Ecological Randomness

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

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.

Written by Eddy.