Research

My interests lie at the interface of mathematics and biology, specifically mathematical modeling of population dynamics in the fields of ecology and epidemiology.  My primary specialization is in model selection, where one tries to answer the question of which mathematical model best represents a system or best explains a set of data.  By selecting the most parsimonious model (the model that best balances simplicity with goodness of fit), we can answer important questions about the populations under study.  Typical questions one can answer with these methods are, “How long will it take for this population to go extinct under the current conditions?” or “How many people do we need to vaccinate to eradicate this disease?”

I’m always interested in working with students to study biological systems using mathematical models!

See my CV for a publication list.

Upcoming Undergraduate Research Projects

Tell me if you’re interested in joining one of these projects!

  • Modeling the Impact of the Invasive Evil Weevil on the Endangered Giant Air Plant Population of Florida:
    We wish to study the endangered giant air plant of Florida (T. utriculata) and its invasive predator, the evil weevil (M. callizona). The air plant in Florida is semelparous, which means it has one, large sexual reproduction event in its lifetime by growing an apical meristem. The weevil consumes this meristem before the plant is able to reproduce, causing it to head towards extinction. We are building and analyzing an agent-based model of this system to determine effective control strategies as well as evolutionary impacts on the plant species.
  • Modeling Pollen Competition:
    Many aspects of plant sex remain a mystery to the biological community. In this project, we will use mathematical and computer simulation models to study the dynamics of pollen competition and to determine successful evolutionary strategies. In particular, we will use an agent-based modeling (ABM) approach. ABMs are models where individuals (agents) are unique and autonomous and interact with each other and their environment locally. ABMs have become a popular modeling process in the last decade due to the rise of computational power so we will be able to answer novel biological problems with new modeling techniques!
  • Modeling the Evolution of Language:
    Language evolution differs significantly from genetic evolution because individuals’ use of language can change during their lifetime.  This difference means that many of the techniques that are used for modeling genetic evolution, such as tracking generations, must be modified.

Previous Undergraduate Research Projects

  1. Charlotte Beckford, Montana Ferita, and Julie Fucarino, “Biomath Modeling: Pollen Competition” VERUM 2019.
  2. Ryan Kulwicki,  “Agent-based Modeling of the Evolution of the Domestic Dog,” MATH 497-498, 2018-19.
  3. Katherine Bassett, in consultation with Dr. Rob Swanson and his student Craig Garzella,”Agent-based Modeling of Pollen Competition,” MATH 496, Spring 2018.
  4. Ashley Hire, Samuel Iselin, Michael Revor “Mathematical Modeling of the Evolution of the Domestic Dog,” MATH 496, 2017-18.
  5. Eva Cornwell, David Elzinga, Shelby Stowe, “Mathematical Modeling in Ecology: White-Nose Syndrome in North American Bats,” VERUM 2017.
  6. Matthew Klapman, “A Simulation of Anthropogenic Mammoth Extinction,” MATH 497-498, 2016-17.
  7. Jordan Bauer, “Mathematical Modeling of Vaccination Noncompliance,” summer 2016, MATH 492, Spring 2017.
  8. Samuel Iselin, Shannon Segin, in consultation with Dr. Laurie Eberhardt and her students Sylas Buller, Kathleen Hebble, “An Agent-Based Modeling Approach to Determine Winter Survival Rates of American Robins and Eastern Bluebirds,” MATH 492, 2015-16.
  9. Erin Boggess, Jordan Collignon, Alanna Riederer, “Mathematical Modeling in Ecology: Simulating the Reintroduction of the Extinct Passenger Pigeon,” VERUM 2015.
  10. Michael Frank, Anneliese Slaton, Teresa Tinta, “Mathematical Modeling in Ecology: What Killed the Mammoth?” VERUM 2013.
  11. Ana Eveler, Tayler Grashel, Abby Kenyon, Jessica Richardson, “Optimizing the Allocation of Vaccines in the Presence of Multiple Strains of the Influenza Virus,” MATH 492, 2012-13.
  12. Sydney Philipps, Dan Rossi, Rachel Von Arb, “Mathematical Models in Infectious Diseases: Multistrain Infections in Metapopulations,” VERUM 2011.
  13. Teryn Gehred, Justin Nettrouer, Patrick Slattery, “Modeling Humans Vs. Zombies with Differential Equations,” MATH 492, 2010-11.

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