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DTSTAMP:20210510T141913Z
DTSTART:20210512T090000Z
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SUMMARY:Lewi Stone -- Random matrices\, biological networks\, and the sta
bility of complex systems
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DESCRIPTION:(via Zoom)\nJoin us for this seminar by Lewi Stone (Melbourne
) as part of the North West Seminar Series in Mathematical Biology and D
ata Sciences. Details of the full series can be found here https://www.c
ms.livjm.ac.uk/APMSeminar/\n\nPlease contact carl.whitfield@manchester.a
c.uk or i.siekmann@ljmu.ac.uk for the zoom link\, or sign up to the mail
ing list.\n\nAbstract: In his theoretical work of the 70’s\, Robert May
introduced “random matrix” theory for studying the stability of large co
mplex biological systems. In contrast to the established paradigm\, May
demonstrated that complexity leads to instability in generic models of b
iological networks having random interaction matrices. Similar analyses
have since appeared in many other disciplines. The “circular law” is cen
tral to assessing stability since it describes the eigenvalue distributi
on for an important class of random matrices\, A. However\, despite its
widespread adoption\, the “circular law” does not apply for the many eco
logical systems in which density-dependence operates (i.e.\, where a spe
cies growth is determined by its density). Instead one needs to study th
e far more complicated eigenvalue distribution of the community matrix S
=DA\, where D is a diagonal matrix of population equilibrium values. Her
e we obtain this eigenvalue distribution in the complex plane and discus
s its consequences\, thereby helping to explain why feasible systems are
often stable.\n\nParticular attention will be paid to state-of-the-art
modelling studies of mutualism\, ranging from plant and animal interacti
ons down to the human microbiome. Mathematical biologists have long port
rayed mutualism as destabilizing leading to exponentially growing popula
tions proliferating in an “orgy of mutual benefaction.” In contrast\, co
mpetition is invariably found stabilizing. Recently\, key theoretical st
udies have used random matrix analysis\, only to further corroborate the
instability of mutualism. Here I reassess these findings to show that c
ooperation and mutualism\, which are observed in nearly all living syste
ms\, can indeed be powerful and positive organizing forces.\n\nTo subscr
ibe to the mailing list for this event series\, please send an e-mail wi
th the phrase “subscribe math-lifesci-seminar” in the message body to li
stserv@listserv.manchester.ac.uk
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