# Near Neutral Selectionist Theories (NNST) for SARS-CoV-2 suggested by the substitution-mutation ratio (c/µ) analysis

## TL;DR

This paper proposes a new theory of molecular evolution for SARS-CoV-2 based on analyzing mutation rates and substitution patterns.

## Contribution

The study introduces formal mathematical frameworks for Near-Neutral Balanced and Unbalanced Selectionist Theories (NNBST and NNUST) to explain SARS-CoV-2 evolution.

## Key findings

- 49 SARS-CoV-2 segments showed L-shaped distributions of fitness effects.
- 24 segments supported molecular clocks and balanced near-neutral mutations (NNBST).
- 25 segments lacked molecular clocks and showed unbalanced near-neutral mutations (NNUST).

## Abstract

A definitive test to measure genome-wide fitness effects of any nucleotide mutation, including translated regions (TRs) and untranslated regions (UTRs), is essential to help resolve the decades-long neutralist–selectionist debate regarding mutation-mediated species evolution. The precise boundary, composition, and abundance of nearly neutral mutations remain disputed, highlighting the need for a rigorous framework supported by empirical sequence data. Our substitution–mutation rate ratio test (c/μ) might provide such a framework. c/μ compares the ratio of how often mutations fix into the population (substitution rate, c) with their expected arrival (mutation rate, µ), which classifies each mutation type (c/µ > 1: adaptive; c/µ = 1: neutral; c/µ < 1: deleterious). We previously showed that SARS-CoV-2 exhibits L-shaped distributions of fitness effects (DFEs) and a strict molecular clock, and mutation type proportions consistent only with the Near-Neutral Balanced Selectionist Theory (NNBST) and not with conventional molecular evolution theories. However, a theoretical explanation for incidences of non-strict clock behavior in several SARS-CoV-2 segments are not formalized. Here, we extended c/μ analysis to 49 segments of SARS-CoV-2 (26 TRs, 12 UTRs, and 10 transcriptional regulatory sequences (TRSs)) and provide formal, mathematical frameworks for our NNBST and Near-Neutral Unbalanced Selectionist Theory (NNUST) to explain non-strict clock behavior. All 49 segments displayed L-shaped DFEs: 24 segments (mostly TRs) supported molecular clocks and balanced effects of near neutral mutations, consistent with NNBST; meanwhile, 25 segments (mostly UTRs/TRSs) did not support molecular clocks or balancing of near neutral mutations, consistent with NNUST. Numerous violations of Selectionist Theory (ST), Kimura’s Neutral Theory (KNT), and Ohta’s Nearly Neutral Theory (ONNT) were observed, but none for NNBST or NNUST. Together, these results support a unified Near-Neutral Selectionist Theory (NNST), combining neutral and selectionist perspectives to better explain the molecular evolution of SARS-CoV-2.