Salt-marsh foraminifera have been instrumental in the production of quantitative high-resolution Holocene relative sea-level reconstructions using both traditional and Bayesian transfer function approaches. To produce the most accurate and precise elevation estimates using a transfer function, the influence of the particular input data must be understood. Here, we used a foraminifera dataset from New Jersey to examine how count size and rare species affect elevation estimates generated by a Bayesian transfer function. We found that increasing count size can reduce elevation estimate uncertainties, but increasing or decreasing total counts does not have a consistent influence on the estimates themselves. Further, the inclusion or exclusion of rare species do not have consistent trends; however, the results vary by location, highlighting the significance of unique foraminiferal assemblages. Finally, we found that count sizes of 60–80 tests minimizes elevation estimate uncertainties and any greater counts will not contribute to further reduced uncertainties.

Reconstructions of relative sea-level (RSL) change through the mid to late Holocene have provided valuable information about the spatial and temporal variability of sea-level change and have contextualized modern climate change and sea-level rise (e.g., Gehrels, 2000; Kemp et al., 2011; Kopp et al., 2016; Walker et al., 2022). Particularly along North American coastlines, salt-marsh foraminifera have proved to be a vital resource as a proxy to reconstruct RSL due to their vertical zonation and strong relationship with tidal elevation in salt-marsh environments (e.g., Scott & Medioli, 1978, 1980; Thomas & Varekamp, 1991; Gehrels, 1994; Kemp et al., 2009).

The abundant and low-diversity assemblages of salt-marsh foraminifera have been used to develop foraminiferal-based transfer functions to quantitatively relate modern assemblages with tidal elevation (e.g., Gehrels, 1999; Horton, 1999). Combined with sediment cores and fossil assemblages to estimate paleomarsh elevations downcore, the transfer function approach has been extensively used to produce continuous records of RSL at decimeter vertical resolution (e.g., Gehrels, 2000; Horton & Edwards, 2006; Kemp & Telford, 2015; Cahill et al., 2016). Commonly used transfer functions include weighted averaging and weighted averaging partial least squares (Barlow et al., 2013; Kemp & Telford, 2015) which represent populations using species proportions or a Bayesian transfer function (BTF) technique which uses raw species counts (Cahill et al., 2016). Transfer function techniques can be broadly classified into two categories depending on whether the underlying model maps environmental variables to species abundances (classical calibration) or vice versa (inverse calibration). Classical approaches are underpinned by the ecologically intuitive assumption that the distribution of species is driven by environmental variables (e.g., Birks, 2012). Inverse approaches invert this association in order to reduce computational complexity (e.g., Birks, 2010) when reconstructing the environmental variable of interest (e.g., elevation). The commonly used weighted averaging transfer function relies on inverse calibration while the BTF method is inherently classical and has in recent years grown in popularity for use in sea-level reconstructions (e.g., Kemp et al., 2017, 2018; Walker et al., 2021, 2023a).

Differences between the BTF and traditional transfer functions are rooted in their treatment of species data and the manner in which species-elevation relationships are quantified. The BTF operates on a multinomial data model for foraminifera counts and employs a penalized spline (P-spline) model, enabling a flexible capture of the interplay between species counts and tidal elevation. The multinomial data model for the counts can take account of the fact that large counts can give reduced uncertainty. In contrast, traditional transfer functions commonly rely on relative abundances as input, potentially leading to the loss of information on the uncertainties inherent in raw counts. Additionally, they often assume a unimodal Gaussian form across all species with respect to elevation. Moreover, the rationale for favoring the BTF over traditional counterparts extends to the explicit quantification of uncertainty. Non-Bayesian methods in transfer function estimation assume fixed model parameters, devoid of direct incorporation of uncertainty into reconstruction estimation. Consequently, the separate generation of uncertainty tends to exhibit minimal variability across reconstructed samples, overlooking inherent biological variations in species composition. In contrast, Bayesian methods explicitly model uncertainty within transfer function parameters, formally integrating uncertainty into the reconstruction process. Hence, Bayesian-based reconstructions comprehensively embrace uncertainties linked to the model and its parameters, surpassing non-Bayesian approaches in accounting for inherent variability.

