The infinitesimal model: Definition, derivation, and implications

Polygenic dynamics underlying the response of quantitative traits to directional selection

We study the response of a quantitative trait to exponential directional selection in a finite haploid population, both at the genetic and the phenotypic level. We assume an infinite sites model, in which the number of new mutations per generation in the population follows a Poisson distribution (with mean Θ) and each mutation occurs at a new, previously monomorphic site. Mutation effects are beneficial and drawn from a distribution. Sites are unlinked and contribute additively to the trait. Assuming that selection is stronger than random genetic drift, we model the initial phase of the dynamics by a supercritical Galton-Watson process. This enables us to obtain time-dependent results. We show that the copy-number distribution of the mutant in generation n, conditioned on non-extinction until n, is described accurately by the deterministic increase from an initial distribution with mean 1. This distribution is related to the absolutely continuous part W+ of the random variable, typically denoted W, that characterizes the stochasticity accumulating during the mutant's sweep. A suitable transformation yields the approximate dynamics of the mutant frequency distribution in a Wright-Fisher population of size N. Our expression provides a very accurate approximation except when mutant frequencies are close to 1. On this basis, we derive explicitly the (approximate) time dependence of the expected mean and variance of the trait and of the expected number of segregating sites. Unexpectedly, we obtain highly accurate approximations for all times, even for the quasi-stationary phase when the expected per-generation response and the trait variance have equilibrated. The latter refine classical results. In addition, we find that Θ is the main determinant of the pattern of adaptation at the genetic level, i.e., whether the initial allele-frequency dynamics are best described by sweep-like patterns at few loci or small allele-frequency shifts at many. The number of segregating sites is an appropriate indicator for these patterns. The selection strength determines primarily the rate of adaptation. The accuracy of our results is tested by comprehensive simulations in a Wright-Fisher framework. We argue that our results apply to more complex forms of directional selection.

Singular effect of linkage on long-term genetic gain in Fisher's infinitesimal model

During the founding of the field of quantitative genetics, Fisher formulated in 1918 his "infinitesimal model" that provided a novel mathematical framework to describe the Mendelian transmission of quantitative traits. If the infinitely many genes in that model are assumed to segregate independently during reproduction, corresponding to having no linkage, directional selection asymptotically leads to a constant genetic gain at each generation. In reality, genes are subject to strong linkage because they lie on chromosomes and thus segregate in a correlated way. Various approximations have been used in the past to study that more realistic case of the infinitesimal model with the expectation that the asymptotic gain per generation is modestly decreased. To treat this system even in the strong linkage limit, we take the genes to lie on continuous chromosomes. Surprisingly, the consequences of genetic linkage are in fact rather singular, changing the nature of the long-term gain per generation: the asymptotic gain vanishes rather than being simply decreased. Nevertheless, the per-generation gain tends to zero sufficiently slowly for the total gain, accumulated over generations, to be unbounded.

Emergence of phenotypic plasticity through epigenetic mechanisms

Plasticity is found in all domains of life and is particularly relevant when populations experience variable environmental conditions. Traditionally, evolutionary models of plasticity are non-mechanistic: they typically view reactions norms as the target of selection, without considering the underlying genetics explicitly. Consequently, there have been difficulties in understanding the emergence of plasticity, and in explaining its limits and costs. In this paper, we offer a novel mechanistic approximation for the emergence and evolution of plasticity. We simulate random "epigenetic mutations" in the genotype-phenotype mapping, of the kind enabled by DNA-methylations/demethylations. The frequency of epigenetic mutations at loci affecting the phenotype is sensitive to organism stress (trait-environment mismatch), but is also genetically determined and evolvable. Thus, the "random motion" of epigenetic markers enables developmental learning-like behaviors that can improve adaptation within the limits imposed by the genotypes. However, with random motion being "goal-less," this mechanism is also vulnerable to developmental noise leading to maladaptation. Our individual-based simulations show that epigenetic mutations can hide alleles that are temporarily unfavorable, thus enabling cryptic genetic variation. These alleles can be advantageous at later times, under regimes of environmental change, in spite of the accumulation of genetic loads. Simulations also demonstrate that plasticity is favored by natural selection in constant environments, but more under periodic environmental change. Plasticity also evolves under directional environmental change as long as the pace of change is not too fast and costs are low.

Plant pangenomes for crop improvement, biodiversity and evolution

Plant genome sequences catalogue genes and the genetic elements that regulate their expression. Such inventories further research aims as diverse as mapping the molecular basis of trait diversity in domesticated plants or inquiries into the origin of evolutionary innovations in flowering plants millions of years ago. The transformative technological progress of DNA sequencing in the past two decades has enabled researchers to sequence ever more genomes with greater ease. Pangenomes - complete sequences of multiple individuals of a species or higher taxonomic unit - have now entered the geneticists' toolkit. The genomes of crop plants and their wild relatives are being studied with translational applications in breeding in mind. But pangenomes are applicable also in ecological and evolutionary studies, as they help classify and monitor biodiversity across the tree of life, deepen our understanding of how plant species diverged and show how plants adapt to changing environments or new selection pressures exerted by human beings.

Drivers of genomic diversity and phenotypic development in early phases of domestication in Hermetia illucens

The black soldier fly (BSF), Hermetia illucens, has the ability to efficiently bioremediate organic waste into usable bio-compounds. Understanding the impact of domestication and mass rearing on fitness and production traits is therefore important for sustainable production. This study aimed to assess patterns of genomic diversity and its association to phenotypic development across early generations of mass rearing under two selection strategies: selection for greater larval mass (SEL lines) and no direct artificial selection (NS lines). Genome-wide single nucleotide polymorphism (SNP) data were generated using 2bRAD sequencing, while phenotypic traits relating to production and population fitness were measured. Declining patterns of genomic diversity were observed across three generations of captive breeding, with the lowest diversity recorded for the F3 generation of both selection lines, most likely due to founder effects. The SEL cohort displayed statistically significantly greater larval weight com the NS lines with pronounced genetic and phenotypic directional changes across generations. Furthermore, lower genetic and phenotypic diversity, particularly for fitness traits, were evident for SEL lines, illustrating the trade-off between selecting for mass and the resulting decline in population fitness. SNP-based heritability was significant for growth, but was low or non-significant for fitness traits. Genotype-phenotype correlations were observed for traits, but individual locus effect sizes where small and very few of these loci demonstrated a signature for selection. Pronounced genetic drift, due to small effective population sizes, is likely overshadowing the impacts of selection on genomic diversity and consequently phenotypic development. The results hold particular relevance for genetic management and selective breeding for BSF in future.

