Autocorrelation in the testate amoeba calibration set

Amesbury et al examine the autocorrelation in their huge calibration set. I thought I would do the same, increasing the resolution of the analysis to get a better handle on what is going on.


An RNE plot for the weighted averaging with tolerance downweighting plotted with ggpalaeo. I have used the pruned calibration set for comparison with the original paper.

This is an RNE plot. It shows the cross-validation performance of the transfer function when samples are removed by deleting samples from the calibration set

  1. at random (open circles)
  2. which are geographic neighbours of the focal sample in the cross-validation (filled circles)
  3. which have similar values of the environmental variable being reconstructed to the focal sample in the cross-validation (red dashed line).

If there is no autocorrelation in the calibration set, deleting samples by geography or at random should yield similar changes in performance. If there is strong autocorrelation, deleting samples by geographic proximity is worse than deleting samples by environmental similarity.

With the testate amoeba WAtol calibration set, a substantial fraction of the loss in performance occurs when samples within 1km of the focal site in cross-validation are deleted. At this distance, deleting samples by geographic proximity is worse than deleting the same number of samples by environmental similarity. At greater distances, the decline in performance is less step (the equivalent plot in Amesbury et al is a little different because they have accidentally plotted the WAinv instead of the WAtol result – I need to improve the rne function to make the selection of model variants clearer).

I interpret the initial steep decline as a bog-specific effect, the type of issue that leave-one-site-out cross-validation is designed to fix. The subsequent decline is probably partly due to some climate effects on testate amoeba (either directly or via bog vegetation composition) and partly due to analyst effects (for example in how water table depths were calculated).

It might be possible to get some (imperfect) handle on the relative importance of these terms by cross-validating the WAtol model in different ways. Leave-one-out cross-validation of the pruned calibration set has an r2 of 0.722; with leave-one-site-out cross-validation, the r2 falls to 0.697; leaving out data from each reference in turn gives an r2 of 0.683. This is equivalent to a geographic exclusion of 500 km. This suggests there might be some analyst effect, but there will still be an element of climate effect in this change in performance. A better analysis would use information on who the taxonomist was for each calibration set.

For this testate amoeba calibration set with WAtol, spatial autocorrelation is not a major problem (see Telford and Birks (2009) for some transfer functions where autocorrelation is a much bigger problem).


About richard telford

Ecologist with interests in quantitative methods and palaeoenvironments
This entry was posted in Palaeohydrology, Peer reviewed literature, transfer function and tagged , , . Bookmark the permalink.

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