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Showing posts with label morphometrics. Show all posts
Showing posts with label morphometrics. Show all posts

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.

PC1 PC2 PC3 PC4 PC5 PC6
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 they did. 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 showed 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.  
 
PS: August 2021:  An quotation (original untraced) from Stacy Marks - "... Many people regarding birds in but three aspects—as things to be either eaten, shot, or worn. ... No natural history of a bird is complete without recording where the last specimen was shot; and should a rare bird visit our shores, the hospitality which we accord to the foreign refugee is denied, and it is bound to be the victim of powder and shot. The fashion of wearing birds or their plumage as part of ladies' attire, threatens to exterminate many beautiful species, such as the humming-birds of South America, the glossy starlings of Africa, and the glorious Impeyan pheasant of the Himalayas, with many other species."
 
5 March 2022: A new work more or less deals with all my comments above - see https://doi.org/10.1111/ele.13960 -  A bird in the hand: Global-scale morphological trait datasets open new frontiers of ecology, evolution and ecosystem science by Joseph A. Tobias.

PS: October 2024: Found this very interesting geometrical analysis of peacock feather patterning by E. T. Seton.



Friday, February 25, 2011

Crunching elephants

Apparently the physict Freeman Dyson came up with a complex formula in 1953 and when Enrico Fermi saw it, he just did not like the complexity. Fermi in his quest for simplicity and elegance apparently quoted John von Neumann who had said:
"With four parameters I can fit an elephant, and with five I can make him wiggle his trunk"
I was recently muddling with some techniques for shape quantification which has applications for field biologists, for instance to match or compare biological shapes. Naturally I decided to try out what are termed as elliptic Fourier descriptors - an idea based on the epicyclic movements of planets that goes back to ancient times although the mathematical forms are relatively new. A lovely demonstration of the concept can be found here. The problem of getting the parameters from a given closed curve however is not shown by that applet. The reduced number of terms to describe a closed curve, elliptic Fourier descriptors, have been widely used in analysing shapes for systematics. 
Mathematically reduced elephant

What got my attention was a 2010 paper (I usually stay away from physics) titled "Drawing an elephant with four complex parameters" where the authors try to reconstruct an elephant with four complex numbers and wiggle its trunk with a fifth ! This was attempted earlier in 1975 with least-squares Fourier series fitting but that apparently took 30 parameters. The figures in the new paper show that they managed to do something close.

Program Screenshot: My elephant clearly beats the math
I decided to write up a program and see for myself but have been able to get a passable elephant only with 8 parameters and that is 8 sets of 4 real numbers (a, b, c and d of Kuhl and Giardina can be considered as two complex numbers) and so not as good as the results of the authors of the 2010 paper.  Maybe my elephant is too complex for the math. In case you want to play around with the idea, download (Windows unfortunately, but works in Wine) the small program  that I wrote today from here - you can also find some Matlab code here.

Further reading