Holocene tropical reef accretion and lagoon sedimentation: A quantitative approach to the influence of sea‐level rise, climate and subsidence (Belize, Maldives, French Polynesia)

Accretion rates of Holocene tropical coral reefs in three areas in the Atlantic, Pacific and Indian Oceans have been quantified in 79 dated core sections in 34 reef cores from Belize, the Maldives and French Polynesia. Holocene vertical reef accretion rate averages 5.05 m/kyr and has decreased during the past 10 kyr. Accretion rates in branched and massive coral facies are statistically similar. Reef accretion rate is positively correlated with the rate of sea‐level rise, that is the degree of creation of accommodation space, and with climate as expressed in a Holocene sea surface temperature anomaly. Accommodation space is also created by subsidence, but at a rate one to two orders of magnitude lower than that created by glacio‐eustasy (0.04 to 0.16 m/kyr). Lagoonal background sedimentation in adjacent reef lagoons averages 0.89 m/kyr as measured in 72 dated core sections in 28 cores. Lagoonal carbonate sedimentation on top of underlying mangrove peat usually starts after a considerable hiatus of ca 3 kyr on average. The lagoonal background sedimentation rate increased during the Holocene, probably due to deepening. The differences between vertical reef accretion and lagoonal background sedimentation rates are a major factor in the production of the widely known saucer shapes typical of tropical reefs and carbonate platforms, that is the creation of unfilled accommodation space. Reef core recovery, used as a proxy for reef consolidation, and core depth exhibit a statistically negative correlation based on data from 326 core barrels. Recovery and marine cement abundance (average volume 8.6%) also decrease from windward to leeward core positions. These observations are presumably a result of both a decrease in the rate of sea‐level rise that is the increase in time available for submarine cementation during the Holocene and the amount of flushing of reef interstices by marine waters.


| INTRODUCTION
Reef accretion rate has been a geoscience focus, especially in sedimentology and sequence stratigraphy, since the classic paper by Schlager (1981) on reef and carbonate platform drowning, a common phenomenon observed throughout Earth history with the potential to produce sequence boundaries. For the Holocene, Neumann and Macintyre (1985) have discussed the response of tropical coral reefs to rising sea-levels in terms of give-up (drowned), catch-up and keep-up types. Each reef type is characterized by specific coral compositions and successions. Reefs with an abundance of branched corals, usually characteristic of keep-up and the late stages of catch-up types, were supposed to accrete faster than those dominated by massive corals, which may be typical of give-up or early catch-up type reefs (Davies & Marshall, 1980;Neumann & Macintyre, 1985). However, Gischler (2008) and Hubbard (2009) have shown for the Caribbean realm that the accretion rates of reefs predominately constructed of either massive or branched corals are statistically similar. As yet, such statistical comparisons for the Indo-Pacific realm are lacking. Drilling in Holocene reefs, the modern counterparts of the fossil record, has generated an increasing body of data with Dullo (2005) and Montaggioni (2005) providing useful compilations of reef accretion and coral growth rates. Potential growth rates of Scleractinian corals and tropical coral reefs are in the range of rates of rise of glacio-eustatic sea-level. Still, major drilling projects in post-glacial (ca 20 to 10 kyr bp) reefs of Barbados, Tahiti and the Great Barrier Reef have shown that reefs do experience drowning and backstepping during periods of very rapid sea-level rise such as during meltwater pulses (Camoin et al., 2012;Fairbanks, 1989;Webster et al., 2018). In addition, because of deteriorating environmental conditions, for example elevated nutrient input and turbidity, hyperthermal events or diseases, the growth potential of reef builders and reef systems may decrease significantly. Holocene reef accretion has become increasingly important both scientifically and socio-economically in the context of the recent decline of tropical coral reefs due to warming and bleaching (Hughes et al., 2017;Pandolfi, Connolly, Marshall, & Cohen, 2011;Pandolfi et al., 2003), ocean acidification (Eyre et al., 2018;Kleypas et al., 1999) and sea-level rise (Intergovernmental Panel on Climate Change; Hubbard et al., 2014;IPCC, 2013;Pala, 2014;Woodruff, Irish, & Camargo, 2013).
