SPONTANEOUS MUTATIONS FOR LIFE-HISTORY CHARACTERS IN AN OBLIGATE PARTHENOGEN

By allowing mutations to accumulate spontaneously in different lines derived from a single female of an obligately parthenogenetic Daphnia, it has become possible to estimate the rate at which new genetic variance for life-history characters arises as well as to identify the average pleiotropic effects of mutant polygenes. The estimated polygenic mutation rates are quite compatible with those available for sexual organisms. The results are therefore in conflict with the hypothesis that parthenogens compensate for the loss of recombination by elevating the mutation rate. Based on these results, it is argued that the rate of phenotypic evolution may be enhanced as much as five-fold by sexuality. However, if dominance or epistatic gene interactions are of major importance, or if the sensitivity to environmental effects is reduced or the rate of polygenic mutation enhanced under asexuality, the full advantage of sex will not be attained and may even be reversed. Regardless of these conditions, it is clear that the mutational rate of production of polygenic variation is sufficient to allow significant rates of phenotypic evolution in purely asexual organisms.     

ON THE INSTABILITY OF POLYGENIC SEX DETERMINATION: THE EFFECT OF SEX-SPECIFIC SELECTION

A combination of analytical and simulation models is used to explore the initial evolution of genic sex determination from polygenic sex determination. Prior studies have indicated that polygenic sex determination is rare or absent in extant species but that it has likely played an important intermediate role in the evolution of other genetic sex-determination systems. This study explores why polygenic sex determination does not persist. Two possibilities are considered. First it is assumed that a major sex-determining gene also pleiotropically increases fitness. Second it is assumed that the sex-determining gene is neutral but linked to another locus segregating for a rare selectively favored allele. The major conclusion from the models is that sex-specific natural selection will cause polygenic sex determination to be a transient state in most populations. Polygenic sex determination may be an important intermediate step in the evolution of genetically controlled sexual differentiation, but it is unlikely to persist unless there is some selective advantage compared to genic sex determination. This may in part explain the relatively small number of extant species that have polygenic sex determination.     

Polygenic variation maintained by balancing selection: pleiotropy, sex-dependent allelic effects and G x E interactions

We investigate three alternative selection-based scenarios proposed to maintain polygenic variation: pleiotropic balancing selection, G x E interactions (with spatial or temporal variation in allelic effects), and sex-dependent allelic effects. Each analysis assumes an additive polygenic trait with n diallelic loci under stabilizing selection. We allow loci to have different effects and consider equilibria at which the population mean departs from the stabilizing-selection optimum. Under weak selection, each model produces essentially identical, approximate allele-frequency dynamics. Variation is maintained under pleiotropic balancing selection only at loci for which the strength of balancing selection exceeds the effective strength of stabilizing selection. In addition, for all models, polymorphism requires that the population mean be close enough to the optimum that directional selection does not overwhelm balancing selection. This balance allows many simultaneously stable equilibria, and we explore their properties numerically. Both spatial and temporal G x E can maintain variation at loci for which the coefficient of variation (across environments) of the effect of a substitution exceeds a critical value greater than one. The critical value depends on the correlation between substitution effects at different loci. For large positive correlations (e.g., rho(ij)2>3/4), even extreme fluctuations in allelic effects cannot maintain variation. Surprisingly, this constraint on correlations implies that sex-dependent allelic effects cannot maintain polygenic variation. We present numerical results that support our analytical approximations and discuss our results in connection to relevant data and alternative variance-maintaining mechanisms.     

Sequence variation and the biological function of genes: methodological and biological considerations

Single nucleotide polymorphisms (SNPs) are expected to facilitate the chromosomal mapping and eventual cloning of genetic determinants of complex quantitative phenotypes. To date, more than 2.5 million non-redundant human SNPs have been reported in the public domain, of which approximately 100000 have been validated by either independent investigators or by independent methods. Equally impressive is the myriad of methods developed for allelic discrimination. Nevertheless, reports of successful applications of SNPs to genome-wide linkage analysis of both mono- and polygenic traits are rare and limited to a few model organisms, that provide affordable platforms to test both novel methodological and biological concepts at a whole-genome scale under conditions that can be reasonably controlled. Progress in the analysis of SNPs needs to be complemented by methods that allow the systematic elucidation of both primary and secondary phenotypes of genes. Importantly, observations made in one species may very well be of immediate applicability to other species including human. This is particularly true for conserved biological processes such as mitochondrial respiration and DNA repair.     

