Cornell Center for Applied Mathematics
Cornell Center for Teaching Excellence
I am a PhD student at Cornell University's Center for Applied Mathematics,
advised by Professor Stephen Ellner.
At the broadest level, my research could be classified as Applied Theoretical Ecology. That is, I spend a lot of time thinking
about how to use mathematics to best manage biological populations.
Ecosystem management is particularly complicated because it involves an understanding of quantitative techniques and ecological
processes along with an understanding of human behavior, economics and politics.
Therefore, my research is highly interdisciplinary and involves collaborations with students, postdocs, and faculty in
Applied Economics and Management,
Ecology and Evolutionary Biology,
I study the use of trap cropping as a tool for sustainable pest management. Trap cropping is a form
of habitat diversification in which the grower plants additional crops to attract, divert, intercept,
and/or retain targeted pests to reduce damage on a main crop. While it has been used with some success
in laboratory and semi field experiments, it most often fails
when scaled up to commercial farms and greenhouses. I use mathematical models to explain
why trap cropping has failed so often in the past and also suggest improvements for future deployment.
Collaborators on this project include entomologists
and Doo Hyung Lee.
The results from past theoretical studies suggest that managers spend too much money sampling for invasive pests.
In this project I explore why simple models and optimization frameworks are suggesting such low sampling effort compared to what managers actually do in the field.
Optimal Harvesting in Stage Structured Fisheries:
Calculating the optimal sustainable harvest of fish populations is perhaps the most classic application of mathematics to ecological resource management.
However, traditional methods focus on one dimensional and, more recently, age structured models.
The sparsity of a nonlinear Leslie matrix makes optimization for small age structured fisheries mathematically tractable.
Unfortunately, this advantage does not exist for size structured populations.
I study the optimal harvest in these more complicated models and also explore the effect of stochasticity on best harvesting practices.
Human Intuition vs. Models:
When managing biological populations whose dynamics are influenced by complicated ecological processes, how well do mathematical
models help improve management in comparison to a manager basing their decisions solely on their data, expertise and years of experience? In this project I conduct experiments where
human subjects manage simulated, hypothetical populations and compare their performance to various mathematical models.
Low, C., S.P. Ellner, & M.H. Holden. 2013. Optimal control and cold war dynamics between plant and herbivore. The American Naturalist. 182: E000 E-Article.
Holden, M.H., S.P. Ellner, D.-H. Lee, J.P. Nyrop, & J.P. Sanderson. 2012. Designing an effective trap cropping strategy: the effects of attraction, retention and plant spatial distribution. Journal of Applied Ecology. 49:3:715-722
(If you cannot access this journal, here is a preprint)
For PDFs of post peer review versions of any of my publications, please email me (firstname.lastname@example.org)
To see quiz and worksheet solutions visit Math 1120 section Solutions
Spring 2012: TA for Math 1106 - Calculus for the Life and Social Sciences
To see quiz and worksheet solutions visit Math 1106 section Solutions
Fall 2011: TA for Math 1710 - Statistical Theory and Application in the Real World
April 2011: Workshop leader for Expand Your Horizons: motivating young women in science + mathematics.
October 2010: Instructor and Co-Organizer for a one day course on Game Theory at the Johns Hopkins Center for Talented Youth: Odyssey Series .
October 2009: Instructor for a one day course on Chaos at the Johns Hopkins Center for Talented Youth: Odyssey Series.
Summer 2008: TA for Chaos and Fractals at Johns Hopkins Center for Talented Youth.