For any transfer function analyses, the foraminifera tests must be individually identified and counted to form a dataset, which can become very time consuming depending on the number of modern samples needed to understand the full range of environments across an elevational transect or the depth of a sediment core for a RSL record extending several thousands of years into the past. However, an adequate count size is necessary to accurately characterize a foraminifera assemblage and therefore produce an accurate RSL reconstruction. Further, a larger count size will likely better incorporate any rare species (e.g., species that make up only 1%, 2%, 5%, or 10% of the total) in an assemblage, but it is not certain how essential those rare species are for describing an assemblage to be used in a sea-level reconstruction. Previous studies have suggested count sizes of at least 100 tests per sample are needed to fully capture non-dominant species within the low-diversity salt-marsh foraminifera assemblages (e.g., Buzas, 1990; Fatela & Taborda, 2002; Horton & Edwards, 2006; Hayek & Buzas, 2010). The influence of count size has been explored for the weighted averaging transfer function approach (Kemp et al., 2020), but varying count sizes have not been analyzed for the BTF approach.

Here, we tested the influence of count size and rare species specifically on BTF results. We used an extensive modern foraminifera dataset from four high marsh stations in southern New Jersey, which were previously analyzed for spatial and temporal variability of dead and live assemblages in Walker et al. (2020) and Walker et al. (2023b). With variations of the actual datasets and individual samples to control for changes in count size and rare species, we used the BTF to predict elevation estimates for the samples from each of the four stations (acting as pseudofossil assemblages) where the elevations are known to test the accuracy and precision of the estimates. In addition, we tested the influence of count size in a regional modern foraminifera training set. Based on these results, we can determine the necessary, as well as most practical, count size to fully understand a foraminifera assemblage and produce accurate RSL reconstructions. This information can be utilized to help maximize the total number of individual samples that can be counted for any particular study.

Test Dataset

To test the influence of foraminifera input data to the Bayesian transfer function (BTF), we used a modern foraminifera dataset from Walker et al. (2020) in order to use test samples with known elevations. This dataset, therefore, acts as a pseudofossil assemblage for subsequent analyses. The dataset includes 72,804 dead foraminiferal tests, comprising 14 different agglutinated species, from four 1 m × 1 m high marsh/high marsh-upland transition stations along a salinity gradient in the Mullica River-Great Bay estuary in southern New Jersey (Fig. 1). We focus our analyses on these samples from high marsh intertidal sites because high marsh sedimentary sequences are primarily used in sea-level studies since foraminiferal zones are narrower compared to the low marsh and can provide more precise elevation estimates (e.g., Gehrels, 2000; Kemp et al., 2011). The samples were collected every three months over three years (September 2014 to June 2017) including 50 samples taken through time and 138 spatial replicate samples. The spatial and temporal distributions of the dead and live assemblages have been previously described in Walker et al. (2020) and Walker et al. (2023b). In this context, we opted to examine the dead assemblages. This choice is rooted in the fact that modern dead assemblages are commonly employed in sea-level studies due to their ability to reduce temporal fluctuations in modern distributions. Consequently, they bear the closest resemblance to subsurface assemblages (e.g., Horton, 1999; Horton & Edwards, 2003; Morvan et al., 2006).

The dead assemblages from the four stations had sample count sizes ranging from 58 to 1196 tests/10 cm3 with an average of 389 ± 221 tests/10 cm3 (1σ). Stations 2 and 3 had greater average count sizes (500 ± 225 tests/10 cm3 and 553 ± 198 tests/10 cm3, respectively) compared to Stations 1 and 4 (229 ± 112 tests/10 cm3 and 252 ± 86 tests/10 cm3, respectively). The dominant foraminifera species across the four monitoring stations from most to least abundant were Jadammina macrescens (21,408 tests), Balticammina pseudomacrescens (14,448 tests), Tiphotrocha comprimata (13,912 tests), Trochammina inflata (9688 tests), Haplophragmoides spp. (5,252 tests), and Ammoastuta inepta (1,982 tests; Walker et al., 2020). On average, Station 3 had the greatest number of taxa among its samples (7.5 taxa), and Station 1 had the fewest (3.6 taxa). Further, Station 3 had the greatest species diversity among the stations with an average Shannon Index among its samples of 1.51 (Fig. 1). Partitioning around medoids (PAM) analysis showed that each site had a unique assemblage as all of the samples fit well into four groups and all but 12 of the 188 samples were assigned to a group corresponding to the station from which they were sampled (Walker et al., 2020).