Fisher's Geometric Model as a Tool to Study Speciation

Interactions between alleles and across environments play an important role in the fitness of hybrids and are at the heart of the speciation process. Fitness landscapes capture these interactions and can be used to model hybrid fitness, helping us to interpret empirical observations and clarify verbal models. Here, we review recent progress in understanding hybridization outcomes through Fisher's geometric model, an intuitive and analytically tractable fitness landscape that captures many fitness patterns observed across taxa. We use case studies to show how the model parameters can be estimated from different types of data and discuss how these estimates can be used to make inferences about the divergence history and genetic architecture. We also highlight some areas where the model's predictions differ from alternative incompatibility-based models, such as the snowball effect and outlier patterns in genome scans.

Geographic variation in evolutionary rescue under climate change in a crop pest-predator system

Species distribution models (SDMs) are often built upon the "niche conservatism" assumption, such that they ignore the possibility of "evolutionary rescue" and may underestimate species' future range limits under climate change. We select aphids and ladybirds as model species and develop an eco-evolutionary model to explore evolutionary rescue in a predator-prey system under climate change. We model the adaptive change of species' thermal performances, accounting for biotic interactions. Our study suggests that, without considering evolutionary adaptation, the warming climate will result in a reduction in aphid populations and the extinction of ladybirds in large parts of the United States. However, when incorporating evolutionary adaptation into the model, aphids can adapt to climate change, whereas ladybirds demonstrate geographic variation in their evolutionary rescue potential. Specifically, ladybirds in southern regions are more likely to be rescued than those in the north. In certain northern regions, ladybirds do not avoid extinction due to severe warming trends and seasonality of the climate. While higher warming trends do prompt stronger evolutionary changes in phenotype, they also lead to reduced aphid population abundance such that ecology constrains ladybird population growth. Higher seasonality induces an ecological effect by limiting the length of reproductive season, thereby reducing the capacity for evolutionary rescue. Together, these findings reveal the complex interplay between ecological and evolutionary dynamics in the context of evolutionary adaptation to climate change.

Limits to species' range: the tension between local and global adaptation

We know that heritable variation is abundant, and that selection causes all but the smallest populations to rapidly shift beyond their original trait distribution. So then, what limits the range of a species? There are physical constraints and also population genetic limits to the effectiveness of selection, ultimately set by population size. Global adaptation, where the same genotype is favoured over the whole range, is most efficient when based on a multitude of weakly selected alleles and is effective even when local demes are small, provided that there is some gene flow. In contrast, local adaptation is sensitive to gene flow and may require alleles with substantial effect. How can populations combine the advantages of large effective size with the ability to specialise into local niches? To what extent does reproductive isolation help resolve this tension? I address these questions using eco-evolutionary models of polygenic adaptation, contrasting discrete demes with continuousspace.

Multi-OMICS approaches in cancer biology: New era in cancer therapy

Innovative multi-omics frameworks integrate diverse datasets from the same patients to enhance our understanding of the molecular and clinical aspects of cancers. Advanced omics and multi-view clustering algorithms present unprecedented opportunities for classifying cancers into subtypes, refining survival predictions and treatment outcomes, and unravelling key pathophysiological processes across various molecular layers. However, with the increasing availability of cost-effective high-throughput technologies (HTT) that generate vast amounts of data, analyzing single layers often falls short of establishing causal relations. Integrating multi-omics data spanning genomes, epigenomes, transcriptomes, proteomes, metabolomes, and microbiomes offers unique prospects to comprehend the underlying biology of complex diseases like cancer. This discussion explores algorithmic frameworks designed to uncover cancer subtypes, disease mechanisms, and methods for identifying pivotal genomic alterations. It also underscores the significance of multi-omics in tumor classifications, diagnostics, and prognostications. Despite its unparalleled advantages, the integration of multi-omics data has been slow to find its way into everyday clinics. A major hurdle is the uneven maturity of different omics approaches and the widening gap between the generation of large datasets and the capacity to process this data. Initiatives promoting the standardization of sample processing and analytical pipelines, as well as multidisciplinary training for experts in data analysis and interpretation, are crucial for translating theoretical findings into practical applications.

The complex relationship between disease resistance and yield in crops

In plants, growth and defence are controlled by many molecular pathways that are antagonistic to one another. This results in a 'growth-defence trade-off', where plants temporarily reduce growth in response to pests or diseases. Due to this antagonism, genetic variants that improve resistance often reduce growth and vice versa. Therefore, in natural populations, the most disease resistant individuals are often the slowest growing. In crops, slow growth may translate into a yield penalty, but resistance is essential for protecting yield in the presence of disease. Therefore, plant breeders must balance these traits to ensure optimal yield potential and yield stability. In crops, both qualitative and quantitative disease resistance are often linked with genetic variants that cause yield penalties, but this is not always the case. Furthermore, both crop yield and disease resistance are complex traits influenced by many aspects of the plant's physiology, morphology and environment, and the relationship between the molecular growth-defence trade-off and disease resistance-yield antagonism is not well-understood. In this article, we highlight research from the last 2 years on the molecular mechanistic basis of the antagonism between defence and growth. We then discuss the interaction between disease resistance and crop yield from a breeding perspective, outlining the complexity and nuances of this relationship and where research can aid practical methods for simultaneous improvement of yield potential and disease resistance.

Bursts of coalescence within population pedigrees whenever big families occur

We consider a simple diploid population-genetic model with potentially high variability of offspring numbers among individuals. Specifically, against a backdrop of Wright-Fisher reproduction and no selection, there is an additional probability that a big family occurs, meaning that a pair of individuals has a number of offspring on the order of the population size. We study how the pedigree of the population generated under this model affects the ancestral genetic process of a sample of size two at a single autosomal locus without recombination. Our population model is of the type for which multiple-merger coalescent processes have been described. We prove that the conditional distribution of the pairwise coalescence time given the random pedigree converges to a limit law as the population size tends to infinity. This limit law may or may not be the usual exponential distribution of the Kingman coalescent, depending on the frequency of big families. But because it includes the number and times of big families, it differs from the usual multiple-merger coalescent models. The usual multiple-merger coalescent models are seen as describing the ancestral process marginal to, or averaging over, the pedigree. In the limiting ancestral process conditional on the pedigree, the intervals between big families can be modeled using the Kingman coalescent but each big family causes a discrete jump in the probability of coalescence. Analogous results should hold for larger samples and other population models. We illustrate these results with simulations and additional analysis, highlighting their implications for inference and understanding of multilocus data.

Are cereal grasses a single genetic system?

In 1993, a passionate and provocative call to arms urged cereal researchers to consider the taxon they study as a single genetic system and collaborate with each other. Since then, that group of scientists has seen their discipline blossom. In an attempt to understand what unity of genetic systems means and how the notion was borne out by later research, we survey the progress and prospects of cereal genomics: sequence assemblies, population-scale sequencing, resistance gene cloning and domestication genetics. Gene order may not be as extraordinarily well conserved in the grasses as once thought. Still, several recurring themes have emerged. The same ancestral molecular pathways defining plant architecture have been co-opted in the evolution of different cereal crops. Such genetic convergence as much as cross-fertilization of ideas between cereal geneticists has led to a rich harvest of genes that, it is hoped, will lead to improved varieties.

