Theoretical considerations for biological control: a case study with scentless chamomile

Abstract

The introduction of invasive species is a significant driving force of global change. Weed scientists, resource managers, conservation and restoration biologists have focused their attention on the control of invasive species trying to understand, mitigate and prevent impacts of biological invasions. Biological control, the control of invading organisms by means of their natural enemy, is one way to prevent impacts of biological invasions. Mathematical models are a useful tool for the design of biological control strategies. These models allow for the analysis of population growth and spread, and for determination of aspects of the life cycle of the organisms which can be manipulated to control populations. In this dissertation I use matrix models to study the life history of invading organisms. First, a new method for the calculation of an analytical net reproductive rate formula is derived. I show with examples how this formula can be applied to study the control of invading organisms, particularly weeds. I extend these results, to calculate a mean and variance of the generation time. Later in the thesis, I use coupled map lattice models, a time and space discrete formalism, to calculate rate of spread for scalar and matrix population models. I derive formulae for the wave speed for constant and stochastic environments for coupled map lattices. I then apply these to scentless chamomile, an invasive weed distributed all across North America. The methods for calculation of net reproductive rate and generation time, and formulae for rate of spread in coupled map lattices, are new to biological invasions and biological control.