Population genetic studies have found evidence for dramatic population growth in recent human history. It is unclear how this recent population growth, combined with the effects of negative natural selection, has affected patterns of deleterious variation, as well as the number, frequencies, and effect sizes of mutations that contribute risk to complex traits. Here I use simulations under population genetic models where a proportion of the heritability of the trait is accounted for by mutations in a subset of the exome. I show that recent population growth increases the proportion of nonsynonymous variants segregating in the population, but does not affect the genetic load relative to that in a population that did not expand. Under a model where a mutation's effect on a trait is correlated with its effect on fitness, rare variants explain a greater portion of the additive genetic variance of the trait in a population that has recently expanded than in a population that did not recently expand. Further, when using a single-marker test, for a given false-positive rate and sample size, recent population growth decreases the expected number of significant association with the trait relative to the number detected in a population that did not expand. However, in a model where there is no correlation between a mutation's effect on fitness and the effect on the trait, common variants account for much of the additive genetic variance, regardless of demography. Moreover, here demography does not affect the number of significant association detected. These finding suggest recent population history may be an important factor influencing the power of association tests in accounting for the missing heritability of certain complex traits.
In the classic view introduced by R. A. Fisher, a quantitative trait is encoded by many loci with small, additive effects. Recent advances in QTL mapping have begun to elucidate the genetic architectures underlying vast numbers of phenotypes across diverse taxa, producing observations that sometimes contrast with Fisher's blueprint. Despite these considerable empirical efforts to map the genetic determinants of traits, it remains poorly understood how the genetic architecture of a trait should evolve, or how it depends on the selection pressures on the trait. Here we develop a simple, populati…
GWAS in humans are revealing the genetic architecture of biomedical and anthropomorphic traits, i.e., the frequencies and effect sizes of variants that contribute to heritable variation in a trait. To interpret these findings, we need to understand how genetic architecture is shaped by basic population genetics processes-notably, by mutation, natural selection and genetic drift. Because many quantitative traits are subject to stabilizing selection and genetic variation that affects one trait often affects many others, we model the genetic architecture of a focal trait that arises under stabili…
Molecular traits, such as gene expression levels or protein binding affinities, are increasingly accessible to quantitative measurement by modern high-throughput techniques. Such traits measure molecular functions and, from an evolutionary point of view, are important as targets of natural selection. We review recent developments in evolutionary theory and experiments that are expected to become building blocks of a quantitative genetics of molecular traits. We focus on universal evolutionary characteristics: these are largely independent of a trait's genetic basis, which is often at least par…
Genetic association data from national biobanks and large-scale association studies have provided new prospects for understanding the genetic evolution of complex traits and diseases in humans. In turn, genomes from ancient human archaeological remains are now easier than ever to obtain, and provide a direct window into changes in frequencies of trait-associated alleles in the past. This has generated a new wave of studies aiming to analyse the genetic component of traits in historic and prehistoric times using ancient DNA, and to determine whether any such traits were subject to natural selec…
Although many phenotypic traits are determined by a large number of genetic variants, how a polygenic trait adapts in response to the changes in the environment is still poorly understood. Here we study the adaptation dynamics of a polygenic trait that is determined by a finite number of genetic loci in an infinitely large population which is evolving under stabilising selection and recurrent mutations. We find that in a changing environment, modeled here by a linearly moving phenotypic optimum, the mean trait also moves linearly with time. But its speed is smaller than that of the phenotypic …
The selection pressures that have shaped the evolution of complex traits in humans remain largely unknown, and in some contexts highly contentious, perhaps above all where they concern mean trait differences among groups. To date, the discussion has focused on whether such group differences have any genetic basis, and if so, whether they are without fitness consequences and arose via random genetic drift, or whether they were driven by selection for different trait optima in different environments. Here, we highlight a plausible alternative, that many complex traits evolve under stabilizing se…
Population genomic studies have shown that genetic draft and background selection can profoundly affect the genome-wide patterns of molecular variation. We performed forward simulations under realistic gene-structure and selection scenarios to investigate whether such linkage effects impinge on the ability of the McDonald-Kreitman (MK) test to infer the rate of positive selection (α) from polymorphism and divergence data. We find that in the presence of slightly deleterious mutations, MK estimates of α severely underestimate the true rate of adaptation even if all polymorphisms with population…
Genetic studies of human traits have revolutionized our understanding of the variation between individuals, and opened the door for numerous breakthroughs in biology, medicine and other scientific fields. And yet, the ultimate promise of this area of research is still not fully realized. In this review, we highlight the major open problems that need to be solved to improve our understanding of the genetic variation underlying human traits, and by discussing these challenges provide a primer to the field. Our focus is on concrete analytical problems, both conceptual and technical in nature. We …
In this article, we review the different models and methods to understand and estimate correlated evolution within the same genome, individual or species. We describe correlated evolution among traits, among genetic components and finally between traits and genetics.