Evolution of Phenotypic Variance Provides Insights into the Genetic Basis of Adaptation

Most traits are polygenic, and the contributing loci can be identified by genome-wide association studies. The genetic basis of adaptation (adaptive architecture) is, however, difficult to characterize. Here, we propose to study the adaptive architecture of traits by monitoring the evolution of their phenotypic variance during adaptation to a new environment in well-defined laboratory conditions. Extensive computer simulations show that the evolution of phenotypic variance in a replicated experimental evolution setting can distinguish between oligogenic and polygenic adaptive architectures. We compared gene expression variance in male Drosophila simulans before and after 100 generations of adaptation to a novel hot environment. The variance change in gene expression was indistinguishable for genes with and without a significant change in mean expression after 100 generations of evolution. We suggest that the majority of adaptive gene expression evolution can be explained by a polygenic architecture. We propose that tracking the evolution of phenotypic variance across generations can provide an approach to characterize the adaptive architecture.

Large effects and the infinitesimal model

The infinitesimal model of quantitative genetics relies on the Central Limit Theorem to stipulate that under additive models of quantitative traits determined by many loci having similar effect size, the difference between an offspring's genetic trait component and the average of their two parents' genetic trait components is Normally distributed and independent of the parents' values. Here, we investigate how the assumption of similar effect sizes affects the model: if, alternatively, the tail of the effect size distribution is polynomial with exponent α<2, then a different Central Limit Theorem implies that sums of effects should be well-approximated by a "stable distribution", for which single large effects are often still important. Empirically, we first find tail exponents between 1 and 2 in effect sizes estimated by genome-wide association studies of many human disease-related traits. We then show that the independence of offspring trait deviations from parental averages in many cases implies the Gaussian aspect of the infinitesimal model, suggesting that non-Gaussian models of trait evolution must explicitly track the underlying genetics, at least for loci of large effect. We also characterize possible limiting trait distributions of the infinitesimal model with infinitely divisible noise distributions, and compare our results to simulations.

Unifying approaches from statistical genetics and phylogenetics for mapping phenotypes in structured populations

In both statistical genetics and phylogenetics, a major goal is to identify correlations between genetic loci or other aspects of the phenotype or environment and a focal trait. In these two fields, there are sophisticated but disparate statistical traditions aimed at these tasks. The disconnect between their respective approaches is becoming untenable as questions in medicine, conservation biology, and evolutionary biology increasingly rely on integrating data from within and among species, and once-clear conceptual divisions are becoming increasingly blurred. To help bridge this divide, we derive a general model describing the covariance between the genetic contributions to the quantitative phenotypes of different individuals. Taking this approach shows that standard models in both statistical genetics (e.g., Genome-Wide Association Studies; GWAS) and phylogenetic comparative biology (e.g., phylogenetic regression) can be interpreted as special cases of this more general quantitative-genetic model. The fact that these models share the same core architecture means that we can build a unified understanding of the strengths and limitations of different methods for controlling for genetic structure when testing for associations. We develop intuition for why and when spurious correlations may occur using analytical theory and conduct population-genetic and phylogenetic simulations of quantitative traits. The structural similarity of problems in statistical genetics and phylogenetics enables us to take methodological advances from one field and apply them in the other. We demonstrate this by showing how a standard GWAS technique-including both the genetic relatedness matrix (GRM) as well as its leading eigenvectors, corresponding to the principal components of the genotype matrix, in a regression model-can mitigate spurious correlations in phylogenetic analyses. As a case study of this, we re-examine an analysis testing for co-evolution of expression levels between genes across a fungal phylogeny, and show that including covariance matrix eigenvectors as covariates decreases the false positive rate while simultaneously increasing the true positive rate. More generally, this work provides a foundation for more integrative approaches for understanding the genetic architecture of phenotypes and how evolutionary processes shape it.

Unraveling Adaptive Evolutionary Divergence at Microgeographic Scales

AbstractStriking examples of local adaptation at fine geographic scales are increasingly being documented in natural populations. However, the relative contributions made by natural selection, phenotype-dependent dispersal (when individuals disperse with respect to a habitat preference), and mate preference in generating and maintaining microgeographic adaptation and divergence are not well studied. Here, we develop quantitative genetics models and individual-based simulations (IBSs) to uncover the evolutionary forces that possibly drive microgeographic divergence. We also perform Bayesian estimation of the parameters in our IBS using empirical data on habitat-specific variation in bill morphology in the island scrub-jay (Aphelocoma insularis) to apply our models to a natural system. We find that natural selection and phenotype-dependent dispersal can generate the patterns of divergence we observe in the island scrub-jay. However, mate preference for a mate with similar bill morphology, even though observed in the species, does not play a significant role in driving divergence. Our modeling approach provides insights into phenotypic evolution occurring over small spatial scales relative to dispersal ranges, suggesting that adaptive divergence at microgeographic scales may be common across a wider range of taxa than previously thought. Our quantitative genetic models help to inform future theoretical and empirical work to determine how selection, habitat preference, and mate preference contribute to local adaptation and microgeographic divergence.

A mathematical framework for evo-devo dynamics

Natural selection acts on phenotypes constructed over development, which raises the question of how development affects evolution. Classic evolutionary theory indicates that development affects evolution by modulating the genetic covariation upon which selection acts, thus affecting genetic constraints. However, whether genetic constraints are relative, thus diverting adaptation from the direction of steepest fitness ascent, or absolute, thus blocking adaptation in certain directions, remains uncertain. This limits understanding of long-term evolution of developmentally constructed phenotypes. Here we formulate a general, tractable mathematical framework that integrates age progression, explicit development (i.e., the construction of the phenotype across life subject to developmental constraints), and evolutionary dynamics, thus describing the evolutionary and developmental (evo-devo) dynamics. The framework yields simple equations that can be arranged in a layered structure that we call the evo-devo process, whereby five core elementary components generate all equations including those mechanistically describing genetic covariation and the evo-devo dynamics. The framework recovers evolutionary dynamic equations in gradient form and describes the evolution of genetic covariation from the evolution of genotype, phenotype, environment, and mutational covariation. This shows that genotypic and phenotypic evolution must be followed simultaneously to yield a dynamically sufficient description of long-term phenotypic evolution in gradient form, such that evolution described as the climbing of a fitness landscape occurs in "geno-phenotype" space. Genetic constraints in geno-phenotype space are necessarily absolute because the phenotype is related to the genotype by development. Thus, the long-term evolutionary dynamics of developed phenotypes is strongly non-standard: (1) evolutionary equilibria are either absent or infinite in number and depend on genetic covariation and hence on development; (2) developmental constraints determine the admissible evolutionary path and hence which evolutionary equilibria are admissible; and (3) evolutionary outcomes occur at admissible evolutionary equilibria, which do not generally occur at fitness landscape peaks in geno-phenotype space, but at peaks in the admissible evolutionary path where "total genotypic selection" vanishes if exogenous plastic response vanishes and mutational variation exists in all directions of genotype space. Hence, selection and development jointly define the evolutionary outcomes if absolute mutational constraints and exogenous plastic response are absent, rather than the outcomes being defined only by selection. Moreover, our framework provides formulas for the sensitivities of a recurrence and an alternative method to dynamic optimization (i.e., dynamic programming or optimal control) to identify evolutionary outcomes in models with developmentally dynamic traits. These results show that development has major evolutionary effects.

