Table 1.
Methods for defining nearly neutral mutation boundaries within a c/µ Distribution of Fitness Effects. The nearly neutral mutation boundaries encompass the weak negative boundary (WNB) and weak positive boundary (WPB) c/µ values of nearly neutral mutations for a genomic segment, and the WNB and WPB c/µ values determined from our SARS-CoV-2 empirical sequence data.
Table 2.
Theory summary concerning the fixation of weakly neutral mutations. Equation description, presence of molecular clock, detailed balance condition, evidence to support theory, as described prior (Ohta, Sella, Gillespie) in comparison to the fixation of nearly neutral mutations as described in the Near-Neutral Selectionist Theory proposed in this study.
Table 3.
Definitions of major symbols.
Fig 1.
Investigation of the site-independent mutation rate across each nucleotide site in the SARS-CoV-2 genome.
The mutation landscape of the SARS-CoV-2 genome in the short time frame (black lines, mutation occurrence following cell passaging) and longer time frame after selection (orange lines, position-based percent substitution rate of each nucleotide site from SARS-CoV-2 genomic sequence data analyzed in this study). See Table of S1 Table for the nucleotide mutations compiled from our previous study.
Fig 2.
The varying presence of the molecular clock feature in SARS-CoV-2 genomic segments.
The total percent nucleotide substitution variation (c) for segments exhibiting strict molecular clock (A) or no strict molecular clock (B) over evolution time, averaged over the three SARS-CoV-2 datasets. The time-based substitution rate for Orf1ab 5’UTR obtained from its timeline and coefficient of determination (R2 = 0.9392) was defined as the fundamental genomic mutation rate (µ = c of Orf1ab 5’UTR). See Figures of S6 and S8 Figs for the individual timelines of segments not exhibiting strict molecular clock and Figures of S7 and S9 Figs for the individual timelines of segments exhibiting strict molecular clock.
Table 4.
Relative rate and mutation fraction values for molecular clock SARS-CoV-2 genomic segments. Time-based c/μ, R2 and percent abundance at three selection type boundaries, the relative percent abundance of sites under five different selection types, proportion ratios and evaluation of KNT, ONNT and ST for the genome and each segment exhibiting strict molecular clock features of SARS-CoV-2 over 19 months using the approximated lower and upper boundaries of µ.
Fig 3.
Cumulative c/µ DFE of Orf1ab 5’UTR, genome, All-TR, All-UTR, All-TRS and Orf1ab.
The segments demonstrate a strict molecular clock, showing the abundance of sites under five different selection types (). The boundaries for weak negative selection (red line) to neutral selection (green line) to weak beneficial selection (orange line) and their determined c/µ positions are shown. Strong negative selection and strong beneficial selection would be to the left and right of the red and orange lines, respectively. A broken line leading on the x-axis represents the distance between c/µ = 3.0 to the weak beneficial selection boundary. See Figure in S11 Fig for the segments not demonstrating a strict molecular clock and Figure in S12 Fig for the remaining segments demonstrating strict molecular clock.
Fig 4.
Percent abundance of different mutation types within SARS-CoV-2 genomic segments.
c/µ values (left column) and abundance of selection type (right column) for segments exhibiting strict molecular clock features (first and second rows) and no strict molecular clock features (third and fourth rows). (Left column) Green, light red and dark red represent segments under neutral selection, weak negative selection and strong negative selection, respectively. (Right column) Blue, green, red and purple (where applicable) colors represent percentage of sites under weak negative, weak beneficial, strong beneficial and strong negative selection, respectively. See Figures in S15 and S16 Figs for the graphs of segments decomposed into other selection types. See Tables in S6 and S7 Tables for tabulated values.
Fig 5.
Summary of the key features of molecular evolution theories.
Two substitution rate models (GSRM and SSRM) and five theories of molecular evolution (ST, KNT, ONNT, NNBST, NNUST) in terms of molecular clock, SSMRSS, DFE and percentage of sites under different selection types. *GSRM (Genomic Substitution Rate Model/Strict neutrality hypothesis); SSRM (Genomic Substitution Rate Model); ST (Selectionist Theory); KNT (Kimura’s Neutral Theory); ONNT (Ohta’s Nearly Neutral Theory); NNBST (Near-Neutral Balanced Selectionist Theory); NNUST (Near-Neutral Unbalanced Selectionist Theory); NNST (Near-Neutral Selectionist Theory): including NNBST and NNUST; (Eq. 24a) and
(Eq. 24b) under SSRM: the mean substitution rate
for a given genomic sequence, segment or collection of sites, can be described as the weighted sum of the substitution rate of the sites under strong negative selection (
), weak negative selection (
), strictly neutral selection (
), weak positive selection (
), and strong positive selection (
) by reducing the discrete c/μ distribution into these five categories;
: total substitution rate;
mean substitution rate of strongly deleterious, weakly deleterious, strictly neutral, weakly beneficial and strongly beneficial sites;
: the fraction of strongly deleterious, weakly deleterious, strictly neutral, weakly beneficial and strongly beneficial sites;
: the fraction of nearly neutral sites; q: time-dependent proportion of deleterious mutations that reach fixation; **Molecular clock presence (Yes/No); SSMRRS: Site Frequency Spectra; DFE: Distribution of Fitness Effects; WNB: weak negative boundary; WPB: weak positive boundary; SN: Strong negative selection (0 ≤ c/µ < WNB) in red color; WN: Weak negative selection (WNB ≤ c/µ < 1) in pink; N: Selectively Neutral selection (c/µ = 1) in dark green; WP: Weak positive selection (1 < c/µ ≤ WPB) in light yellow; SP: Strong positive selection (c/µ > WPB) in dark yellow.
Table 5.
Relative rate and mutation fraction values for non-molecular clock SARS-CoV-2 genomic segments. Position-based c/μ, R2 and percent abundance at three selection type boundaries, the relative percent abundance of sites under five different selection types, proportion ratios and evaluation of KNT, ONNT and ST for each segment not exhibiting strict molecular clock of SARS-CoV-2 over 19 months, in order of descending average c R2.
Table 6.
Evaluation of KNT, ONNT, ST, NNBST and NNUST for all SARS-CoV-2 segments. See Tables 2 and 3 for the evaluation at each segment. The number and percentage of violations calculated for applicable segments are presented.