A key goal in studies of ecology and evolution is understanding the causes of phenotypic diversity in nature. Most traits of interest, such as those relating to morphology, life-history, immunity and behaviour are quantitative, and phenotypic variation is driven by the cumulative effects of genetic and environmental variation. The field of quantitative genetics aims to quantify the additive genetic component of this trait variance (i.e. the "heritability"), often with the underlying assumption that trait variance is driven by many loci of infinitesimal effects throughout the genome. This appro…
A crop can be represented as a biotechnical system in which components are either chosen (cultivar, management) or given (soil, climate) and whose combination generates highly variable stress patterns and yield responses. Here, we used modeling and simulation to predict the crop phenotypic plasticity resulting from the interaction of plant traits (G), climatic variability (E) and management actions (M). We designed two in silico experiments that compared existing and virtual sunflower cultivars (Helianthus annuus L.) in a target population of cropping environments by simulating a range of indi…
Individual success in group-structured populations has two components. First, an individual gains by outcompeting its neighbors for local resources. Second, an individual's share of group success must be weighted by the total productivity of the group. The essence of sociality arises from the tension between selfish gains against neighbors and the associated loss that selfishness imposes by degrading the efficiency of the group. Without some force to modulate selfishness, the natural tendencies of self interest typically degrade group performance to the detriment of all. This is the tragedy of…
Genetic data are often used to infer demographic history and changes or detect genes under selection. Inferential methods are commonly based on models making various strong assumptions: demography and population structures are supposed \textit{a priori} known, the evolution of the genetic composition of a population does not affect demography nor population structure, and there is no selection nor interaction between and within genetic strains. In this paper, we present a stochastic birth-death model with competitive interactions and asexual reproduction. We develop an inferential procedure fo…
By exploiting an analogy between population genetics and statistical mechanics, we study the evolution of a polygenic trait under stabilizing selection, mutation, and genetic drift. This requires us to track only four macroscopic variables, instead of the distribution of all the allele frequencies that influence the trait. These macroscopic variables are the expectations of: the trait mean and its square, the genetic variance, and of a measure of heterozygosity, and are derived from a generating function that is in turn derived by maximizing an entropy measure. These four macroscopics are enou…
When polygenic traits are under stabilizing selection, many different combinations of alleles allow close adaptation to the optimum. If alleles have equal effects, all combinations that result in the same deviation from the optimum are equivalent. Furthermore, the genetic variance that is maintained by mutation-selection balance is $2 μ/S$ per locus, where $μ$ is the mutation rate and $S$ the strength of stabilizing selection. In reality, alleles vary in their effects, making the fitness landscape asymmetric, and complicating analysis of the equilibria. We show that that the resulting genetic …
Background and Aims: Prediction of phenotypic traits from new genotypes under untested environmental conditions is crucial to build simulations of breeding strategies to improve target traits. Although the plant response to environmental stresses is characterized by both architectural and functional plasticity, recent attempts to integrate biological knowledge into genetics models have mainly concerned specific physiological processes or crop models without architecture, and thus may prove limited when studying genotype x environment interactions. Consequently, this paper presents a simulation…
A phenomenon that strongly influences the demography of small introduced populations and thereby potentially their genetic diversity is the Allee effect, a reduction in population growth rates at small population sizes. We take a stochastic modeling approach to investigate levels of genetic diversity in populations that successfully overcame a strong demographic Allee effect, a scenario in which populations smaller than a certain critical size are expected to decline. Our results indicate that compared to successful populations without Allee effect, successful Allee-effect populations tend to …
In addition to natural selection, adaptive evolution requires genetic variation to proceed. Yet the G-matrix may have limited 'genetic degrees of freedom', with certain combinations of trait values unavailable to evolution. Such limitations are often referred to as genetic constraints. Unfortunately, clear predictions about when to expect constraints are rarely available. Therefore, we developed an experimental system that provides specific predictions regarding constraints. Such tests are important as disagreements persist regarding the evidence for genetic constraints, possibly due to differ…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in continuous time of a population with (continuous) age and trait structures. The individuals reproduce asexually, age, interact and die. The 'trait' is an individual heritable property (d-dimensional vector) that may influence birth and death rates and interactions between individuals, and vary by mutation. In a large population limit, the random process con…
