Ratio of valid to invalid (REPORT)

Thu Oct 5 12:16:18 CDT 2000

Dear Taxofolks,

Here is the promised summary of public and private messages on this thread.
I hope that I have not inadvertently misrepresented anyone's ideas while
presenting them so briefly. Tables are difficult to format on listservers,
so I disassembled the table at the end. For a Word version of this file,
please email me (privately!).

I have not had the stamina to thank all of you individually for writing to
me. Please be assured that I enjoyed receiving every note (yes, even the
critical ones!) and got something interesting out of each one. It has been
an interesting conversation.

Andrew

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Number of species per genus

Andrew K. Rindsberg
Geological Survey of Alabama
P.O. Box 869999
Tuscaloosa, AL 35486-6999 USA
arindsberg at gsa.state.al.us

"What I tell you three times is true."
                        Lewis Carroll (C. L. Dodgson), 1876, The Hunting of the Snark

What is the average number of species per genus? How many of these species
are valid? I posted variants of these questions on the taxonomic listserver,
Taxacom, on September 25, 2000, and received more than twenty replies,
mostly by private email. Evidently, the questions struck a chord. I asked
because I am embarking on a large taxonomic revision of trace fossils, and
wanted to know to what degree the processes of human thinking, particularly
of categorization, affect systematics. This is particularly apposite for
trace fossils, because ichnotaxa form a parallel taxonomic system that is
not organized phylogenetically.

The problem of objectivity immediately came to the fore. Taxonomic
categories are not objective above the species rank, and arguably not even
at that rank. As Pierre Deleporte said, "A genus of bacteria and a genus of
mammals have no common grounds." Moreover, it is a commonplace that
attractive organisms such as birds and butterflies tend to be subdivided
more finely than unattractive, uninteresting, or simply "difficult" groups
of organisms. Thus, even if we can determine the average number of species
per genus, we will not necessarily have a number that represents any kind of
objective reality.

If genera were truly comparable from group to group, or if the differences
could be evened out by taking a sufficiently large data set, then we would
have a rough measure of evolutionary rate. Genera with unusually large
numbers of species should, at least in theory, be those that are evolving
quickly. Contrariwise, genera of "living fossils" should be monospecific or
nearly so.

Zdenek Skala stated that the distribution of taxa within higher taxa tends
to follow a hollow Willis curve, so that the commonest number of species per
genus is 1, the next commonest is 2, and so on. The names of human family
names show the same pattern. "Hence, the 'average' genus does not represent
some central tendency." As a former student of linguistics, I can state that
similar trends are found in language, e.g., the number of syllables per word
as used in a text, as shown by Zipf many years ago. It would be interesting
to follow up these ideas, although, As Peter Stevens said, the underlying
causes of such patterns are difficult to interpret.

Regardless of the subjectivity of genera, it is not unscientific or
worthless to ask how taxonomy is affected by human preferences. The answers
may help us to be more objective.

On Taxacom, I suggested that the average number of valid or available
species per genus might be about 3, and that this might have to do more with
human convenience than with anything objective. Richard Jensen pointed out,
"A simple bar bet is to show someone the integers 1, 2, 3, 4 and bet that
you can predict the one they will choose -- about 75% of the time, people
choose 3 (3 blind mice, holy trinity, 3 wise men, 3 on a match, 3 medals in
sporting events, etc,). There is also, apparently, a predilection for odd
numbers." Peter Stevens said that 5 seems to be a convenient number for
humans when bundling items. Indeed, 5 is the largest number of objects that
most people can count at a glance without breaking the group up mentally
first. Ken Kinman's (1994) classification has about 5 to 6 classes per
phylum, and 6 to 7 orders per class.

Peter Stevens (1997, 1998) also said that human classification into
categories is sometimes "entirely structured by explicit concerns about
memory," e.g., Bentham and Hooker's classification of plants. This was
certainly the general case among early biologists, including Linnaeus.

