Populations and Evolution (q-bio.PE)

Abstract: 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 {\it fitness proportional} selection, but other fitness schemes are conceivable as well. Inspired by the work of Etheridge et al. ([EPW09]) we propose a parameter scaling which fits well to the ``near-critical'' regime that was in the focus of [EPW09] (and in which the mutation-selection ratio diverges logarithmically as $N\to \infty$). Using a Moran model, we investigate the``rule of thumb'' given in [EPW09] 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, which (other than that of the classical ratchet) follows an autonomous dynamics up to the time of its extinction. In [GSW23] it was discovered that the tournament ratchet has a hierarchy of dual processes which can be constructed on top of an Ancestral Selection graph with a Poisson decoration. For a regime in which the mutation/selection-ratio remains bounded away from 1, this was used in [GSW23] to reveal the asymptotics of the click rates as well as that of the type frequency profile between clicks. We will describe how these ideas can be extended to the near-critical regime in which the mutation-selection ratio of the tournament ratchet converges to 1 as $N\to \infty$.

Abstract: Digital contact tracing/notification was initially hailed as a promising strategy to combat SARS-CoV-2, but in most jurisdictions it did not live up to its promise. To avert a given transmission event, both parties must have adopted the tech, it must detect the contact, the primary case must be promptly diagnosed, notifications must be triggered, and the secondary case must change their behavior to avoid the focal tertiary transmission event. Achieving a 26% reduction in R(t) requires 80% success rates at each of these six points of failure. Here we review the six failure rates experienced by a variety of digital contact tracing/notification schemes, including Singapore's TraceTogether, India's Aarogya Setu, and leading implementations of the Google Apple Exposure Notification system. This leads to a number of recommendations, e.g. that tracing/notification apps be multi-functional and integrated with testing, manual contact tracing, and the gathering of critical scientific data, and that the narrative be framed in terms of user autonomy rather than user privacy.