Lecturer: Prof. Yoram Louzoun
Affiliation: Department of Mathematics,
Bar-Ilan University
Abstract:
Cooperative interactions, their stability and
evolution, provide an interesting context in
which to study the interface between cellular
and population levels of organization. Such
interactions also open the way for the
discovery of new population dynamics
mechanisms.
We have studied a version of the public
goods model relevant to microorganism
populations actively extracting a growth
resource from their environment. Cells can
display one of two phenotypes – a
productive phenotype that extracts the
resources at a cost, and a non-productive
phenotype that only consumes the same
resource. We analyze the continuous
differential equation model as well as
simulate the full stochastic dynamics. It is
found that the two sub-populations, which
cannot coexist in a well-mixed environment,
develop spatio-temporal patterns that enable
long-term coexistence in the shared
environment. These patterns are solely
fluctuation-driven, since the continuous
system does not display Turing instability.
The average stability of the coexistence
patterns derives from a dynamic mechanism
in which one sub-population holds the
environmental resource close to an
extinction transition of the other, causing it
to constantly hover around its critical
transition point, forming a mechanism
reminiscent of self-organized criticality.
Accordingly, power-law distributions and
long-range correlations are found.
When a time scale separation occurs
between two dynamic parameters is defined,
a structurally unstable point emerges and
any small perturbation of the dynamics with
additive noise leads to an equilibrium
distribution in which both species coexist in
context of additive but not multiplicative
noise.