Refuge effects in food chains (Spring 2020)

A food web 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 the population dynamics of food chains is an important problem in Mathematical Biology, with applications to species conservation, endangered species protection, as well as the control of invasive species.

We will investigate food chains, where various predator populations can blow-up or explode in finite time, and certain prey populations can go extinct in finite time. Next we will explore the impact of providing refuge or "protection zones" for the prey, on the overall population dynamics, in the food chain.

Various questions will be explored.

• Could one prove what are the size and shape of a refuge, required to prevent blow-up or extinction, given a specific initial condition? 

• Do the relationship between refuge size and finite time dynamics follow power laws?

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

How would adding network structure to the model, such as in the case of a larger food web, change the overall population dynamics?

Students will first be introduced to the concept of finite time blow up and finite time extinction in differential equations. They will be introduced to network models, statistical methods in data fitting, and mathematical biology concepts pertaining to food chain dynamics and prey refuge.

People:

• Kushani DeSilva (Postdoc)

• Ethan Herron (Undergrad)

• Catherine Larson (Undergrad)

• Hannah Lo (Undergrad)

• Audrey McCombs (Grad)

• Rana Parshad (Faculty)

• David Uselman (Undergrad)

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