Rapid genomic evolution in Brassica rapa with bumblebee selection in experimental evolution

BACKGROUND

Insect pollinators shape rapid phenotypic evolution of traits related to floral attractiveness and plant reproductive success. However, the underlying genomic changes remain largely unknown despite their importance in predicting adaptive responses to natural or to artificial selection. Based on a nine-generation experimental evolution study with fast cycling Brassica rapa plants adapting to bumblebees, we investigate the genomic evolution associated with the previously observed parallel phenotypic evolution. In this current evolve and resequencing (E&R) study, we conduct a genomic scan of the allele frequency changes along the genome in bumblebee-pollinated and hand-pollinated plants and perform a genomic principal component analysis (PCA).

RESULTS

We highlight rapid genomic evolution associated with the observed phenotypic evolution mediated by bumblebees. Controlling for genetic drift, we observe significant changes in allelic frequencies at multiple loci. However, this pattern differs according to the replicate of bumblebee-pollinated plants, suggesting putative non-parallel genomic evolution. Finally, our study underlines an increase in genomic variance implying the putative involvement of multiple loci in short-term pollinator adaptation.

CONCLUSIONS

Overall, our study enhances our understanding of the complex interactions between pollinator and plants, providing a stepping stone towards unravelling the genetic basis of plant genomic adaptation to biotic factors in the environment.

Host-Parasite Coevolution in Continuous Space Leads to Variation in Local Adaptation across Spatial Scales

AbstractPrevious host-parasite coevolutionary theory has focused on understanding the determinants of local adaptation using spatially discrete models. However, these studies fall short of describing patterns of host-parasite local adaptation across spatial scales. In contrast, empirical work demonstrates that patterns of adaptation depend on the scale at which they are measured. Here, we propose a mathematical model of host-parasite coevolution in continuous space that naturally leads to a scale-dependent definition of local adaptation. In agreement with empirical research, we find that patterns of adaptation vary across spatial scales. In some cases, not only the magnitude of local adaptation but also the identity of the locally adapted species will depend on the spatial scale at which measurements are taken. Building on our results, we suggest a way to consistently measure parasite local adaptation when continuous space is the driver of cross-scale variation. We also describe a way to test whether continuous space is driving cross-scale variation. Taken together, our results provide a new perspective that can be used to understand empirical observations previously unexplained by theoretical expectations and deepens our understanding of the mechanics of host-parasite local adaptation.

Repeatability of adaptation in sunflowers reveals that genomic regions harbouring inversions also drive adaptation in species lacking an inversion

Local adaptation commonly involves alleles of large effect, which experience fitness advantages when in positive linkage disequilibrium (LD). Because segregating inversions suppress recombination and facilitate the maintenance of LD between locally adapted loci, they are also commonly found to be associated with adaptive divergence. However, it is unclear what fraction of an adaptive response can be attributed to inversions and alleles of large effect, and whether the loci within an inversion could still drive adaptation in the absence of its recombination-suppressing effect. Here, we use genome-wide association studies to explore patterns of local adaptation in three species of sunflower: Helianthus annuus, Helianthus argophyllus, and Helianthus petiolaris, which each harbour a large number of species-specific inversions. We find evidence of significant genome-wide repeatability in signatures of association to phenotypes and environments, which are particularly enriched within regions of the genome harbouring an inversion in one species. This shows that while inversions may facilitate local adaptation, at least some of the loci can still harbour mutations that make substantial contributions without the benefit of recombination suppression in species lacking a segregating inversion. While a large number of genomic regions show evidence of repeated adaptation, most of the strongest signatures of association still tend to be species-specific, indicating substantial genotypic redundancy for local adaptation in these species.

Pervasive G × E interactions shape adaptive trajectories and the exploration of the phenotypic space in artificial selection experiments

Quantitative genetics models have shown that long-term selection responses depend on initial variance and mutational influx. Understanding limits of selection requires quantifying the role of mutational variance. However, correlative responses to selection on nonfocal traits can perturb the selection response on the focal trait; and generations are often confounded with selection environments so that genotype by environment (G×E) interactions are ignored. The Saclay divergent selection experiments (DSEs) on maize flowering time were used to track the fate of individual mutations combining genotyping data and phenotyping data from yearly measurements (DSEYM) and common garden experiments (DSECG) with four objectives: (1) to quantify the relative contribution of standing and mutational variance to the selection response, (2) to estimate genotypic mutation effects, (3) to study the impact of G×E interactions in the selection response, and (4) to analyze how trait correlations modulate the exploration of the phenotypic space. We validated experimentally the expected enrichment of fixed beneficial mutations with an average effect of +0.278 and +0.299 days to flowering, depending on the genetic background. Fixation of unfavorable mutations reached up to 25% of incoming mutations, a genetic load possibly due to antagonistic pleiotropy, whereby mutations fixed in the selection environment (DSEYM) turned to be unfavorable in the evaluation environment (DSECG). Global patterns of trait correlations were conserved across genetic backgrounds but exhibited temporal patterns. Traits weakly or uncorrelated with flowering time triggered stochastic exploration of the phenotypic space, owing to microenvironment-specific fixation of standing variants and pleiotropic mutational input.

Unraveling the Molecular Basis of Stabilizing Selection by Experimental Evolution

Stabilizing selection provides a challenge to molecular population genetics. Although stabilizing selection is ubiquitous, its genomic signature is difficult to distinguish from demographic signals. Experimental evolution provides a promising approach to characterize genomic regions exposed to stabilizing selection. A recent experimental evolution study of Aedes aegypti populations evolving either with or without sexual selection found a pattern of genetic differentiation suggestive of relaxed stabilizing selection. I argue that this study could not have detected the signal of relaxed stabilizing selection. I highlight why incorrect statistical methods resulted in a high number of false positive candidate single nucleotide polymorphism (SNPs) and discuss the fallacy of functional validation of candidate SNPs for polygenic traits by RNA-mediated knockdown.

