My autocorrelation papers

I’m making the papers I have published about the effects of autocorrelation on transfer functions available below for easy reference.

Telford RJ, Birks HJB. 2005. The secret assumption of transfer functions: problems of spatial autocorrelation in evaluating model performance. Quaternary Science Reviews 24: 2173-2179.

The estimation of the predictive power of transfer functions assumes that the test sites are independent of the modelling sites. Cross-validation in the presence of spatial autocorrelation seriously violates this assumption. This assumption and the consequences of its violation have not been discussed before. We show, by simulation, that the expected r2 of a transfer function model from an autocorrelated environment can be high, and is not near zero as commonly assumed. We investigate a foraminiferal sea surface temperature training set for the North Atlantic, for which, with cross-validation, the modern analogue technique (MAT) and artificial neural networks (ANN) outperform transfer function methods based on a unimodal species-environment response model. However, when a spatially independent test set, the South Atlantic, is used, all models have a similar predictive power. We show that there is a spatial structure in the foraminiferal assemblages even after accounting for temperature, presumably due to autocorrelations in other environmental variables. Since the residuals from MAT show little spatial structure, in contrast to the residuals of unimodal response models, we contend that MAT has inappropriately internalized the non-temperature spatial structure to improve its performance. We argue that most, if not all, estimates of the predictive power of MAT and ANN models for sea surface temperatures hitherto published are over-optimistic and misleading.

Telford RJ. 2006. Limitations of dinoflagellate cyst transfer functions. Quaternary Science Reviews 25: 1375-1382.

Organic-walled dinoflagellate cysts have become an important proxy for reconstructing Quaternary sea-surface conditions, with transfer functions generating quantitative estimates of summer and winter sea-surface temperatures, salinity, and ice cover. I critically reassess these transfer functions and argue that the uncertainty of the summer temperature and ice cover transfer functions has been substantially underestimated because the strong spatial structure in the data set has been ignored, and that there is little evidence that either winter sea-surface temperature or salinity can be independently reconstructed.

Telford RJ, Birks HJB. 2009. Evaluation of transfer functions in spatially structured environments. Quaternary Science Reviews 28: 1309-1316.

Transfer function training set sites close to each other tend to have similar species assemblages and environmental conditions in both oceanic and terrestrial data sets. This is unremarkable, but as this lack of independence between sites violates the assumptions of many statistical tests, it has severe consequences for transfer function evaluation, possibly resulting in inappropriate model choice and misleading and over-optimistic estimates of a transfer function’s performance. In this paper, we develop a simple graphical method to test if spatial autocorrelation affects a training set, develop a Monte Carlo geostatistical simulation as a null model to test the significance of transfer functions in autocorrelated environments, and introduce a cross-validation scheme that is more robust to autocorrelation. We use these tests to show that some recently-published transfer functions have no predictive power, and strongly recommend the use of these tests to make transfer functions more robust to autocorrelation.

Telford RJ, Birks HJB. 2011. QSR Correspondence “Is spatial autocorrelation introducing biases in the apparent accuracy of palaeoclimatic reconstructions?” Quaternary Science Reviews, 30: 3210-3213.

Guiot and de Vernal (2011) comment on three of our papers, Telford and Birks (2005, 2009) and Telford (2006), that concern the implications of spatial autocorrelation for quantitative palaeoecological transfer functions. Here we show that (1) they do not address the central predictions of these papers, (2) they test a prediction based on a misrepresentation of our work, (3) they mis-state the assumptions of the methods they use, and (4) they incorrectly interpret their results.

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