Explicit spatial modelling of territories

1. A mathematical approach to modeling movement patterns, signalling and response behaviors.

   I will discuss one approach to modeling explicit spatial and temporal aspects of behavior, using wolf territorial interactions and scent-marking as an example. The result is a model that describes changing probability density functions for the locations of individuals. Territories typically arise from the interactions and are not assumed a priori. The model is then used to understand the effect of behavioral rules on territory formation.

   
   
2. Deriving models explicitly from data vs. modeling based on behavioral assumptions.

   It is possible to simply assume a basic class of models and to then attempt to fit the data. The other possibility is to make explicit assumptions about behavioral responses. Both approaches can lead to similar models (such as diffusion convection equations), but answer very different questions.

   
   
3. Interactions between territorial predators and a prey population.

   I will focus on how territoriality can affect predator prey interactions. I will discuss buffer zones between territories acting as prey refuges, and the effect that prey distribution may have on the process of territorial pattern formation. The organisms discussed will be wolves and white-tailed deer in NE Minnesota.

   
   
4. Optimizing movement behavior when competing for a spatially distributed resource.

   I will discuss how optimal control theory can be used to formulate a game where territorial individuals interact with interference and exploitation competition.