Population Genetic Models Research Articles

Models of Fluctuating Selection Between Generations: A Solution for the Theoretical Inconsistency.

The theory of selection fluctuation between generations has been a topic with much activities in population genetics and molecular evolution in 1970's. Most studies suggested that, as the result of fluctuating selection between generations, the frequency of an (on average) neutral mutation may fluctuate around 0.5 during the long-term evolution before it was ultimately fixed or lost. However, this pattern can only be derived from a specific type Wright-Fisher additive model, coined by the Nei-Yokoyama puzzle. In this commentary, I revisited this issue and figured out a theoretical assumption that has never been claimed explicitly, the notion of reference phenotype. Consider one locus with two-alleles: A is the wildtype allele and A' is the mutation. The fluctuating selection model actually requires a constraint that one of three genotypes (AA, AA', or A'A') must maintain a constant fitness without fluctuating between generations. It appears that the balancing selection at a frequency of 0.5 emerges only when the heterozygote (AA') is the reference genotype. Because it is difficult to determine which genotype could be the reference genotype in a real population, a desirable population genetics model should take all three possibilities into account. To this end, I propose a mixture model, where each genotype has a certain chance to be the reference genotype. My analysis showed that the emergence of balancing selection depends on the relative proportions of three different reference genotypes.

Modeling the velocity of evolving lineages and predicting dispersal patterns

Accurate estimation of the dispersal velocity or speed of evolving organisms is no mean feat. In fact, existing probabilistic models in phylogeography or spatial population genetics generally do not provide an adequate framework to define velocity in a relevant manner. For instance, the very concept of instantaneous speed simply does not exist under one of the most popular approaches that models the evolution of spatial coordinates as Brownian trajectories running along a phylogeny. Here, we introduce a family of models-the so-called Phylogenetic Integrated Velocity (PIV) models-that use Gaussian processes to explicitly model the velocity of evolving lineages instead of focusing on the fluctuation of spatial coordinates over time. We describe the properties of these models and show an increased accuracy of velocity estimates compared to previous approaches. Analyses of West Nile virus data in the United States indicate that PIV models provide sensible predictions of the dispersal of evolving pathogens at a one-year time horizon. These results demonstrate the feasibility and relevance of predictive phylogeography in monitoring epidemics in time and space.

Making sense of recent models of the "sheltering" hypothesis for recombination arrest between sex chromosomes.

In their most extreme form, sex chromosomes exhibit a complete lack of genetic recombination along much of their length in the heterogametic sex. Some recent models explain the evolution of such suppressed recombination by the "sheltering" of deleterious mutations by chromosomal inversions that prevent recombination around a polymorphic locus controlling sex. This sheltering hypothesis is based on the following reasoning. An inversion that is associated with the male-determining allele (with male heterogamety) is present only in the heterozygous state. If such an inversion carries a lower-than-average number of deleterious mutations, it will accrue a selective advantage, and will be sheltered from homozygosity for any mutations that it carries due to the enforced heterozygosity for the inversion itself. It can therefore become fixed among all carriers of the male-determining allele. Recent population genetics models of this process are discussed. It is shown that, except under the unlikely scenario of a high degree of recessivity of most deleterious mutations, inversions of this type that lack any other fitness effects will have at best a modest selective advantage; they will usually accumulate on proto-Y chromosomes at a rate close to, or less than, the neutral expectation. While the existence of deleterious mutations does not necessarily prevent the spread of Y-linked inversions, it is unlikely to provide a significant selective advantage to them.

The role of pleiotropy and population structure in the evolution of altruism through the greenbeard effect.

