In the 2002/February/9th edition of New Scientist (yes, its dates are
nominal; I'm writing this in the small hours of the morning before the given
date) there appears an article, Law of the Jungle

, covering a model
proposed by Steve Hubbell, based on selection neutral

randomness, which
produces reasonably good predictions of bio-diversity. New Scientist (in an
entirely familiar pattern) makes a big gosh-wow out of this.

My main observation about this model is quite simple: that, for
inter-species competition, it is no surprise, however shocking orthodoxy (or, at
least, Oliver Baker, the author, described by New Scientist as a freelance
science writer in Davis, California

) may find it. The basic truth of
species is that each is well adapted to its environment; so that the success of
species relative to one another should, indeed, be largely random. Each species
is this well adapted for the simple reason that intra-species competition
selects those members of the species which are well enough adapted to their
environment to succeed at competition with the other species competing with
them. Each individual vies with all the other creatures competing to fill the
same niche as it, not just with those of its own species.

There is a diagram included with the article, giving a bar chart of
number of species

vertically against number of individuals per
species

horizontally, for forest trees on Barro Colorado Island, Panama.
The horizontal axis is logarithmic (its given values are 1, 2, 4, ..., 512,
1024; I presume some clumping has been done). Steve Hubbell's model is given by
a curve which fits the data fairly well. The other curve given, labelled
standard model

, is quite clearly a Gaussian (so the dumbed-down article
calls it a bell curve) on the logarithmic co-ordinate and isn't as good a fit as
Steve Hubbell's model. This should be no surprise: the Gaussian curve would (if
it had not been truncated) give a non-zero number of species with half an
individual (and likewise quarter, eighth, etc.); the alleged standard model is
manifestly broken.

The Gaussian model is invariably inappropriate for any variate whose values
can never be negative, though excusable when the mean of the distribution is
very much larger than the standard deviation. In the present case, it is used
for the log (to base 2) of the number of members of a species; which can never
be negative; the mean is 4 (the log of 16 to base 2) and the standard deviation
appears to be about 3 (i.e. a factor of 8), so the excusable exception does not
apply. It is invariably better, for never-negative distributions, to use a
Gamma distribution (the simplest family of distributions which matches the
never negative

constraint); like the Gaussian family, Gamma has two free
parameters (the order

parameter, which controls the shape of the
distribution near zero, and the scale

parameter, which (given the order
parameter) controls the moments (mean, variance, etc.) of the distribution).
Thus Steve Hubbell's model is shown to be better than a straw man, which is no
information. Which is not to argue against it, merely to show that the alleged
orthodoxy is an easy opponent to beat; New Scientist can be irritatingly
touchy-feely at times.

It is interesting to note the four variables in Steve Hubbell's model: they are given to be

- number of trees in study area
- number of trees in the
universe

- immigration rate
- rate of emergence of new species in the
universe

where the universe

is the domain from which immigration to the
study area is feasible. Somewhere between the second and last of these I must
suppose some hypothesis is being inserted which says how many species exist in
the universe

, but this is merely my supposition.

The best thing about this model is that it is a natural null
hypothesis

against which one can test theories of selective advantage. Its
presumed data are well-chosen (though I would expect some datum relating to
distribution of trees among species, in the external universe

). It is,
thus, a good back-ground, using which to filter available data in search of the
cases where selective advantage reveals itself. Given my observation that
competing species are always roughly equally good, this model can be read as
describing the equilibrium

which serves as background to evolutionary
dynamics.