Transfer Function Input Analyses

We used a BTF that takes raw foraminifera counts as input (Cahill et al., 2016) with a regional modern foraminifera training dataset including 207 total samples from 13 sites in southern New Jersey (Kemp et al., 2013) and one site in northern New Jersey (Walker et al., 2021). As in analyses in Walker et al. (2020), Jadammina macrescens and Balticammina pseudomacrescens were combined, as well as Trochammina inflata and Siphotrocha lobata. In the BTF, we also inform the prior distribution that describes the random variation of the individual foraminifera species based on the results from Walker et al. (2020) to formally account for spatial and temporal variability of modern foraminifera distributions. In the BTF we describe the relationship between a latent species response, λl, and elevation such that:
formula
formula
where gl is a P-spline function that governs the shape of the response curve of species l and em are elevations from the modern training data. The error term ϵl is added to the P-spline for each species to account for over/under dispersion in the raw species data and forumlais a species-specific variance term. A truncated t-distribution prior is placed on forumlaand the analysis in Walker et al., (2020) provided estimates and justification for the values of the hyperparameters of this prior distribution, hence providing informative priors for the variation associated with individual foraminifera species.

As in Walker et al. (2020), the BTF was applied to the regional modern foraminifera training dataset with the foraminifera data (raw counts) from each of the four monitoring stations to provide an elevation estimate for each station to compare to the known elevation, and to examine spatial and temporal variability in elevation estimates. Here, we performed two new analyses to determine the influence of how changes in the raw pseudofossil data (count size and rare species) influence elevation estimates derived from the BTF:

  • 1) For each sample, maintain the relative abundance of individual species, but decrease the total count of tests to 10%, 20%, 30% … 80%, 90% of the original total count for the sample (count size values were rounded to the nearest whole number). For each scenario, we produced a new elevation estimate using the BTF.

  • 2) For each sample, include only species that make up at least 1%, 2%, 5%, or 10% of the total assemblage. For each scenario, we produced a new elevation estimate using the BTF.

Through these two analyses, we tested the influence of count size and rare species on elevation estimates derived from the BTF. By using a modern foraminifera dataset acting as a pseudofossil assemblage, we could compare these estimates with the known elevations of the samples from the four monitoring stations in southern New Jersey. All elevations are reported in a standardized water level index (SWLI), following the approach of Horton et al. (1999) due to differences in tidal range among the monitoring stations, where a value of 100 corresponds to local mean tide level (MTL) and a value of 200 corresponds to local mean higher high water (MHHW).

Further, we also conducted a separate analysis to test the influence of count size in the regional modern foraminifera training dataset (which includes samples from southern New Jersey (Kemp et al., 2013) and northern New Jersey (Walker et al., 2021). For each sample in the modern training set, we maintained the relative abundance of individual species, but decreased the total count of tests to 20%, 30% … 80%, 90% of the original total count for the sample. Due to convergence issues with estimating model parameters using only 10%, likely because count size is so low, we excluded the 10% of the total count scenario. For each scenario, we re-calibrated the BTF using the new training set and produced a new elevation estimate for each sample from the original Walker et al. (2020) dataset. We note that for each of these scenarios, the full count was retained for the pseudofossil assemblages.

Influence of Count Size on Pseudofossil Assemblages

All samples from each station, regardless of count size (e.g., 10% of total count, 20% of total count, etc.) predicted an elevation estimate within a 95% uncertainty interval consistent with the observed elevation of that station. However, there was no clear trend in the range of SWLI estimates as the percentage of the samples used with the BTF increases (Fig. 2) and the SWLI estimates did not converge with increased count sizes. We used ANOVA, a method used to compare differences of means among more than two groups, to test for differences in SWLI estimates across the count size groups. The p-value for the ANOVA is 0.912 (>0.05) and hence we can conclude that there is no significant difference in the average SWLI across the groups of varying count sizes. For example, at Station 1, the range of SWLI estimates with samples that used 10% of the total count is 195–217, while using the total sample was 191–220.

While the actual SWLI estimates did not have a clear relationship with count size, the uncertainties of SWLI estimates did decrease with larger count sizes (Fig. 3). Across all four stations, the SWLI uncertainty decreased from an average of 42 SWLI units when using 10% of the total count to 34 SWLI units when using the total sample. The p-value using ANOVA for differences in SWLI uncertainty across the count size groups is 0.002 (<0.05) and hence we can conclude that the uncertainties are significantly different with varying count sizes. At individual stations, SWLI uncertainty had the greatest reduction at Station 4 with an average of 41 SWLI units when using the total sample compared to 55 SWLI units when using 10% of the total count. A reduction in SWLI uncertainty was least apparent at Station 3 with an average of 37 SWLI units when using the total sample compared to 41 SWLI units when using 10% of the total count.

