Dynamics of food chains with refuge and finite time extinction (Spring 2021)

A food web is a classical representation of a community that consists of all the predator-prey relationships in an ecosystem. A food chain is a linear sequence of links in such a web. A better understanding of food chains' population dynamics is an essential problem in Mathematical Biology, with applications to endangered species protection, invasive species control, and stability of ecological communities.

We will investigate food chains, where various predator or prey populations can go extinct in finite time. Next, we will explore the impact of providing refuge or "protection zones" for the prey, predator or both, on the overall population dynamics. Moreover, we will explore different interaction types among the species in multi-level food chains to understand their effects on the ecological community stability. Various questions will be explored.

  • Could one prove what are the size and shape of a refuge, required to prevent extinction, given specific initial predator and prey populations?

  • Could there be a link between the population dynamics at a certain trophic level, and refuge size at a lower trophic level?

  • What types of interactions (antagonistic, competitive or mutualistic) will provide community stability in a multi-level food chain?

  • How well would these models fit real predator-prey data, and could they help in forecasting population trends?

Students will first be introduced to the relevant concept in differential equations. They will also be introduced to statistical methods in data fitting, and theoretical ecology concepts pertaining to food chain dynamics and refuge theory.

For more information contact Kushani De Silva (kdesilva@iastate.edu)

People:

  • Kushani De Silva (Postdoc)

  • Rana Parshad (Faculty)

  • Eric Takyi (Grad)

Pre-requisites:

  • Programming (Matlab/R/Python) is desirable, but not required.

  • Experience with differential equations (Math 266/267) is desirable, but not required.

  • Experience with applied statistics (at the level of an introductory statistics course) is desirable, but not required.