student research

summer 2020

Students play an integral role in my research. This page includes descriptions of past student projects related to my long-term program on modeling 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 2021

Prof Jasper Weinburd and Prof Andrew Bernoff anticipate working with three research students on problems related to modeling how and why locusts swarm.

You will work in a group of students on related projects and will meet our collaborators to learn how your research fits into the larger program. Our students often continue their work in a senior thesis, present their findings at conferences, and may coauthor resulting publications.

To Apply:

Visit the HMC Undergraduate Research Opportunities website. You must be an HMC student to apply.

Successful applicants need no prior research experience; should have completed core courses in differential equations and linear algebra; programming experience, especially in Matlab, is highly desirable; courses in statistics, data science, and modeling/mathematical biology would be very helpful.

Applications open Monday Feb 1st and close on Sunday Feb 21st.

If you have any questions please be in touch: jweinburd [at] hmc [dot] edu

Past Projects

Overview

Locusts form swarms with distinctive geometries that appear to aid in foraging. Fig A shows locusts moving perpendicular to the line of advancing insects through a lush agricultural field. In contrast, Fig C shows locusts moving parallel to the collective stream towards an isolated patch of vegetation. No leader directs the swarm to aggregate or move in these ways, instead both collective behaviors can be attributed to the interaction of rules that dictate an individual locust's attraction to food and social attraction/repulsion from other locusts. Understanding that interaction may eventually help identify efficient strategies for controlling locust outbreaks.

A Locusts travel in a planar front moving to the right as insects forage, leaving behind destroyed crops (brown) with uneaten crops ahead (green), from ABC. B Traveling pulse solution to our agent-based model of the the behavior observed in A. C Locusts forming a columnar stream over bare ground, from Wiki, in contrast with perpendicular movement in A. D Simulation of a first 2D agent-based model shows similar columnar structures to C. E Complex band shapes, with both clear fronts and extending columns, from AUS Dept of Agriculture. A NetLogo simulation of foraging locusts; the color scale indicates food density and the red points are foraging locusts.

a. The Crucial Role of Repulsion

Existing agent-based models of locust swarms are capable of reproducing qualitatively the columnar structures observed in swarms, however our studies have revealed that existing models have the unbiological characteristic that the density of the swarm becomes infinite as the number of locusts increase . It is clear that, while our models of locusts adequately capture alignment and attraction, our modeling of repulsion (a collision avoidance mechanism) is wanting. The two promising strategies seem to be to build in anticipation and by generalizing ideas of nearest neighbor repulsion from one-dimension to two-dimensions. Preliminary work suggests that the right strategy may to be to combine both of these mechanisms. The goal of this project is to determine macroscopic swarm density as a function of the repulsion mechanism chosen and then to tune these models with actual field data.

b. 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 plan to formulate a this as a question in game theory and verify the predictions using an extension of the agent-based model developed by Hannah Larson (HMC 2020) shown in 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 is to explain mathematically why locust behavior is bimodal.

"Heat map" showing the likelihood of neighbor positions around an individual locust, generated from numerical data.

c. Deducing Insect Interactions from Field Data

The form, speed, and density of these swarms is partly due to social interactions, such as a locust orienting itself to move in the same direction as its neighbors. In this project we will work with field data to deduce biologically realistic rules for these interactions. These rules will inform the creation of an agent-based model that we hope will produce swarms comparable to those observed in nature.