Math 485 -- Mathematical Modeling

Ecology and evolutionary biology

Parasitism and predation

The first paper considers a model of coupled ordinary differential equations describing the effect of water mites on mosquito populations. The second article investigates a discrete model (coupled maps) describing parasitoid-host interactions.

• Modelling parasitism and predation of mosquitoes by water mites by L Esteva, G Rivas, and H M Yang. J. Math. Biol. 53 (2006) pp 540-555
• Dynamic complexities in a mutual interference host-parasitoid model by C Xu and M S Boyce. Chaos, Solitons and Fractals 24 (2005) pp 175-182

Modeling evolution

The following paper discusses a model of evolution which takes into account the way individuals within a population interact with one another.

• Evolutionary dynamics on graphs by E Lieberman, C Hauert, and M A Nowak. Nature 433 (2005) pp 312-316

Chaotic dynamics in an insect population

Animal populations are often assumed to be either steady or cyclical (periodic). The following paper examines theoeretically and experimentally a situation in which the population size fluctuates chaotically.

• Chaotic dynamics in an insect population by R F Costantino, R A Desharnais, J M Cushing, and B Dennis. Science 17 (1997) pp 389-391

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