Spatial structure in population dynamics: from individuals to populations
30 Abril 2015 ·
- Quem: Michael Raghib
- Onde: FGV - Praia de Botafogo, 190, room 317
- Quando: 30 de Abril de 2015 às 16:00h
Most models of population dynamics that deal with space explicitly, do so in terms of mean population densities (global or local);reaction-diffusion equations being a case in point. This allows modeling efforts to focus in choosing the most useful expressions for population growth and dispersal that control the dynamics of a single state variable, the mean (local or global) density. This approach implicitly assumes a fully mixed population, where all individuals interact with everyone else and thus have equal access to the uniformly distributed limiting resource. Nature, however,is diverse and heterogeneous. She always surprises us. In many cases of real populations, the different characteristic spatial scales associated with fundamental biological processes lead to spatially structured populations, characterized by clumping or (stochastic) regularity. In those cases, the mean density alone is insufficient to characterize the state of the population at any given time. In this talk I will address the problem of modeling spatially explicit populations that link the individual scale with the population via a more general set of summary statistics that keep track of spatial correlations for various higher order configurations. This will require the development of new theory, based on applications of measure-valued stochastic processes, renormalization techniques, and information theory. Future extensions of this work involve problems in epidemiology requiring the synthesis of classical mathematical modeling techniques with machine learning.
Speaker
Michael Raghib is a civil engineer, applied mathematician and theoretical ecologist interested in mathematical & computational modeling in biology and the geosciences. His work focuses on merging tools from complex systems and machine learning with classical physical modeling, and applying these tools to find solutions for real-world problems in energy, healthcare, agriculture and the environment. He is Ph.D. in Applied Mathematics at the University of Glasgow in 2006, and postdoc at Los Alamos National Laboratory. He joined IBM Research-Brazil as a Research Staff Member in the Physically-based analytics group in January 2015. His research interests include stochastic processes, complex systems, machine learning and cognitive computing. Current focus explores applications of these areas of applied mathematics and computer science to problems in applied geosciences and biology. Current research focus include problems in applied geosciences and mathematical biology.
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