A Continuous Model of Locust Alignment and Feeding

Throughout 2020, a massive locust plague threatened food security in southwest Asia, the Arabian Peninsula, and eastern Africa. This plague is composed of swarms that originate as groups of juvenile locusts called hopper bands (incapable of flight). Hopper bands contain up to millions of locusts, all walking and foraging in apparent coordination. Our aim is to study the aggregation, propagation, and feeding of these hopper bands by understanding the link between individual and collective behaviors.

When a locust outbreak occurs, the resulting hopper bands can exhibit shapes that range from planar fronts to columnar fingers. We recently published a paper on locust fronts in which we showed that a one-dimensional model, incorporating food and feeding behavior, quantitatively reproduces field observations of fronts of foraging locusts. However, this model cheats in the sense that it assumes that all the locusts are aligned and therefore it can only produce front solutions that are uniform in the direction transverse to the motion.  Recently we’ve borrowed some ideas from continuum mechanics to derive a novel partial differential equation (PDE) model that represents locust swarms via a continuous density that depends on position, time, and locust orientation.

Our goal over the summer is to simulate this system numerically.  Our hope is that the numerical scheme will allow us to identify which parameters in the model manifest the observed morphologies and to characterize them using tools from dynamical system theory. A summer student would continue code development, validate the accuracy of the code, explore the model’s parameter space, and classify the observed behaviors. Developing effective visualizations of the data will also be a key component of the project.  Finally, we will try and relate the parameters and behavior in the model to those observed in the field and the lab as reported in the literature and in our own studies of field data provided by our collaborator, Dr. Jerome Buhl, a locust biologist at the University of Adelaide.

 

Name of research group, project, or lab
Locust Group (with Prof. Bernoff and Prof. Weinburd)
Why join this research group or lab?

Profs Weinburd and Bernoff are partners in an international collaboration of mathematicians, data scientists, and field ecologists. Among them, a prominent locust biologist Dr. Jerome Buhl studies locust outbreaks in Australia and has provided us with video field data. Last summer, our student researchers extracted numerical trajectories via motion tracking. This summer we are excited to leverage this field data to inform and validate our locust model.

You will work in a group of three 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.

 

Representative publication
Logistics Information:
Project categories
Mathematics
Mathematical Biology
Numerical Modeling
Student ranks applicable
First-year
Sophomore
Junior
Senior
Student qualifications
  • The student should have completed core courses in Linear Algebra & Differential Equations.
  • Experience programming, particularly in MATLAB, is highly desirable.
  • Experience with Partial Differential Equations (such as Math 115 or Math 180) is extremely helpful.
  • Courses in Dynamical Systems, Mathematical Biology, Statistical Mechanics, and/or Continuum Mechanics would be useful (but we realize many students will not have seen this material). 
Time commitment
Summer - Full Time
Compensation
Paid Research
Number of openings
1
Techniques learned

A summer student would learn:

  • How to build partial differential equation (PDE) models of biological systems, specifically the interaction of foraging locusts and resources.
  • How to simulate a partial differential equation numerically (incorporating ideas for linear algebra and Fast Fourier Transforms.
  • How to validate the accuracy of a numerical code for a PDE.
  • Strategies for exploring behavior of a model with a large dimensional parameter space
  • How to develop effective visualizations and metrics of the numerical data generated.
  • Finally (if time) how to relate the parameters and behavior in the model to those observed in the field and the lab as reported in the literature and in our own studies of field data provided by our collaborator, Dr. Jerome Buhl, a locust biologist at the University of Adelaide.

 

Contact Information:
Mentor name
Andrew Bernoff
Mentor email
bernoff@g.hmc.edu
Mentor position
Professor of Mathematics
Name of project director or principal investigator
Prof. Bernoff (and Prof. Weinburd)
Email address of project director or principal investigator
bernoff@g.hmc.edu
1 sp. | 9 appl.
Hours per week
Summer - Full Time
Project categories
Mathematics (+2)
MathematicsMathematical BiologyNumerical Modeling