# Mathematical Sciences

UAH’s Department of Mathematical Sciences is dedicated to education, scholarship, and service in the mathematical sciences. We offer programs of study leading to bachelor’s and master’s degrees in mathematics and to the doctor of philosophy degree in applied mathematics.

“Mathematics…is indispensable as an intellectual technique. In many subjects, to think at all is to think like a mathematician.”

## Dr. Karen A. Ames Memorial Lecture Series on Applied Mathematics

### Dr. Azmy S. Ackleh

Devon Endowed Professor of Mathematics, Dean of the College of Sciences, The University of Louisiana at Lafayette

## Competitive exclusion for selection-mutation models with discrete or continuous trait spaces:  A unifying measure-valued modeling approach

DATE:               March 31, 2017

TIME:                3:00 p.m.

LOCATION:     SST Room 218

Competitive interactions between organisms play a significant role in structuring ecological communities. The questions of when do competing species coexist and when do they exclude each other have long intrigued both ecologists and mathematicians. In 1932, Gause formulated the well-known Competitive Exclusion Principle, which states that two species competing for the same resources cannot coexist if other ecological factors are constant.  Thereafter, experiments and mathematical models (beginning with the Lotka-Volterra model) have been used to support or violate this tenet.  Recently efforts have been devoted to understanding this phenomenon in selection-mutation models in which individuals are distributed over a phenotypical trait space and compete with one another.  In this talk, a few recent selection-mutation models formulated using discrete or continuous trait spaces will be reviewed.  Then, a measure-valued selection-mutation modeling approach will be presented. This approach has the advantage of combining models with discrete or continuous trait spaces under one formulation. The long-time behavior of solutions of this measure-valued model is discussed and competitive exclusion or coexistence between traits is demonstrated.

Dr. Azmy S. Ackleh is the Dean of the College of Sciences and the Devon Endowed Professor of Mathematics at the University of Louisiana at Lafayette.  Ackleh received his Ph.D. from the University of Tennessee at Knoxville in 1993. He then joined the Center of Research in Scientific Computation at North Carolina State University as a postdoctoral fellow until 1995 where he became an Assistant Professor of Mathematics at the University of Louisiana at Lafayette and rose through the ranks to become a Full Professor in 2003. In 2007 he received the University Distinguished Professor award and was selected to become the R.P. Authement Eminent Scholar and Endowed Chair in Computational Mathematics. From 2011-2013 he served as the Head of the Department of Mathematics at the University of Louisiana at Lafayette and has been serving as the Dean of the College of Science since 2013.