Evolutionary analysis of genomes of SARS-CoV-2-related bat viruses suggests old roots, constant effective population size, and possible increase of fitness

It is of vital practical interest to understand the co-evolution of bat {beta}-coronaviruses with their hosts, since a number of these most likely crossed the species boundaries and infected humans. Complete sequences of 47 consensus genomes are available for bat {beta}-coronaviruses related to the SARS-CoV-2 human virus. We carried out several types of evolutionary analyses using these data. First, using the publicly available BEAST 2 software, we generated phylogenetic trees and skyline plots. The roots of the trees, both for the entire sequences and subsequences coding for the E and S proteins as well as the 5 and 3 UTR regions, are estimated to be located from several decades to more than a thousand years ago, while the effective population sizes remained largely constant. Motivated by this, we developed a simple estimator of the effective population size in a Moran model with constant population, which, under the model is equal to the expected age of the MRCA measured in generations. Comparisons of these estimates to those produced by BEAST 2 shows qualitative agreement. We also compared the site frequency spectra (SFS) of the bat genomes to those provided by the Moran Tug-of-War model. Comparison does not exclude the possibility that overall fitness of the bat {beta}-coronaviruses was increasing over time as a result of directional selection. Stability of interactions of bats and their viruses was considered likely on the basis of specific manner in which bat immunity is tuned, and it seems consistent with our analysis.