Paternal age at conception has been found to predict the number of new genetic mutations. We examined the effect of father's age at birth on offspring intelligence, head circumference and personality traits. Using the Minnesota Twin Family Study sample we tested paternal age effects while controlling for parents' trait levels measured with the same precision as offspring's. From evolutionary genetic considerations we predicted a negative effect of paternal age on offspring intelligence, but not on other traits. Controlling for parental IQ had the effect of turning a positive-zero order associa…
We consider an infinitely large population under stabilising selection and mutation in which the allelic effects determining a polygenic trait vary between loci. We obtain analytical expressions for the stationary genetic variance as a function of the distribution of effects, mutation rate and selection coefficient. We also study the dynamics of the allele frequencies, focussing on short-term evolution of the phenotypic mean as it approaches the optimum after an environmental change. We find that when most effects are small, the genetic variance does not change appreciably during adaptation, a…
Both evolution and ecology have long been concerned with the impact of variable environmental conditions on observed levels of genetic diversity within and between species. We model the evolution of a quantitative trait under selection that fluctuates in space and time, and derive an analytical condition for when these fluctuations promote genetic diversification. As ecological scenario we use a generalized island model with soft selection within patches in which we incorporate generation overlap. We allow for arbitrary fluctuations in the environment including spatio-temporal correlations and…
We study fixation probabilities and times as a consequence of neutral genetic drift in subdivided populations, motivated by a model of the cultural evolutionary process of language change that is described by the same mathematics as the biological process. We focus on the growth of fixation times with the number of subpopulations, and variation of fixation probabilities and times with initial distributions of mutants. A general formula for the fixation probability for arbitrary initial condition is derived by extending a duality relation between forwards- and backwards-time properties of the m…
All non-human great apes are endangered in the wild, and it is therefore important to gain an understanding of their demography and genetic diversity. To date, however, genetic studies within these species have largely been confined to mitochondrial DNA and a small number of other loci. Here, we present a genome-wide survey of genetic variation in gorillas using a reduced representation sequencing approach, focusing on the two lowland subspecies. We identify 3,274,491 polymorphic sites in 14 individuals: 12 western lowland gorillas (Gorilla gorilla gorilla) and 2 eastern lowland gorillas (Gori…
Insights into human evolution from large genetic biobanks
Institute for Human Genetics, University of California, San Francisco（加州大学旧金山分校人类遗传学研究所）；Department of Epidemiology & Biostatistics, University of California, San Francisco（加州大学旧金山分校流行病学与生物统计系）；Department of Data Science, University of Oregon（俄勒冈大学数据科学系）；Institute for Ecology and Evolution, University of Oregon（俄勒冈大学生态与进化研究所）
We are interested in a stochastic model of trait and age-structured population undergoing mutation and selection. We start with a continuous time, discrete individual-centered population process. Taking the large population and rare mutations limits under a well-chosen time-scale separation condition, we obtain a jump process that generalizes the Trait Substitution Sequence process describing Adaptive Dynamics for populations without age structure. Under the additional assumption of small mutations, we derive an age-dependent ordinary differential equation that extends the Canonical Equation. …
Transgenerational inheritance of a trait is presumably affected by both genetic and environmental factors but remains poorly understood. We studied the effect of genetic polymorphisms on transgenerational inheritance of yeast segregants that were derived from a cross between a laboratory strain and a wild strain of Saccharomyces cerevisiae. For each SNP analyzed, the parental allele present in less than half of the segregants panel was called the minor allele (MA). We found a nonrandom distribution of MAs in the segregants, indicating natural selection. We compared segregants with high MA cont…
Whether or not biodiversity dynamics tend toward stable equilibria remains an unsolved question in ecology and evolution with important implications for our understanding of diversity and its conservation. Phylo/population genetic models and macroecological theory represent two primary lenses through which we view biodiversity. While phylo/population genetics provide an averaged view of changes in demography and diversity over timescales of generations to geological epochs, macroecology provides an ahistorical description of commonness and rarity across contemporary co-occurring species. Our g…
We describe the simulation method of modelling the population evolution using Monte Carlo based on the Penna model. Individuals in the populations are represented by their diploid genomes. Genes expressed after the minimum reproduction age are under a weaker selection pressure and accumulate more mutations than those expressed before the minimum reproduction age. The generated gradient of defective genes determines the ageing of individuals and age-structured populations are very similar to the natural, sexually reproducing populations. The genetic structure of a population depends on the way …
