Strong evidence for the evolution of decreasing compositional heterogeneity in SARS-CoV-2 genomes during the pandemic.

Using phylogenetic ridge regression of S 1 against time, we observed a highly significant decreasing trend in S 1 for K = 1 (Fig. 2 a, slope = −149.18, p < 0.001, Table 1 ) and, to a lesser extent, for K = 3 (not shown).

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Analysis of S 1 rate values points to the existence of a strong trend for increased rates, yet it is positive using search.trend (slope = 1056.07, p = 1), but negative under the Brownian motion model (AIC BMT = −13423.167, slope = −548.20, LRT p-value < 0.001, Table 2 ).

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BMT suggests a negative trend (decrease over time) and has lower AIC than ordinary BM (AIC BMT = −12998.195, slope = −0.316; AIC BM = −12997.511), but the difference with BM is not statistically significant (likelihood ratio test, LRT p-value = 0.10, Table 1 ).).

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However, it must be noted that both SCC (K = 0.28, p = 0.078) and SCC_RY (K = 0.44, p = 0.022) have a low and marginally significant phylogenetic signal (as measured by Blomberg’s K 32 , Table 2 ) implying the BM is probably a poor representation of compositional metrics evolution.

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We present consistent evidence for a decreasing trend in SCC, indicating a robust long-term adaptive tendency in SARS-CoV-2 evolution.

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