I am an applied mathematician. My research is largely concerned with the development and analysis of mathematical models that capture and make accessible important aspects of physical systems. Most of my work is inspired by biology.
Current and ongoing projects
Persistence of cooperation
Why do we (or any living organisms) cooperate? Cooperation, the act of expending one's own energy or resources for the good of the group, is a necessary part of life, but is also exploitable by so-called "free-loaders" who choose not to help out yet still reap the benefits that cooperation yields. In fact, under fairly general assumptions, every rational individual will (theoretically) choose to defect, thereby extinguishing cooperation and dooming society. Of course, cooperation has not been extinguished and is in fact quite common in the natural world. This observation brings us back to the question at the beginning of this paragraph. With Andrew Belmonte, we are investigating the cooperation-stabilizing effects of migration on networks in which individuals face an ecological public goods dilemma. You can find our first paper on the subject below.
G. Young and A. Belmonte, "Fast cheater migration stabilizes coexistence in a public
goods dilemma on networks" Theoretical Population Biology 121, 12-25 (2018) pdf
Bacterial collective behavior and pulse interaction
Collective behavior of cellular species that move by chemical sensing, or chemotaxis, (e.g., E. coli, slime mold) is a classic area of mathematical study, revolutionized in 1970 by Evelyn Keller and Lee Segel's partial differential equations model for cellular aggregation, now known as the Keller-Segel model. Along with Hanna Salman, Jonathan Rubin , and Bard Ermentrout , we use the Keller-Segel model to study the interaction of two bacterial pulses in a one-dimensional nutrient gradient. Simulations predict that as the two pulses approach one another, they either combine and move as a single pulse or, anomalously, change direction and begin moving away from each other in the direction from which they originated. To study this phenomenon, we introduced a heuristic approximation to the spatial profiles of the pulses in the Keller-Segel model and derive a system of ordinary differential equations approximating the dynamics of the pulse centers of mass and widths. Our approximation simplifies analysis of the global dynamics of the bacterial system and allows us to efficiently explore qualitative behavior changes under a range of parameter variations. Experiments from Hanna Salman's lab support our theoretical predictions.
G Young, M Demir, H Salman, GB Ermentrout, JE Rubin. "Interactions of Solitary Pulses
of E. coli in a One-Dimensional Nutrient Gradient" Physica D: Nonlinear Phenomena 395, 24-36 (2019)
I am currently investigating the interaction of two bacterial pulses with Lotka-Volterra
competitive dynamics. Under fairly general parameter conditions, the ''space-free''
Lotka-Volterra competition model predicts that one population will necessarily outcompete
the other, driving that population to extinction. Under the same parameter conditions,
two competitive species that move according to Keller-Segel dynamics can coexist.
In this way, chemotaxis stabilizes coexistence. This work is ongoing with Jeremy Mysliwiec,
an undergraduate student at Penn State.
With Andrew Belmonte, I am currently investigating fixation probabilities in stochastic competition models with fluctuating population sizes. Classic work in the area typically assumes a constant (total) population size, say N, allowing two competitive species' respective sizes, N1 and N2, to be given by proportions x=N1/N and 1-x=N2/N, thus reducing the stochastic process to a single stochastic variable. Determining fixation probabilities is thereby greatly simplified. I recently derived a novel approximation to the probability of fixation in the stochastic Lotka-Volterra competition model that agrees quite well with simulations. I am currently using this approximation to study competitive trade-offs (for example, increased reproduction rate at a cost of reduced competitive fitness).
Ryan Murray and I are currently investigating the effects of periodic fitness fluctuations
in a Wright-Fisher-type model.
With Jonathan Rubin and Bard Ermentrout, I analyzed the within-host competition dynamics between Salmonella Typhimurium and the native gut bacteria. S. Typhimurium invades the gut in two distinct phenotypic populations, one fast-growing and avirulent, the other slow-growing and virulent. Somehow, invading with a combination of these two phenotypes provides the species with an environmental advantage over the host's gut bacteria that neither phenotype enjoys if invading by itself. We derived and analyzed a system of ordinary differential equations that combines a Lotka-Volterra-like competition model with a simple model of the host's immune response, and show that our model captures important aspects of the competition. We then use our model to make predictions about optimal invasion strategies.
G. Young, B Ermentrout, JE Rubin. "A Boundary Value Approach to Optimization with
an Application to Salmonella Competition" Bulletin of Mathematical Biology 77 (7), 1327-1348 (2015) preprint pdf
Rotavirus transmission and vaccination
With Eunha Shim and Bard Ermentrout, I explored the effects of a monovalent vaccination on the transmission of multiple strains of rotavirus. We found conditions under which major-strain replacement is a likely consequence of vaccine introduction.
G. Young, E Shim, GB Ermentrout. "Qualitative effects of monovalent vaccination against
rotavirus: a comparison of North America and South America" Bulletin of Mathematical Biology 77 (10), 1854-1885 (2015) preprint pdf