Potato Bug Packs a Punch; Math Student Fights Back with Numbers

Senior Karissa Smith’s distinguished honors research paper weaves differential equations with biological data to examine what happens when plant diversity increases or decreases. The results just might help alfalfa farmers fend off pesky (and ravenous) insects and fight a million-dollar agriculture problem.

Her research was supervised by Mohammed Yahdi, assoicate professor of Math and chair of the Math department. Smith used data from the Ursinus Biology Department and Cory Straub, assistant professor of Biology, who has been researching ways to reduce the damage done to the plant, alfalfa, by the pest, Potato Leaf Hoppers (PLH).

“This damage costs farmers millions of dollars each year,” says Smith. “The research tests the enemies’ hypothesis. A predator insect, Nabis, is introduced to the system to control the Potato Leaf Hopper population and plant diversity was also tested.”

Her paper, Modeling the Effect of Diversity in Host Plant-Herbivore-Predator Interactions , a Summer Fellows project, was accepted this fall for presentation. She was awarded funding from the National Institute for Mathematical & Biological Synthesis (NIMBioS) to attend the Research Conference at the Interface of Biology and Mathematics at NIMBioS.

Last month, the same project was an Outstanding Presentation award winner, placing among the top poster presentations at the 2012 Joint Mathematics Meetings MAA (Mathematical Association of America) Undergraduate Poster Session. The research used an enclosure field experiment that had four different types of plots: monoculture, meaning containing only alfalfa, with the predator, and without the predator, polyculture, meaning containing half alfalfa and half orchard grass, with and without the predator. Smith created a system of differential equations using information from literature about similar experiments and new mathematical approaches. The three variables were the abundance of PLH, the abundance of Nabis, and the damage caused to alfalfa by PLH.

“Using the data, we found many parameters that measure the level interactions in the system, such as birth, consumption and damage rates,” says Smith. “Then I ran different simulations to find starting points for the parameters in the equations. I was able to get these models to match the graphs that were based on the data, and incorporate the roles of plant diversity and the abundance of predators.”

Smith’s student partner, senior Allison Bugenis, worked with the 2011 data that used an open field experiment, getting similar results. Smith used this model to find ideal conditions.  “I found that a polyculture plot of 80 percent alfalfa with a predator present is ideal for farming alfalfa,” says Smith, who worked about forty hours a week for this Summer Fellows project. This included meetings with Professor Yahdi and Professor Straub. During both semesters, she worked a few hours a week doing more analysis on the model and fixing problems she didn’t initially see.
Success and Surprise

“I honestly didn’t think the model would work so well so quickly,” says Smith, who is planning to attend graduate school in the fall. “I knew there were a lot of ‘tricks’ to mathematical modeling, especially with ecological systems, but I still expected to face more failures than I did. The model matches well with the experimental data, despite needing to exclude some factors due to lack of information.”

“The close match between the model results and results from our field experiment indicate that the model is doing a good job capturing what is going on in the system. Now we can use the model to make predictions about what planting strategy is optimal to reduce pest damage, and we can test these predictions with experiments” says professor Straub. “The combined approach of modeling and experimentation allows us to make progress much more quickly”.

Professor Yahdi credits Straub’s generosity in providing insight about the biology and results and data of his experiments. “I believe there is more interdisciplinary work to be done as a continuation of this project,” says Yahdi. “The goal of the project is to provide mathematically a frame work for designing cost-effective and environmentally safe strategies to minimize alfalfa damage, and utilize enemies’ hypothesis and polyculture diversity. This could inform and give biologists tangible directions for limited field experiments without the cost involved in broad experiments.”