Predicting loneliness with polygenic scores of social,psychological and psychiatric traits

Loneliness is a heritable trait that accompanies multiple disorders. The association between loneliness and mental health indices may partly be due to inherited biological factors. We constructed polygenic scores for 27 traits related to behavior, cognition and mental health and tested their prediction for self‐reported loneliness in a population‐based sample of 8798 Dutch individuals. Polygenic scores for major depressive disorder (MDD), schizophrenia and bipolar disorder were significantly associated with loneliness. Of the Big Five personality dimensions, polygenic scores for neuroticism and conscientiousness also significantly predicted loneliness, as did the polygenic scores for subjective well‐being, tiredness and self‐rated health. When including all polygenic scores simultaneously into one model, only 2 major depression polygenic scores remained as significant predictors of loneliness. When controlling only for these 2 MDD polygenic scores, only neuroticism and schizophrenia remain significant. The total variation explained by all polygenic scores collectively was 1.7%. The association between the propensity to feel lonely and the susceptibility to psychiatric disorders thus pointed to a shared genetic etiology. The predictive power of polygenic scores will increase as the power of the genome‐wide association studies on which they are based increases and may lead to clinically useful polygenic scores that can inform on the genetic predisposition to loneliness and mental health.     

Genome scan methods against more complex models: when and how much should we trust them?

The recent availability of next‐generation sequencing (NGS) has made possible the use of dense genetic markers to identify regions of the genome that may be under the influence of selection. Several statistical methods have been developed recently for this purpose. Here, we present the results of an individual‐based simulation study investigating the power and error rate of popular or recent genome scan methods: linear regression, Bayescan, BayEnv and LFMM. Contrary to previous studies, we focus on complex, hierarchical population structure and on polygenic selection. Additionally, we use a false discovery rate (FDR)‐based framework, which provides an unified testing framework across frequentist and Bayesian methods. Finally, we investigate the influence of population allele frequencies versus individual genotype data specification for LFMM and the linear regression. The relative ranking between the methods is impacted by the consideration of polygenic selection, compared to a monogenic scenario. For strongly hierarchical scenarios with confounding effects between demography and environmental variables, the power of the methods can be very low. Except for one scenario, Bayescan exhibited moderate power and error rate. BayEnv performance was good under nonhierarchical scenarios, while LFMM provided the best compromise between power and error rate across scenarios. We found that it is possible to greatly reduce error rates by considering the results of all three methods when identifying outlier loci.     

Using the mixed model for interval mapping of quantitative trait loci in outbred line crosses

Interval mapping by simple regression is a powerful method for the detection of quantitative trait loci (QTLs) in line crosses such as F2 populations. Due to the ease of computation of the regression approach, relatively complex models with multiple fixed effects, interactions between QTLs or between QTLs and fixed effects can easily be accommodated. However, polygenic effects, which are not targeted in QTL analysis, cannot be treated as random effects in a least squares analysis. In a cross between true inbred lines this is of no consequence, as the polygenic effect contributes just to the residual variance. In a cross between outbred lines, however, if a trait has high polygenic heritability, the additive polygenic effect has a large influence on variation in the population. Here we extend the fixed model for the regression interval mapping method to a mixed model using an animal model. This makes it possible to use not only the observations from progeny (e.g. F2), but also those from the parents (F1) to evaluate QTLs and polygenic effects. We show how the animal model using parental observations can be applied to an outbred cross and so increase the power and accuracy of QTL analysis. Three estimation methods, i.e. regression and an animal model either with or without parental observations, are applied to simulated data. The animal model using parental observations is shown to have advantages in estimating QTL position and additive genotypic value, especially when the polygenic heritability is large and the number of progeny per parent is small.     