The distribution and heritability of many traits depends on numerous loci in the genome. In general, the astronomical number of possible genotypes makes the system with large numbers of loci difficult to describe. Multilocus evolution, however, greatly simplifies in the limit of weak selection and frequent recombination. In this limit, populations rapidly reach Quasi-Linkage Equilibrium (QLE) in which the dynamics of the full genotype distribution, including correlations between alleles at different loci, can be parameterized by the allele frequencies. This review provides a simplified exposit…
Non-selective effects, like genetic drift, are an important factor in modern conceptions of evolution, and have been extensively studied for constant population sizes. Here, we consider non-selective evolution in the case of growing populations that are of small size and have varying trait compositions (e.g. after a population bottleneck). We find that, in these conditions, populations never fixate to a trait, but tend to a random limit composition, and that the distribution of compositions 'freezes' to a steady state This final state is crucially influenced by the initial conditions. We obtai…
Concomitant with the evolution of biological diversity must have been the evolution of mechanisms that facilitate evolution, due to the essentially infinite complexity of protein sequence space. We describe how evolvability can be an object of Darwinian selection, emphasizing the collective nature of the process. We quantify our theory with computer simulations of protein evolution. These simulations demonstrate that rapid or dramatic environmental change leads to selection for greater evolvability. The selective pressure for large scale genetic moves, such as DNA exchange, becomes increasingl…
Identifying drivers of complex traits from the noisy signals of genetic variation obtained from high throughput genome sequencing technologies is a central challenge faced by human geneticists today. We hypothesize that the variants involved in complex diseases are likely to exhibit non-neutral evolutionary signatures. Uncovering the evolutionary history of all variants is therefore of intrinsic interest for complex disease research. However, doing so necessitates the simultaneous elucidation of the targets of natural selection and population-specific demographic history. Here we characterize …
Genome-wide association studies (GWAS) have identified many genetic factors underlying complex human traits. However, these factors have explained only a small fraction of these traits' genetic heritability. It is argued that many more genetic factors remain undiscovered. These genetic factors likely are weakly associated at the population level and sparsely distributed across the genome. In this paper, we adapt the recent innovations on Tukey's Higher Criticism (Tukey [The Higher Criticism (1976) Princeton Univ.]; Donoho and Jin [Ann. Statist. 32 (2004) 962-994]) to SNP-set analysis of GWAS, …
Trait differences between species may be attributable to natural selection. However, quantifying the strength of evidence for selection acting on a particular trait is a difficult task. Here we develop a population-genetic test for selection acting on a quantitative trait which is based on multiple-line crosses. We show that using multiple lines increases both the power and the scope of selection inference. First, a test based on three or more lines detects selection with strongly increased statistical significance, and we show explicitly how the sensitivity of the test depends on the number o…
Heritability is a central parameter in quantitative genetics, both from an evolutionary and a breeding perspective. For plant traits heritability is traditionally estimated by comparing within and between genotype variability. This approach estimates broad-sense heritability, and does not account for different genetic relatedness. With the availability of high-density markers there is growing interest in marker based estimates of narrow-sense heritability, using mixed models in which genetic relatedness is estimated from genetic markers. Such estimates have received much attention in human gen…
Many plants harbor complex mechanisms that promote outcrossing and efficient pollen transfer. These include floral adaptations as well as genetic mechanisms, such as molecular self-incompatibility (SI) systems. The maintenance of such systems over long evolutionary timescales suggests that outcrossing is favorable over a broad range of conditions. Conversely, SI has repeatedly been lost, often in association with transitions to self-fertilization (selfing). This transition is favored when the short-term advantages of selfing outweigh the costs, primarily inbreeding depression. The transition t…
Classical stochastic demography predicts that environmental stochasticity reduces population growth rates and, thereby, can increase extinction risk. In contrast, the SAS-CFF model demonstrates that environmental stochasticity can promote genetic diversity. Extending the SAS-CFF to account for demography, I examine the simultaneous effects of environmental stochasticity on genetic diversity and population persistence. Consistent with Gillespie's analysis, if the log-fitness function is concave and allelic responses to the environment are not perfectly correlated, then per-capita growth rates o…
Methods to effectively detect multi-locus genetic association are becoming increasingly relevant in the genetic dissection of complex trait in humans. Current approaches typically consider a limited number of hypotheses, most of which are related to the effect of a single locus or of a relatively small number of neighboring loci on a chromosomal region. We have developed a novel method that is specifically designed to detect genetic association involving multiple disease-susceptibility loci, possibly on different chromosomes. Our approach relies on the efficient discovery of patterns comprisin…
