no picture to see here

Contact:

Program in Applied
     Mathematics
 
University of Arizona

Office: Math 303
Phone: (520)621-1163
Email: rrael@math.arizona.edu
Curriculum Vitae

 Links:

 PEaCE Lab
RMBL
LAGSES
 
Teaching     |     Research     |     Publications     |     About 


     Welcome - I am a Ph.D. student in the Interdisciplinary Program in Applied Mathematics at the University of Arizona.  My background is in mathematics and biology, and currently I am studying how evolution changes outcomes between interacting organisms over time.  Species in nature are constantly adapting not only to changes in their environment, but also to changes in the community around them.  When populations that interact with a species increase or decrease in abundance, this can influence such factors as competition, predatory pressure, and prey availabilty, and thereby affect the evolution of the species.   I am using mathematical models to discover how such adaptations can change the course of population dynamics.  In particular, I am currently using evolutionary game theory to study competition and predator-prey relationships.

Press
A Science News article (Jan. 6, 2009) on our evolution of coexistence project can be found here : "Mathematicians Show How Beetles Can Share a Niche"

Teaching

Current Course:
       Spring 2008:  MATH 120R - Preparation for Calculus

Past Courses:
  • Fall 2008: MATH 120R - Preparation for Calculus
  • Spring 2007:  MATH 110 - College Algebra
  • Fall 2006:  MATH 110 - College Algebra

Research   [UNDER CONSTRUCTION......  check back soon!]

Advisors: T. L. Vincent, J. M. Cushing

Evolution of Coexistence

Evolution of a Genetic Polymorphism

Food Webs

Publications

R. C. Rael, R. F. Costantino, and J. M. Cushing, T. L. Vincent.  Using stage-structured evolutionary game theory to model the experimentally observed evolution of a genetic polymorphism, Evolutionary Ecology Research.  (In review).

R. C. Rael, T. L. Vincent, R. F. Costantino, and J. M. Cushing.  Evolution of corn oil sensitivity in the flour beetle, Annals of the International Society of Dynamic Games, vol. 9: Advances in Dynamic Game Theory. Birkhäuser, 2007.

R. C. Rael and B. Starzomski.  Effects of extinctions on food webs.  Proceedings of the Complex Systems Summer School, 2004.

 J. M. Restrepo, R. C. Rael, and J. M. Hyman.  Modeling the influence of polls on elections: A population dynamics approach,. (accepted at Public Choice)

R. C. Rael, R. F. Costantino, J. M. Cushing, and T. L. Vincent.  Evolution changes competive outcomes.  (in preparation).