GENOTYPE-ENVIRONMENT INTERACTION AND THE EVOLUTION OF PHENOTYPIC PLASTICITY

Studies of spatial variation in the environment have primarily focused on how genetic variation can be maintained. Many one-locus genetic models have addressed this issue, but, for several reasons, these models are not directly applicable to quantitative (polygenic) traits. One reason is that for continuously varying characters, the evolution of the mean phenotype expressed in different environments (the norm of reaction) is also of interest. Our quantitative genetic models describe the evolution of phenotypic response to the environment, also known as phenotypic plasticity (Gause, 1947), and illustrate how the norm of reaction (Schmalhausen, 1949) can be shaped by selection. These models utilize the statistical relationship which exists between genotype-environment interaction and genetic correlation to describe evolution of the mean phenotype under soft and hard selection in coarse-grained environments. Just as genetic correlations among characters within a single environment can constrain the response to simultaneous selection, so can a genetic correlation between states of a character which are expressed in two environments. Unless the genetic correlation across environments is ± 1, polygenic variation is exhausted, or there is a cost to plasticity, panmictic populations under a bivariate fitness function will eventually attain the optimum mean phenotype for a given character in each environment. However, very high positive or negative correlations can substantially slow the rate of evolution and may produce temporary maladaptation in one environment before the optimum joint phenotype is finally attained. Evolutionary trajectories under hard and soft selection can differ: in hard selection, the environments with the highest initial mean fitness contribute most individuals to the mating pool. In both hard and soft selection, evolution toward the optimum in a rare environment is much slower than it is in a common one. A subdivided population model reveals that migration restriction can facilitate local adaptation. However, unless there is no migration or one of the special cases discussed for panmictic populations holds, no geographical variation in the norm of reaction will be maintained at equilibrium. Implications of these results for the interpretation of spatial patterns of phenotypic variation in natural populations are discussed.     

An Approximate Model of Polygenic Inheritance

The finite polygenic model approximates polygenic inheritance by postulating that a quantitative trait is determined by n independent, additive loci. The 3(n) possible genotypes for each person in this model limit its applicability. CANNINGS, THOMPSON, and SKOLNICK suggested a simplified, nongenetic version of the model involving only 2n + 1 genotypes per person. This article shows that this hypergeometric polygenic model also approximates polygenic inheritance well. In particular, for noninbred pedigrees, trait means, variances, covariances, and marginal distributions match those of the ordinary finite polygenic model. Furthermore as n -> &, the trait values within a pedigree collectively tend toward multivariate normality. The implications of these results for likelihood evaluation under the polygenic threshold and mixed models of inheritance are discussed. Finally, a simple numerical example illustrates the application of the hypergeometric polygenic model to risk prediction under the polygenic threshold model.     

Persistence of accuracy of genome-wide breeding values over generations when including a polygenic effect

Background

When estimating marker effects in genomic selection, estimates of marker effects may simply act as a proxy for pedigree, i.e. their effect may partially be attributed to their association with superior parents and not be linked to any causative QTL. Hence, these markers mainly explain polygenic effects rather than QTL effects. However, if a polygenic effect is included in a Bayesian model, it is expected that the estimated effect of these markers will be more persistent over generations without having to re-estimate the marker effects every generation and will result in increased accuracy and reduced bias.

Methods

Genomic selection using the Bayesian method, ''BayesB'' was evaluated for different marker densities when a polygenic effect is included (GWpEBV) and not included (GWEBV) in the model. Linkage disequilibrium and a mutation drift balance were obtained by simulating a population with a Ne of 100 over 1,000 generations.

Results

Accuracy of selection was slightly higher for the model including a polygenic effect than for the model not including a polygenic effect whatever the marker density. The accuracy decreased in later generations, and this reduction was stronger for lower marker densities. However, no significant difference in accuracy was observed between the two models. The linear regression of TBV on GWEBV and GWpEBV was used as a measure of bias. The regression coefficient was more stable over generations when a polygenic effect was included in the model, and was always between 0.98 and 1.00 for the highest marker density. The regression coefficient decreased more quickly with decreasing marker density.