Tropical coral reefs accrete due to a complex interplay of simultaneous processes (Scoffin, 1992). The collective carbonate production of organisms such as reef corals, molluscs, foraminifera and other invertebrates, and calcareous algae leads to reef construction. At the same time, destructive processes both biologically (via bioerosion) and physically (via cyclones) counteract reef construction. Reef sediments are produced, redeposited and distributed in the reef system, and considerable quantities are exported. Early submarine cementation plays an important role in reef consolidation. Still, studies which have quantified all of these processes are extremely rare (Hubbard, Miller, & Scaturo, 1990). Therefore, more data are necessary to constrain our understanding of reef accretion and the possible controlling factors, and to make extrapolations into the near future (Camoin & Webster, 2015). Reef accretion rates have been summarized earlier (Dullo, 2005;Montaggioni, 2005); however, they have not been statistically analysed or quantitatively compared with controlling environmental factors. For these reasons, vertical accretion-rate data from three prominent tropical reef systems in the Atlantic, Pacific and Indian Oceans has been compiled and analysed, and statistically compared with sea-level and climate proxy data.

| STUDY AREAS AND METHODS
Data on reef accretion from 34 cores extracted with a wireline rotary drill system and 1.5-m long core barrels have been compiled and quantitatively analysed in three regions during this study ( Figure 1; Table S1). These include the Belize barrier and atoll reefs (western Atlantic), Rasdhoo Atoll in | 517 GISCHLER and HUdSOn the central Maldives (western Indian Ocean) and the oceanic barrier reef system of Bora Bora in the Society Islands (south Pacific). From Belize, 11 rotary cores drilled on the barrier reef and five rotary cores taken on the offshore atolls have been included (Gischler, 2008). From the Maldives, data from four rotary cores collected on the reef were analysed (Gischler, Hudson, & Pisera, 2008) and included with data from 14 rotary cores from the barrier and fringing reefs of Bora Bora (Gischler et al., , 2019. In Belize and Bora Bora, core traverses were drilled in order to obtain two-dimensional sections of reef architecture. Individual Holocene reef core penetration is up to 31.5 m (average 12.6 m; total 503.5 m). Cores are composed in decreasing abundance of both branched and massive coral, grainstone to rudstone, and unconsolidated sand facies (Gischler, 2008;Gischler et al., 2008Gischler et al., , 2016Gischler et al., , 2019. Branched coral facies are dominated by acroporids; massive corals by Orbicella (Atlantic) and Porites (Indo-Pacific). Microbialite facies occur usually in sections older than 6 kyr ( Figure 2). Core recovery ranged from 0% to 100% and averaged 27.2% (Table  S2). Absolute age data include calibrated radiocarbon and U/ Th ages from corals. Ideally, corals for dating were selected utilising shallow-water acroporids with the sampling distances between corals kept more or less equal and averaging 3 to 4 m. The elevation of samples has been reported relative to mean sea-level. Elevation (D) and elevation error (±D) were calculated based on recovery in individual core barrels ( Figure 3) using the formulas: (1) D = 2d m + 1.5 − r ∕2 (2) ±D = 2d m + 1.5 − r ∕2 − d m F I G U R E 2 Representative rotary core logs from the three regions investigated (modified from Gischler, 2008;Gischler et al., 2008Gischler et al., , 2016.
TEV 1 from Bora Bora; Rasdhoo 1 from the Maldives; BBR 1 from Belize. Note that there are individual legends for the three core logs where d m is the measured depth in barrel in metres and r is the recovery in %.
