Evolutionary Game Theory: Theoretical Concepts and Applications to Microbial Communities

Ecological systems are complex assemblies of large numbers of
individuals, interacting competitively under multifaceted
environmental conditions. Recent studies using microbial laboratory
communities have revealed some of the self-organization principles
underneath the complexity of these systems. A major role of the
inherent stochasticity of its dynamics and the spatial segregation
of different interacting species into distinct patterns has thereby
been established. It ensures the viability of microbial colonies by
allowing for species diversity, cooperative behavior and other
kinds of “social” behavior. A synthesis of evolutionary game
theory, nonlinear dynamics, and the theory of stochastic processes
provides the mathematical tools and a conceptual framework for a
deeper understanding of these ecological systems. We give an
introduction into the modern formulation of these theories and
illustrate their effectiveness focussing on selected examples of
microbial systems. Intrinsic fluctuations, stemming from the
discreteness of individuals, are ubiquitous, and can have an
important impact on the stability of ecosystems. In the absence of
speciation, extinction of species is unavoidable. It may, however,
take very long times. We provide a general concept for defining
survival and extinction on ecological time-scales. Spatial degrees
of freedom come with a certain mobility of individuals. When the
latter is sufficiently high, bacterial community structures can be
understood through mapping individual-based models, in a continuum
approach, onto stochastic partial differential equations. These
allow progress using methods of nonlinear dynamics such as
bifurcation analysis and invariant manifolds. We conclude with a
perspective on the current challenges in quantifying bacterial
pattern formation, and how this might have an impact on fundamental
research in non-equilibrium physics.