In nature, most microbial populations have complex spatial structures that can affect their evolution. Evolutionary graph theory predicts that some spatial structures modelled by placing individuals on the nodes of a graph affect the probability that a mutant will fix. Evolution experiments are beginning to explicitly address the impact of graph structures on mutant fixation. However, the assumptions of evolutionary graph theory differ from the conditions of modern evolution experiments, making the comparison between theory and experiment challenging. Here, we aim to bridge this gap by using our new model of spatially structured populations. This model considers connected subpopulations that lie on the nodes of a graph, and allows asymmetric migrations. It can handle large populations, and explicitly models serial passage events with migrations, thus closely mimicking experimental conditions. We analyze recent experiments in light of this model. We suggest useful parameter regimes for future experiments, and we make quantitative predictions for these experiments. In particular, we propose experiments to directly test our recent prediction that the star graph with asymmetric migrations suppresses natural selection and can accelerate mutant fixation or extinction, compared to a well-mixed population. Predicting how mutations spread through a population and eventually take over is important for understanding evolution. Complex spatial structures are ubiquitous in natural microbial populations, and can impact the fate of mutants. Theoretical models have been developed to describe this effect. They predict that some spatial structures have mutant fixation probabilities that differ from those of well-mixed populations. Experiments are beginning to probe these effects in the laboratory. However, there is a disconnect between models and experiments, because they consider different conditions. In this work, we connect them through a new model that closely matches experimental conditions. We analyze recent experiments and propose new ones that should allow testing the effects of complex population spatial structures on mutant fate.

In this paper an exact rejection algorithm for simulating paths of the coupled Wright- Fisher diffusion is introduced. The coupled Wright-Fisher diffusion is a family of multivariate Wright-Fisher diffusions that have drifts depending on each other through a coupling term and that find applications in the study of networks of interacting genes. The proposed rejection algorithm uses independent neutral Wright-Fisher diffusions as candidate proposals, which are only needed at a finite number of points. Once a candidate is accepted, the remainder of the path can be recovered by sampling from neutral multivariate Wright-Fisher bridges, for which an exact sampling strategy is also provided. Finally, the algorithm's complexity is derived and its performance demonstrated in a simulation study.