Seventy-nine vertical accretion rates were calculated by dividing in core absolute age data by the vertical reef thickness between data points. To compare reefal accretion with adjacent lagoonal background sedimentation, 72 sedimentation rates in adjacent lagoons were calculated by dividing absolute age data (radiocarbon method) by measured distance between age data points in 28 vibracores. Vibracore thickness and sample elevation were corrected for compaction (Table S1); recovery in all vibracores is 100%. Vibracores include 11 cores from Belize atoll lagoons (Gischler, 2003;Schultz, Gischler, & Oschmann, 2010), 11 cores from the lagoon at Rasdhoo Atoll (Klostermann & Gischler, 2015) and 6 cores from the Bora Bora lagoon . Individual lagoon cores are up to 6 m long (average 3.8 m; total 111.5 m) and largely comprise packstone, wackestone and mudstone with abundant mollusc, foraminifer and Halimeda remains ( Figure 4). Ideal successions contain basal soil, mangrove peat, shell-rich beds and carbonate sediments indicative of deepening upward (Gischler, 2003;Isaack et al., 2016;Klostermann & Gischler, 2015). In both calculated reef F I G U R E 3 Schematic drawing of core barrel to illustrate how sample elevation is calculated in the case of less than 100% recovery during rotary drilling F I G U R E 4 Representative vibracore logs from the three regions investigated (modified from Gischler, 2003;Klostermann & Gischler, 2015;Isaack et al., 2016). FAA 1B from Bora Bora; MV-16 from the Maldives; G 5 from Belize. Absolute age data in years | 519 GISCHLER and HUdSOn F I G U R E 5 Elevation and age data (n = 79) used in this study and regional sea-level curves. Elevation data have been corrected for minimum subsidence F I G U R E 6 Vertical reef accretion and lagoon sedimentation rates from Belize, the Maldives and Bora Bora including regression lines as well as the Holocene climate (SST) anomaly of Marcott et al. (2013). Note that reef accretion rates decrease and lagoonal sedimentation rates increase during the Holocene. Both trends are statistically significant. Average values in upper left corner. Note that modern SST anomaly increases significantly. SST: sea surface temperature 520 |  ) accretion and lagoon sedimentation rates, the linear error propagation (ep) was calculated using the formula: where d is the difference in core depths (D) in metres; dd is the error in difference in core depth; t 12 is the difference in age dates in kyr; and dt 12 is the error in difference in age dates.
When the linear error propagation, which is a conservative measure of variability, exceeded calculated accretion and sedimentation rates, values were excluded from further analysis. This was the case when sampling points were close together, typically less than 1 or 2 m apart. In order to compare reef accretion rates with the influence of sea-level, rates of sea-level rise were calculated for intervals of 500 years based on local Holocene sea-level reconstructions for these three regions ( Figure 5). In situ corals were identified using taphonomic screening for corallites oriented upcore, together with the presence/absence of marine encrustation and bioerosion (Blanchon & Perry, 2004). Palaeoecologic reconstructions were then used to estimate palaeobathymetry (Abbey et al., 2011). The vertical distance from each datum to the respective local sea-level curve was taken as palaeo-water depth ( Figure 5). The regional sea-level curves exhibit steep slopes during the early-to-mid Holocene and gentle slopes during the late Holocene. Although the Belize and Maldives curves are characterized by sea-level rise, the Bora Bora curve exhibits a rise and a fall that is after an early-to-mid Holocene rise, late T A B L E 1 (Continued) | 527

GISCHLER and HUdSOn
Holocene sea-level exceeds modern level and then falls to the present level. The Holocene sea surface temperature (SST) data set of Marcott, Shakun, Clark, and Mix (2013), which is based on 73 globally distributed Holocene climate records, was used as a climate proxy. Subsidence rates originate from calculations that are based on core depths, palaeobathymetry reconstructions and U-series dates from corals selected from underlying Pleistocene sections in cores (Gischler, Lomando, Hudson, & Holmes, 2000;Gischler et al., 2008Gischler et al., , 2016. The composition of 40 petrographic thin sections along three cores of Glovers Reef (Belize), one core from Rasdhoo Atoll (Maldives) and four cores from Bora Bora (French Polynesia) have been quantified using a point counter, counting 300 items per section (van der Plas & Tobi, 1965). Five categories were counted including reef framework (largely coral and coralline algae), porosity, aragonite cement, high-Mg calcite cement and fine-grained internal sediment. The Glovers Reef core holes were used to install 3 m deep wells for water sampling. Ordinary PVC pipes, slotted over the lower 0.5 m, were inserted into the core holes with the open space outside of the pipes being filled along the main part with reef sand and at the top with hydraulic cement. Water samples were taken four times in each well and from surface waters during 16 to 20 August 1996 and 4 to 8 April 1997. Samples were analysed for oxygen concentration and alkalinity by titration in the field using a HacH portable water analysis kit. Two dye experiments were performed by injecting a rhodamine solution (1 g dissolved in 10 l ocean water) in to each well and subsequently sampling the well water over time periods of up to 100 hr during August 1996 and April 1997. Water samples were pumped out of the wells and dyed water into the wells using a small peristaltic pump.
