TRANSFER FUNCTION PERFORMANCE

Using altitude as the only constraining environmental variable, DCCA revealed gradient lengths that indicated strongly linear species distributions along the environmental gradient ranging from between 0.775 and 1.536 SD units for site specific training sets JDT and BLT. In combining datasets together (TCD), the gradient length was still strongly linear at 1.173 SD units. As a result, PLS linear regression models suggested the strength of relationship (r2

jack) was relatively weak for an unscreened training set (0.32; component 3). Whilst this may appear poor, it is directly related to the short environmental gradient of the contemporary training set. Indeed, in combining local training sets to create a single combined training set, the strength of correlation between foraminiferal assemblages and the environmental variable (e.g. elevation) is reduced. Whilst this may seem counterintuitive to do so, a regional combined dataset provides an increased range of modern environments from which the fossil assemblages can be compared with, as discussed below (Gehrels et al., 2001). The sampled vertical range of the contemporary training set has a strong impact on model predictive ability (Barlow et al., 2013). The small r2 jack values in this study therefore reflect the bias in sampling towards in the upper part of the elevational gradient. In such cases, RMSEPjack may offer a more realistic assessment of the model performance (Gehrels et al., 2001; Leorri et al., 2010). This suggested model predictions of sea-level to within 0.11 m for an unscreened training set. In order to improve model performance, sample outliers in modern training sets are often excluded on the basis of their poor relationship with elevation (Edwards et al., 2004a; Gehrels et al., 2005; Horton and Edwards, 2006; Leorri et al., 2008;

Page | 172 Rossi et al., 2011). The performance of transfer function models are sensitive to such ‘tuning’ processes (Woodroffe, 2009). However, tuning helps by improving the predictive ability of the training set whilst increasing the strength of relationship. In this study, by removing all samples with an absolute residual (observed minus predicted) greater than the standard deviation of altitude, the strength of relationship improved to r2 jack = 0.54 whilst prediction errors (RMSEPjack)decreased to 0.08 m.

Linear regression and calibration methods are less common in quantitative sea-level reconstructions due to the often observed unimodal distribution of species in response to elevation. However, the results of this study are comparable to other research where PLS transfer functions have been applied. For example, in a study of foraminiferal distributions from Brittany, France, Rossi et al. (2011) also observed short environmental gradients (0.67 SD units). Based on a modern training set comprising 36 samples, the authors demonstrated robust transfer function performance (r2 jack = 0.70 ; RMSEP jack = 0.07 m) and applied the model to reconstruct relative sea-level changes back to AD 1850 showing comparable rates of change to direct observations from the Brest tide-gauge. Callard et al. (2011) also used PLS regression to construct a transfer model for sea-level studies in Tasmania. Their results showed that whilst PLS produced good statistical parameters, comparable to unimodal regression WA-PLS, when the model was applied to core sediments but was unreliable when used for predictions due to estimates larger than the modern sampling range and also exceeding the tidal range.

As discussed, the strength of relationship of foraminiferal assemblages from microtidal environments is typically weaker by comparison to macrotidal settings and can be directly related to the small vertical range of the samples studied (Horton and Edwards, 2006). Counter to this however are the small vertical prediction errors associated with microtidal settings. As such, microtidal environments are regarded as ideal settings for quantitative sea-level reconstructions based on microfossils (Callard et al., 2011). In a theoretical scenario, a tidal range of 20 cm should provide prediction errors of approximately 10% of the tidal range (i.e. 2 cm) (Barlow et al., 2013). Whilst this is achievable (e.g. Kemp et al., 2009a), if the vertical relationship between foraminiferal assemblages and elevation is less defined, a microtidal environment may offer little benefit in terms of prediction errors. Inspection of model prediction errors for a screened TCD training set in this study revealed precise sea-level reconstructions were possible to within 0.07 m. At first, while these results may seem promising, when taken as a percentage of the mean tidal range, prediction errors are actually greater by comparison to those studies conducted in larger tidal ranges (table 7.2). In this study the mean tidal range at the samples sites was 0.23 m equating to prediction error of almost a third of the mean tidal range (30%). Nonetheless the data can

Page | 173 still be used to interpret trends of past sea level providing the record is independently assessed (i.e. tide gauge records).

Table 7.2. Comparison table of microfossil transfer function prediction errors (RMSEP jack) and as a percentage of the tidal range with published studies.

Location Model RMESP (m) RMESP (m)

% tidal range

Reference

Central Croatia PLS 0.07 30 This study

New Zealand WA-Tol 0.05 3.3 Southall et al. (2006)

Maine, USA WA-PLS 0.25 8 Gehrels (2000)

Western Denmark WA-Tol 0.16 10.7 Gehrels and Newman (2004) Nova Scotia, Canada WA-Tol 0.06 3.7 Gehrels et al. (2005)

Biscay, Spain WA-PLS 0.19 7.6 Leorri et al. (2008)

Tasmania WA-PLS 0.10 16.7 Callard et al. (2011)

Brittany, France PLS 0.07 2.3 Rossi et al. (2011) Southern Portugal PLS 0.10 4.8 Leorri et al. (2010) Brittany, France PLS 0.13 4.9 Leorri et al. (2010) North Carolina, USA WA-PLS 0.04 14.8 Kemp et al. (2009b) Hokkaido, Japan WA-PLS 0.29 27.6 Sawai et al. (2004) North Carolina, USA WA-PLS 0.08 22.9 Horton et al. (2006)