Conclusions

Including a polygenic effect had no impact on the selection accuracy, but showed reduced bias, which is especially important when estimates of genome-wide markers are used to estimate breeding values over more than one generation.     

The genetic, molecular and phenotypic consequences of selection for insecticide resistance

Studies of insecticide resistance allow theories of the adaptive process to be tested where the selective agent, the insecticide, is unambiguously defined. Thus, the consequences of selection of phenotypic variation can be investigated in genetic, biochemical, molecular, population biological and, most recently, developmental contexts. Are the options limited biochemically and molecularly? Is the genetic mechanism monogenic or polygenic, general or population/species specific? Are fitness and developmental patterns associated? These questions of general evolutionary significance can be considered with experimental approaches to determine how insecticide resistance evolves.     

Polygenic modeling of genome-wide association studies: an application to prostate and breast cancer

Genome-wide association studies (GWAS) have successfully detected and replicated associations with numerous diseases, including cancers of the prostate and breast. These findings are helping clarify the genomic basis of such diseases, but appear to explain little of disease heritability. This limitation might reflect the focus of conventional GWAS on a small set of the most statistically significant associations with disease. More information might be obtained by analyzing GWAS using a polygenic model, which allows for the possibility that thousands of genetic variants could impact disease. Furthermore, there may exist common polygenic effects between potentially related phenotypes (e.g., prostate and breast cancer). Here we present and apply a polygenic model to GWAS of prostate and breast cancer. Our results indicate that the polygenic model can explain an increasing--albeit low--amount of heritability for both of these cancers, even when excluding the most statistically significant associations. In addition, nonaggressive prostate cancer and breast cancer appear to share a common polygenic model, potentially reflecting a similar underlying biology. This supports the further development and application of polygenic models to genomic data.     

Conditional Polygenic Effects in the Sternopleural Bristle System of DROSOPHILA MELANOGASTER

The chromosomal architecture of genotype x environment interactions was investigated in lines of Drosophila melanogaster selected for increased or decreased sternopleural bristle number at 18°, 25° and 29°. In general, interactions were found to have a stabilizing effect upon the bristle phenotype, in the sense that the genotype x environment interaction tended to increase bristle number under conditions in which temperature alone reduced bristle number and vice versa. The polygenic modifiers of mean bristle number were often separable from modifiers of the response to temperature both at the chromosomal level and intrachromosomally. In one of the low selection lines, a temperature-dependent polygenic locus was mapped on chromosome 3. It is suggested that genotype x environment interactions be thought of in terms of conditional polygenic expression. Such conditionality may be one of the ways in which polygenic variation is maintained in a population in the face of selection for an optimum phenotype.     

Unmasking of heterozygosity by inherited balanced translocations. Implications for prenatal diagnosis and gene mapping

Phenotypic abnormalities in individuals with balanced chromosome rearrangements can be caused by loss of function at the break points and consequent functional homozygosity for recessive genes. This has obvious implications in prenatal diagnosis. Relevant cases are presented and discussed. Mendelian disorders and possibly also disorders which are under polygenic control may be assigned to certain chromosome regions or bands by means of such translocations. Several assignments have been accomplished lately, the approach being much the same as with deletion mapping.     

Does cutting herbicide rates threaten the sustainability of weed management in cropping systems?

Evolution of herbicide resistance in weeds is a growing problem across the world, and it has been suggested that low herbicide rates may be contributing to this problem. An individual-based simulation model that represents weed population dynamics and the evolution of polygenic herbicide resistance was constructed and used to investigate whether using lower herbicide rates or standard rates at reduced efficacy could reduce the sustainability of cropping systems by causing faster increases in weed population density as herbicide resistance develops. A number of different possible genetic bases for resistance were considered, including monogenic resistance and polygenic resistance conferred by several genes. The results show that cutting herbicide rates does not affect the rate at which weed densities reach critical levels when resistance is conferred exclusively by a single dominant gene. In some polygenic situations, cutting herbicide rates substantially reduces sustainability, due to a combination of faster increase in resistance gene frequency and reduced kill rates in all genotypes, while in other polygenic situations the effect is small. Differences in sustainability depend on combined strength of the resistance genes, variability in phenotypic susceptibility and rate delivered, level of control due to alternative measures, and degree of genetic dominance and epistasis. In the situation where resistance can be conferred by both a single dominant major gene or a number of co-dominant minor genes in combination, the difference made by low rates depends on the relative initial frequency of the major and minor genes. These results show that careful consideration of herbicide rate and understanding the genetic basis of resistance are important aspects of weed management.     