Dye concentrations were measured in 36 water samples at the hydrogeology laboratory, University of Tübingen, Germany, using a spectrofluorometer in September 1996 and May 1997. The δ 18 O of water and the δ 13 C of dissolved inorganic carbon (DIC) were measured using a ThermoFinnigan DeltaPlus mass spectrometer at the stable isotope laboratory, University of Miami, USA, in June 1997, and reported relative to standard mean ocean water (SMOW). Analytical precision was 0.2‰ for δ 18 O and δ 13 C.
Statistical analyses during this work were made using the software past (Hammer, Harper, & Ryan, 2001).

| RESULTS
Vertical reef accretion rates range from below 1 m/kyr in the late Holocene to more than 20 m/kyr in the early Holocene (Figures 6 and 7; Table 1). There is a statistically significant, overall trend of decreasing accretion rates throughout the Holocene. The total mean vertical reef accretion rate amounts to 5.05 m/kyr. The standard deviation (SD) equals 4.14. The Indo-Pacific accretion rates are significantly higher than the Atlantic rates that is the mean values for Rasdhoo Atoll (7.25 m/kyr) and Bora Bora (5.84 m/kyr) clearly exceed the Belize mean value (2.91 m/kyr). Accretion rates in core sections with predominantly branched corals (mean 5.18 m/ kyr; SD 4.47) are statistically similar to those in reef sections dominated by massive corals (mean 5.07 m/kyr; SD 3.28) (Figure 8; Table 1). The average palaeodepth amounts to 3.06 m in the branched coral reef facies and to 7.46 m with massive coral reef facies (Tables 1, 2). Correlations between accretion rate and potential controlling factors such as rate of In the Belize (r = 0.547, p < 0.003) and the Maldives examples (r = 0.861, p < 0.0003), there are statistically significant positive correlations between accretion rate and rate of sealevel rise (Table 3). In all data, this correlation is also significant (r = 0.569, p < 0.000). In Belize (r = 0.812, p < 0.004), the Maldives (r = 0.808, p < 0.005), Bora Bora (r = 0.830, p < 0.003) and in all data (r = 0.626, p < 0.0002), accretion rates show statistically significant correlations with the SST anomaly ( Figures 6 and 7). There are no significant correlations between reef accretion rate and palaeodepth (Table 3). Background sedimentation rates in adjacent reef lagoons are much lower when compared to vertical reef accretion rates (Figures 6 and 9). Most values are below 1 m/kyr. The highest numbers reach 5 m/kyr that is in the late Holocene Belize examples. There is a statistically significant trend towards higher sedimentation rates during the Holocene. The overall mean lagoonal sedimentation rate is 0.89 m/kyr (SD 0.85), with the lowest means found at Bora Bora (0.54 m/kyr), moderate means found at Rasdhoo Atoll (0.68 m/kyr) and the highest means occurring in the Belize atoll lagoons (1.44 m/kyr). The contact of the basal lagoonal carbonate and the underlying mangrove peat is characterized in 14 examples by hiatuses ranging from 1.70 to 5.38 kyr with a mean of 3.05 kyr (Table 4).