To further examine the influence of raw count sizes, the percentages of total counts were translated into actual number of tests. The average total count size for each station was 215 tests/cm3 at Station 1, 450 tests/cm3 at Station 2, 541 tests/cm3 at Station 3, and 209 tests/cm3 at Station 4. Across all four stations, the average total count, therefore, ranged from 354 tests/cm3 for 100% of the sample to 35 tests/cm3 for 10% of the sample. The average SWLI uncertainty was compared to sample count size in 20-test bins (e.g., samples with 0–20 tests, 20–40 tests, etc.). Across all four stations, there was a declining trend in average uncertainty from SWLI estimates with samples with 0–20 tests (average of 49 SWLI units) to 60–80 tests (average of 34 SWLI units; Fig. 4). Samples with greater than 80 tests did not produce any consistent further reduction in uncertainty. From samples with count sizes ranging from 80 to 600 tests, the SWLI uncertainties ranged from 30–38 SWLI units, with an average of 34 SWLI units.

Influence of Rare Species on Pseudofossil Assemblages

All but five samples (all from Station 4), regardless of rare species included (e.g., those with at least 1% relative abundance, 2% relative abundance, etc.) predicted an elevation estimate within a 95% uncertainty interval consistent with the observed elevation of that station. However, there was no clear trend across all four stations in the range of SWLI estimates as the range of rare species used with the BTF changed (Fig. 5). The p-value using ANOVA for differences in SWLI across the rare species groups is 0.109 (>0.05) and hence we can conclude that the average SWLI estimates are not significantly different across groups. Further, the influence of rare species had different effects at each station. At Station 1, as the rare species were limited and moved towards only species that had at least a 10% relative abundance in a sample, the SWLI estimates converged closer to the observed SWLI range. For example, using all species with at least 1% relative abundance resulted in a SWLI range of 180–222, whereas using all species with at least 10% relative abundance resulted in a SWLI range of 201–226 compared to the observed SWLI range of 212–223. At Station 3, using all species with at least 10% relative abundance also resulted in the most accurate SWLI estimates with a range of 191–228 compared to the observed SWLI range of 192–227. However, using 1%, 2%, or 5% relative abundances at Station 3 did not show any further trends towards more accurate SWLI estimates. In contrast, at Stations 2 and 4, no inclusion or exclusion of rare species resulted in significantly more precise or accurate SWLI estimates compared to the observed SWLI range for each station.

When comparing SWLI uncertainties with the percentage of rare species included across all four stations, the greatest uncertainties occur when using only species with at least 10% relative abundances (an average of 39 SWLI units compared to 32–35 SWLI units for all other scenarios; Fig. 6). The p-value using ANOVA for differences in SWLI uncertainty across the rare species groups is 0.000007 (<0.05) and hence we can conclude that the SWLI uncertainties are significantly different across groups. However, similar to the SWLI estimate results, there are distinct differences among the stations. The SWLI uncertainty increases at Stations 1, 2, and 4 when using only species with at least 10% relative abundances. The increase is largest at Stations 2 and 4 where the average uncertainty is 45 SWLI units compared to 33 SWLI units when using all data at Station 2, and 54 SWLI units compared to 40 SWLI units when using all data at Station 4. The opposite trend occurred at Station 3 where the SWLI uncertainty is smallest (average of 30 SWLI units) when using only species with at least 10% relative abundances compared to an average of 40 SWLI units when using all data.

Modern Training Set Count Size Analysis

All samples from each station, regardless of the modern training set count size (e.g., 20% of total count, 30% of total count, etc.) predicted an elevation estimate within a 95% uncertainty interval consistent with the observed elevation of that station. However, there was no clear trend in the range of SWLI estimates as the percentage of the samples used in the training set increases (Fig. 7) and the SWLI estimates did not converge with increased count sizes. The p-value using ANOVA for differences in SWLI estimates across the count size groups is 0.522 (>0.05) and hence we can conclude that the average SWLI estimates are not significantly different with varying modern training set count sizes.

