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Due to the emergence of new variants of the SARS-CoV-2 coronavirus, the question of how the viral genomes evolved, leading to the formation of highly infectious strains, becomes particularly important. Three major emergent strains, Alpha, Beta and Delta, characterized by a significant number of missense mutations, provide a natural test field. We accumulated and aligned 4.7 million SARS-CoV-2 genomes from the GISAID database and carried out a comprehensive set of analyses. This collection covers the period until the end of October 2021, i.e., the beginnings of the Omicron variant. First, we explored combinatorial complexity of the genomic variants emerging and their timing, indicating very strong, albeit hidden, selection forces. Our analyses show that the mutations that define variants of concern did not arise gradually but rather co-evolved rapidly, leading to the emergence of the full variant strain. To explore in more detail the evolutionary forces at work, we developed time trajectories of mutations at all 29,903 sites of the SARS-CoV-2 genome, week by week, and stratified them into trends related to (i) point substitutions, (ii) deletions and (iii) non-sequenceable regions. We focused on classifying the genetic forces active at different ranges of the mutational spectrum. We observed the agreement of the lowest-frequency mutation spectrum with the Griffiths–Tavaré theory, under the Infinite Sites Model and neutrality. If we widen the frequency range, we observe the site frequency spectra much more consistently with the Tung–Durrett model assuming clone competition and selection. The coefficients of the fitting model indicate the possibility of selection acting to promote gradual growth slowdown, as observed in the history of the variants of concern. These results add up to a model of genomic evolution, which partly fits into the classical drift barrier ideas. Certain observations, such as mutation “bands” persistent over the epidemic history, suggest contribution of genetic forces different from mutation, drift and selection, including recombination or other genome transformations. In addition, we show that a “toy” mathematical model can qualitatively reproduce how new variants (clones) stem from rare advantageous driver mutations, and then acquire neutral or disadvantageous passenger mutations which gradually reduce their fitness so they can be then outcompeted by new variants due to other driver mutations.

Inference of demographic history from genetic data is a primary goal of population genetics of model and nonmodel organisms. Whole genome-based approaches such as the pairwise/multiple sequentially Markovian coalescent methods use genomic data from one to four individuals to infer the demographic history of an entire population, while site frequency spectrum (SFS)-based methods use the distribution of allele frequencies in a sample to reconstruct the same historical events. Although both methods are extensively used in empirical studies and perform well on data simulated under simple models, there have been only limited comparisons of them in more complex and realistic settings. Here we use published demographic models based on data from three human populations (Yoruba, descendants of northwest-Europeans, and Han Chinese) as an empirical test case to study the behavior of both inference procedures. We find that several of the demographic histories inferred by the whole genome-based methods do not predict the genome-wide distribution of heterozygosity, nor do they predict the empirical SFS. However, using simulated data, we also find that the whole genome methods can reconstruct the complex demographic models inferred by SFS-based methods, suggesting that the discordant patterns of genetic variation are not attributable to a lack of statistical power, but may reflect unmodeled complexities in the underlying demography. More generally, our findings indicate that demographic inference from a small number of genomes, routine in genomic studies of nonmodel organisms, should be interpreted cautiously, as these models cannot recapitulate other summaries of the data.

Ease of worldwide travel provides increased opportunities for organisms not only to colonize new environments but also to encounter related but diverged populations. Such events of reconnection and secondary contact of previously isolated populations are widely observed at different time scales. For example, during the quaternary glaciation, sea water level fluctuations caused temporal isolation of populations, often to be followed by secondary contact. At shorter time scales, population isolation and reconnection of viruses are commonly observed, and such events are often associated with epidemics and pandemics. Here, using coalescent theory and simulations, we describe the temporal impact of population reconnection after isolation on nucleotide differences and the site frequency spectrum, as well as common summary statistics of DNA variation. We identify robust genomic signatures of population reconnection after isolation. We utilize our development to infer the recent evolutionary history of human immunodeficiency virus 1 (HIV-1) in Asia and South America, successfully retrieving the successive HIV subtype colonization events in these regions. Our analysis reveals that divergent HIV-1 subtype populations are currently admixing in these regions, suggesting that HIV-1 may be undergoing a process of homogenization, contrary to popular belief.

The Site Frequency Spectrum (SFS) and the heterozygosity of allelic variants are among the most important summary statistics for population genetic analysis of diploid organisms. We discuss the generalization of these statistics to populations of autopolyploid organisms in terms of the joint Site Frequency/Dosage Spectrum and its expected value for autopolyploid populations that follow the standard neutral model. Based on these results, we present estimators of nucleotide variability from High-Throughput Sequencing (HTS) data of autopolyploids and discuss potential issues related to sequencing errors and variant calling. We use these estimators to generalize Tajima's D and other SFS-based neutrality tests to HTS data from autopolyploid organisms. Finally, we discuss how these approaches fail when the number of individuals is small. In fact, in autopolyploids there are many possible deviations from the Hardy–Weinberg equilibrium, each reflected in a different shape of the individual dosage distribution. The SFS from small samples is often dominated by the shape of these deviations of the dosage distribution from its Hardy–Weinberg expectations.

In population genetics, parameters describing forces such as mutation, migration and drift are generally inferred from molecular data. Lately, approximate methods based on simulations and summary statistics have been widely applied for such inference, even though these methods waste information. In contrast, probabilistic methods of inference can be shown to be optimal, if their assumptions are met. In genomic regions where recombination rates are high relative to mutation rates, polymorphic nucleotide sites can be assumed to evolve independently from each other. The distribution of allele frequencies at a large number of such sites has been called “allele-frequency spectrum” or “site-frequency spectrum” (SFS). Conditional on the allelic proportions, the likelihoods of such data can be modeled as binomial. A simple model representing the evolution of allelic proportions is the biallelic mutation-drift or mutation-directional selection-drift diffusion model. With series of orthogonal polynomials, specifically Jacobi and Gegenbauer polynomials, or the related spheroidal wave function, the diffusion equations can be solved efficiently. In the neutral case, the product of the binomial likelihoods with the sum of such polynomials leads to finite series of polynomials, i.e., relatively simple equations, from which the exact likelihoods can be calculated. In this article, the use of orthogonal polynomials for inferring population genetic parameters is investigated.

The allotetraploid species Brassica napus L. is a global crop of major economic importance, providing canola oil (seed) and vegetables for human consumption and fodder and meal for livestock feed. Characterizing the genetic diversity present in the extant germplasm pool of B. napus is fundamental to better conserve, manage and utilize the genetic resources of this species. We used sequence-based genotyping to identify and genotype 30,881 SNPs in a diversity panel of 782 B. napus accessions, representing samples of winter and spring growth habits originating from 33 countries across Europe, Asia and America. We detected strong population structure broadly concordant with growth habit and geography, and identified three major genetic groups: spring (SP), winter Europe (WE), and winter Asia (WA). Subpopulation-specific polymorphism patterns suggest enriched genetic diversity within the WA group and a smaller effective breeding population for the SP group compared to WE. Interestingly, the two subgenomes of B. napus appear to have different geographic origins, with phylogenetic analysis placing WE and WA as basal clades for the other subpopulations in the C and A subgenomes, respectively. Finally, we identified 16 genomic regions where the patterns of diversity differed markedly from the genome-wide average, several of which are suggestive of genomic inversions. The results obtained in this study constitute a valuable resource for worldwide breeding efforts and the genetic dissection and prediction of complex B. napus traits.