Recovery in reefal rotary cores ranged from 0% to 100% with a mean of 27.3% or 0.41 m per barrel ( Figure 10; Table  S2). There is a trend to lower recovery, or, in other words, an increase in the unconsolidated sand and rubble facies downcore. This trend is statistically significant in that a negative correlation between recovery and depth exists (r = −0.217, p < 0.000). A comparable downcore trend does not exist in the absolute amounts of cements in cores (Table 5). Acicular aragonite and microcrystalline high-Mg calcite cements are most common, and make up 2.4% to 27.5% of the rock volume (average 8.6%; SD = 4.6%). Volumes of internal sediment amount to 25.4%, that of framework builders to 51% and porosity to 14.8% on average (Table 5). There is also a trend towards increasing amounts of the unconsolidated sand and rubble facies from windward towards leeward locations visible in the Glovers Reef, Lighthouse Reef and the Bora Bora fringing reef cores ( Figure 11). Likewise, marine cements are more abundant on windward, compared to leeward and lagoonal core positions (Table 5). Reef well water samples from Glovers Reef exhibit lower oxygen and higher alkalinity values in leeward versus windward positions (Table 6). There are no significant or meaningful differences in oxygen concentration and alkalinity in surface water samples. The same is true for δ 18 O and δ 13 C values of surface waters, which do not show significant differences and range from 0 to +1‰ SMOW ( Table 6). The δ 18 O values of well waters are between 0 to + 1‰ SMOW. The δ 13 C values of well water ranges from −2.1 to +0.83‰ SMOW, with the heaviest values measured in the windward well and the lightest values in the leeward well. Rhodamine experiments in the Glovers Reef wells showed that dye concentrations decreased most quickly in the windward well and most slowly in the leeward well (Figure 12).

| Reef accretion
The rates of Holocene vertical reef accretion in Belize, the Maldives and Bora Bora are in the range of existing F I G U R E 1 0 Core recovery data show a statistically significant decreasing trend downcore. Recovery is interpreted as a proxy of reef consolidation that is the degree of marine cementation compilations. Dullo (2005) reported average accretion rates of 4.4 m/kyr for the Indo-Pacific and 6.1 m/kyr for the Caribbean realms. Montaggioni (2005) noted highly variable vertical accretion rates in the Indo-Pacific region ranging from 1 to 30 m/kyr (mode 6 to 7 m/kyr) in framework-dominated reefs. High variability in accretion rate may be seen even in reefs of the same local area such as in the Capricorn Bunker Group of the southern Great Barrier Reef (Dechnik, Webster, Davies, Braga, & Reimer, 2015). Hubbard (2009) reported average vertical accretion rates of 3.1 to 3.8 m/kyr for the Caribbean region and Toth, Kuffner, Stathakopoulos, and Shinn (2018) ca 3 m/kyr for the Florida Reef Tract that is lower than the Caribbean rates of Dullo (2005). In all of these studies, however, quantitative correlations with environmental controlling factors are largely lacking. The decreasing trend in reef accretion rate in Belize, the Maldives and Bora Bora during the Holocene is most probably related to the decrease in the rate of sea-level rise, that is the reduction in accommodation space, and to climate variation as expressed in the SST anomaly (Marcott et al., 2013). The rate of sea-level rise ( Figure 5; Table 2) and, hence, the creation of accommodation space is crucial for vertical reef growth and accretion, and therefore shows statistically significant correlations with reef accretion rate. Lateral accretion (reef progradation), as observed in Bora Bora , has not been taken into account here. Rates of sea-level rise in 500 year time bins are as high as 14 m/kyr and average 1.96 m/kyr (Table 2). Somewhat warmer and wetter conditions during the early to mid Holocene Climate Optimum apparently also supported increased reef accretion during this time window as seen in the positive correlations of accretion rates with the Holocene SST climate anomaly (Marcott et al., 2013). This climate anomaly exhibits a high fluctuating around 0.4°C from ca 10 to 5 kyr bp, a subsequent decreasing trend towards −0.4°C, and a strong modern increase to 0.6°C ( Figure 6). The data set comprises only a few archives from the Pacific; however, Stott et al. (2004) have shown that SSTs in the western tropical Pacific have decreased over the past 10 kyr, as in the compilation of Marcott et al. (2013). Recently, Toth et al. (2018) concluded also that the Holocene decline in reef accretion in the Florida Reef Tract was largely controlled by a cooling climate.