Numerous traits under migration-selection balance are shown to exhibit complex patterns of genetic architecture with large variance in effect sizes. However, the conditions under which such genetic architectures are stable have yet to be investigated, because studying the influence of a large number of small allelic effects on the maintenance of spatial polymorphism is mathematically challenging, due to the high complexity of the systems that arise. In particular, in the most simple case of a haploid population in a two-patch environment, while it is known from population genetics that polymor…
Modelling genetic phenomena affecting biological traits is important for the development of agriculture as it allows breeders to predict the potential of breeding for certain traits. One such phenomenon is heterosis or hybrid vigor: crossing individuals from genetically distinct populations often results in improvements in quantitative traits, such as growth rate, biomass production and stress resistance. Heterosis has become a very useful tool in global agriculture, but its genetic basis remains controversial and its effects hard to predict. We have taken a computational approach to studying …
Over the last fifty years, geneticists have made great strides in understanding how our species' evolutionary history gave rise to current patterns of human genetic diversity classically summarized by Lewontin in his 1972 paper, 'The Apportionment of Human Diversity'. One evolutionary process that requires special attention in both population genetics and statistical genetics is admixture: gene flow between two or more previously separated source populations to form a new admixed population. The admixture process introduces unique patterns of genetic variation within and between populations, w…
Adaptation in response to selection on polygenic phenotypes may occur via subtle allele frequencies shifts at many loci. Current population genomic techniques are not well posed to identify such signals. In the past decade, detailed knowledge about the specific loci underlying polygenic traits has begun to emerge from genome-wide association studies (GWAS). Here we combine this knowledge from GWAS with robust population genetic modeling to identify traits that may have been influenced by local adaptation. We exploit the fact that GWAS provide an estimate of the additive effect size of many loc…
A crop can be viewed as a complex system with outputs (e.g. yield) that are affected by inputs of genetic, physiology, pedo-climatic and management information. Application of numerical methods for model exploration assist in evaluating the major most influential inputs, providing the simulation model is a credible description of the biological system. A sensitivity analysis was used to assess the simulated impact on yield of a suite of traits involved in major processes of crop growth and development, and to evaluate how the simulated value of such traits varies across environments and in rel…
Although a number of studies have shown that natural and laboratory populations initially well-adapted to their environment can evolve rapidly when conditions suddenly change, the dynamics of rapid adaptation are not well understood. Here a population genetic model of polygenic selection is analyzed to describe the short-term response of a quantitative trait after a sudden shift of the phenotypic optimum. We provide explicit analytical expressions for the time scales over which the trait mean approaches the new optimum. We find that when the effect sizes are small relative to a scaled mutation…
Sexual selection theory models evolution of sexual signals and preferences using simple life histories. However, life-history models predict that males benefit from increasing sexual investment approaching old age, producing age-dependent sexual traits. Age-dependent traits require time and energy to grow, and will not fully mature before individuals enter mating competition. Early evolutionary stages pose several problems for these traits. Age-dependent traits suffer from strong viability selection and gain little benefit from mate choice when rare. Few males will grow large traits, and they …
Deleterious genetic variants can be evaluated as quantitative traits using information theory-based sequence analysis of recognition sites. To assess the effect of such variants, fitness and genetic load of SNPs which alter binding site affinity are derived from changes in individual information and allele frequencies. Human SNPs that alter mRNA splicing are partitioned according to their genetic load. SNPs with high genetic loads (>0.5) are common in the genome and, in many instances, predicted effects are supported by gene expression studies.
SLiM is an efficient forward population genetic simulation designed for studying the effects of linkage and selection on a chromosome-wide scale. The program can incorporate complex scenarios of demography and population substructure, various models for selection and dominance of new mutations, arbitrary gene and chromosomal structure, and user-defined recombination maps.
The phenotypic consequences of individual mutations are modulated by the wild type genetic background in which they occur.Although such background dependence is widely observed, we do not know whether general patterns across species and traits exist, nor about the mechanisms underlying it. We also lack knowledge on how mutations interact with genetic background to influence gene expression, and how this in turn mediates mutant phenotypes. Furthermore, how genetic background influences patterns of epistasis remains unclear. To investigate the genetic basis and genomic consequences of genetic ba…
