From: Pete Seiler <guiness@vehicle.ME.Berkeley.EDU>
Subject: Re: models of competitive/evolutionary systems
Date: Fri, 12 May 2000 15:33:08 -0700
Newsgroups: sci.math
Summary: [missing]

> Can anyone point me to some simple mathematical models that
> describe the "core" features of competitive or evolutionary
> systems?  I'm looking for a somewhat abstract model that
> incorporates the critical notions of competition and mutation,
> but that doesn't necessarily seek to describe a particular
> biological reality.  (A "toy" problem would certainly be
> appreciated.)  I would especially like to see any models
> expressible as a simple system of differential equations.

The Lotka-Volterra model is a very simple set of nonlinear differential
equations that model interactions between predators and their prey
I snagged the following from:
http://www.stolaf.edu/people/mckelvey/envision.dir/lotka-volt.html 

For concreteness let us assume that the prey in our model are rabbits,
and that the predators are foxes. If we let R(t) and F(t) represent the
number of rabbits and foxes, respectively, that are alive at time t, then
the Lotka-Volterra model is: 
	dR/dt = a*R - b*R*F
	dF/dt = e*b*R*F - c*F
where the parameters are defined by: 
  a is the natural growth rate of rabbits in the absence of predation, 
  c is the natural death rate of foxes in the absence of food (rabbits), 
  b is the death rate per encounter of rabbits due to predation, 
  e is the efficiency of turning predated rabbits into foxes. 


Pete