A Wolf in Sheep's Clothing: Idealisations and the aims of polygenic scores

Research in pharmacogenomics and precision medicine has recently introduced the concept of Polygenic Scores (PGSs), namely, indexes that aggregate the effects that many genetic variants are predicted to have on individual disease risk. The popularity of PGSs is increasing rapidly, but surprisingly little attention has been paid to the idealisations they make about phenotypic development. Indeed, PGSs rely on quantitative genetics models and methods, which involve considerable theoretical assumptions that have been questioned on various grounds. This comes with epistemological and ethical concerns about the use of PGSs in clinical decision-making. In this paper, I investigate to what extent idealisations in genetics models can impact the data gathering and clinical interpretation of genomics findings, particularly the calculation and predictive accuracy of PGSs. Although idealisations are considered ineliminable components of scientific models, they may be legitimate or not depending on the epistemic aims of a model. I thus analyse how various idealisations have been introduced in classical models and progressively readapted throughout the history of genetic theorising. Notably, this process involved important changes in the epistemic purpose of such idealisations, which raises the question of whether they are legitimate in the context of contemporary genomics.

The limitations of phenotype prediction in metabolism

Phenotype prediction is at the center of many questions in biology. Prediction is often achieved by determining statistical associations between genetic and phenotypic variation, ignoring the exact processes that cause the phenotype. Here, we present a framework based on genome-scale metabolic reconstructions to reveal the mechanisms behind the associations. We calculated a polygenic score (PGS) that identifies a set of enzymes as predictors of growth, the phenotype. This set arises from the synergy of the functional mode of metabolism in a particular setting and its evolutionary history, and is suitable to infer the phenotype across a variety of conditions. We also find that there is optimal genetic variation for predictability and demonstrate how the linear PGS can still explain phenotypes generated by the underlying nonlinear biochemistry. Therefore, the explicit model interprets the black box statistical associations of the genotype-to-phenotype map and helps to discover what limits the prediction in metabolism.

A theory of oligogenic adaptation of a quantitative trait

Rapid phenotypic adaptation is widespread in nature, but the underlying genetic dynamics remain controversial. Whereas population genetics envisages sequential beneficial substitutions, quantitative genetics assumes a collective response through subtle shifts in allele frequencies. This dichotomy of a monogenic and a highly polygenic view of adaptation raises the question of a middle ground, as well as the factors controlling the transition. Here, we consider an additive quantitative trait with equal locus effects under Gaussian stabilizing selection that adapts to a new trait optimum after an environmental change. We present an analytical framework based on Yule branching processes to describe how phenotypic adaptation is achieved by collective changes in allele frequencies at the underlying loci. In particular, we derive an approximation for the joint allele-frequency distribution conditioned on the trait mean as a comprehensive descriptor of the adaptive architecture. Depending on the model parameters, this architecture reproduces the well-known patterns of sequential, monogenic sweeps, or of subtle, polygenic frequency shifts. Between these endpoints, we observe oligogenic architecture types that exhibit characteristic patterns of partial sweeps. We find that a single compound parameter, the population-scaled background mutation rate Θbg, is the most important predictor of the type of adaptation, while selection strength, the number of loci in the genetic basis, and linkage only play a minor role.

The infinitesimal model with dominance

The classical infinitesimal model is a simple and robust model for the inheritance of quantitative traits. In this model, a quantitative trait is expressed as the sum of a genetic and an environmental component, and the genetic component of offspring traits within a family follows a normal distribution around the average of the parents' trait values, and has a variance that is independent of the parental traits. In previous work, we showed that when trait values are determined by the sum of a large number of additive Mendelian factors, each of small effect, one can justify the infinitesimal model as a limit of Mendelian inheritance. In this paper, we show that this result extends to include dominance. We define the model in terms of classical quantities of quantitative genetics, before justifying it as a limit of Mendelian inheritance as the number, M, of underlying loci tends to infinity. As in the additive case, the multivariate normal distribution of trait values across the pedigree can be expressed in terms of variance components in an ancestral population and probabilities of identity by descent determined by the pedigree. Now, with just first-order dominance effects, we require two-, three-, and four-way identities. We also show that, even if we condition on parental trait values, the "shared" and "residual" components of trait values within each family will be asymptotically normally distributed as the number of loci tends to infinity, with an error of order 1/M. We illustrate our results with some numerical examples.

The evolutionary ecology of variation in labile traits: selection on its among- and within-individual components

Closer integration between behavioral ecology and quantitative genetics has resulted in a recent increase in studies partitioning sources of variation in labile traits. Repeatable between-individual differences are commonly documented, and their existence is generally explained using adaptive arguments, implying that selection has shaped variation at the among- and within-individual level. However, predicting the expected pattern of non-adaptive phenotypic variation around an optimal phenotypic value is difficult, hampering our ability to provide quantitative assessments of the adaptive nature of observed patterns of phenotypic variation within a population. We argue that estimating the strength of selection on trait variation among and within individuals provides a way to test adaptive theory concerned with phenotypic variation. To achieve this aim, we describe a nonlinear selection analysis that enables the study of the selective pressures on trait means and their among- and within-individual variation. By describing an integrative approach for studying the strength of selection on phenotypic variation at different levels, we hope to stimulate empirical studies investigating the ecological factors that can shape the repeatability, heritability, and coefficients of variation of labile and other repeatedly expressed traits.

The genotype-phenotype relationship and evolutionary genetics in the light of the Metabolic Control Analysis

Metabolic control analysis has long been used as a systemic model of the genotype-phenotype (GP) relationship. By considering kinetic parameters and enzyme concentrations as reflecting the genotype level and metabolic fluxes or pools as phenotypes related to fitness, MCA has given a biological basis to the relationship between these two levels. The non-linear and concave relationship between enzymes and fluxes can account for common genetic effects that reductionist approaches have been powerless to explain, such as the dominance of active alleles over less active alleles, the various types of epistasis and heterosis, and reveals the structural links between these genetic effects. The summation property of the flux control coefficients accounts for the L-shaped distribution of Quantitative Trait Locus (QTL) effects, irrespective of other possible causes. Metabolic models of response to selection results in evolutionary scenarios that are markedly different from those derived from the classical infinitesimal model of quantitative genetics. In particular, evolution towards selective neutrality appears to be a consequence of the diminishing return of the flux-enzyme relationship. In this paper, we survey the historical and recent achievements of MCA in genetics, quantitative genetics and evolution, focusing on epistasis and the evolution of flux in relation to enzyme concentrations.

