C I SS-37 Ap SS C I SS-38 Ap SS C I SS-39 Ma SS C I SS-40 Ds SS C I m SS C II SS-31 Ap SS C II SS-32 Ds SS C II SS-33 Ap SS C II SS-34 Dc SS C II SS-35 Dc SS C II SS-41 Ap SS C II SS-42 Ap SS C II m SS C IIc SS-44 Ap SS C IIc SS-45 Ap

23 SS C IIc SS-46 Ap SS C IIc SS-47 Ap SS C IIc SS-48 Ap SS C IIc m SS C top SS-30 Ap SS C top SS-36 Ap SS C top m SS other top SS-67 Dc SS other top i (SS) San Salvador Island, Bahamas; (GI) Great Inagua Island, Bahamas 2 Stratigraphic units: I: ; lowest unit; in situ head coral, planed off by a wave-cut bench. II: I; in situ head coral growing on top of the wave-cut bench, except where mixed head and branching corals occur. IIb: I; rubble of branching corals with occasional in situ individuals, draping in situ corals of and II. IIc: I; rubble of branching corals, consistent I ages; may not be stratigraphically in place with respect to other I sub-units (reworked). Top: In situ corals at the top of the stratigraphic sequence, with significantly younger ages. 3 Species (Ap) Acropora palmata, (Ac) Acropora cervicornis, (Ma) Montastraea annularis, (Ds) Diploria strigosa, (Dc) Diploria clivosa, (Ss) Siderastrea siderea. Type of : ages from discrete samples of an individual coral (i), ages from closely associated samples within the same stratigraphic unit (m). 4 Ages calculated from the age-correction equations of Thompson & Goldstein Ages calculated from conventional U/Th age equations 18. All error estimates are 2 SE. 23

24 Supplementary Table 4: Mean ages of stratigraphic units Site 1 Unit 2 Type 3 Age 4 ± 5 Raw age ± n 6 (ka) (ka) I I I m GI-J I I GI-B I I GI-H I m I I GI-F I m GI-I I I GI-E I m I m II I II m II I II m GI-D II I IIc m IIc m IIb m GI-D IIb m SS-O top I top m top m GI-G top I (SS) San Salvador, Bahamas; (GI) Great Inagua, Bahamas. 2 Stratigraphic units: I: ; lowest unit; in situ head coral, planed off by a wave-cut bench. II: I; in situ head coral growing on top of the wave-cut bench, except where mixed head and branching corals occur. IIb: I; rubble of branching corals with occasional in situ individuals, draping in situ corals of and II. IIc: I; rubble of branching corals, consistent I ages; may not be stratigraphically in place with respect to other I sub-units (reworked). Top: In situ corals at the top of the stratigraphic sequence, with significantly younger ages. 3 Type of : ages from discrete samples of an individual coral (i), ages from closely associated samples within the same stratigraphic unit (m). 4 Ages calculated from the age-correction equations of Thompson & Goldstein Ages calculated from conventional U/Th age equations Number of samples. All error estimates are 2 SE. 24