L-shaped distribution of the relative substitution rate (c/μ) observed for SARS-COV-2's genome, inconsistent with the selectionist theory, the neutral theory and the nearly neutral theory but a near-neutral balanced selection theory: Implication on “neutralist-selectionist” debate

The genomic substitution rate (GSR) of SARS-CoV-2 exhibits a molecular clock feature and does not change under fluctuating environmental factors such as the infected human population (10°-10⁷), vaccination etc. The molecular clock feature is believed to be inconsistent with the selectionist theory (ST). The GSR shows lack of dependence on the effective population size, suggesting Ohta's nearly neutral theory (ONNT) is not applicable to this virus. Big variation of the substitution rate within its genome is also inconsistent with Kimura's neutral theory (KNT). Thus, all three existing evolution theories fail to explain the evolutionary nature of this virus. In this paper, we proposed a Segment Substitution Rate Model (SSRM) under non-neutral selections and pointed out that a balanced mechanism between negative and positive selection of some segments that could also lead to the molecular clock feature. We named this hybrid mechanism as near-neutral balanced selection theory (NNBST) and examined if it was followed by SARS-CoV-2 using the three independent sets of SARS-CoV-2 genomes selected by the Nextstrain team. Intriguingly, the relative substitution rate of this virus exhibited an L-shaped probability distribution consisting with NNBST rather than Poisson distribution predicted by KNT or an asymmetric distribution predicted by ONNT in which nearly neutral sites are believed to be slightly deleterious only, or the distribution that is lack of nearly neutral sites predicted by ST. The time-dependence of the substitution rates for some segments and their correlation with the vaccination were observed, supporting NNBST. Our relative substitution rate method provides a tool to resolve the long standing “neutralist-selectionist” controversy. Implications of NNBST in resolving Lewontin's Paradox is also discussed.