And who is Thomas Malthus?

Kenelm Philip fnkwp at
Mon Apr 29 05:36:18 EDT 2002

> But the next question then becomes: What stops the predators from eating
> up all of their prey?

> The most obvious answer is that bunny rabbits bred up faster than cruel
> fox can catch them.

It's not just the paleontologists that tell us this is a fairy tale. Con-
sider the work of Gause in the 1930s. Theory at that time said that a
single species with a fixed food supply would show the logistic curve: an
initial exponential growth which then decreased and approached asymptot-
ically to a steady state. Gause's experiments with _Paramecium caudatum_
yielded just such a curve. So far so good...

Theory also said that adding a predator would follow the Lotka-Volterra
equations, yielding either a steady oscillation (with the prey and
predator populations out of phase), or a damped oscillation asymptotic to
a steady state. So Gause added _Didinium nasutum_ to his _Paramecium_--
and nothing of the sort happened. The _Paramecium_ increased until the
_Didinium_ were introduced--whereupon the _Paramecium_ started to
decrease and went extinct. The _Didinium_ increased at first, but went
extinct after the prey were all consumed. He repeated the experiments,
trying to get the predicted Lotka-Volterra oscillations, but failed to
so so. Even this simplest conceivable system did not follow the theory.
Despite these results, the Lotka-Volterra model was used for for decades

	Note that in this simple case the 'foxes' did indeed eat up all
the 'bunny rabbits'.

	Conclusion: real ecosystems are much more complex than these
simple models.

						   Ken Philip

P.S. This runs from mammals to protozoa--but we can assume that leps
are subject to similar constraints.


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