It has been observed earlier that reefs with a massive coral framework accrete as fast as reefs dominated by branched corals, both in the Caribbean (Gischler, 2008;Hubbard, 2009)  . Different growth strategies and bathymetrical variation in bioerosion have been used to explain this phenomenon (Gischler, 2008;Hubbard, 2009). Massive corals grow relatively slowly but continuously in somewhat deeper water, whereas branched corals grow relatively quickly in shallower water but are repeatedly broken down by storms. At the same time, rates of bioerosion decrease with increasing water depth (Kiene & Hutchings, 1994;Vogel, Gektidis, Golubic, Kiene, & Radtke, 2000). These findings, and the fact that the reefs studied here largely kept up with sea-level, underline that there is not necessarily a correlation between reef architecture, that is coral composition (massive vs. branched) and response to sea-level rise in the Holocene as assumed earlier (Davies & Marshall, 1980;Neumann & Macintyre, 1985). More studies from other regions are needed, which compare massive and branched coral reefs statistically, in order to further validate these new findings. The increase in accommodation space for reef growth via relative sea-level rise may also be caused by subsidence. Existing late Quaternary subsidence data for the three study areas range from 0.04 to 0.11 m/kyr in Belize , 0.09 to 0.16 m/kyr in the Maldives (Gischler et al., F I G U R E 1 1 Schematical crosssections through Glovers Reef, Lighthouse Reef, Rasdhoo Atoll and Bora Bora showing core composition. Numbers on pie diagrams are in percent. Missing core recovery corresponds to unconsolidated sand and rubble facies. Sections are oriented so that the windward reef side is on the right hand side of the figure. Note that cores were considered only when they comprised complete or close to complete Holocene sections 2008) and 0.05 to 0.14 m/kyr for Bora Bora . This translates into a range of absolute subsidence values of 0.4 to 1.6 m during the past 10 kyr. Because these numbers are one to two orders of magnitude lower than accommodation space provided by glacio-eustasy, subsidence is regarded as much less significant for reef accretion when compared to the effects of sea-level rise.
Only the Indo-Pacific rates of vertical reef accretion from the Maldives and French Polynesia, at least in part, exceed the rates of sea-level rise of the 21st century predicted by the IPCC (2013) or by other scenarios that are on the same order of magnitude (DeConto & Pollard, 2016;Woodruff et al., 2013). It remains to be seen whether even the Indo-Pacific examples will be able to keep up with rising sea-level in the light of the fact that SSTs, the occurrences of bleaching events and disease, and ocean acidification will increase probably (Eyre et al., 2018;Hughes et al., 2017;Pandolfi et al., 2011). Recently, Perry et al. (2018 stated that few reefs in both the Caribbean, including Belize, and the Indian Ocean, including the Maldives, would be able to match projected 21st century rates of sea-level rise based on estimates of vertical growth potential.

| Lagoon sedimentation
The increase in lagoonal background sedimentation rates during the Holocene may be related to progressive deepening that is a slight but continuous increase in accommodation space over time. This assumption is supported by the existence of fining-upward trends observed in the lagoonal successions (Gischler, 2003;Isaack et al., 2016;Klostermann & Gischler, 2015). The quantitative comparison of lower background sedimentation rates (0.89 m/kyr on average) as compared to the significantly higher reef accretion rates (5.05 m/ kyr on average) explains why many modern reefs and carbonate platforms are unfilled buckets that is have saucer-shaped cross-sections (Purdy & Gischler, 2005;Schlager, 1981). Only the accommodation space in small reefs and platforms occupying a few hundred square kilometres or less has been filled during the Holocene, largely by lateral sediment transport via sand aprons (Purdy & Gischler, 2005; and references therein). Over longer time scales during the Pleistocene, the saucer-shape of reefs and carbonate platforms is usually exacerbated by preferential karst dissolution in platform interiors during glacial sea-level lowstands as demonstrated by Purdy (1974) and Purdy and Winterer (2001) both in experiments and by the existence of Pleistocene reef island examples with central topographic depressions. Schlager and Purkis (2013) have shown that the bucket shape of carbonate platforms may also be a consequence of biotic self organization, based on the fact that carbonate producers at the margin potentially have easier access to food and nutrients and are less prone to be buried in sediment.
