Reply to: Evolutionary rescue effect can disappear under non-neutral mutations—a reply to Zhang et al. (2022)

In their comment, Hinsch et al. raise two concerns regarding our recent paper1. Epidemic spreading under mutually independent intra- and inter-host pathogen evolution, published in the October 2022 edition of Nature Communications: (i) Model assumptions. While our paper focuses on neutral intra-host evolutionary dynamics ( ), they argue that it is more realistic to assume that mutations are, on average, deleterious. In our formulation this maps to adding a negative drift to the effective random walk in fitness space. (ii) Results. The comment then proceeds to report that when such negative drift is introduced, the effect of our predicted mutation-driven phase is suppressed, and rather quickly, it ceases to exist altogether. Below we address both issues in detail, but first let us cut to the bottom line. Regarding (i), while a negative mutation fitness bias is certainly an important factor, we reject the notion that it is necessarily more realistic. To the best of our knowledge, the question whether mutations are neutral or negatively biased simply lacks one clear answer, and both assumptions are equally realistic, depending on the specific context. Most crucially, our modeling framework is agnostic to this discussion, and can be applied under negative, zero or positive , as needed. This flexibility is clearly demonstrated by the Matters Arising itself, which, indeed, used our formulation to simulate the case of mean-deleterious mutations. As for item (ii), the Authors’ implementation of their proposed negative drift is not fully consistent with our proposed modeling framework, and therefore gives the impression that even the slightest deviation from neutrality eliminates the mutation-driven phase. This, we believe is unrealistic, and as we show, there is, in fact a significant window in which we continue to observe our mutation-driven phase, even under a mean-deleterious mutation regime. It is precisely within this window that we focus our results.