Theory predicts that the approach of catastrophic thresholds in natural systems (e.g., ecosystems, the climate) may result in an increasingly slow recovery from small perturbations, a phenomenon called critical slowing down. We used replicate laboratory populations of the budding yeast Saccharomyces cerevisiae for direct observation of critical slowing down before population collapse. We mapped the bifurcation diagram experimentally and found that the populations became more vulnerable to disturbance closer to the tipping point. Fluctuations of population density increased in size and duration near the tipping point, in agreement with the theory. Our results suggest that indicators of critical slowing down can provide advance warning of catastrophic thresholds and loss of resilience in a variety of dynamical systems.

Results for mutation, selection, genetic drift, and migration in a one-dimensional continuous population are reviewed and extended. The population is described by a continuous limit of the stepping stone model, which leads to the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation with additional terms describing mutations. Although the stepping stone model was first proposed for population genetics, it is closely related to "voter models" of interest in nonequilibrium statistical mechanics. The stepping stone model can also be regarded as an approximation to the dynamics of a thin layer of actively growing pioneers at the frontier of a colony of micro-organisms undergoing a range expansion on a Petri dish. The population tends to segregate into monoallelic domains. This segregation slows down genetic drift and selection because these two evolutionary forces can only act at the boundaries between the domains; the effects of mutation, however, are not significantly affected by the segregation. Although fixation in the neutral well-mixed (or "zerodimensional") model occurs exponentially in time, it occurs only algebraically fast in the onedimensional model. An unusual sublinear increase is also found in the variance of the spatially averaged allele frequency with time. If selection is weak, selective sweeps occur exponentially fast in both well-mixed and one-dimensional populations, but the time constants are different. The relatively unexplored problem of evolutionary dynamics at the edge of an expanding circular colony is studied as well. Also reviewed are how the observed patterns of genetic diversity can be used for statistical inference and the differences are highlighted between the well-mixed and one-dimensional models. Although the focus is on two alleles or variants, q-allele Potts-like models of gene segregation are considered as well. Most of the analytical results are checked with simulations and could be tested against recent spatial experiments on range expansions of inoculations of Escherichia coli and Saccharomyces cerevisiae.

Cancer progression is driven by the accumulation of a small number of genetic alterations. However, these few driver alterations reside in a cancer genome alongside tens of thousands of additional mutations termed passengers. Passengers are widely believed to have no role in cancer, yet many passengers fall within protein-coding genes and other functional elements that can have potentially deleterious effects on cancer cells. Here we investigate the potential of moderately deleterious passengers to accumulate and alter the course of neoplastic progression. Our approach combines evolutionary simulations of cancer progression with an analysis of cancer sequencing data. From simulations, we find that passengers accumulate and largely evade natural selection during progression. Although individually weak, the collective burden of passengers alters the course of progression, leading to several oncological phenomena that are hard to explain with a traditional driver-centric view. We then tested the predictions of our model using cancer genomics data and confirmed that many passengers are likely damaging and have largely evaded negative selection. Finally, we use our model to explore cancer treatments that exploit the load of passengers by either (i) increasing the mutation rate or (ii) exacerbating their deleterious effects. Though both approaches lead to cancer regression, the latter is a more effective therapy. Our results suggest a unique framework for understanding cancer progression as a balance of driver and passenger mutations.

The fight against cancer has drawn researchers from a wide variety of disciplines, ranging from molecular biology to physics, but the perspective of an ecological theorist has been mostly overlooked. By thinking about the cells that make up a tumour as an endangered species, cancer vulnerabilities become more apparent. Studies in conservation biology and microbial experiments indicate that extinction is a complex phenomenon, which is often driven by the interaction of ecological and evolutionary processes. Recent advances in cancer research have shown that tumours, like species striving for survival, harbour intricate population dynamics, which suggests the possibility to exploit the ecology of tumours for treatment.