Although work on transfer functions started by using planktonic foraminifera for reconstructing sea surface temperature, I am most familiar with palaeolimnological transfer functions. In a standard palaeolimnological transfer function, the calibration set has one observation per lake, little or no spatial autocorrelation and typically many species. These are the ideal conditions.
Since palaeolimnological transfer functions were developed for reconstructing pH from diatoms during the acid rain debate (Birks et al 1990), many other variables have been reconstructed from many different microfossil groups. Importantly, there have been changes to the original calibration set design, so there are now calibration sets with many observations per site, spatial autocorrelated observations, or few species. One strand of my research over the past few years has been to investigate how these changes from the ideal set-up affect transfer functions.
I’ve tested how spatial autocorrelation affects transfer functions, concluding that it will make the transfer function’s performance appear to be better than is justified by the data, and in extremis, can make ecologically irrelevant variables appear possible to reconstruct.
I’ve tested the effect of having multiple observations per site (essentially a special case of spatial autocorrelation), and promoted more appropriate cross-validation procedures than the usual leave-one-out cross-validation.
I’ve tested the behaviour of intra-lake calibration sets, the extreme case where all the observations are from one lake, and am very doubtful about their utility.
I still want to test the calibration-in-time approach that has been developed for chironomid-temperature reconstructions.
My most recent transfer function paper explored foram sea-level transfer functions. These have their own set of peculiarities, with multiple observations per transect across the salt-marsh, and, potentially, spatial autocorrelation both within and between the transects. The paper largely ignored the potential for autocorrelation between transects, but found that the multiple observations per transect, and therefore the within-transect autocorrelation, was a minor issue – at least in the New Jersey calibration set investigated.
One interesting issue is that my test of reconstruction significance failed, probably because at the site investigated, sediment accumulation kept up with sea-level rise leading to only small changes in tidal exposure.
Of course, sea-level reconstructions still needed to be evaluated for the “sick science” problems, but I think they are reasonably robust if used with care.
Kemp, AC, Telford, RJ, Horton, BP, Anisfeld, SC & Sommerfield, CK (2013) Reconstructing Holocene sea level using salt-marsh foraminifera and transfer functions: lessons from New Jersey, USA. Journal of Quaternary Science 28: 617-629 http://dx.doi.org/10.1002/jqs.2657
We present an expanded training set of salt-marsh foraminifera for reconstructing Holocene relative sea-level change from 12 sites in New Jersey that represent varied physiographic environments. Seven groups of foraminifera are recognized, including four high- or transitional-marsh assemblages and a low-salinity assemblage. A weighted-averaging transfer function trained on this dataset was applied to a dated core from Barnegat Bay to reconstruct sea level with uncertainties of ± 14% of tidal range. We evaluate the transfer function using seven tests. (1) Leave-one-site-out cross validation suggests that training sets of salt-marsh foraminifera are robust to spatial autocorrelation caused by sampling along transects. (2) Segment-wise analysis shows that the transfer function performs best at densely sampled elevations and overall estimates of model performance are over optimistic. (3) Dissimilarity and (4) non-metric multi-dimensional scaling evaluated the analogy between modern and core samples. The closest modern analogues for core samples were drawn from six sites demonstrating the necessity of a multi-site training set. (5) Goodness-of-fit statistics assessed the validity of reconstructions. (6) The transfer function failed a test of significance because of the unusual properties of some cores selected for sea-level reconstruction. (7) Agreement between reconstructed sea level and tide-gauge measurements demonstrates the transfer function’s utility.