The considerable hiatus between mangrove peat and basal carbonates observed in a number of cores has also been described from other reefal successions and has been modelled (Kim, Fouke, Quinn, Kerans, & Taylor, 2012;Tipper, 1997, and references therein). A reasonable explanation is the inimical bank water model, which underlines the deleterious effect of turbid and nutrient-rich waters created after the initial flooding of subaerially exposed reef banks with soil cover (Lighty, Macintyre, & Stuckenrath, 1978;Schlager, 1981

| Reef consolidation
Recovery during rotary drilling is largely a function of reef consolidation that is the degree of early marine cementation. A downcore decrease in recovery was common in the reef cores analysed here. Comparable observations have been made by James, Ginsburg, Marszalek, and Choquette (1976) who noticed that the most extensive cementation occurred in the upper portions (0.5 to 1 m) of excavated Belize barrier and atoll reef margin pavements. The most probable explanation for this observation is the time available for marine cementation (Tucker & Wright, 1990, pp. 325-327, and references therein). During the relatively rapid early to mid Holocene sea-level rise, much less time was available for submarine cementation in the reef framework as compared to the mid to late Holocene time window when sea-level rise had decelerated significantly. This interpretation may be somewhat biased by the existence of reef cavities, which would also reduce core recovery during drilling. It is not entirely clear why the downcore trend in core recovery is not matched by a similar decrease in cement abundance (Table 5). Possible explanations might be the patchiness of cement distribution and the relatively low amounts of cementation (<10% on average) in general. Another problem is the difficulty of identifying microcrystalline cement (Friedman, 1985;Reid, Macintyre, & James, 1990;Scoffin, 1993) and its quantification in the internal sediment portions, which make up 25.4% of the reef on average (Table 5). The windward-to-leeward decrease in core recovery that is the increase in the unconsolidated sand and rubble facies, underlines the importance of flushing reef interstices with marine waters saturated with regard to calcium carbonate during cementation. This trend is also seen in the distribution of marine cements in that average abundances are higher at windward rather than leeward core positions ( Table 5). The dye experiments and the measured gradient in oxygen concentration in well waters in Belize have shown that flushing with marine waters is indeed stronger on the windward side. The lower alkalinities measured in the windward well compared to the leeward and lagoon locations suggest that cementation preferentially occurs at a higher rate at the former position, presumably reducing alkalinity in pore waters. The negative δ 13 C values measured in the lagoon and leeward well water may indicate the influence of heterotrophic bacteria, which introduce light, 12 C-enriched carbon into the DIC pool. Pigott and Land (1986) have shown that microbial sulphate reduction may trigger calcium carbonate precipitation in reef cavities. In general, stronger cementation at windward rather than leeward reef positions has been reported from various other Holocene reef sites, for example from the southern and central Great Barrier Reef (Marshall, 1985;Marshall & Davies, 1981) and from Mururoa Atoll (Aissaoui & Purser, 1985). In order to further validate these interpretations, a challenging task will be the conduction of further studies quantifying the comparatively low volumes of cements in Holocene reef core material.

| CONCLUSIONS
Holocene tropical reef accretion and adjacent lagoonal sedimentation rates from Belize, the Maldives and French Polynesia have been quantified, statistically analysed, and compared with climate proxy data. Vertical reef accretion rates, which average 5.05 m/kyr, have been decreasing during the Holocene, probably due to both decreases in the rate of sea-level rise and in SST. Only a minor portion of the accommodation space has been added by subsidence compared to that provided by glacio-eustatic sea-level rise. Accretion rates in reefs dominated by massive corals are statistically similar to accretion rates in reefs dominated by branched corals. While lagoonal background sedimentation rates average 0.89 m/kyr they have been increasing during the past 10 kyr, most probably due to lagoon deepening. Lagoonal background sedimentation rates are insufficient to fill available accommodation space in the examples studied. Lagoonal carbonate sedimentation usually started with a considerable hiatus after marine inundation and mangrove peat formation. Time and flushing appear to be major controlling environmental factors affecting reef consolidation, which is strongest on windward positions and in mid to late Holocene sections, respectively. Reef cements have been quantified and average 8.6% of the reef volume.