Clonal interference can cause wavelet-like oscillations of multilocus linkage disequilibrium

Selection-recombination-mutation dynamics: Gradient, limit cycle, and closed invariant curve

In this paper, the replicator dynamics of the two-locus two-allele system under weak mutation and weak selection is investigated in a generation-wise nonoverlapping unstructured population of individuals mating at random. Our main finding is that the dynamics is gradient-like when the point mutations at the two loci are independent. This is in stark contrast to the case of one-locus-multi-allele where the existence gradient behavior is contingent on a specific relationship between the mutation rates. When the mutations are not independent in the two-locus-two-allele system, there is the possibility of nonconvergent outcomes, like asymptotically stable oscillations, through either the Hopf bifurcation or the Neimark-Sacker bifurcation depending on the strength of the weak selection. The results can be straightforwardly extended for multilocus-two-allele systems.

Extinction scenarios in evolutionary processes: a multinomial Wright-Fisher approach

We study a discrete-time multi-type Wright-Fisher population process. The mean-field dynamics of the stochastic process is induced by a general replicator difference equation. We prove several results regarding the asymptotic behavior of the model, focusing on the impact of the mean-field dynamics on it. One of the results is a limit theorem that describes sufficient conditions for an almost certain path to extinction, first eliminating the type which is the least fit at the mean-field equilibrium. The effect is explained by the metastability of the stochastic system, which under the conditions of the theorem spends almost all time before the extinction event in a neighborhood of the equilibrium. In addition to the limit theorems, we propose a maximization principle for a general deterministic replicator dynamics and study its implications for the stochastic model.

Contrasting Epidemiology and Population Genetics of COVID-19 Infections Defined by Multilocus Genotypes in SARS-CoV-2 Genomes Sampled Globally

Since its emergence in 2019, SARS-CoV-2 has spread and evolved globally, with newly emerged variants of concern (VOCs) accounting for more than 500 million COVID-19 cases and 6 million deaths. Continuous surveillance utilizing simple genetic tools is needed to measure the viral epidemiological diversity, risk of infection, and distribution among different demographics in different geographical regions. To help address this need, we developed a proof-of-concept multilocus genotyping tool and demonstrated its utility to monitor viral populations sampled in 2020 and 2021 across six continents. We sampled globally 22,164 SARS-CoV-2 genomes from GISAID (inclusion criteria: available clinical and demographic data). They comprised two study populations, “2020 genomes” (N = 5959) sampled from December 2019 to September 2020 and “2021 genomes” (N = 16,205) sampled from 15 January to 15 March 2021. All genomes were aligned to the SARS-CoV-2 reference genome and amino acid polymorphisms were called with quality filtering. Thereafter, 74 codons (loci) in 14 genes including orf1ab polygene (N = 9), orf3a, orf8, nucleocapsid (N), matrix (M), and spike (S) met the 0.01 minimum allele frequency criteria and were selected to construct multilocus genotypes (MLGs) for the genomes. At these loci, 137 mutant/variant amino acids (alleles) were detected with eight VOC-defining variant alleles, including N KR203&204, orf1ab (I265, F3606, and L4715), orf3a H57, orf8 S84, and S G614, being predominant globally with > 35% prevalence. Their persistence and selection were associated with peaks in the viral transmission and COVID-19 incidence between 2020 and 2021. Epidemiologically, older patients (≥20 years) compared to younger patients (<20 years) had a higher risk of being infected with these variants, but this association was dependent on the continent of origin. In the global population, the discriminant analysis of principal components (DAPC) showed contrasting patterns of genetic clustering with three (Africa, Asia, and North America) and two (North and South America) continental clusters being observed for the 2020 and 2021 global populations, respectively. Within each continent, the MLG repertoires (range 40−199) sampled in 2020 and 2021 were genetically differentiated, with ≤4 MLGs per repertoire accounting for the majority of genomes sampled. These data suggested that the majority of SARS-CoV-2 infections in 2020 and 2021 were caused by genetically distinct variants that likely adapted to local populations. Indeed, four GISAID clade-defined VOCs - GRY (Alpha), GH (Beta), GR (Gamma), and G/GK (Delta variant) were differentiated by their MLG signatures, demonstrating the versatility of the MLG tool for variant identification. Results from this proof-of-concept multilocus genotyping demonstrates its utility for SARS-CoV-2 genomic surveillance and for monitoring its spatiotemporal epidemiology and evolution, particularly in response to control interventions including COVID-19 vaccines and chemotherapies.