The uncertainties of SWLI estimates also did not have a clear relationship with modern training set count size (Fig. 8). Across all four stations, the SWLI uncertainty was an average of 28 SWLI units when using 20% of the total count compared to 35 SWLI units when using 90% of the total count. At each individual station, SWLI uncertainty was also lowest when using only 20% of the total sample. It is possible that with smaller count sizes in the modern training set, some of the counts for low abundance species are removed altogether, resulting in less noise in the modern training set overall and hence a reduction in the uncertainty. However, the p-value using ANOVA for differences in SWLI uncertainty across the count size groups is 0.08 (>0.05) and hence we can conclude that the uncertainties are not significantly different with varying modern training set count sizes.

Effects of Varying Input Data

Adjusting the total count of foraminifera samples to derive elevation estimates from the BTF did not produce consistent changes in the accuracy of the elevation estimates with increased or decreased count sizes. So, while the BTF is sensitive to total count sizes, even though the relative abundances of each individual species remain the same in this analysis, adjusting the total count size does not produce consistent effects. In particular, more accurate SWLI estimates are not produced with increased count sizes. Notably, however, the uncertainty of SWLI estimates did decrease with increased count sizes across all four monitoring stations. Across all the stations in this study, the decreasing elevation estimate uncertainty is limited in its effectiveness with count sizes larger than 60–80 tests. Therefore, for the BTF approach, the nature of a particular foraminifera assemblage seems to be reliably determined with a relatively small count size, with reduced uncertainties as long as at least 60–80 tests are counted. This result is under the assumption that the lower count sizes still provide an accurate reflection of the “true” relative abundances, since in this study, the count sizes were reduced but the relative abundances were kept constant. The magnitude of the decreased uncertainty did vary among the stations, underscoring the role of unique foraminiferal assemblages from different environments. While the particular influence of count size is likely influenced by assemblage diversity (Kemp et al., 2020), samples from salt-marsh environments are still generally dominated by relatively few distinct species even in high diversity areas (Wright et al., 2011), which also makes it more likely to capture the “true” relative abundances at low count sizes. For example, on the North American Atlantic coast, Kemp et al. (2020) found that the number of taxa that make up at least 5% or 10% of a foraminiferal assemblage is very similar from sites extending from Newfoundland to North Carolina. Therefore, due to the low diversity of salt-marsh foraminifera and the strong spatial similarities among assemblages particularly along the Atlantic coast, the results from this study are likely applicable to other regions beyond New Jersey.

The influence of more or fewer rare species being included in the BTF analyses also highlighted the differences among assemblages from each of the four monitoring stations. Both the accuracy and precision of the SWLI estimates and their uncertainties varied by station as rare species were included or excluded. While results from Stations 1, 2, and 4 suggest excluding more rare species will increase the uncertainty in elevation estimates, the results from Station 3 suggest the opposite as uncertainties decrease as more rare species are excluded in the analysis. The distinction with Station 3 could be because Station 3 had the most diverse assemblage of foraminifera among the stations, which may be due to the uneven surface topography at this site, creating increased variability in assemblages due to microtopography (Walker et al., 2020). Therefore, including all of the additional rare species in this case may decrease the capability of the BTF to produce the most accurate and precise elevation estimate.

While we also examined the influence of count size on SWLI estimates in the modern training set of foraminifera, these results were inconclusive. There were no statistically significant trends in the SWLI estimates or uncertainties. Therefore, SWLI estimates using a BTF are influenced more by count size in fossil assemblages compared to count size in modern training sets. SWLI estimates are likely more influenced by the range of local environments and elevational gradients included in a modern training set, as count sizes of individual samples do not affect overall results.

Implications for Sea-Level Studies

For relative sea-level reconstructions using salt-marsh foraminifera as a proxy, clearly defining the necessary input data for a transfer function will lead to the most efficient and accurate result. Although salt-marsh assemblages are low diversity, it is uncertain how individual rare species may influence estimates of elevation when they only make up a small proportion of an assemblage. In this study, due to the discrepancies in results of the rare species analysis among stations, we suggest including all foraminifera data in analyses using the BTF approach or to include those species with at least a 1% or 2% relative abundance as the results across these categories were comparable. Similar tests using the BTF with additional site locations within or outside of New Jersey could contribute to a broader analysis of the influence of rare species on elevation estimates, but it is likely not necessary to capture all rare species in individual samples. Since excluding species that only make up 1%, 2%, or even 5% of an assemblage did not significantly alter the elevation estimate results, the dominant taxa are clearly the drivers and key components of the elevation results. In some cases, just a few tests of a rare species could even produce an anomalous and less accurate elevation estimate (Walker et al., 2020). Other paleoenvironmental microfossil proxies, such as testate amoebae, have also produced stable transfer function reconstructions with relatively low count sizes of 50–100, showing a similar lack of sensitivity to rare species that would not be captured without higher count sizes (Payne & Mitchell, 2009). Those proxies with significantly greater diversity, however, such as diatoms, where hundreds of species can be found across just a few sites (Hong et al., 2021), would need to be thoroughly evaluated for the influence of rare species on transfer function results. For foraminifera, larger count sizes in order to capture more rare species are likely not necessary for the purposes of RSL reconstructions using low-diversity salt-marsh foraminifera assemblages.

