On the asymptotic speed of a stochastic invasion

                              by

                    Mark Lewis  (U. of U. Math)
   

            INSCC 110, 3:30pm  Tuesday, May 26, 1998


                          Abstract

In this talk I will propose a set of equations which describe the
dynamics of spatial moments of a nonlinear stochastic invasion
process.  In general the problem can not be expressed in closed form,
but a mixture of moment closure approximations and comparison methods
can be used to find upper and lower bounds for the rate of spread of the
nonlinear stochastic invasion process.  Both bounds inidicate slower 
spread than than the corresponding deterministic model predicts.  
The slowness of spread arises from the tendency of the stochastic models
to give rise to spatial clumps of individuals.  Here the spatial 
correlations between individuals mean that nonlinear effects are 
significant even when expected densities are low.  Applications to 
biological invasions will be discussed.

Requests for preprints and reprints to: mlewis@math.utah.edu
This source can be found at http://www.math.utah.edu/applied-math/