Research
Research
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My interests lie at the interface of mathematics and biology, specifically mathematical modeling of population dynamics in the fields of ecology, evolutionary biology, and epidemiology. My favorite quantitative tools are:
1) Model selection: This is 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?”
2) Agent-based models: Many questions in ecology and evolutionary biology require detailed (mathematical) descriptions of the systems involved. Models used to be limited to what we could analytically study, such as simple differential equation models like the Lotka-Volterra predator-prey model. Now that we have vast computing capabilities, researchers no longer need to limit themselves to structured models that aggregate individuals into a population; instead, we can track individuals, each with their own properties and behavior, in an agent-based model (ABM). ABMs are models where individuals (agents) are unique and autonomous and interact with each other and their environment locally. An agent-based model is most useful when we want to demonstrate the causality of a property of the system. We make as few assumptions as possible on the behavior of individuals (just the behaviors we want to consider causal) so that when a property emerges, it shows those behaviors are sufficient to cause it.
I have applied these tools to a variety of biological scenarios including dog domestication (see press in National Geographic, Live Science, and American Kennel Club), pollen competition, white-nose syndrome in bats, overkill of mammoths, and de-extinction of passenger pigeons.
Publication List:
Undergraduate Research Projects Mentored
My most cherished part of my job is using original research as a method of teaching and mentoring undergraduate students. I have been particularly active as a research advisor for undergraduates.
Undergraduate Research Projects Mentored
My most cherished part of my job is using original research as a method of teaching and mentoring undergraduate students. I have been particularly active as a research advisor for undergraduates.
James Madison University
19. Clarissa Azurin, Lois Carpenter, and Grace Gorreck, "Optimizing the Distribution of Fruiting Agave on Bat-Friendly Tequila Plantations" JMU Math REU 2025.
18. Bethany Droubay, “Modeling Bacterial Control of White-Nose Syndrome in Bats" Summer 2025.
17. Josephine Funderburg, “A Simulation of the Population Dynamics and Life History of Maiasaura,” FYRE 2025.
16. Haynes Scholar Program cohort of 17 students, co-mentored with Dr. Laura Tipton, “Modeling White-Nose Syndrome in Bats," MATH 297 Spring 2025.
15. Griffin Mahoney, “A Simulation of the Population Dynamics and Life History of Maiasaura,” FYRE 2024.
Valparaiso University
14. Nathan Randle, “Estimating Average Boston Marathon Time from the Winning Times,” Summer 2020.
13. Charlotte Beckford, Montana Ferita, and Julie Fucarino, “Biomath Modeling: Pollen Competition” VERUM 2019.
12. Ryan Kulwicki, “Agent-based Modeling of the Evolution of the Domestic Dog,” MATH 497-498, 2018-19.
11. Katherine Bassett, in consultation with Dr. Rob Swanson and his student Craig Garzella,”Agent-based Modeling of Pollen Competition,” MATH 496, Spring 2018.
10. Ashley Hire, Samuel Iselin, Michael Revor “Mathematical Modeling of the Evolution of the Domestic Dog,” MATH 496, 2017-18.
9. Eva Cornwell, David Elzinga, Shelby Stowe, “Mathematical Modeling in Ecology: White-Nose Syndrome in North American Bats,” VERUM 2017.
8. 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.
6. 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.
5. Erin Boggess, Jordan Collignon, Alanna Riederer, “Mathematical Modeling in Ecology: Simulating the Reintroduction of the Extinct Passenger Pigeon,” VERUM 2015.
4. Michael Frank, Anneliese Slaton, Teresa Tinta, “Mathematical Modeling in Ecology: What Killed the Mammoth?” VERUM 2013.
3. 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.
2. Sydney Philipps, Dan Rossi, Rachel Von Arb, “Mathematical Models in Infectious Diseases: Multistrain Infections in Metapopulations,” VERUM 2011.
1. Teryn Gehred, Justin Nettrouer, Patrick Slattery, “Modeling Humans Vs. Zombies with Differential Equations,” MATH 492, 2010-11.
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