# Mathbio Colloquium Thursday Dec. 2 at 3:30 in MG2050

*November 29, 2010*

The last Math bio colloquium of the semester will be held on Thursday, Dec 2 at 3:30 in MG2050. Truman Physics professor Peter Rolnick will be presenting

Paramecia and Two Issues in Population Modeling: Inertial Effects; Prey-Dependence in Predator-Prey Systems

There are lots of things to consider in coming up with a general model for the dynamics of a population. One is whether or not the differential equations used in modeling need to be second-order in time. Models that include a second-order time derivative are sometimes called inertial models, because they allow populations to behave as if they have “inertia”, analogous to the inertia of objects in classical physics. These models are also sometimes called maternal effect models, because, biologically, they require some kind of passing-down from parent to off-spring of environmental effects experienced by the parent. Another modeling issue is whether or not, in predator-prey systems, the interaction term in the model should depend on the density of prey, or on the prey-predator ratio. There are supporters of both views, and each comes with its own reasonable biological justification. In our lab at Truman, we are looking to gather empirical data to support or refute the various points of view on these two issues. Paramecium aurelia can be grown in a nice controlled system which can be tweaked in various ways, and population can be tracked relatively easily, with large changes happening over short time periods. When coupled with its predator Didinium nasutum, we have a nice controlled predator-prey system. I will discuss the issues of inertial effects and prey-dependence from both a mathematical and a biological perspective. Finally, I will explain our efforts to empirically study the presence (or not) of an inertial effect in Paramecium aurelia, and to find which of prey-dependence or prey-predator ratio dependence are most important in describing the Paramecium-Didinium system.