The long-term effects of genomic selection: 2. Changes in allele frequencies of causal loci and new mutations

Genetic selection has been applied for many generations in animal, plant, and experimental populations. Selection changes the allelic architecture of traits to create genetic gain. It remains unknown whether the changes in allelic architecture are different for the recently introduced technique of genomic selection compared to traditional selection methods and whether they depend on the genetic architectures of traits. Here, we investigate the allele frequency changes of old and new causal loci under 50 generations of phenotypic, pedigree, and genomic selection, for a trait controlled by either additive, additive and dominance, or additive, dominance, and epistatic effects. Genomic selection resulted in slightly larger and faster changes in allele frequencies of causal loci than pedigree selection. For each locus, allele frequency change per generation was not only influenced by its statistical additive effect but also to a large extent by the linkage phase with other loci and its allele frequency. Selection fixed a large number of loci, and 5 times more unfavorable alleles became fixed with genomic and pedigree selection than with phenotypic selection. For pedigree selection, this was mainly a result of increased genetic drift, while genetic hitchhiking had a larger effect on genomic selection. When epistasis was present, the average allele frequency change was smaller (∼15% lower), and a lower number of loci became fixed for all selection methods. We conclude that for long-term genetic improvement using genomic selection, it is important to consider hitchhiking and to limit the loss of favorable alleles.

Selection and the direction of phenotypic evolution

Predicting adaptive phenotypic evolution depends on invariable selection gradients and on the stability of the genetic covariances between the component traits of the multivariate phenotype. We describe the evolution of six traits of locomotion behavior and body size in the nematode Caenorhabditis elegans for 50 generations of adaptation to a novel environment. We show that the direction of adaptive multivariate phenotypic evolution can be predicted from the ancestral selection differentials, particularly when the traits were measured in the new environment. Interestingly, the evolution of individual traits does not always occur in the direction of selection, nor are trait responses to selection always homogeneous among replicate populations. These observations are explained because the phenotypic dimension with most of the ancestral standing genetic variation only partially aligns with the phenotypic dimension under directional selection. These findings validate selection theory and suggest that the direction of multivariate adaptive phenotypic evolution is predictable for tens of generations.

Management of diversity and inbreeding when importing new stock into an inbred population

This article relates to breeding programs that seek to manage genetic diversity. The method maximizes a multicomponent objective function, applicable across breeding scenarios. However, this paper focuses on breeding decisions following immigration of 10 unrelated individuals into a highly inbred simulated population (F ≈ 0.34). We use Optimal Contribution Selection to maximize retention of genetic diversity. However, some treatments add Coancestry Assortative Mating (CAM). This helps to avoid early dilution of immigrant genetic material, maximizing its ability to contribute to genetic diversity in the longer term. After 20 generations, this resulted in considerably increased genetic diversity, with mean coancestries 59% of what random pairing gave. To manage progeny inbreeding, common practice is to reject matings above an upper limit. As a suboptimal rules-based approach, this resulted in 26% decreased genetic diversity and 8% increased inbreeding in the long term, compared with random pairing. In contrast, including mean progeny inbreeding as a continuous variable in the overall objective function decreased final inbreeding by 37% compared with random pairing. Adding some emphasis on selection for a single trait resulted in a similar pattern of effects on coancestry and inbreeding, with 12% higher trait response under CAM. Results indicate the properties of alternative methods, but we encourage users to do their own investigations of particular scenarios, such as including inbreeding depression. Practical implementation of these methods is discussed: they have been widely adopted in domestic animal breeding and are highly flexible to accommodate a wide range of technical and logistical objectives and constraints.

Genetic Architecture of Flowering Time Differs Between Populations With Contrasting Demographic and Selective Histories

Understanding the evolutionary factors that impact the genetic architecture of traits is a central goal of evolutionary genetics. Here, we investigate how quantitative trait variation accumulated over time in populations that colonized a novel environment. We compare the genetic architecture of flowering time in Arabidopsis populations from the drought-prone Cape Verde Islands and their closest outgroup population from North Africa. We find that trait polygenicity is severely reduced in the island populations compared to the continental North African population. Further, trait architectures and reconstructed allelic histories best fit a model of strong directional selection in the islands in accord with a Fisher-Orr adaptive walk. Consistent with this, we find that large-effect variants that disrupt major flowering time genes (FRI and FLC) arose first, followed by smaller effect variants, including ATX2 L125F, which is associated with a 4-day reduction in flowering time. The most recently arising flowering time-associated loci are not known to be directly involved in flowering time, consistent with an omnigenic signature developing as the population approaches its trait optimum. Surprisingly, we find no effect in the natural population of EDI-Cvi-0 (CRY2 V367M), an allele for which an effect was previously validated by introgression into a Eurasian line. Instead, our results suggest the previously observed effect of the EDI-Cvi-0 allele on flowering time likely depends on genetic background, due to an epistatic interaction. Altogether, our results provide an empirical example of the effects demographic history and selection has on trait architecture.

The contributions of rare inherited and polygenic risk to ASD in multiplex families

Autism spectrum disorder (ASD) has a complex genetic architecture involving contributions from both de novo and inherited variation. Few studies have been designed to address the role of rare inherited variation or its interaction with common polygenic risk in ASD. Here, we performed whole-genome sequencing of the largest cohort of multiplex families to date, consisting of 4,551 individuals in 1,004 families having two or more autistic children. Using this study design, we identify seven previously unrecognized ASD risk genes supported by a majority of rare inherited variants, finding support for a total of 74 genes in our cohort and a total of 152 genes after combined analysis with other studies. Autistic children from multiplex families demonstrate an increased burden of rare inherited protein-truncating variants in known ASD risk genes. We also find that ASD polygenic score (PGS) is overtransmitted from nonautistic parents to autistic children who also harbor rare inherited variants, consistent with combinatorial effects in the offspring, which may explain the reduced penetrance of these rare variants in parents. We also observe that in addition to social dysfunction, language delay is associated with ASD PGS overtransmission. These results are consistent with an additive complex genetic risk architecture of ASD involving rare and common variation and further suggest that language delay is a core biological feature of ASD.

Adaptation of a quantitative trait to a changing environment: New analytical insights on the asexual and infinitesimal sexual models

Predicting the adaptation of populations to a changing environment is crucial to assess the impact of human activities on biodiversity. Many theoretical studies have tackled this issue by modeling the evolution of quantitative traits subject to stabilizing selection around an optimal phenotype, whose value is shifted continuously through time. In this context, the population fate results from the equilibrium distribution of the trait, relative to the moving optimum. Such a distribution may vary with the shape of selection, the system of reproduction, the number of loci, the mutation kernel or their interactions. Here, we develop a methodology that provides quantitative measures of population maladaptation and potential of survival directly from the entire profile of the phenotypic distribution, without any a priori on its shape. We investigate two different systems of reproduction (asexual and infinitesimal sexual models of inheritance), with various forms of selection. In particular, we recover that fitness functions such that selection weakens away from the optimum lead to evolutionary tipping points, with an abrupt collapse of the population when the speed of environmental change is too high. Our unified framework allows deciphering the mechanisms that lead to this phenomenon. More generally, it allows discussing similarities and discrepancies between the two systems of reproduction, which are ultimately explained by different constraints on the evolution of the phenotypic variance. We demonstrate that the mean fitness in the population crucially depends on the shape of the selection function in the infinitesimal sexual model, in contrast with the asexual model. In the asexual model, we also investigate the effect of the mutation kernel and we show that kernels with higher kurtosis tend to reduce maladaptation and improve fitness, especially in fast changing environments.

