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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(More)
We investigate the effects of a strong number fluctuations on traveling waves in the Fisher-Kolmogorov reaction-diffusion system. Our findings are in stark contrast to the commonly used deterministic and weak-noise approximations. We compute the wave velocity in one and two spatial dimensions, for which we find a linear and a square-root dependence of the(More)
It is widely accepted that population-genetics theory is the cornerstone of evolutionary analyses. Empirical tests of the theory, however, are challenging because of the complex relationships between space, dispersal, and evolution. Critically, we lack quantitative validation of the spatial models of population genetics. Here we combine analytics, on- and(More)
Mutualism is a major force driving evolution and sustaining ecosystems. Although the importance of spatial degrees of freedom and number fluctuations is well known, their effects on mutualism are not fully understood. With range expansions of microbes in mind, we show that, even when mutualism confers a selective advantage, it persists only in populations(More)
1 Abstract We review and extend results for mutation, selection, genetic drift, and migration in a one-dimensional continuous population. 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(More)
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(More)
Evolutionary experiments with microbes are a powerful tool to study mutations and natural selection. These experiments, however, are often limited to the well-mixed environments of a test tube or a chemostat. Since spatial organization can significantly affect evolutionary dynamics, the need is growing for evolutionary experiments in spatially structured(More)
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(More)
Slower recovery from perturbations near a tipping point and its indirect signatures in fluctuation patterns have been suggested to foreshadow catastrophes in a wide variety of systems. Recent studies of populations in the field and in the laboratory have used time-series data to confirm some of the theoretically predicted early warning indicators, such as(More)
The relationship between the host and its microbiota is challenging to understand because both microbial communities and their environments are highly variable. We have developed a set of techniques based on population dynamics and information theory to address this challenge. These methods identify additional bacterial taxa associated with pediatric Crohn(More)