Document: In this implementation, two categories of sites were assumed, those for which ω neg ≤ 1, in 149 . CC-BY-NC-ND 4.0 International license is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/539239 doi: bioRxiv preprint 8 proportion p, and those for which ω pos > 1, that are under positive selection, in propor-150 tion 1 − p. Evidence for selection was derived by means of a likelihood ratio test between 151 this model, and a null model where ω pos was constrained to take its value between 0 152 and 1. Linear models were fitted through robust regressions Yohai et al. (1991) . All R 153 scripts and HyPhy source files are available from https://github.com/sarisbro (file 154 "API scripts.zip," in "data"). The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/539239 doi: bioRxiv preprint our original hypothesis, there were no differences between dsDNA and dsRNA viruses 176 (X 2 = 0.26, df = 1, P = 0.6110), or between ssDNA and ssRNA viruses in terms of 177 prevalence of diversifying selection (X 2 = 2.07, df = 1, P = 0.1503). Note that these 178 differences cannot be attributed to genetic diversity, as dsDNA and dsRNA, which have 179 similar levels of selection, have however different levels of diversity ( Figure S3 ). However, 180 it is unlikely that "strandedness" (single vs. double stranded genetic material) alone drives The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/539239 doi: bioRxiv preprint dsDNA, while it is mostly peptidase activity and methylation on the viral envelope in 226 ssRNA viruses (Table S1 ; P < 0.01). In spite of these differences, we note that episodic 227 diversifying selection mostly affects genes involved in viral replication (Table S1 ). Genes (Table S2) . Again, most of these 231 functions and processes are involved in viral replication (Table S2 ). At the intersect of 232 these evolutionary processes however, the genes that are jointly affected by selection and Table S3 ). This suggests that despite key differences in life history strategies adopted Altogether, we showed that episodic diversifying selection is mostly found in single stranded 281 viruses, while correlated evolution is more prevalent in DNA viruses. More critically, we 282 also showed that the genes affected by each process, when acting independently, are in-283 volved in viral replication. However, the genes that are jointly affected by both processes 284 are mostly involved in viral stability (cell entry, integrity, assembly, immune escape), and 285 that the same amino acid sites tend to be affected by both processes. In retrospect, this 286 . CC-BY-NC-ND 4.0 International license is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/539239 doi: bioRxiv preprint tight relationship between selection and correlated evolution may not be surprising, as 296 We note however that we neglected some aspects of viral structure: indeed, viruses can 297 be segmented or not, with a circular or linear genome, with positive or negative strands, 298 overlapping reading frames, complications that we could not consider here due to the 299 resulting small samp
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