Using Pair Approximations to Predict Takeover Dynamics in Spatially Structured Populations
Proceedings of the 9th annual conference companion on Genetic and evolutionary computation, , 2557-2564, 2007
Abstract: The topological properties of a network directly impact the flow of information through a system. For example, in natural populations, the network of inter-individual contacts affects the rate of flow of infectious disease. Similarly, in evolutionary systems, the topological properties of the underlying population structure affect the rate of flow of genetic information, and thus affect selective pressure. One commonly employed method for quantifying the influence of the population structure on selective pressure is through the analysis of takeover time. In this study, we reformulate takeover time analysis in terms of the well-known Susceptible-Infectious-Susceptible (SIS) model of disease spread. We then adapt an analytical technique, called the pair approximation, to provide a general model of takeover dynamics. We compare the results of this model to simulation data on a total of six regular population structures and discuss the strengths and limitations of the approximation.
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Bongard's work focuses on understanding the general nature of cognition, regardless of whether it is found in humans, animals or robots. This unique approach focuses on the role that morphology and evolution plays in cognition. Addressing these questions has taken him into the fields of biology, psychology, engineering and computer science.
Danforth is an applied mathematician interested in modeling a variety of physical, biological, and social phenomenon. He has applied principles of chaos theory to improve weather forecasts as a member of the Mathematics and Climate Research Network, and developed a real-time remote sensor of global happiness using messages from Twitter: the Hedonometer. Danforth co-runs the Computational Story Lab with Peter Dodds, and helps run UVM's reading group on complexity.
Laurent studies the interaction of structure and dynamics. His research involves network theory, statistical physics and nonlinear dynamics along with their applications in epidemiology, ecology, biology, and sociology. Recent projects include comparing complex networks of different nature, the coevolution of human behavior and infectious diseases, understanding the role of forest shape in determining stability of tropical forests, as well as the impact of echo chambers in political discussions.
Hines' work broadly focuses on finding ways to make electric energy more reliable, more affordable, with less environmental impact. Particular topics of interest include understanding the mechanisms by which small problems in the power grid become large blackouts, identifying and mitigating the stresses caused by large amounts of electric vehicle charging, and quantifying the impact of high penetrations of wind/solar on electricity systems.
Bagrow's interests include: Complex Networks (community detection, social modeling and human dynamics, statistical phenomena, graph similarity and isomorphism), Statistical Physics (non-equilibrium methods, phase transitions, percolation, interacting particle systems, spin glasses), and Optimization(glassy techniques such as simulated/quantum annealing, (non-gradient) minimization of noisy objective functions).