Predator-Prey Dynamics of Intra-Host Simian Immunodeficiency Virus Evolution Within the Untreated Host

The dynamic nature of the SIV population during disease progression in the SIV/macaque model of AIDS and the factors responsible for its behavior have not been documented, largely owing to the lack of sufficient spatial and temporal sampling of both viral and host data from SIV-infected animals. In this study, we detail Bayesian coalescent inference of the changing collective intra-host viral effective population size (N_e ) from various tissues over the course of infection and its relationship with what we demonstrate is a continuously changing immune cell repertoire within the blood. Although the relative contribution of these factors varied among hosts and time points, the adaptive immune response best explained the overall periodic dynamic behavior of the effective virus population. Data exposing the nature of the relationship between the virus and immune cell populations revealed the plausibility of an eco-evolutionary mathematical model, which was able to mimic the large-scale oscillations in N_e through virus escape from relatively few, early immunodominant responses, followed by slower escape from several subdominant and weakened immune populations. The results of this study suggest that SIV diversity within the untreated host is governed by a predator-prey relationship, wherein differing phases of infection are the result of adaptation in response to varying immune responses. Previous investigations into viral population dynamics using sequence data have focused on single estimates of the effective viral population size (N_e ) or point estimates over sparse sampling data to provide insight into the precise impact of immune selection on virus adaptive behavior. Herein, we describe the use of the coalescent phylogenetic frame- work to estimate the relative changes in N_e over time in order to quantify the relationship with empirical data on the dynamic immune composition of the host. This relationship has allowed us to expand on earlier simulations to build a predator-prey model that explains the deterministic behavior of the virus over the course of disease progression. We show that sequential viral adaptation can occur in response to phases of varying immune pressure, providing a broader picture of the viral response throughout the entire course of progression to AIDS.

Fast and strong amplifiers of natural selection

Selection and random drift determine the probability that novel mutations fixate in a population. Population structure is known to affect the dynamics of the evolutionary process. Amplifiers of selection are population structures that increase the fixation probability of beneficial mutants compared to well-mixed populations. Over the past 15 years, extensive research has produced remarkable structures called strong amplifiers which guarantee that every beneficial mutation fixates with high probability. But strong amplification has come at the cost of considerably delaying the fixation event, which can slow down the overall rate of evolution. However, the precise relationship between fixation probability and time has remained elusive. Here we characterize the slowdown effect of strong amplification. First, we prove that all strong amplifiers must delay the fixation event at least to some extent. Second, we construct strong amplifiers that delay the fixation event only marginally as compared to the well-mixed populations. Our results thus establish a tight relationship between fixation probability and time: Strong amplification always comes at a cost of a slowdown, but more than a marginal slowdown is not needed.

Directional Selection Rather Than Functional Constraints Can Shape the G Matrix in Rapidly Adapting Asexuals

Genetic covariances represent a combination of pleiotropy and linkage disequilibrium, shaped by the population's history. Observed genetic covariance is most often interpreted in pleiotropic terms. In particular, functional constraints restricting which phenotypes are physically possible can lead to a stable G matrix with high genetic variance in fitness-associated traits, and high pleiotropic negative covariance along the phenotypic curve of constraint. In contrast, population genetic models of relative fitness assume endless adaptation without constraint, through a series of selective sweeps that are well described by recent traveling wave models. We describe the implications of such population genetic models for the G matrix when pleiotropy is excluded by design, such that all covariance comes from linkage disequilibrium. The G matrix is far less stable than has previously been found, fluctuating over the timescale of selective sweeps. However, its orientation is relatively stable, corresponding to high genetic variance in fitness-associated traits and strong negative covariance-the same pattern often interpreted in terms of pleiotropic constraints but caused instead by linkage disequilibrium. We find that different mechanisms drive the instabilities along vs. perpendicular to the fitness gradient. The origin of linkage disequilibrium is not drift, but small amounts of linkage disequilibrium are instead introduced by mutation and then amplified during competing selective sweeps. This illustrates the need to integrate a broader range of population genetic phenomena into quantitative genetics.