Imbrie and Kipp (1971) were first to utilize the transfer function methodology whereby deep- sea foraminiferal assemblages were employed to reconstruct paleo-sea-surface temperatures from sediment cores. Its application in salt-marsh environments however did not occur until much later in the 1990s when Guilbault et al. (1995) used the approach to quantify the amount of subsidence during a late Holocene earthquake using fossil tidal salt- marsh foraminifera from Vancouver Island, Canada. The term ‘transfer function’ is used to describe a set of regression equations that attempts to model the contemporary distribution of microfossil assemblages and their relationship with an associated environmental variable. Essentially the goal of a transfer function is to mathematically relate the species abundance of biological data as a function of an environmental variable, as illustrated in figure 2.4 (Birks, 1995). Its success in quantifying microfossil assemblages and reconstructing palaeoenvironmental change has since spawned numerous papers investigating Holocene sea-level change to become the mainstay in quantitative sea-level reconstructions conducted in salt-marsh environments (Horton et al., 1999a; Zong and Horton, 1999; Gehrels, 2000; Edwards, 2001; Gehrels et al., 2001; Gehrels et al., 2002; Edwards et al., 2004; Gehrels et al., 2005; Horton and Edwards, 2006; Kemp et al., 2009b; Leorri and Cearreta, 2009; Woodroffe, 2009; Woodroffe and Long, 2010; Callard et al., 2011).
Figure 2.4. Principles of quantitative palaeoenvironmental reconstruction showing X0, the unknown environmental variable to be reconstructed from fossil assemblage Y0, and the role
of a modern training set consisting of modern biological Y (foraminifera) and environmental data X (elevation). Modified after Birks (1995).
Page | 16 With reference to foraminifera-based transfer function reconstructions from salt-marsh environments, the method is centered around fossil foraminifera preserved in sediment cores that can be quantitatively related to their modern counterparts found on the contemporary salt-marsh surface (Gehrels et al., 2001). As the vertical zonation of contemporary foraminifera have been shown to be strongly influenced by tidal level, they can be used as ‘proxies’ for elevation in which the faunal data are converted into environmental data and applied to fossil analogues found in sediment cores to reconstruct relative sea-level changes when combined with chronostratigraphic techniques (e.g. radiocarbon dating) (Gehrels, 2000).
A detailed investigation into the contemporary environment and the relationship between microfossil assemblages and environmental variables is therefore prerequisite in transfer function based sea-level reconstructions. The relationship between foraminiferal assemblages and elevation must first be investigated to confirm their suitably before they can be confidently used as ‘proxy’ indicators of sea-level change. The development of a transfer function begins with the compilation a modern dataset, commonly referred to as a ‘training set’, that accurately depicts the modern environment which is reflected in the fossil sequence (Barlow et al., 2013). It contains information on the relative abundance of foraminiferal taxa and associated environmental data (e.g. elevation, pH, salinity etc). Whilst there are no strict guidelines as to an ideal size of a training set, it should be as large as possible since smaller training sets will be more susceptible to errors (Horton and Edwards, 2006). More importantly however is that it should contain foraminiferal assemblages that are from the same environmental conditions repeated in the fossil sequence to be reconstructed (Horton and Edwards, 2006). With this in mind, the spatial scale from which a training set is derived, collectively termed ‘local’ or ‘regional’, can have a significant effect on transfer function performance (e.g. Woodroffe and Long, 2010; Watcham et al., 2013).