Several empirical examples and theoretical models suggest that the greenbeard effect may be an important mechanism in driving the evolution of altruism. However, previous theoretical models rely on assumptions such as spatial structure and specific sets of pleiotropic loci, the importance of which for the evolution of altruism has not been studied. Here, we develop a population-genetic model that clarifies the roles of extrinsic assortment (e.g., due to population viscosity) and pleiotropy in the maintenance of altruism through the greenbeard effect. We show that, when extrinsic assortment is too weak to promote the evolution of altruism on its own, the greenbeard effect can only promote altruism significantly if there is a pleiotropic locus controlling both altruism and signaling. Further, we show that indirect selection via genetic associations is too weak to have a noticeable impact on altruism evolution. We also highlight that, if extrinsic assortment is strong enough to promote the evolution of altruism on its own, it also favors the spread of alleles encoding the other functions of a greenbeard trait (signaling and discriminatory behavior), as well as genetic associations. This occurs despite the fact that the greenbeard effect did not favor the evolution of altruism in the first place. This calls for caution when inferring the causality between greenbeard traits and the evolution of altruism.

Apollo: A comprehensive GPU-powered within-host simulator for viral evolution and infection dynamics across population, tissue, and cell.

Modern sequencing instruments bring unprecedented opportunity to study within-host viral evolution in conjunction with viral transmissions between hosts. However, no computational simulators are available to assist the characterization of within-host dynamics. This limits our ability to interpret epidemiological predictions incorporating within-host evolution and to validate computational inference tools. To fill this need we developed Apollo, a GPU-accelerated, out-of-core tool for within-host simulation of viral evolution and infection dynamics across population, tissue, and cellular levels. Apollo is scalable to hundreds of millions of viral genomes and can handle complex demographic and population genetic models. Apollo can replicate real within-host viral evolution; accurately recapturing observed viral sequences from an HIV cohort derived from initial population-genetic configurations. For practical applications, using Apollo-simulated viral genomes and transmission networks, we validated and uncovered the limitations of a widely used viral transmission inference tool.

Reconciling Santa Rosalia: Both Reproductive Isolation and Coexistence Constrain Diversification.

AbstractUnderstanding patterns of diversification necessarily requires accounting for both the generation and the persistence of species. Formal models of speciation genetics, however, focus on the generation of new species without explicitly considering the maintenance of biodiversity (e.g., coexistence, the focus of ecological studies of diversity). Consequently, it remains unclear whether and how new species will coexist following a speciation event, a gap limiting our ability to understand the rate-limiting controls of diversification over macroevolutionary timescales. To connect coexistence and speciation theory and assess the relative importance of ecological versus genetic constraints in diversification events, we develop a deterministic, three-locus, population-genetic model that includes a skewed distribution of available resources (to generate variation in fitness differences), frequency-dependent competition, and assortative mating. Both ecology and genetics play vital and interacting roles in shaping initial speciation events and long-term eco-evolutionary outcomes. Ecological constraints are especially important when fitness differences are large and competition remains strong among dissimilar phenotypes. Ephemeral species can occur in our model and are typically lost because of competitive exclusion, a result demonstrating that species persistence may serve as the rate-limiting control of long-term diversification rates. More broadly, our model adds evidence that the unification of ecological and evolutionary (including genetic) perspectives on biodiversity is needed to predict large-scale patterns.

The contributions of direct and indirect selection to the evolution of mating preferences.

Many influential mathematical models of sexual selection have stressed that mating preferences evolve due to correlations that build between mating preferences and preferred display traits - that is, through indirect selection. Nevertheless, there is a perception that indirect selection should generally be overwhelmed by direct selection, for example in the form of search costs. Recent work by Fry has used quantitative genetic models to argue that in many cases, including when there are direct benefits (a fecundity advantage to mating with the preferred male), direct and indirect selection may be of similar magnitude. Here I use population genetic models, in which the strength of the genetic correlation is an emergent property of evolution at mating preference and display trait loci, to assess the relative contributions of direct and indirect selection to the evolution of mating preferences. For the cases of direct benefits and of indirect benefits with fixed and frequency-dependent search costs, I outline parameter values of fecundity benefits, preference strengths, and search costs for which indirect selection on female preferences can potentially predominate. I also analyze male mate choice under polygyny, showing that direct selection will always outweigh indirect selection except when there are direct benefits.

