Matstat seminar fredagen 30 maj 2001

The time-evolution of small populations:
  stochastic dynamics is not just determinism plus noise

Hernan G. Solari, Universidad de Buenos Aires

ABSTRACT
A few hundred rabbits share a patch of land, less than a hundred
share the same warren. They are not sane, the virus of the
mixomatosis has taken part of the population. How will the population
evolve? Will the illness become endemic? Which strand of virus will
be the prevalent one? The problem has been posed for about 50 years,
the standard (deterministic) models give clear answers to these
questions, but Nature does not behave according to them. What is
wrong with our models?

At a can-making factory the manager goes berserk! Once again the
process is out of control and one complete roll of steel will have to
be re-processed. Why our nosy-deterministic models cannot account for
this situation? Why we have been unable to solve this problem so far?

We will discuss these and related problems of small populations where
stochasticity is not just a correction to the deterministic dynamics
but a fundamental element of the dynamics.