GCI2016: Mini-course 4: Structured dynamical models for biological invasions - Lecture 2: Mark Lewis

Mini-course 4: Structured dynamical models for biological invasions
Mark Lewis (University of Alberta)
Lecture 1: Stage structured models including matrix models, eigenvalues, elasticity, net
reproductive rate, etc., with examples taken from invasive species
This lecture will focus on how to determine the growth rate of an invader as a function of
stage-structured demographic parameters, such as survival, stage-transition probability and
stage-specific fecundity in discrete time. We will review classical theory of geometric
growth rates, eigenvalues and elasticity and develop some newer theory that links the net
reproductive rate of an invader to its life-cycle graph. Applications will be made to invasive
species where parameters have been measured.
Lecture 2: Spatially structured models involving integrodifference equations with long
distance dispersal and the analysis of spreading speeds
The spreading speed of a species is an essential characterization of its invasive potential.
Here long-distance dispersal plays a crucial role in determining the spreading speed. For
example, a small fraction of propagules that travel a long distance can increase the
spreading speed by an order of magnitude. We consider spreading speeds for spatial extensions of the stage-structured models from Lecture 1. Here dispersal kernels describe
the spatial redistribution of different stages of invader, giving rise to an integrodifference
equation problem. It turns out that the spreading speed can be described in terms of a
minimal eigenvalue problem, providing a compact and easy to use characterization for
invasive potential as a function of demographic and dispersal parameters.
Lecture 3: Study of models in the computer lab
We will use R code to calculate eigenvalues, elasticities, net reproductive rates and
spreading speeds for invasive species, and will also numerically simulate solutions to the
integrodifference equations.