Mathematical Models for Carnivore Territories
Abstract
Mathematical models can help us understand the formation of complex spatial patterns, including the territories of wolves and coyotes. Here scent marks provide important cues regarding the use of space. In this talk I will show how biologically-based mechanistic rules can be put into a mathematical model which predicts the process of territorial formation as individuals create and respond to scent marks. The model predicts complex spatial patterns which are seen in nature, such stable `buffer zones' between territories which act as refuges for prey such as deer. The mathematical work is supported by detailed radio-tracking studies of animals. I will also employ the approach of game theory, where each pack attempts to maximize its fitness by increasing intake of prey (deer) and while decreasing interactions with hostile neighboring packs. Here the predictions are compared with radio-tracking data for wolves and coyotes.
About the Speaker
Mark Lewis is Professor and Canada Research Chair in both Mathematical Sciences and Biological Sciences at the University of Alberta, and Director for the Centre for Mathematical Biology at Alberta. Professor Lewis' has broad research interests in mathematical ecology. He works on biological problems including the modeling of territorial pattern formation in wolves, predicting population spread in biological invasions, calculating optimal strategies for biocontrol, and assessing the effect of habitat fragmentation on species survival. Par of his research involves the formulation and verification of quantitative models, in collaboration with field ecologists.
Mark obtained his doctorate at Oxford University in Mathematical Biology in 1990. His recent awards and grants include the CRM-Fields-PIMS Prize Distinction (2010-2011, from the Centre de Recherches Math/Fields/Pacific Institute for Mathematical Sciences); a Lee Segel Prize for Best Original Research Paper published in the Bulletin of Math Biology (2008, from the Society for Mathematical Biology); an American Society of Naturalists Presidential Award Distinction for Best Paper published in The American Naturalist (2006, from the American Society of Naturalists), and two Senior Canada Research Chair (Tier I) Research awards (2001-2008 and 2008-2015, from the University of Alberta). He has published over 150 papers.
Mark enjoys outdoor activities, including canoeing and cross country skiing and sailing. He lives with his family in Edmonton Alberta.
The Howard Rowlee Lecture Series is made possible through a generous donation by Mr. Howard E. Rowlee, Jr., a Lincoln resident and friend of the department, who has established a fund at the University of Nebraska Foundation to support research in mathematics. The Howard Rowlee Lecture is an annual event which seeks to bring internationally acclaimed scholars in the mathematical sciences to UNL to promote public understanding of mathematical research and to stimulate the environment for mathematics research at UNL. The inaugural Howard Rowlee Lecture was given in 1997, by Efim Zelmanov, Professor of Mathematics at Yale University and the winner of the Fields Medal in 1994, for his seminal contributions to algebra.
Complete Listing of Howard Rowlee Lecturers
| Year | Speaker | Institution |
|---|---|---|
| 2012 | Mark Lewis | University of Alberta |
| 2011 | David Eisenbud | University of California-Berkeley |
| 2010 | Carlos Kenig | University of Chicago |
| 2009 | Mike Hopkins | Harvard University |
| 2008 | Peter Sarnak | Institute for Advanced Study |
| 2007 | Béla Bollobás | Trinity College, Cambridge, and the University of Memphis |
| 2006 | Ingrid Daubechies | Princeton University |
| 2005 | James P. Keener | University of Utah |
| 2004 | Donald Saari | University of California, Irvine |
| 2003 | Mark J. Ablowitz | University of Colorado, Boulder |
| 2002 | Ron Graham | University of California, San Diego |
| 2001 | Vaughan F. R. Jones | University of California, Berkeley |
| 2000 | Melvin Hochster | University of Michigan |
| 1999 | Bradley Efron | Stanford University |
| 1998 | Avner Friedman | University of Minnesota |
| 1997 | Efim Zelmanov | Yale University |
Previous lectures in this series have also been supported by the Department of Mathematics, the College of Arts and Sciences, and the University of Nebraska–Lincoln Research Council.