The factor of time is important when considering the ratio of accepted and
unused names, as Daniel Geiger pointed out (among others). As time goes on,
nomina nuda and nomina oblita tend to accumulate while understanding of
systematic relationships becomes more complete. John Noyes argued that
groups whose inventory is relatively incomplete (e.g., parasitic
Hymenoptera) may have fewer synonyms. I have not found this to be the case
with trace fossils, some ichnogenera of which are grossly overnamed
(especially the pretty ones). Still, it is arguable that the splitting of
genera into additional genera may dynamically offset this trend.

With all this discussion behind us, what are the numbers themselves? They
are given in table 1. Obviously the method is not standardized and the
sample is insufficient, at least in zoology. Still, the range of numbers is
impressive. They tend to support the idea that the more a group is studied,
for whatever reason, the more useless names tend to accumulate. They also
support the idea that attractive groups tend to accumulate more synonyms
than unattractive groups. At least for plants, the number of valid species
per genus hovers around 4 or 5, for whatever that is worth. I would say that
the questions were worth asking.

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Acknowledgments
Thanks to the following Taxacom correspondents for stimulating ideas and
references: Nicolas Bailly, James Bass, Jim Croft, Pierre Deleporte, Susan
B. Farmer, Daniel L. Geiger, Richard J. Jensen, Ken Kinman, John S. Noyes,
Richard L. Pyle, Peter Rauch, Geoff Read, Hendrik Segers, Teresa Sholars,
Zdenek Skala, Peter Stevens, F. Christian Thompson, Mark F. Watson, Paul H.
Williams, and Karen L. Wilson.

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Bibliography
I've made no effort to track these down yet, so the citations are only as
complete as the information that was sent to me. Sorry for the
inconvenience!

Bentham and Hooker. Genera plantarum.
Berlin, Brent [folk taxonomy]
Catalog of Fishes. URL
http://www.calacademy.org/research/ichthyology/catalog/descrip.html and
http://www.fishbase.org
Kinman, Ken, 1994
Mayr, Ernst
Segers, H., 1998. An analysis of taxonomic studies on Rotifera: a case
study. Hydrobiologia, 387/388: 9-14.
Stevens, P., 1997. How to interpret botanical classifications -- suggestions
from history: BioScience 47: 243-250 [relationship between taxonomic
structure and mnemonics]
______1998. Mind, memory and history: how classifications are shaped by and
through time, and some consequences: Zoologica Scripta, 26: 293-301.
Williams, P. H., 1988. An annotated checklist of bumble bees with an
analysis of patterns of description (Hymenoptera: Apidae, Bombini): Bulletin
of the Natural History Museum (Entomology), 67: 79-152.

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Table 1. Approximate number of species per genus in selected groups.

(A) Group
(B) Number of named species
(C) Number of valid species per genus (percentage): not supplied in each
case
(D) Source (email messages, 2000)

A. Index Kewensis (plants)
B. (~25%)
D. Brummitt in Wilson

A. Australian Plant Names Index
B. ~60,000 taxa
C. ~17,500 taxa (17%)
D. Croft

A. Trilliaceae
B. 575 taxa
C. 70 taxa (12%)
D. Farmer

A. Apiaceae
B. ~15,000
C. ~3000 (20%)
D. Watson

A. California lupines
B. ~400
C. 64 (16%)
D. Sholars

A. genus Lupinus
B. ~500-1000
D. Sholars

A. Rotifera
B. 1817
C. (~77%)
D. Segers

A. Haliotidae (abalones)
B. ~200
C. 55 (27.5%)
D. Geiger

A parasitic Hymenoptera
B. "huge"
C. (>90%)
D. Noyes

A. recent Bombini (bumblebees)
B. 239
C. (>11 species per genus)
D. Williams

A. Pisces
B. >54,300
C. ~26,000 (48%)
D. Bailly