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Fermi Problems and Systematics R. H. Zander Res January 29, 2010 return to home |
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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 |
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