Due to the time-consuming nature of counting individual foraminifera tests, it is helpful to determine what count size is best to fully understand a foraminifera assemblage and therefore most accurately and precisely estimate elevations using that assemblage. A previous simulation of the influence of count size from Walker et al. (2020) showed a reduction of SWLI estimate uncertainties with increasing count sizes, which stabilized with count sizes greater than 100 tests. Other previous studies have also suggested count sizes of at least 100 to fully capture non-dominant species (e.g., Buzas, 1990; Fatela & Taborda, 2002; Hayek & Buzas, 2010). Using a weighted averaging transfer function approach, Kemp et al. (2020) showed stability in elevation estimates at low counts (∼50 tests) and recommended count sizes of at least 75 tests for high-resolution RSL reconstructions. Using the BTF to produce elevation estimates here, we found count sizes of 60–80 tests will minimize the elevation estimate uncertainties, and count sizes greater than 80 tests do not result in any further appreciable reduction in uncertainty. Therefore, we recommend a count size of a minimum of 60–80 tests to produce reliable elevation estimates when using the BTF. By continuing future analyses with these lower count sizes, the time and effort saved from reduced counts can therefore be spent on analysis of a greater total number of samples counted both in modern environments and sediment cores to expand and strengthen RSL reconstructions. Further, since the count size analysis for modern training sets did not produce conclusive results, it is likely that similarly lower count sizes are suitable for modern training set samples as long as the relative abundances are accurately reflected and an appropriate number of total samples are included in the dataset to capture a range of local environments and elevational gradients. Overall, in comparison of the count size analyses for the pseudofossil assemblages and the modern training set, time is likely better spent counting fossil foraminifera up to 60–80 tests as there is a reduction in SWLI uncertainty; since the SWLI uncertainty does not significantly change with increasing count size for samples in the modern training set, it is likely beneficial to prioritize increasing the total number of modern training set samples to capture the greatest variety in modern environments.

Salt-marsh foraminifera are a valuable tool in the production of high-resolution Holocene RSL reconstructions. The transfer function approach, in particular, has led to the quantified understanding of modern foraminifera distributions which can be applied to fossil assemblages in salt-marsh sediment cores. An examination of the influence of the input data, such as count size and rare species, into the transfer function allows for the most efficiently produced, as well as accurate and precise, estimates of elevation. Using a Bayesian transfer function approach, we tested the influence of count size and rare species on elevation estimates using a modern foraminifera dataset from southern New Jersey. We found that the effects of including or excluding more rare species is dependent on the specific foraminifera assemblage. We would generally recommend including all species in an assemblage in Bayesian transfer function analyses or at least include all species that make up at least 1% or 2% of an assemblage to produce the most accurate and precise estimates of elevation. Further, we found that increasing count size can result in decreased elevation estimate uncertainties. In particular, count sizes up to 60–80 tests will minimize the elevation estimate uncertainties, but counting any greater numbers will not result in further reduced uncertainties. These results are consistent with recent studies exploring the most practical and suitable count sizes for foraminifera-based RSL reconstructions and, here specifically, provide a basis for those using a Bayesian transfer function approach.

The authors acknowledge PALSEA (Palaeo-Constraints on Sea-Level Rise), a working group of the International Union for Quaternary Sciences (INQUA) and Past Global Changes (PAGES), which in turn received support from the Swiss Academy of Sciences and the Chinese Academy of Sciences. This work is a contribution to IGCP Project 725 ‘Forecasting Coastal Change’. Cahill’s work was conducted with the financial support of Science Foundation Ireland and co-funded by Geological Survey Ireland under grant number 20/FFP-P/8610.