Research
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.
Research areas
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.
Ecological competition
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
Past projects
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
