Seminars

Martin Luther King Day (No Seminar)

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Spring Break (No Seminar)

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Memorial Day

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Matthew Asker University of Leeds

Fixation and Extinction in Fluctuating Meta-populations with Migration Subject to Bottlenecks

Microbial populations evolve within spatially structured and dynamically changing environments, a reality often overlooked by classical modelling approaches. From microbial infections spreading across host organs to environmental pollutants altering ecological niches, understanding the effects of and interplay between spatial structure and environmental change is essential for developing insights into the evolutionary dynamics of microbial communities. Here, we present a comprehensive analysis of a two-species metapopulation model, incorporating selection bias, to investigate how microbial species evolve while competing under stochastic population bottlenecks. Our analytical framework provides insights into the long-lived behavior of the system: will we see total extinction of all species, or will a species take over and remain, and how long does this take? Additionally, stochastic simulations offer a deeper understanding of the complex dynamics on various networks, extending beyond the scope of analytical predictions where we find the qualitative behavior remains. By combining analytical and computational methodologies, we uncover the rich dynamics underlying microbial population evolution in spatially structured and dynamically changing environments.

Host: Prof. Uwe Tauber

"Labor Day" (No Seminar)

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Veterans Day

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Spring Break (No Seminar)

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Dr. Jorge Puebla /b> RIKEN

Host:Prof. Satoru Emori

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Final Exams Week (No Seminar)

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Prof. Alastair Rucklidge

University of Leeds, Germany

"Cycling behavior and spatial structure in a hetero-clinic network model of Rock-Paper-Scissors-Spock-Lizard

The well-known game of Rock-Paper-Scissors can be used as a simple model of competition between three species. When modeled in continuous time using ordinary differential equations, the resulting system contains a hetero-clinic cycle between the three equilibrium solutions that represent the existence of only a single species. The game can be extended in asymmetric fashion by the addition of two further strategies (`Spock' and `Lizard'):now each strategy is dominant over two of the other four strategies, and is dominated by the remaining two. The ODE model contains coupled hetero-clinic cycles forming a hetero-clinic network. We develop a technique, based on the concept of fragmentary asymptotic stability, to understand the stability of arbitrarily long periodic sequences of visits made to the neighborhoods of the equilibrium. The regions of stability form a complicated pattern in parameter space. By adding spatial diffusion, we extend to a partial differential equation model and investigate the spatiotemporal evolution of these periodic itineraries.

Host: Prof. Uwe Tauber