The effects of intersexual interactions on survival can drive the evolution of female ornaments in the absence of mate limitation.

The evolution of sexual ornaments in animals is typically attributed to reproductive competition. However, sexual ornaments also arise in contexts where the ornamented sex is neither mate nor gamete limited, and explanations for ornamentation in these cases remain incomplete. In many species, particularly those with slow life histories, lifetime reproductive success depends more strongly on adult survival than fecundity, and survival can depend on intersexual interactions. We develop a population genetic model to investigate how the effect of intersexual interactions on survival may contribute to ornament evolution in the absence of competition for mates. Using female ornamentation in polygynous mating systems as a case study, we show that, indeed, ornaments can evolve when the ornament functions to modify interactions with males in ways that enhance a female's own survival. The evolutionary dynamics depend qualitatively on the specific behavioral mechanism by which the ornament modifies social interactions. In all cases, the ornament's long-term persistence is ultimately determined by the coevolution of the male locus that determines how males affect female survival. We outline the scenarios that are most likely to favor the evolution of female ornaments through the effects of intersexual interactions on survival, and we urge empirical researchers to consider the potential for this social selection mechanism to shape traits of interest across taxa.

A martingale approach to Gaussian fluctuations and laws of iterated logarithm for Ewens–Pitman model

The Ewens–Pitman model refers to a distribution for random partitions of [n]={1,…,n}, which is indexed by a pair of parameters α∈[0,1) and θ>−α, with α=0 corresponding to the Ewens model in population genetics. The large n asymptotic properties of the Ewens–Pitman model have been the subject of numerous studies, with the focus being on the number Kn of partition sets and the number Kr,n of partition subsets of size r, for r=1,…,n. While for α=0 asymptotic results have been obtained in terms of almost-sure convergence and Gaussian fluctuations, for α∈(0,1) only almost-sure convergences are available, with the proof for Kr,n being given only as a sketch. In this paper, we make use of martingales to develop a unified and comprehensive treatment of the large n asymptotic behaviours of Kn and Kr,n for α∈(0,1), providing alternative, and rigorous, proofs of the almost-sure convergences of Kn and Kr,n, and covering the gap of Gaussian fluctuations. We also obtain new laws of the iterated logarithm for Kn and Kr,n.

Prevalence Estimates and Genetic Diversity for Autosomal Dominant Retinitis Pigmentosa Due to RHO, c.68C>A (p.P23H) Variant

ObjectiveTo provide the most up-to-date clinical prevalence estimate for autosomal dominant retinitis pigmentosa (adRP) patients due to RHO c.68C>A, (p.P23H) in the United States, supported by two independent approaches; literature based meta-analysis of reported patients and population genetics modeling. DesignSystematic review and meta-analysis plus population genetics modeling. MethodsSystematic review of the literature describing RP patients attributed to RHO variants was conducted to support a meta-analysis used to estimate the clinical prevalence of the RHO P23H patients diagnosed in the US. In parallel, large-scale genetic diversity studies describing the US population and non-European cohorts of the Americas (PAGE II), were evaluated to ascertain the allele frequencies of variant RHO c.68C>A, (p.P23H). The genetic prevalence for variant RHO c.68C>A, (p.P23H) was calculated using Hardy-Weinberg equilibrium. Further demographic data, including age and average age of onset for visual impairment were incorporated into a basic distribution model to estimate clinical prevalence of genetically predisposed persons. ResultsThe estimated clinical prevalence of adRP due to RHO P23H based on literature review was approximately 2000-3000 patients. In comparison the genetic prevalence of persons with RHO c.68C>A, (p.P23H) in the United States was an estimated 6176 (90% CI: 3333-11398) and only half of them are expected to cluster with European genetic ancestry. This variant was found enriched in subgroups of African American or other non-European biogeographic ancestries. Of the estimated 6200 persons carrying this variant in the US, ∼3500 (estimate range: 1900-6500) are expected to show clinical signs of visual impairment as modeled by average age of onset previously reported for patients with this variant. ConclusionsWe utilized two independent approaches to estimate the total number of adRP patients due to RHO c.68C>A, (p.P23H) in the United States; systematic literature review based meta-analysis and population genetics modeling. Both approaches yielded similar, overlapping estimates of adRP patients due to RHO P23H. However, comparison of these estimates provides some indication for a diagnosis gap. Unexpectedly, this variant is present at relatively higher frequency in some predominantly non-European genetic ancestries in the US. While this genetic analysis supports our estimates of clinical prevalence of adRP due to RHO P23H in the United States, it also has implications for diagnosing potential adRP patients due to this variant, raising questions of genotype-phenotype correlation and access to genetic testing.