A Theoretical Framework for Trait-Based Eco-Evolutionary Dynamics: Population Structure, Intraspecific Variation, and Community Assembly

AbstractHow is trait diversity in a community apportioned between and within coevolving species? Disruptive selection may result in either a few species with large intraspecific trait variation (ITV) or many species with different mean traits but little ITV. Similar questions arise in spatially structured communities: heterogeneous environments could result in either a few species that exhibit local adaptation or many species with different mean traits but little local adaptation. To date, theory has been well-equipped to either include ITV or to dynamically determine the number of coexisting species, but not both. Here, we devise a theoretical framework that combines these facets and apply it to the above questions of how trait variation is apportioned within and between species in unstructured and structured populations, using two simple models of Lotka-Volterra competition. For unstructured communities, we find that as the breadth of the resource spectrum increases, ITV goes from being unimportant to crucial for characterizing the community. For spatially structured communities on two patches, we find no local adaptation, symmetric local adaptation, or asymmetric local adaptation, depending on how much the patches differ. Our framework provides a general approach to incorporate ITV in models of eco-evolutionary community assembly.

Adaption, neutrality and life-course diversity

Heterogeneity among individuals in fitness components is what selection acts upon. Evolutionary theories predict that selection in constant environments acts against such heterogeneity. But observations reveal substantial non-genetic and also non-environmental variability in phenotypes. Here, we examine whether there is a relationship between selection pressure and phenotypic variability by analysing structured population models based on data from a large and diverse set of species. Our findings suggest that non-genetic, non-environmental variation is in general neither truly neutral, selected for, nor selected against. We find much variations among species and populations within species, with mean patterns suggesting nearly neutral evolution of life-course variability. Populations that show greater diversity of life courses do not show, in general, increased or decreased population growth rates. Our analysis suggests we are only at the beginning of understanding the evolution and maintenance of non-genetic non-environmental variation.

Variation in mutational (co)variances

Because of pleiotropy, mutations affect the expression and inheritance of multiple traits and, together with selection, are expected to shape standing genetic covariances between traits and eventual phenotypic divergence between populations. It is therefore important to find if the M matrix, describing mutational variances of each trait and covariances between traits, varies between genotypes. We here estimate the M matrix for six locomotion behavior traits in lines of two genotypes of the nematode Caenorhabditis elegans that accumulated mutations in a nearly neutral manner for 250 generations. We find significant mutational variance along at least one phenotypic dimension of the M matrices, but neither their size nor their orientation had detectable differences between genotypes. The number of generations of mutation accumulation, or the number of MA lines measured, was likely insufficient to sample enough mutations and detect potentially small differences between the two M matrices. We then tested if the M matrices were similar to one G matrix describing the standing genetic (co)variances of a population derived by the hybridization of several genotypes, including the two measured for M, and domesticated to a lab-defined environment for 140 generations. We found that the M and G were different because the genetic covariances caused by mutational pleiotropy in the two genotypes are smaller than those caused by linkage disequilibrium in the lab population. We further show that M matrices differed in their alignment with the lab population G matrix. If generalized to other founder genotypes of the lab population, these observations indicate that selection does not shape the evolution of the M matrix for locomotion behavior in the short-term of a few tens to hundreds of generations and suggests that the hybridization of C. elegans genotypes allows selection on new phenotypic dimensions of locomotion behavior.

How development affects evolution

Natural selection acts on developmentally constructed phenotypes, but how does development affect evolution? This question prompts a simultaneous consideration of development and evolution. However, there has been a lack of general mathematical frameworks mechanistically integrating the two, which may have inhibited progress on the question. Here, we use a new mathematical framework that mechanistically integrates development into evolution to analyse how development affects evolution. We show that, while selection pushes genotypic and phenotypic evolution up the fitness landscape, development determines the admissible evolutionary pathway, such that evolutionary outcomes occur at path peaks rather than landscape peaks. Changes in development can generate path peaks, triggering genotypic or phenotypic diversification, even on constant, single-peak landscapes. Phenotypic plasticity, niche construction, extra-genetic inheritance, and developmental bias alter the evolutionary path and hence the outcome. Thus, extra-genetic inheritance can have permanent evolutionary effects by changing the developmental constraints, even if extra-genetically acquired elements are not transmitted to future generations. Selective development, whereby phenotype construction points in the adaptive direction, may induce adaptive or maladaptive evolution depending on the developmental constraints. Moreover, developmental propagation of phenotypic effects over age enables the evolution of negative senescence. Overall, we find that development plays a major evolutionary role.

Adaptive Evolution of Rhizobial Symbiosis beyond Horizontal Gene Transfer: From Genome Innovation to Regulation Reconstruction

There are ubiquitous variations in symbiotic performance of different rhizobial strains associated with the same legume host in agricultural practices. This is due to polymorphisms of symbiosis genes and/or largely unexplored variations in integration efficiency of symbiotic function. Here, we reviewed cumulative evidence on integration mechanisms of symbiosis genes. Experimental evolution, in concert with reverse genetic studies based on pangenomics, suggests that gain of the same circuit of key symbiosis genes through horizontal gene transfer is necessary but sometimes insufficient for bacteria to establish an effective symbiosis with legumes. An intact genomic background of the recipient may not support the proper expression or functioning of newly acquired key symbiosis genes. Further adaptive evolution, through genome innovation and reconstruction of regulation networks, may confer the recipient of nascent nodulation and nitrogen fixation ability. Other accessory genes, either co-transferred with key symbiosis genes or stochastically transferred, may provide the recipient with additional adaptability in ever-fluctuating host and soil niches. Successful integrations of these accessory genes with the rewired core network, regarding both symbiotic and edaphic fitness, can optimize symbiotic efficiency in various natural and agricultural ecosystems. This progress also sheds light on the development of elite rhizobial inoculants using synthetic biology procedures.

Sibling variation in polygenic traits and DNA recombination mapping with UK Biobank and IVF family data

We use UK Biobank and a unique IVF family dataset (including genotyped embryos) to investigate sibling variation in both phenotype and genotype. We compare phenotype (disease status, height, blood biomarkers) and genotype (polygenic scores, polygenic health index) distributions among siblings to those in the general population. As expected, the between-siblings standard deviation in polygenic scores is [Formula: see text] times smaller than in the general population, but variation is still significant. As previously demonstrated, this allows for substantial benefit from polygenic screening in IVF. Differences in sibling genotypes result from distinct recombination patterns in sexual reproduction. We develop a novel sibling-pair method for detection of recombination breaks via statistical discontinuities. The new method is used to construct a dataset of 1.44 million recombination events which may be useful in further study of meiosis.

