Fermi Problems and Systematics

R. H. Zander

Res Botanica, Missouri Botanical Garden

January 29, 2010


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Fermi Problems and Systematics

Richard H. Zander


Traditional evolutionary taxonomy has long been criticized as overly subjective. Yet, today, only the most simplistic (though often internally mathematically complex) methods have been offered to replace seasoned judgments of evolutionary relationships of expressed traits involved in evolution. Simplifying, reducing analyses are, of course, valuable but a mono-methodological classification system almost entirely focused on tree-like relationships of lineages cannot generate the most useful classification for science.


By analogy, Fermi problems (Mertens 2008) are “impossible” parlor games involving questions asked when not enough data or distributions of data are available, e.g. “how long is a piece of string?” The best way to guess is to use the geometric mean, namely the square root of the product of the upper and lower bounds. A piece of string cannot be less than 0.5 centimeter or it would be a bit of fluff, and not longer than 20 centimeters or it would be useful and thus a “length of twine”, and the square root of the product is about 3.5 centimeters, thus the length of a piece of string. The geometric mean is used because the bounds are usually an order of magnitude or more apart, and indeed provides a good guess.


Methods like phenetics and cladistics deal in the same superficial way with problems for which only a small sample of data is available, and the results can be quite wrong though plausible because “in the ball park” or because the method seemed to work for other groups.


These highly methodologically dependent results can appear to be useful because evolutionary relationships usually cannot be directly checked in nature. The study of evolution must not allow a simplistic method (molecular phylogenetics usually using few sequences and small sampling of organisms) replace seasoned, reasoned judgments based on massive sampling, well-grounded in evolutionary theory, and backed up by morphometry, allozymes, mating behavior, cultivation, cytology, biogeography, and other ancillary tools for determining a useful classification with maximum evolutionary information.


Mertens S (2007) On the back of an envelope. Science 321:1160