Diffusion approximations in population genetics and the rate of Muller's ratchet

Mutant fate in spatially structured populations on graphs: Connecting models to experiments

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.

Muller's ratchet in a near-critical regime: Tournament versus fitness proportional selection

Muller's ratchet, in its prototype version, models a haploid, asexual population whose size N is constant over the generations. Slightly deleterious mutations are acquired along the lineages at a constant rate, and individuals carrying less mutations have a selective advantage. The classical variant considers fitness proportional selection, but other fitness schemes are conceivable as well. Inspired by the work of Etheridge et al. (2009) we propose a parameter scaling which fits well to the "near-critical" regime that was in the focus of Etheridge et al. (2009) (and in which the mutation-selection ratio diverges logarithmically as N→∞). Using a Moran model, we investigate the"rule of thumb" given in Etheridge et al. (2009) for the click rate of the "classical ratchet" by putting it into the context of new results on the long-time evolution of the size of the best class of the ratchet with (binary) tournament selection. This variant of Muller's ratchet was introduced in González Casanova et al. (2023), and was analysed there in a subcritical parameter regime. Other than that of the classical ratchet, the size of the best class of the tournament ratchet follows an autonomous dynamics up to the time of its extinction. It turns out that, under a suitable correspondence of the model parameters, this dynamics coincides with the so called Poisson profile approximation of the dynamics of the best class of the classical ratchet.

Operator model for evolutionary dynamics

Drift, selection, and mutation are integral evolutionary factors. In this article, operator model is newly suggested to intuitively represent those evolutionary factors into mathematical operators, and to ultimately offer unconventional methodology for understanding evolutionary dynamics. To be specific, each of the drift, selection, and mutation was respectively interpreted as operator which in essence is a random matrix that acts upon the vector which contains population distribution information. The simulation results from the operator model coincided with the previous theoretical results for beneficial mutation accumulation rate in concurrent and successional regimes for asexually reproducing case. Furthermore, beneficial mutation accumulation in strong drift regime for asexually reproducing case was observed from the simulation while allowing the interactions of mutations with diverse selection coefficients. Lastly, methods to justify, reinforce, apply, and expand the operator model were discussed to scrutinize the implications of the model. With the operator model's unique characteristics, the model is expected to broaden perspective and to offer effective methodology for understanding the evolutionary process.