Publications and Research

Document Type


Publication Date

Summer 8-7-2015


The goal of this talk is to present a student research project in computational population biology, which aims at creating a computer simulation and animation of the spatial dynamics of interactions between two kinds of species living on a torus-shaped universe. The habitat for spatial interactions is modeled by a 2D lattice with periodic boundary conditions, which wrap the rectangular grid into a torus. The spatial interactions between the species have two components: 1. Population dynamics modeled by the classical Nicholson-Bailey two-parameter family of models for coupled interactions between species, extended to incorporate space and 2. Two-parameter migration dynamics, modeled by the weighted average of the current population density and the average inflow of migrating species from the nearest 8-neighbor migration zone, applied to any given cell in the inner core of the grid (inside the reflecting boundary layer). All simulations are coded using the high-level programming language R, which allows for very compact code that can be quickly developed by using functional, matrix-based, programing. This programming approach allows the entire model dynamics to be coded in less than 50 lines of code, making it ideal for student projects. The main goal of the student research project is to create a video, animating the spatial interactions between the two species living on a torus, based on the given population and migration dynamics, initial conditions and parameter values. The resulting beautiful spatial wave patterns, produced by the interfering waves of the spatial population density, visualize the fluctuating abundance of the species in their torus-shaped universe over time.

This is an html presentation, as given at the MAA MathFest 2015. We also provide an additional pdf document that contains the model animation. The pdf must be opened in Adobe Acrobat Reader for the animation to run. Preview on the Mac will not run the animation since it is not JavaScript enabled.


This presentation was given at the MAA MathFest 2015 in Washington DC, on August 7, 2015.

To advance the html version of the presentation in your browser, use the up and down arrows or pageup or pagedown buttons.

Two different .pdf versions are attached as a supplement. The second .pdf has video embedded.

MAA_MathFest2015_BK_Presentation.pdf (1244 kB)
.pdf of presentation

VideoPDFMAAMathFest2015.pdf (152 kB)
.pdf with embedded video