MS03 - ECOP-2
Brutus Buckeye Room (#3044) in The Ohio Union

Modeling and Analysis of Evolutionary Dynamics Across Scales and Areas of Application

Tuesday, July 18 at 10:30am

SMB2023 SMB2023 Follow Tuesday during the "MS03" time block.
Room assignment: Brutus Buckeye Room (#3044) in The Ohio Union.
Note: this minisymposia has multiple sessions. The other session is MS04-ECOP-2 (click here).

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Daniel Cooney, Olivia Chu


The dynamics of evolution shape the natural world across all scales, from the evolution of multicellularity to the formation of complex human and animal societies. In this session, we aim to highlight recent work on the mathematical modeling of evolutionary dynamics, bringing together researchers focused both on mathematical and biological developments in evolutionary game theory and population genetics and mathematical modelers tackling problems in biological and cultural evolution. The talks in our session will focus on applications ranging from the evolution of treatment-resistant cancers to the spatial evolution of invasive species to mutualism within and across species, while mathematical approaches will range from stochastic processes and network models for social interactions in finite populations to the derivation and analysis of ODEs and PDEs in mean-field models.

Anuraag Bukkuri

Moffitt Cancer Center (Integrated Mathematical Oncology)
"Evolution of Resistance in Structured Neuroblastoma Populations"
Neuroblastoma is a pediatric brain cancer of variable clinical presentation. The causes behind the initiation, progression, and ultimate resistance of this cancer is unknown, though it is recognized that two cellular phenotypes underpin its deadliness: adrenergic (ADRN) and mesenchymal (MES). How these phenotypes influence the eco-evolutionary dynamics of neuroblastoma cell populations (especially under therapy) remains a mystery. This is due to the confu- sion surrounding whether the ADRN and MES phenotypes represent different cell types (species) or cell states (stages in the life cycle of a single species). This distinction is critical in understanding and ultimately treating neuroblas- toma. In this talk, we will introduce theoretical methods to model the eco- evolutionary dynamics in state-structured neuroblastoma populations and use these models to tease apart cell type vs. cell state hypotheses. We will then expand and generalize this framework to continuous-structured models and discuss implications for cancer and bacterial resistance more generally.
Additional authors: Stina Andersson, Sofie Mohlin

Olivia J. Chu

Dartmouth College (Mathematics)
"An Evolutionary Game Theory Model of Altruism via Arrhenotoky"
Arrhenotoky is a unique biological mechanism in which unfertilized eggs give rise to haploid male offspring, while fertilized eggs give rise to diploid female offspring. In this work, we build a mathematical model for the arrhenotoky replicator dynamics of a beehive by adopting an evolutionary game theory framework. Using this model, we investigate the evolution of altruistic behavior in a beehive, looking particularly at hive success over a variety of parameters, controlling for altruism in workers and the queen. We find that the most reproductively successful hives have completely altruistic workers that donate all of their resources to the queen, as well as a somewhat altruistic queen that donates a small proportion of her resources to drone bees. Through these results, our model explains in part the evolutionary adoption of altruistic behavior by insects with arrhenotoky reproductive dynamics.
Additional authors: Zachary Nathan

Nicole Creanza

Vanderbilt University (Department of Biological Sciences)
"Modeling and analysis of cultural evolution: insights from humans and birds"
Cultural traits—behaviors that are learned from others—can change more rapidly than genes and can be inherited not only from parents but also from teachers and peers. How does this complex process of cultural evolution differ from and interact with genetic evolution? In this talk, I will discuss the dynamics of culturally transmitted behaviors on dramatically different evolutionary timescales: the learned songs of a family of songbirds and the spoken languages of modern human populations. Both of these behaviors enable communication between individuals and facilitate complex social interactions that can affect genetic evolution. My lab's work on models and analyses of these two systems demonstrate that learned behaviors, while less conserved than genetic traits, can retain evolutionary information across great distances and over long timescales.

Wai-Tong (Louis) Fan

Indiana University (Mathematics)
"Stochastic waves on metric graphs and their genealogies"
Stochastic reaction-diffusion equations are important models in spatial population genetics and ecology. These equations arise as the scaling limit of discrete systems such as interacting particle models, and so they are robust against model perturbation. In this talk, I will discuss methods to compute the probability of extinction, the quasi-stationary distribution, the asymptotic speed and other long-time behaviors for stochastic reaction-diffusion equations of Fisher-KPP type. Importantly, we consider these equations on general metric graphs that flexibly parametrize the underlying space. This enables us to not only bypass the ill-posedness issue of these equations in higher dimensions, but also assess the impact of space and stochasticity on the coexistence and the genealogies of interacting populations.
Additional authors: Rick Durrett (Duke), Wenqing Hu (Missouri), Greg Terlov (UIUC), Johnny Yang (Indiana), John Yin (UW-Madison)

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Annual Meeting for the Society for Mathematical Biology, 2023.