Phase transitions in evolutionary dynamics.

Sharp changes in state, such as transitions from survival to extinction, are hallmarks of evolutionary dynamics in biological systems. These transitions can be explored using the techniques of statistical physics and the physics of nonlinear and complex systems. For example, a survival-to-extinction transition can be characterized as a non-equilibrium phase transition to an absorbing state. Here, we review the literature on phase transitions in evolutionary dynamics. We discuss directed percolation transitions in cellular automata and evolutionary models, and models that diverge from the directed percolation universality class. We explore in detail an example of an absorbing phase transition in an agent-based model of evolutionary dynamics, including previously unpublished data demonstrating similarity to, but also divergence from, directed percolation, as well as evidence for phase transition behavior at multiple levels of the model system's evolutionary structure. We discuss phase transition models of the error catastrophe in RNA virus dynamics and phase transition models for transition from chemistry to biochemistry, i.e., the origin of life. We conclude with a review of phase transition dynamics in models of natural selection, discuss the possible role of phase transitions in unraveling fundamental unresolved questions regarding multilevel selection and the major evolutionary transitions, and assess the future outlook for phase transitions in the investigation of evolutionary dynamics.

Phase transition behaviour in yeast and bacterial populations under stress.

Non-equilibrium phase transitions from survival to extinction have recently been observed in computational models of evolutionary dynamics. Dynamical signatures predictive of population collapse have been observed in yeast populations under stress. We experimentally investigate the population response of the budding yeast Saccharomyces cerevisiae to biological stressors (temperature and salt concentration) in order to investigate the system's behaviour in the vicinity of population collapse. While both conditions lead to population decline, the dynamical characteristics of the population response differ significantly depending on the stressor. Under temperature stress, the population undergoes a sharp change with significant fluctuations within a critical temperature range, indicative of a continuous absorbing phase transition. In the case of salt stress, the response is more gradual. A similar range of response is observed with the application of various antibiotics to Escherichia coli, with a variety of patterns of decreased growth in response to antibiotic stress both within and across antibiotic classes and mechanisms of action. These findings have implications for the identification of critical tipping points for populations under environmental stress.