# Undergraduate Math/Stat Colloquium

## Dr. Kathleen Hoffman on predator-prey models

Monday, October 27, 2014

12:00 PM – 1:00 PM

12:00 PM – 1:00 PM

Mathematics/Psychology : 401

**Title:**

*From Classic Results to Recent Advances: The Lotka-Volterra Model of the Predator-Prey Cycle*

**Speaker:**Dr. Kathleen Hoffman

**Abstract:**

Lotka and Volterra profoundly impacted mathematical ecology with their development of the a set of differential equations that successfully predicted the rise and fall ofÂ predator and prey populations. The classic data set of lynx and hare from the Hudson Bay trading company spanning over 100 years exhibits the behavior predicted the the Lotka-Volterra model. In this talk I will discuss two recent developments. The first describes the dynamics of the food chainÂ with an additional scavenger added to the classical predator-prey model. The second provides a mathematical description of the Hairston, Smith and Slobodkin conjecture in ecology that describes how top-down and bottom-up forces in a food chain affect the dynamics of the food chain.