Where a training set has been collected in close proximity to the fossil sequence (i.e. a local training set), assumptions are made in that the modern data is a true analogue for environmental conditions similar to that preserved in a sediment core. However where the depositional environment is not represented by the modern day environment or has significantly changed through time, a local training set may be inadequate to account for the changes in palaeoenvironment and microfossil assemblages (Barlow et al., 2013). To compensate for such variations, regional training sets that are comprised of foraminiferal assemblages and associated environmental data from a wide range of sites may provide better analogues of environmental change permitting a more accurate reconstruction (Edwards and Horton, 2000; Gehrels, 2000; Edwards et al., 2004; Horton and Edwards,
Page | 17 2005; Leorri et al., 2008; Watcham et al., 2013). When regional training sets are used in transfer function reconstructions they are able to capture much wider spatial variability and are capable of achieving reliable results where modern environmental conditions differ from those in the past (Horton and Edwards, 2005). Merging datasets together to form a regional training set however necessitates the need for elevation to be standardized to a water level index (SWLI) to account for differences in tidal range between the sample sites (Horton, 1999). An example of such procedure from Horton and Edwards (2006) is presented below where Altab is the altitude of sample a at site b (measured to vertical datum m OD); MLWSTb is the mean low water spring tide level at site b (m OD); and MHWSTb is the mean high water spring tide at site b (m OD). Whilst other tidal parameters are available (e.g. HAT) and are indeed employed by different authors (e.g. Woodroffe and Long, 2010), in this instance MHWST and MLWST were used as they improved correlations with tide levels from lower elevation environments (Horton and Edwards, 2006). Care must be taken when choosing tidal levels for this process however as transfer function performance can be impeded where tidal levels do not accurately standardize water levels in the tidal frame being reconstructed (Woodroffe and Long, 2010).
Establishing a modern training set that is deemed suitable for palaeosea-level studies is followed by an analysis of the species response along the environmental gradient to derive ‘ecological response functions’ (Horton and Edwards, 2006). As the transfer function models the relationship between microfossil assemblages and the environmental variable to be reconstructed (e.g. elevation), it is important to understand whether the modern species- environment response is linear or unimodal so that the appropriate statistical technique can be applied (Birks, 1995; 2010). To achieve this, regression methods are applied to express the biological data as a function of elevation (the ‘classical’ approach) or elevation as a function of biological data (the ‘inverse’ approach) (Horton and Edwards, 2006). Detrended canonical correspondence analysis (DCCA) is used to quantify this relationship to provide a measure of gradient length which is measured in standard deviation (SD) units (ter Braak and Juggins, 1993; Birks, 1995). Assessment of this gradient length provides information concerning the species response (Telford and Birks, 2005). Generally, where the gradient length is greater than two SD units, the species data are regarded as unimodal where assemblages have their optima along the environmental gradient displaying a Gaussian distribution (Gauch and Whittaker, 1972). Standard deviations units less than two however
Page | 18 suggests several taxa increase or decrease with the environmental variable of interest and therefore the data are linear (figure 2.5) (ter Braak and Prentice, 1988; Birks, 1995; 2010).
Figure 2.5. Taxon-environment response models showing (a) Gaussian unimodal distribution and (b) linear distribution between species abundance (y) and the environmental
variable (x). u = optimum and t = tolerance (Horton and Edwards, 2006: ; modified after Birks, 1995).
In most Holocene sea-level investigations however, species distributions are generally unimodal due the nature of foraminiferal assemblages displaying a Gaussian distribution in relation to the environmental variable of interest (Barlow et al., 2013). Indeed unimodal response models such as Weighted Averaging (WA) (Ter Braak and Barendregt, 1986) and Weighted Averaging Partial Least Squares (WA-PLS) (ter Braak and Juggins, 1993) are considered robust and reliable reconstruction techniques (ter Braak and Juggins, 1993; ter Braak et al., 1993; Birks, 1995; Telford et al., 2004; Telford and Birks, 2005) and are widely applied in salt-marsh microfossil based sea-level reconstructions (e.g. Edwards and Horton, 2000; Edwards et al., 2004; Gehrels et al., 2005; Horton and Edwards, 2005; 2006; Woodroffe and Long, 2010; Leorri et al., 2011; Kemp et al., 2012; Barlow et al., 2013). Unimodal regression models such as WA consider the variance along a single environmental gradient where foraminiferal taxa are assigned an ecological optimal elevation and tolerance in which they may be observed (Horton and Edwards, 2006). However there are several disadvantages associated with this approach, for example WA considers each environmental variable separately and also disregards the residual correlations in the biological data when other variables affecting the data are not considered after fitting the environmental variable of interest (Birks, 1995). Whilst the environmental controls that govern contemporary foraminiferal distributions in salt-marsh environments show a strong correlation with elevation, other environmental factors such as salinity (e.g. de Rijk and Troelstra, 1997) can introduce ‘noise’ and disrupt the unimodal response of species data to
