Matthew Holden

Center for Applied Mathematics
657 Rhodes Hall, Cornell University
Ithaca, NY 14853


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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, Computer Science, Ecology and Evolutionary Biology, Entomology, Mathematics, and Natural Resources.


Sustainable Agriculture: 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 Jan Nyrop, John Sanderson, and Doo Hyung Lee.

Invasive Species: 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 (