Mathematical Modeling of Genetic Pest Control

Colloquium in Celebration of Mathematics Awareness Month

Roy Magnuson

Department of Biological Sciences
University of Alabama in Huntsville

April 17, 2002

Abstract

Meiotic drive elements result in the preferential transmission of element-bearing chromosomes over element-free chromosomes. Thus they will tend to sweep through a population and displace the homologous element-free chromosome. Meiotic drive elements have been described in mice, mosquitoes, fungi and fruit flies. When located on a sex chromosome these drive elements will distort the sex ratio and ultimately drive the species extinct for lack of mates unless suppressed.

In his paper "Extraordinary Sex Ratios," (1967) WD Hamilton developed a mathematical model for the spread of meiotic drive elements. For this model, Hamilton assumed that:

• the meiotic drive element had no deleterious effects on the number or quality of the progeny,
• the meiotic drive element was transmitted to 100% of their progeny, and
• mating within the target population was panmictic (random),

Hamilton calculated that a population seeded with a frequency of 1/1000 with a meiotic drive bearing Y chromosome would go extinct in just 15 generations. We are reworking Hamilton's model under less ideal, more biologically plausible assumptions. We are particularly interested in modeling the effects of the following three parameters:

• Fertility of element-bearing individuals, c, (1.0 to 2.0)
• Transmission efficiency of element, d, (0.5 to 1.0)
• Degree of panmicticity (random mating), p, (0.0 to 1.0)

Through these studies, we hope to understand the evolution and propagation of these elements and to assess their potential utility in the genetic control of pest species.