Geographical and genetic clines in Dracocephalum kotschyi X Dracocephalum oligadenium hybrids: landscape genetics and genocline analyses

Conservation and management of medicinally important plants are among the necessary tasks all over the world. The genus Dracocephalum (Lamiaceae) contains about 186 perennials, or annual herb species that have been used for their medicinal values in different parts of the world as an antihyperlipidemic, analgesic, antimicrobial, antioxidant, as well as anticancer medicine. Producing detailed data on the genetic structure of these species and their response against climate change and human landscape manipulation can be very important for conservation purposes. Therefore, the present study was performed on six geographical populations of two species in the Dracocephalum genus, namely, Dracocephalum kotschyi, and Dracocephalum oligadenium, as well as their inter-specific hybrid population. We carried out, population genetic study, landscape genetics, species modeling, and genetic cline analyses on these plants. We present here, new findings on the genetic structure of these populations, and provide data on both geographical and genetic clines, as well as morphological clines. We also identified genetic loci that are potentially adaptive to the geographical spatial features and genocide conditions. Different species distribution modeling (SDM) methods, used in this work revealed that bioclimatic variables related to the temperature and moisture, play an important role in Dracocephalum population’s geographical distribution within IRAN and that due to the presence of some potentially adaptive genetic loci in the studied plants, they can survive well enough by the year 2050 and under climate change. The findings can be used for the protection of these medicinally important plant.

Population Genomic Scans for Natural Selection and Demography.

Uncovering the fundamental processes that shape genomic variation in natural populations is a primary objective of population genetics. These processes include demographic effects such as past changes in effective population size or gene flow between structured populations. Furthermore, genomic variation is affected by selection on nonneutral genetic variants, for example, through the adaptation of beneficial alleles or balancing selection that maintains genetic variation. In this article, we discuss the characterization of these processes using population genetic models, and we review methods developed on the basis of these models to unravel the underlying processes from modern population genomic data sets. We briefly discuss the conditions in which these approaches can be used to infer demography or identify specific nonneutral genetic variants and cases in which caution is warranted. Moreover, we summarize the challenges of jointly inferring demography and selective processes that affect neutral variation genome-wide.

36-year study reveals stability of a wild wheat population across microhabitats.

Long-term genetic studies of wild populations are very scarce, but are essential for connecting ecological and population genetics models, and for understanding the dynamics of biodiversity. We present a study of a wild wheat population sampled over a 36-year period at high spatial resolution. We genotyped 832 individuals from regular sampling along transects during the course of the experiment. Genotypes were clustered into ecological microhabitats over scales of tens of metres, and this clustering was remarkably stable over the 36 generations of the study. Simulations show that it is difficult to determine whether this spatial and temporal stability reflects extremely limited dispersal or fine-scale local adaptation to ecological parameters. Using a common-garden experiment, we showed that the genotypes found in distinct microhabitats differ phenotypically. Our results provide a rare insight into the population genetics of a natural population over a long monitoring period.

