Monday, March 13, 2017

The mismeasure of birds

This is a remarkable painting by Henry Stacy Marks (1829-1888). He titled it "Science is Measurement" based on suggestions from his artist and scientist friends. Like a good painting, it is open to interpretation.

According to Stacy Marks, he was inspired to consider the scene when he went to measure some skeletons to draw some accurate illustrations. He thought what he was doing would be interesting to depict and he made this scene for his diploma from the Royal Academy in 1879. The title actually came later - and is probably influenced by the discussions of the day. In 1871, Lord Kelvin in his address to the British Association for the Advancement of Science noted:
Accurate and minute measurement seems to the non-scientific imagination a less lofty and dignified work than looking for something new. But nearly all the grandest discoveries of science have been the rewards of accurate measurement and patient long-continued labour in the minute sifting of numerical results.
 By 1883, Lord Kelvin had repeated the idea enough to make it sound more pompous:
I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be.
It is unclear where Stacy Marks and his friends came across the version that seems to differentiate science from art and it appears that Marks and the other artists saw it as being somewhat absurd. His commentary in the elevation of the dead bird (a greater adjutant from Calcutta, incidentally), the "scientist" looking up at the dead bird (while pictures of the living animal lie on the floor), the contrasts of the dark and well dressed man with the light and unfleshed bird all make for an interesting setup.

Now there is something to be said about the measurement of birds - it might looks easy and objective but there are enough pitfalls. Measurement of anything looks easy but getting multiple people to measure in the same way is fraught. There are errors in how things are measured but there are also absolutely horrific things one can do after making measurements. Here is an example of a set of individual birds and their measurements from W.E. Brooks published in Stray Feathers 1875 - the author, a railways engineer, places the measurements of each individual bird in a single row.

What this table does tell us is that the observer recognizes that birds have their parts having proportionate parts. A slightly larger winged bird probably has a slightly longer beak. The proportion may however not be linear during the growth phase of a bird as some parts tend to grow faster than others. Two hundred and twenty five years later, an ordinary reader like me can take this data and put it through a simple Principal Components Analysis and see that the data has internal relationships which allow me to reduce it to a single dimension consisting of a linear combination of the variables that explains 99.8% of the variation among the specimens. The principal component consist of the following variable loadings.

Length -4.93 0.11 -0.01 -0.00 -0.00 -0.00
Wing -0.54 -0.11 0.11 -0.00 0.00 0.00
Tail -0.94 -0.18 -0.08 0.00 -0.00 0.00
Bill 1.89 0.04 -0.02 -0.02 0.00 -0.00
Tarsus 1.34 0.03 0.00 0.01 0.00 -0.00
Mid toe and claw 1.47 0.06 -0.00 0.01 0.01 0.00
Hind toe and claw 1.70 0.05 -0.01 -0.00 -0.01 0.00

This further opens up the possibility of comparing two populations for comparison in meaningful ways. You can even predict missing measurements based on multivariate regression.

The remarkable thing is that this simple approach to documenting bird measurements has been lost subsequently in India. It is unclear how the idea of reducing all data to ranges (maxima and minima) was come upon but a likely reason may have been to reduce space usage. The use of ranges seems to have been introduced by Stuart Baker but surprisingly, with no addition of even simple ideas as means and medians, was continued by Dillon Ripley and Salim Ali in their Handbook - and there was no improvement made to this by later cataloguers like Humayun Abdulali and Saraswathy Unnithan which vastly reduces the value of the work that they published. Reduction of data could have been accomplished through many means, graphical and numerical. This failure to improve upon methodology is especially difficult to understand given that Salim Ali counted J.B.S. Haldane and P.C. Mahalanobis as his friends (Mahalanobis of course pioneered morphometrics in physical anthropology and introduced what is now known as the Mahalanobis distance). Interestingly, I asked a few ringers of the BNHS about the protocols they used for morphometrics and was told that they only thought it worthy to measure waders and that all other birds just showed slight variations that were unworthy of recording!

Typical entry from the Handbook (1978, volume 1. p 10 for Daption capensis)

Meanwhile, ringers in other parts of the world have produced such excellent works as this one from Deutsche Ornithologen-Gesellschaft, this one from South Africa or this one. Even this rather old work from 1931 is worth examining.

I wonder if anyone has ever thought of a global morphometric database for any organism group.

PS: September 6, 2019: On the topic of artists as scientists, I have recently learnt of Tanto Che Basti (1682) by Carlo Maratta with inspirations from  Giovan Pietro Bellori (1613–1696).
Tanto Che Basti ("as much as necessary") showing how art involves geometry, mathematical, and anatomical understanding.