Multi-omics peripheral and core regions of cancer

Thousands of genes are perturbed by cancer, and these disturbances can be seen in transcriptome, methylation, somatic mutation, and copy number variation omics studies. Understanding their connectivity patterns as an omnigenic neighbourhood in a molecular interaction network (interactome) is a key step towards advancing knowledge of the molecular mechanisms underlying cancers. Here, we introduce a unified connectivity line (CLine) to pinpoint omics-specific omnigenic patterns across 15 curated cancers. Taking advantage of the universality of CLine, we distinguish the peripheral and core genes for each omics aspect. We propose a network-based framework, multi-omics periphery and core (MOPC), to combine peripheral and core genes from different omics into a button-like structure. On the basis of network proximity, we provide evidence that core genes tend to be specifically perturbed in one omics, but the peripheral genes are diversely perturbed in multiple omics. And the core of one omics is regulated by multiple omics peripheries. Finally, we take the MOPC as an omnigenic neighbourhood, describe its characteristics, and explore its relative contribution to network-based mechanisms of cancer. We were able to present how multi-omics perturbations percolate through the human interactome and contribute to an integrated periphery and core.

Social interaction can select for reduced ability

Animals, including humans, differ in a wide range of physical and cognitive abilities ranging from measures of running speed and physical strength to learning ability and intelligence. We consider the evolution of ability when individuals interact pairwise over their contribution to a common good. In this interaction, the contribution of each is assumed to be the best given their own ability and the contribution of their partner. Since there is a tendency for individuals to partially compensate for a low contribution by their partner, low-ability individuals can do well. As a consequence, for benefit and cost structures for which individuals have a strong response to partner's contribution, there can be selection for reduced ability. Furthermore, there can be disruptive selection on ability, leading to a bimodal distribution of ability under some modes of inheritance.

Accumulation and maintenance of information in evolution

Selection accumulates information in the genome-it guides stochastically evolving populations toward states (genotype frequencies) that would be unlikely under neutrality. This can be quantified as the Kullback-Leibler (KL) divergence between the actual distribution of genotype frequencies and the corresponding neutral distribution. First, we show that this population-level information sets an upper bound on the information at the level of genotype and phenotype, limiting how precisely they can be specified by selection. Next, we study how the accumulation and maintenance of information is limited by the cost of selection, measured as the genetic load or the relative fitness variance, both of which we connect to the control-theoretic KL cost of control. The information accumulation rate is upper bounded by the population size times the cost of selection. This bound is very general, and applies across models (Wright-Fisher, Moran, diffusion) and to arbitrary forms of selection, mutation, and recombination. Finally, the cost of maintaining information depends on how it is encoded: Specifying a single allele out of two is expensive, but one bit encoded among many weakly specified loci (as in a polygenic trait) is cheap.

Using Polygenic Risk Scores Related to Complex Traits to Predict Production Performance in Cross-Breeding of Yeast

The cultivation of hybrids with favorable complex traits is one of the important goals for animal, plant, and microbial breeding practices. A method that can closely predict the production performance of hybrids is of great significance for research and practice. In our study, polygenic risk scores (PRSs) were introduced to estimate the production performance of Saccharomyces cerevisiae. The genetic variation of 971 published isolates and their growth ratios under 35 medium conditions were analyzed by genome-wide association analysis, and the precise p-value threshold for each phenotype was calculated. Risk markers for the above 35 phenotypes were obtained. By estimating the genotype of F1 hybrids according to that of the parents, the PRS of 613 F1 hybrids was predicted. There was a significant linear correlation between the maximum growth rate at 40 °C and PRS in F1 hybrids and their parents (R² = 0.2582, R² = 0.2414, respectively), which indicates that PRS can be used to estimate the production performance of individuals and their hybrids. Our method can provide a reference for strain selection and F1 prediction in cross-breeding yeasts, reduce workload, and improve work efficiency.

Genetic architecture and QTL selection response for Kernza perennial grain domestication traits

Analysis of multi-year breeding program data revealed that the genetic architecture of an intermediate wheatgrass population was highly polygenic for both domestication and agronomic traits, supporting the use of genomic selection for new crop domestication. Perennial grains have the potential to provide food for humans and decrease the negative impacts of annual agriculture. Intermediate wheatgrass (IWG, Thinopyrum intermedium, Kernza®) is a promising perennial grain candidate that The Land Institute has been breeding since 2003. We evaluated four consecutive breeding cycles of IWG from 2016 to 2020 with each cycle containing approximately 1100 unique genets. Using genotyping-by-sequencing markers, quantitative trait loci (QTL) were mapped for 34 different traits using genome-wide association analysis. Combining data across cycles and years, we found 93 marker-trait associations for 16 different traits, with each association explaining 0.8-5.2% of the observed phenotypic variance. Across the four cycles, only three QTL showed an F_ST differentiation > 0.15 with two corresponding to a decrease in floret shattering. Additionally, one marker associated with brittle rachis was 216 bp from an ortholog of the btr2 gene. Power analysis and quantitative genetic theory were used to estimate the effective number of QTL, which ranged from a minimum of 33 up to 558 QTL for individual traits. This study suggests that key agronomic and domestication traits are under polygenic control and that molecular methods like genomic selection are needed to accelerate domestication and improvement of this new crop.

Ancestral Lineages in Mutation Selection Equilibria with Moving Optimum

Many populations can somehow adapt to rapid environmental changes. To understand this fast evolution, we investigate the genealogy of individuals inside those populations. More precisely, we use a deterministic model to describe the phenotypic density of a population under selection when the fitness optimum moves at constant speed. We study the inside dynamics of this population using the neutral fractions approach. We then define a Markov process characterizing the distribution of ancestral phenotypic lineages inside the equilibrium. This construction yields qualitative as well as quantitative properties on the phenotype of typical ancestors. In particular, we show that in asexual populations typical ancestors of present individuals carried traits much closer to the fitness optimum than most individuals alive at the same time. We also investigate more deeply the asymptotic regime of small mutation effects. In this regime, we obtain an explicit formula for the typical ancestral lineage using the description of the solutions of the Hamilton Jacobi equation as a minimizer of an optimization problem. In addition, we compare our deterministic results on lineages with the lineages of stochastic models.

The "New Synthesis"

When Mendel’s work was rediscovered in 1900, and extended to establish classical genetics, it was initially seen in opposition to Darwin’s theory of evolution by natural selection on continuous variation, as represented by the biometric research program that was the foundation of quantitative genetics. As Fisher, Haldane, and Wright established a century ago, Mendelian inheritance is exactly what is needed for natural selection to work efficiently. Yet, the synthesis remains unfinished. We do not understand why sexual reproduction and a fair meiosis predominate in eukaryotes, or how far these are responsible for their diversity and complexity. Moreover, although quantitative geneticists have long known that adaptive variation is highly polygenic, and that this is essential for efficient selection, this is only now becoming appreciated by molecular biologists—and we still do not have a good framework for understanding polygenic variation or diffuse function.