Approximate Bayesian Inference Based on Expected Evaluation

Approximate Bayesian computing (ABC) and Bayesian Synthetic likelihood (BSL) are two popular families of methods to evaluate the posterior distribution when the likelihood function is not available or tractable. For existing variants of ABC and BSL, the focus is usually first put on the simulation algorithm, and after that the form of the resulting approximate posterior distribution comes as a consequence of the algorithm. In this paper we turn this around and firstly define a reasonable approximate posterior distribution by studying the distributional properties of the expected discrepancy, or more generally an expected evaluation, with respect to generated samples from the model. The resulting approximate posterior distribution will be on a simple and interpretable form compared to ABC and BSL. Secondly a Markov chain Monte Carlo (MCMC) algorithm is developed to simulate from the resulting approximate posterior distribution. The algorithm was evaluated on a synthetic data example and on the Stepping Stone population genetics model, demonstrating that the proposed scheme has real world applicability. The algorithm demonstrates competitive results with the BSL and sequential Monte Carlo ABC algorithms, but is outperformed by the ABC MCMC.

The structure of the environment influences the patterns and genetics of local adaptation

Abstract Environmental heterogeneity can lead to spatially varying selection, which can, in turn, lead to local adaptation. Population genetic models have shown that the pattern of environmental variation in space can strongly influence the evolution of local adaptation. In particular, when environmental variation is highly autocorrelated in space local adaptation will more readily evolve. However, there have been few attempts to test this prediction empirically or characterize the consequences it would have for the genetic architecture underlying local adaptation. In this study, I analyze a large-scale provenance trial conducted on lodgepole pine and find suggestive evidence that spatial autocorrelation in environmental variation is related to the strength of local adaptation that has evolved in that species. Motivated by those results, I use simulations to model local adaptation to different spatial patterns of environmental variation. The simulations confirm that local adaptation is expected to increase with the degree of spatial autocorrelation in the selective environment, but also show that highly heterogeneous environments are more likely to exhibit high variation in local adaptation, a result not previously described. I find that the spatial pattern of environmental variation influences the genetic architectures underlying local adaptation. In highly autocorrelated environments, the genetic architecture of local adaptation tends to be composed of high-frequency alleles with small phenotypic effects. In weakly autocorrelated environments, locally adaptive alleles may have larger phenotypic effects but are present at lower frequencies across species’ ranges and experience more evolutionary turnover. Overall, this work emphasizes the profound importance that the spatial pattern of selection can have on the evolution of local adaptation and how spatial autocorrelation should be considered when formulating hypotheses in ecological and genetic studies.

Measuring the burden of hundreds of BioBricks defines an evolutionary limit on constructability in synthetic biology

Engineered DNA will slow the growth of a host cell if it redirects limiting resources or otherwise interferes with homeostasis. Escape mutants that alleviate this burden can rapidly evolve and take over cell populations, making genetic engineering less reliable and predictable. Synthetic biologists often use genetic parts encoded on plasmids, but their burden is rarely characterized. We measured how 301 BioBrick plasmids affected Escherichia coli growth and found that 59 (19.6%) were burdensome, primarily because they depleted the limited gene expression resources of host cells. Overall, no BioBricks reduced the growth rate of E. coli by >45%, which agreed with a population genetic model that predicts such plasmids should be unclonable. We made this model available online for education (https://barricklab.org/burden-model) and added our burden measurements to the iGEM Registry. Our results establish a fundamental limit on what DNA constructs and genetic modifications can be successfully engineered into cells.

The evolutionary cost of homophily: social stratification facilitates stable variant coexistence and increased rates of evolution in host-associated pathogens.

