Mathematical Biology Seminar - Spring 2025

For questions about the seminar schedule, please contact James MacLaurin.

February 12

Dirk Bucher, NJIT

Consistency vs. flexibility: Convergent co-modulation decreases inter-individual variability and increases intra-individual similarity of neural circuit activity

Neural circuits are always under the influence of multiple neuromodulators that tune synaptic interactions and neuronal excitability. Therefore, neuromodulation is thought to be at the core of the nervous system’s ability to produce different versions of activity to adapt to different behavioral needs. As such, different neuromodulators are often associated with different behavioral contexts and co-modulation with multiple signaling molecules is thought to vastly expand the repertoire of possible circuit states. However, different modulators can have overlapping cellular and subcellular targets, and thus convergence and occlusion may limit that repertoire.

Our experimental data from recordings of rhythmic motor activity in the crustacean stomatogastric nervous system shows that convergent co-modulation with different neuropeptides results in consistent circuit activation that, with increasing numbers of modulators, becomes less dependent on the specific identity of the modulators involved. In addition, we show that convergent co-modulation reduces variability across individuals, i.e., co-modulation increases consistency of circuit activation at the population level. Both results do not contradict the notion of neuromodulation as key to neural flexibility but rather suggest a push-pull mechanism between converging and diverging cellular effects that promotes both flexibility and stability.

I will present some of our experimental results and discuss theoretical and mathematical considerations of possible underlying mechanisms.

February 19

Nir Gavish, Technion Israel Institute of Technology

Challenging Conventional Epidemiological Theories: Coexistence and Oscillations in Multi-Strain Epidemic

During the COVID-19 pandemic, variants constantly emerged and interacted with existing ones. Our data-driven research showed that a variant with a basic reproduction number as high as 10 can defy conventional theory. Motivated by this, the talk will present two works on the dynamics of epidemic systems with two strains that provide partial cross-immunity to each other.

In the first part, we challenge the validity of the exclusion principle at a limit in which one strain has a vast competitive advantage over the other strains.  We show that when one strain is significantly more transmissible than the other, an epidemic system with partial cross-immunity can reach a stable endemic equilibrium in which both strains coexist with comparable prevalence.  Thus, the competitive exclusion principle does not always apply.

The second part explores conditions under which a two-strain epidemic model with partial cross-immunity can lead to self-sustained oscillations. Contrary to previous findings, our results indicate that oscillations can occur even with weak cross-immunity and weak asymmetry. Using asymptotic methods, we reveal that the steady state of coexistence becomes unstable near specific curves in the parameter space, leading to oscillatory solutions for any basic reproduction number greater than one. Numerical simulations support our theoretical findings, highlighting an unexpected oscillatory region.

February 26

Toshiyuki Ogawa, Meiji University

Pattern dynamics appearing on compact metric graph

The study of reaction-diffusion equations on metric graphs has been drawing attention recently. Here, we focus on pattern dynamics on compact metric graphs. We consider systems of reaction-diffusion equations on compact metric graphs with natural boundary conditions, namely, Neumann‒Kirchhoff conditions. Suppose additionally the system has Turing or Wave instability. Then, we may see pattern onsets depending on the lengths of the edges. By using the normal form analysis and symmetry arguments we study the local bifurcation structures around the bifurcation points.

This talk is based on the ongoing joint work between Shunsuke Kobayashi(Miyazaki University) and Takashi Sakamoto(Meiji University).

March 12

Denis Patterson, Durham University

Spatial models of forest-savanna bistability

Empirical studies suggest that for vast tracts of land in the tropics, closed-canopy forests and savannas are alternative stable states, a proposition with far-reaching implications in the context of ongoing climate change. Consequently, numerous spatially implicit and explicit mathematical models have been proposed to capture the mechanistic basis of this bistability and quantify the stability of these ecosystems. We present an analysis of a spatially extended version of the so-called Staver-Levin model of forest-savanna dynamics (a system of nonlinear partial integro-differential equations). On a homogeneous domain, we uncover various types of pattern-forming bifurcations in the presence of resource limitation, which we study as a function of the resource constraints and length scales in the problem. On larger (continental) spatial scales, heterogeneity plays a significant role in determining observed vegetative cover. Incorporating domain heterogeneity leads to interesting phenomena such as front-pinning, complex waves, and extensive multi-stability, which we investigate analytically and numerically.

March 26

Joshua Meisel, The City University of New York (CUNY)

Cutoff for activated random walk

Self-organized criticality (SOC) is an influential theory that explains how critical behavior, like that seen in lab-tuned phase transitions, occurs throughout nature despite no apparent external tuning. The originally proposed model for SOC, the abelian sandpile, was gradually disqualified primarily due to slow mixing. Activated random walk (ARW) is a stochastic variant of the abelian sandpile conjectured to remedy this and other issues. We prove that ARW on an interval mixes as desired in a model of SOC; it exhibits cutoff at a time proportional to the critical density for ARW on Z. Based on joint work with Chris Hoffman, Toby Johnson and Matt Junge.

April 2

Evelyn Sander, George Mason University (GMU)

Computing Manifolds for Billiard Maps on Perturbed Elliptical Tables

Dynamical billiards consist of a particle on a two-dimensional table, bouncing elastically each time it hits the boundary. The successive bounce location plus bounce angle forms a two-dimensional iterated map, which was first studied by Birkhoff. I will give a general introduction to the theory of dynamical billiards, accessible to a general audience.

One notable shape of a billiard table is that of an ellipse, in which case the dynamics of billiard maps are completely integrable, meaning that all orbits are ordered and no chaos occurs. The Birkhoff conjecture is a long standing conjecture that elliptical tables are the only smooth convex table for which complete integrability occurs. In this spirit,   my current research focuses on perturbed elliptical tables. I will describe an implicit real analytic method for billiard maps on. This method allows us to compute stable and unstable manifolds using the parametrization method. While the results as yet are numerical only, our method is devised so it can in future be validated.  This is joint work with Patrick Bishop, George Mason University and Jay Mireles James, Florida Atlantic University

April 16

Pejman Sanaei, Georgia State University

Title/Abstract Forthcoming

April 23

Sungsik Kong, ICERM/Brown University

Towards the Network of Life: Inferring Phylogenetic Networks in the Genomic Era

While phylogenetic trees—branching diagrams that depict the evolutionary history of different organisms—have been essential for understanding species evolution, they do not fully capture certain evolutionary processes, such as hybridization. In these cases, a phylogenetic network, which extends a phylogenetic tree by allowing two branches to merge into one and create reticulations, is needed. However, existing methods for estimating networks from genomic data become computationally prohibitive as dataset size and topological complexity increase. In this talk, I present the performance of popular computational methods that detect hybridization from genomic data as an alternative to the network inference, discussing their significance and limitations. I then explain how phylogenetic networks generalize trees to represent complex evolutionary histories and explore the biological interpretations that can be drawn from various branching patterns. Finally, I introduce PhyNEST (Phylogenetic Network Estimation using SiTe patterns), a novel method that efficiently and accurately infers phylogenetic networks directly from sequence data using composite likelihood. PhyNEST is implemented as an open-source Julia package and is available at https://github.com/sungsik-kong/PhyNEST.jl.

April 30

Jana Gevertz, The College of New Jersey

Title/Abstract Forthcoming

Last Updated: March 31, 2025