Weighted averaging regression and calibration was applied to the 34 lakes and the 127 selected diatom taxa in the training dataset to infer past lake water pH in Llyn Hir, a small upland lake in mid-Wales.
I have identified and removed the outlier sample (CW020) as well as…
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The RMSE gives a measure of the ‘apparent’ error in the model and thus over-optimistic while the RMSE calculated using bootstrap is a more reliable indicator of the true predictive ability of a transfer function.
Analysis of the dataset with both simple weighted averaging (WA) and weighted averaging with tolerance down-weighting (WA(tol)) resulted in the selection of WA for pH reconstructions as it gave lower estimates of the RMSEP (Table 2).
After having decided on criteria that maximize the performance of the model, I have applied it to a lake sediment core, Llyn Hir to perform a pH reconstruction. In WA reconstructions, averages are taken twice, once in WA regression and once in WA calibration. The resulting shrinkage of the inferred environmental variable is corrected for using inverse or classical deshrinking regression (Birks et al., 1990). Following analyses using both methods, trends in residuals revealed that inverse deshrinking was more prone to be biased than classical deshrinking technique (Table 3).
The resulting WA classical deshrinked transfer function was applied to fossil diatom assemblages enumerated from the Llyn Hir sediment core. WA regression and calibration (both with and without tolerance down-weighting) were performed using C2 Programme.
The WA model shows a strong predicted relationship between observed pH and diatom-inferred pH values (r2 = 0.83) (Figure 2). Statistical results for both simple and tolerance down-weighted WA show that the predictive ability of the WA and WA(tol) models, in terms of the predicted r2 and the RMSEP, are comparable (Table 2). Simple WA was chosen as it gives slightly higher predicted correlation between measured and diatom-inferred pH and lower predicted estimates of the error in this model.
A total of 124 diatom taxa were observed throughout the Llyn Hir core, 8 of which did not occur in the training dataset. This means that over 90% of the diatoms occurred in training set which makes our
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