Coexistence of multiple strains of a pathogen in a host population can present significant challenges to vaccine development or treatment efficacy. Here we discuss a novel mechanism that can increase rates of long-lived strain polymorphism, rooted in the presence of social structure in a host population. We show that social preference of interaction, in conjunction with differences in immunity between host subgroups, can exert varying selection pressure on pathogen strains, creating a balancing mechanism that supports stable viral coexistence, independent of other known mechanisms. We use population genetic models to study rates of pathogen heterozygosity as a function of population size, host population composition, mutant strain fitness differences and host social preferences of interaction. We also show that even small periodic epochs of host population stratification can lead to elevated strain coexistence. These results are robust to varying social preferences of interaction, overall differences in strain fitnesses, and spatial heterogeneity in host population composition. Our results highlight the role of host population social stratification in increasing rates of pathogen strain diversity, with effects that should be considered when designing policies or treatments with a long-term view of curbing pathogen evolution.

How should we measure population-level inbreeding depression? Impacts of standing genetic associations between selfing rate and deleterious mutations.

Inbreeding depression (ID) is a major selective force during mating system evolution primarily contributed by highly to partially recessive deleterious mutations. Theories suggest that transient genetic association with fitness alleles can be important in affecting the evolution of alleles that modify the selfing rate during its sweep. Nevertheless, empirical tests often focus on the pre-existing genetic association between selfing rate and ID maintained under mutation-selection balance. Therefore, how this standing genetic association is affected by key factors and its impacts on the evolution of selfing remain unclear. I show that as the selection coefficient of deleterious mutations increases, the association between selfing rate and ID declines from positive to negative. These results predict that association between selfing and ID tends to be negative in populations with low selfing rates, while positive in highly selfing populations. Using population genetic and quantitative genetic models, I show that standing genetic associations between selfing rate and fitness alleles can significantly impact the evolution of the mean selfing rate of a population. I present better metrics of population-level ID, which can be calculated based on the correlation coefficient between individual selfing rate and the fitness of selfed and outcrossed offspring.

Bayesian estimation of gene constraint from an evolutionary model with gene features.

Measures of selective constraint on genes have been used for many applications, including clinical interpretation of rare coding variants, disease gene discovery and studies of genome evolution. However, widely used metrics are severely underpowered at detecting constraints for the shortest ~25% of genes, potentially causing important pathogenic mutations to be overlooked. Here we developed a framework combining a population genetics model with machine learning on gene features to enable accurate inference of an interpretable constraint metric, shet. Our estimates outperform existing metrics for prioritizing genes important for cell essentiality, human disease and other phenotypes, especially for short genes. Our estimates of selective constraint should have wide utility for characterizing genes relevant to human disease. Finally, our inference framework, GeneBayes, provides a flexible platform that can improve the estimation of many gene-level properties, such as rare variant burden or gene expression differences.

On the connections between the spatial Lambda–Fleming–Viot model and other processes for analysing geo-referenced genetic data

The introduction of the spatial Lambda-Fleming–Viot model (ΛV) in population genetics was mainly driven by the pioneering work of Alison Etheridge, in collaboration with Nick Barton and Amandine Véber about ten years ago (Barton et al., 2010; Barton et al., 2013). The ΛV model provides a sound mathematical framework for describing the evolution of a population of related individuals along a spatial continuum. It alleviates the “pain in the torus” issue with Wright and Malécot’s isolation by distance model and is sampling consistent, making it a tool of choice for statistical inference. Yet, little is known about the potential connections between the ΛV and other stochastic processes generating trees and the spatial coordinates along the corresponding lineages. This work focuses on a version of the ΛV whereby lineages move rapidly over small distances. Using simulations, we show that the induced ΛV tree-generating process is well approximated by a birth–death model. Our results also indicate that Brownian motions modelling the movements of lines of descent along birth–death trees do not generally provide a good approximation of the ΛV due to habitat boundaries effects that play an increasingly important role in the long run. Accounting for habitat boundaries through reflected Brownian motions considerably increases the similarity to the ΛV model however. Finally, we describe efficient algorithms for fast simulation of the backward and forward in time versions of the ΛV model.