Page | 19 the environmental variable of interest (e.g. elevation) (Horton and Edwards, 2006). In WA, these correlations are not taken into account and as a result WA-PLS (ter Braak and Juggins, 1993; ter Braak et al., 1993), was developed to allow for such variability. WA-PLS is an extension of WA where the incorporation of partial least squares (PLS) considers the residual correlations in the biological data to improve estimation of the optima for the taxa (Birks, 1995) by considering the effect of other potentially influential environmental variables (ter Braak and Juggins, 1993). Indeed ter Braak and Juggins (1993) consider WA-PLS to be a simple and robust method and recommend its use until other more sophisticated methods are developed. Where the lengths of gradient fall between 2 and 3 SD units, suggesting species response is neither strongly linear or unimodal, Birks (1998) states WA-PLS will in most instances, outperform linear techniques due to the fewer components required by WA- PLS to create an adequate model.
Linear-based regressions models, including Imbrie and Kipp Factor Analysis (IKFA), principal components regression (PCR) and PLS, are suitable for use where data exhibit a linear distribution in relation to the tested environmental variable (i.e. less than 2 SD units as identified from DCCA). In PLS regression, developed by Wold et al. (1984), components are maximised to the covariance with the response variable and thus requires fewer components usually giving lower prediction errors in comparison to other linear methods such as PCR. More importantly however are the added benefits of cross-validation procedures available in PLS which are not possible with PCR (Birks, 1995). Using the same number of components a PLS model always improves on the coefficient of determination (r2)in comparison to PCR and is thus the preferred reconstruction technique (Birks, 1995). Linear-based regression and calibration models are comparatively rare in proxy sea-level studies due to the unimodal relationship commonly observed between foraminifera and elevation. It has however been successfully applied in regions where foraminiferal training sets are derived from short vertical ranges in relationship to the tidal frame (Barlow et al., 2013) such as Leorri et al. (2010) and Rossi et al. (2011).
Following the construction of a transfer function, calibration is performed in which the developed regression linear or unimodal statistical models are applied to fossil counterparts found in sediment cores to reconstruct estimates of paleo-marsh surface (Birks, 1995; Horton and Edwards, 2006). When combined with detailed chronological information (e.g. Marshall et al., 2007), usually acquired through radiocarbon dating and/or short-lived radionuclides, changes in relative sea-level can then be investigated (Horton and Edwards, 2006). Statistical parameters produced from the transfer function models allow an assessment of the reconstruction performance and predictive ability of the training set in
Page | 20 reconstructing past environmental change (further details regarding these parameters are provided in section 6.2). However, quantitative transfer function reconstructions will produce a result regardless of the data used and so the accuracy of the reconstruction should be tested (Birks, 1995). In microfossil-based sea-level reconstructions from salt-marsh environments a common goal of the transfer function technique is to reconstruct relative sea- level over the history of deposition for a core sequence.
As a validation tool and to assess the reconstruction performance it is useful to compare the reconstructed results with direct observations from local instrumental records (e.g. tide gauges). This has proved successful in a number of studies where rates of change are comparable to instrumental records, but provides the added ability of extrapolating the sea- level record further back into the Holocene (Gehrels, 2000; Edwards, 2001; Gehrels et al., 2002; Donnelly et al., 2004; Gehrels et al., 2005; Edwards and Horton, 2006; Kemp et al., 2011). In this respect salt-marsh environments can be regarded as natural archives of sea- level change comparable to tide-gauge records (e.g. Barlow et al., 2013) permitting sea-level observations as far back in time as the sediments allow. Significantly, the transfer function approach has the potential to bridge the crucial gap that exists between instrumental and geological records of sea-level change (Edwards and Horton, 2006).
Page | 21