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Hello! Are you wondering, "What is data science and applied math research, anyway?" This page describes recent student projects related to my long-term program to understand collective behavior in locusts. Check these out to get a sense of what doing research with me might be like, and shoot me an email if you have any questions.
Summer 2027
Summer 2027
I'm currently looking for student researchers to join my group for this summer! I hope to work with 2 or more students this summer, or perhaps starting early as this coming spring. We would work on some aspect of my locust data and modeling work. Your summer research could be related to any aspect of my locust project, from data curation to statistical inference to modeling with differential equations. You can see examples of past projects on this webpage.
If you are a University of St. Thomas student, I encourage you to apply to the Center for Applied Mathematics (CAM) summer research program when they post their positions in Spring 2027. I plan to have a project in their program but it's never too early to be in touch with me if you're interested!
If you want to work with me sooner, there may be options for starting in Spring 2027. One option has an upcoming deadline Nov 2nd.
Motion State as Markov Process
Motion State as Markov Process
Juvenile locusts marching in a group switch between three primary motion states: Stationary, Walking, and Hopping. Do locusts remember which state they were in recently while marching or are their switches completely dependent on their present state, environment, and neighbors? To answer this fundamental question we modeled memory-less switching using a Markov process. We calculated the time spent in each state from the empirical data extracted from video (see the Motion Tracking project below) and compared it to the Poisson distribution that we would expect for a Markov process. We used a Chi-square goodness of fit test to check check whether the data supported or could reject the memory-less hypothesis. The figure below and on the right shows the results of these tests with columns and rows corresponding to various hyper-parameters. We found that we needed to clean the data by removing very short states (just one or two frames of video) which likely occurred due to classification error. With this adjustment we could not find sufficient evidence to reject the hypothesis of memory-less switching.
This project was supported through the Summer Collaborative Undergraduate Research program at Hamline University.
Markov switching between motion states (S, W, H).
Motion Tracking Individual Locusts in a Swarm
Motion Tracking Individual Locusts in a Swarm
The form, speed, and density of these swarms is in large part due to social interactions, such as a locust orienting itself to move in the same direction as its neighbors. In order to deduce these interactions, we extracted numerical trajectories from raw video footage of locusts marching in the field. The video was provided by our collaborator Jerome Buhl (University of Adelaide), an eminent locust biologist. We conducted exploratory analysis of these trajectories, which continued in additional projects below.
On the left is a visual representation of our tracking process. Top: Locusts (dark dots) walk and hop in a naturally occurring swarm. Bottom: Processed video shows locusts (bright spots) detected by the algorithm (purple circles) and linked into trajectories (rainbow lines).
This project was part of the HMC Data Science REU, supported by NSF Grant DMS - 1757952.
Classifying Motion State with Support Vector Machines
Classifying Motion State with Support Vector Machines
Starting with the trajectories we collected from video, we investigated the movement behavior of individuals within the swarm. We developed a support vector machine (SVM) to classify motion into three states: stationary, walking, and hopping. The SVM used motion characteristics of the trajectories such as mean speed averaged over the near future and near past and standard deviation of speed over the same time window. We trained the SVM with data from diligently collected manual classification. Through cross-validation we estimated that the SVM was between 85-90% accurate. Approximately half the data was classified as hopping and the other half was split almost evenly between stationary and walking. This provided the first quantitative insight into how locusts move in a natural swarm!
The figure on the right shows an iteration of our SVM that shows clear clustering of the data. Figure credit to our collaborator Michael Culshaw-Maurer.
Deducing Insect Interactions from Field Data
Deducing Insect Interactions from Field Data
We set out to infer how individuals interacted with their nearby neighbors. Our aim was to deduce biologically realistic rules for these interactions that could inform the creation of a future agent-based model that can produce swarms comparable to those observed in nature.
On the right, we plotted two-dimensional histograms of the position of nearby neighbors relative to a focal locust (red arrow) that is stopped (top) and crawling (bottom). Yellow indicates higher counts of neighbors while blue indicates lower counts. Note that crawling locusts have fewer neighbors in front of them. This suggested to us that when a crawling locust sees a neighbor directly in front, it either stops moving or turns to avoid a collision.
Figure credit goes to Jacob Landsberg (Haverford College '21) who conducted the bulk of this work as part of his senior thesis!
The Sociobiology of Foraging Strategies
The Sociobiology of Foraging Strategies
Perhaps the most striking characteristic of locust behavior is that they manifest an epigenetic phase change where they transition from solitary individuals (when resources are plentiful) to gregarious foragers (when resources are sparse). It is believed that this behavioral transition evolved independently in multiple locust species on at least three continents.
Our hypothesis is that this behavioral transition increases foraging efficiency for the swarm and survival potential for the species. We formulated this as a question in game theory and compared predictions using an extension of the agent-based model developed by Hannah Larson (HMC 2020) shown in the Overview Fig F. Dominant ecological theories of foraging describe the optimal search strategy of an individual only. Whereas game theory provides routes for optimizing strategies for groups. Our goal was to explain mathematically why locust behavior is bimodal.
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