Modeling Projects

Population dynamics

- Predator-prey dynamics

The first paper discusses the use of experimental measurements to create an age-structured model for ginseng plant populations, and to analyze the effect of deer browsing. The second article models predator-prey dynamics in a chemostat, in terms of ordinary differential equations. The third paper discusses foodwebs. The fourth article discusses tri-trophic food chains, and the fifth considers possible consequences of the eradication of a predator.

• Deer Browsing and Population Viability of a Forest Understory Plant, by J.B. McGraw and M.A. Furedi,
  Science 307, 920 - 922 (2005).
• Stability and bifurcation of a simple food chain in a chemostat with removal rates, by M.M.A. El-Sheikh and S.A.A. Mahrouf,
  Chaos, Solitons and Fractals 23, 1475-1489 (2005).
• Stabilization of Large Generalized Lotka-Volterra Foodwebs By Evolutionary Feedback, by G. J. Ackland and I. D. Gallagher,
  Phys. Rev. Lett. 93, 158701 (2004).
• Allometric degree distributions facilitate food-web stability, by S.B. Otto, B.C. Rall, and U. Brose,
  Nature 450, 1226-1230 (2008).
• Cats, rats and seabirds, by M. Le Corre,
  Nature 451, 134-135 (2007).

- 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, 540-555 (2006).
• Dynamic complexities in a mutual interference host-parasitoid model, by C. Xu and M.S. Boyce,
  Chaos, Solitons and Fractals 24, 175-182 (2005).

- Competing species

• Coexistence and chaos in complex ecologies, by J.C. Sprott, J.A. Vano, J.C. Wildenberg, M.B. Anderson, and J.K. Noel,
  Phys. Lett. A 335, 207-212 (2005).