If I can make it there,
I’ll make it anywhere.
It’s up to you, New York, New York.
Palaeoecologists typically try to choose sites where the environmental variable they want to reconstruct is likely an important, ideally the most important, variable determining microfossil assemblages in the past. If other environmental variables are important, the basic assumptions of transfer functions risk being violated and the reconstruction may be spurious, driven by the other variables.
5. Other environmental variables than the one(s) of interest (Xf) have had negligible influence on Yf during the time window of interest, the joint distribution of these variables of interest in the past was the same as today, or their effect on Yf did not lead to past changes in assemblage states resembling shifts indicative in the modern environment of changes in the variable of interest
Most palaeoecologists also try to minimise non-analogue problems by choosing sites that are similar to the calibration set that the transfer function uses.
These two site-selection guidelines make Speke Hall Lake, a polluted eutrophic lake near Liverpool, a curious lake to choose to try to reconstruct July air temperature from chironomid head capsules using the Norwegian chironomid calibration set. But this is what Lang et al (2017) have done. They find a statistically significant correlation between the reconstruction and instrumental records of July temperature from Anglesey (r = 0.620; n = 16; p = 0.01) and declare that
This study demonstrated that a chironomid-based temperature inference model can produce reliable estimates of mean July air temperature, even from a lake that has experienced large changes in heavy metal and sulphur inputs, and trophic status.
Or in other words, if you can reconstruct temperature in Speke Hall Lake, you can reconstruct temperature anywhere.
I would not be so hasty to ignore the assumptions of transfer functions, lest we exemplify the “sick science” problem (curiously, Juggins (2013) is not cited despite its relevance ). Given the enormous ecological, chronological, and taphonomic difficulties that high-resolution chironomid reconstructions face (insurmountable at annual resolution, challenging at decadal resolution), I would judge it far more likely that the reported correlation is due to chance than that everything we know about the limitations of transfer functions is wrong. No single study at p = 0.01 is going to change my mind (you can find homoeopathy studies with lower p-values), and the review of high-resolution reconstructions that I am writing, shows there are serious problems with many of the ten sub-decadal chironomid-temperature reconstructions that I have found.
I am entirely happy to ascribe the key result from Speke Hall Lake to chance, but there are some other aspects of the paper which merit attention.
Lang et al use the constant rate of supply (CRS) model to produce a chronology from their 210Pb data. The CRS model is
where A(0) is the total unsupported 210Pb inventory and A is the inventory below the sample being dated. This resulting age-depth model will always be monotonic as the inventory below the sample being dated will always decline with depth. The CRS model shown in Lang et al is not monotonic (fig 1b)
Lang et al Fig 1. Speke Hall Lake location (a), chronology (b), and core matching with magnetic susceptibility measurements (c).
From the timing of the impossible wiggle, it looks like the 137Cs peak from atmospheric bomb testing might have been included as an age rather than a check on the CRS model. I hope this is simply a plotting problem and that the ages of the chironomid samples are unaffected.
The 210Pb dates are on a different core from the chironomid samples. The chronology is transferred to the chironomid stratigraphy by aligning the magnetic susceptibility record. The overall agreement between the two mag sus records is excellent (Fig 1c), but the details are not perfectly reproduced. Since these details are used to align the records, there will inevitably be some error in the alignment. It is not clear from the paper if this uncertainty is accounted for (even an error of 2 years would seriously degrade the expected correlation between the reconstruction and the instrumental record).
Lang et al do a constrained ordination and find that their variables explain 68% of the variance in the chironomid stratigraphy. This seems impressive until you realise that they used seven predictor variables and have fourteen fossil samples. Given the strong autocorrelation, especially in the geochemical variables, I suspect this result is little better than chance. Had 13 variables been used, they would have explained 100% of the variance!
Lang et al Fig. 5. Canonical correspondence analysis (CCA) for the upper sections (1932–2005) of the Speke Hall record. Anglesey is the July temperature data.
Note that in the ordination the temperature arrow is inversely correlated with most of the pollution indicators.
Lang et al include some reconstruction diagnostics, a plot of residual squared distances and a timetrack plot. Unfortunately, they conflate their residual squared distances (goodness-of-fit) with analogue quality making it difficult to be sure of what they have done. It is possible to have fossil samples that have excellent analogues (short squared chord distance) in the calibration set but a poor goodness-of-fit, and vice versa. What I would like to have seen is a plot of the fossil abundance against calibration set abundance.
Interpreting the correlation
There is a strong trend in the instrumental temperature data (r2 = 0.5) and the assemblage composition is autocorrelated. It would therefore seem prudent to correct the p-value of the correlation between the reconstruction and the instrumental record for autocorrelation. Of course, with a only 16 fossil data points covered by the Anglesey record, this will be difficult, but the corrected p-value is bound to be higher.
The apparent inverse correlation between the temperature and pollution indicators could also help to inflate the correlation between the reconstruction and the instrumental record.
The correlation with the longer CET series is only 0.25. No explanation for this much weaker (and non-significant) correlation is given.
Final questions for the authors
Had the correlation between the reconstruction and the instrumental record not appeared significant would you (and would the editors/reviewers have let you) publish a paper which could be summarised as ‘unpromising ponds cannot be used for high-resolution climate reconstructions’? I wonder if there are any failed high-resolution reconstructions decorating the interior of filing cabinets.
As I have started asking in all my reviews: where are the data going to be archived?