Lewi Stone -- Random matrices, biological networks, and the stability of complex systems
|Dates:||12 May 2021|
|Times:||10:00 - 11:00|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
|Who is it for:||University staff, External researchers, Current University students|
Join us for this seminar by Lewi Stone (Melbourne) as part of the North West Seminar Series in Mathematical Biology and Data Sciences. Details of the full series can be found here https://www.cms.livjm.ac.uk/APMSeminar/
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Abstract: In his theoretical work of the 70’s, Robert May introduced “random matrix” theory for studying the stability of large complex biological systems. In contrast to the established paradigm, May demonstrated that complexity leads to instability in generic models of biological networks having random interaction matrices. Similar analyses have since appeared in many other disciplines. The “circular law” is central to assessing stability since it describes the eigenvalue distribution for an important class of random matrices, A. However, despite its widespread adoption, the “circular law” does not apply for the many ecological systems in which density-dependence operates (i.e., where a species growth is determined by its density). Instead one needs to study the far more complicated eigenvalue distribution of the community matrix S=DA, where D is a diagonal matrix of population equilibrium values. Here we obtain this eigenvalue distribution in the complex plane and discuss its consequences, thereby helping to explain why feasible systems are often stable.
Particular attention will be paid to state-of-the-art modelling studies of mutualism, ranging from plant and animal interactions down to the human microbiome. Mathematical biologists have long portrayed mutualism as destabilizing leading to exponentially growing populations proliferating in an “orgy of mutual benefaction.” In contrast, competition is invariably found stabilizing. Recently, key theoretical studies have used random matrix analysis, only to further corroborate the instability of mutualism. Here I reassess these findings to show that cooperation and mutualism, which are observed in nearly all living systems, can indeed be powerful and positive organizing forces.
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Organisation: Royal Melbourne Institute of Technology (RMIT)
Biography: Lewi Stone has spent his research career innovating at the interface of mathematics, ecology, biology and the environmental sciences. Having trained at Monash University (Melbourne), with a PhD focusing on biomathematics, Stone gained postdoctoral experience in theoretical biology at the University of Melbourne (epidemiology), and the Weizmann Institute. This was followed by twenty years at Tel Aviv University (TAU), where he directed a BioMathematical Unit. In the main, Stone uses nonlinear dynamical systems approaches for studying epidemics and devastating pandemic scenarios, population dynamics and anything he can that connects with biology. Currently Stone is on the staff in the Math department at RMIT University (Melbourne).
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