BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:When Google meets Lotka-Volterra
DTSTART;VALUE=DATE-TIME:20180712T053000Z
DTEND;VALUE=DATE-TIME:20180712T060000Z
DTSTAMP;VALUE=DATE-TIME:20241113T060011Z
UID:indico-contribution-140@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Lewi Stone (RMIT/Tel Aviv University)\nIn his theore
tical work of the 70’s\, Robert May introduced a Random Matrix Theory (R
MT) approach for studying the stability of large complex biological system
s. Unlike the established paradigm\, May demonstrated that complexity lea
ds to instability in generic models of biological networks having random i
nteraction matrices A. Similar random matrix models have since been applie
d in many disciplines. Central to assessing stability is the “circular l
aw” since it describes the eigenvalue distribution for an important clas
s of random matrices\, $A$. However\, despite widespread adoption\, the
“circular law” does not apply for ecological systems in which density-
dependence operates (i.e.\, where a species growth is determined by its de
nsity). Instead one needs to study the far more complicated eigenvalue dis
tribution of the community matrix $S=DA$\, where $D$ is a diagonal matrix
of population equilibrium values. Here we obtain this eigenvalue distribut
ion. We show that if the random matrix\, $A$\, is locally stable\, the com
munity matrix\, $S=DA$\, will also be locally stable\, providing the syste
m is feasible (i.e.\, all species have positive equilibria $D>0$). This he
lps explain why\, unusually\, nearly all feasible systems studied here are
locally stable. Large complex systems may thus be even more fragile than
May predicted\, given the difficulty of assembling a feasible system. The
degree of stability\, or resilience\, was found to depend on the minimum
equilibrium population\, rather than factors such as network topology. Fo
r studying competitive and mutualistic systems\, our analysis is only achi
evable upon introducing a simplifying “Google-matrix” reduction scheme
. In this talk we will explain what happens “when Google meets Lotka-Vo
lterra.”\n\nhttps://conferences.maths.unsw.edu.au/event/2/contributions/
140/
LOCATION:University of Sydney New Law School/--104
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/140/
END:VEVENT
END:VCALENDAR