Complex segregation analysis of dental morphological variants

A set of 20 morphological variants of the dental crowns and four characteristics of the jaws are tested for probable mode of inheritance using the complex segregation analysis method of Morton et al. (Am. J. Hum. Genet. 23:602-611, 1971). Models tested include three two-allele single-locus models (dominant, codominant, and recessive) and a model employing the polychotomized normal distribution of liability (an additive polygenic model), with transmissibility estimated via maximum likelihood. Most of the traits studied are observed using ordinal scales with several grades, and many are tested using more than one dichotomy of their scale. These multiple analyses allow for an examination of such factors as trait incidence on the results of the statistical analysis. The results of the analysis yield propositions of major genes for 13 of the 24 traits examined. Two traits give good evidence of being polygenic in origin. The remaining nine characters present methodological problems that do not allow for a definite conclusion on their mode of inheritance at this time. The ability to test varying levels of transmissibility in the polygenic model allows for an estimation of the percentage of trait variance determined by familial factors. Estimates of transmissibility for all characters examined range from 0 to 1, with a mean of 0.36. These findings may suggest a large environmental role in the development of dental crown morphology. However, the possibility exists that difficulties in the ability to classify the expression of certain traits consistently result in overestimates of the environmental influences on the development of those characters.     

Maintenance of polygenic sex determination in a fluctuating environment: an individual‐based model

R. A. Fisher predicted that individuals should invest equally in offspring of both sexes, and that the proportion of males and females produced (the primary sex ratio) should evolve towards 1:1 when unconstrained. For many species, sex determination is dependent on sex chromosomes, creating a strong tendency for balanced sex ratios, but in other cases, multiple autosomal genes interact to determine sex. In such cases, the maintenance of multiple sex‐determining alleles at multiple loci and the consequent among‐family variability in sex ratios presents a puzzle, as theory predicts that such systems should be unstable. Theory also predicts that environmental influences on sex can complicate outcomes of genetic sex determination, and that population structure may play a role. Tigriopus californicus, a copepod that lives in splash‐pool metapopulations and exhibits polygenic and environment‐dependent sex determination, presents a test case for relevant theory. We use this species as a model for parameterizing an individual‐based simulation to investigate conditions that could maintain polygenic sex determination. We find that metapopulation structure can delay the degradation of polygenic sex determination and that periods of alternating frequency‐dependent selection, imposed by seasonal fluctuations in environmental conditions, can maintain polygenic sex determination indefinitely.     

Polygenic score accuracy in ancient samples: Quantifying the effects of allelic turnover

Polygenic scores link the genotypes of ancient individuals to their phenotypes, which are often unobservable, offering a tantalizing opportunity to reconstruct complex trait evolution. In practice, however, interpretation of ancient polygenic scores is subject to numerous assumptions. For one, the genome-wide association (GWA) studies from which polygenic scores are derived, can only estimate effect sizes for loci segregating in contemporary populations. Therefore, a GWA study may not correctly identify all loci relevant to trait variation in the ancient population. In addition, the frequencies of trait-associated loci may have changed in the intervening years. Here, we devise a theoretical framework to quantify the effect of this allelic turnover on the statistical properties of polygenic scores as functions of population genetic dynamics, trait architecture, power to detect significant loci, and the age of the ancient sample. We model the allele frequencies of loci underlying trait variation using the Wright-Fisher diffusion, and employ the spectral representation of its transition density to find analytical expressions for several error metrics, including the expected sample correlation between the polygenic scores of ancient individuals and their true phenotypes, referred to as polygenic score accuracy. Our theory also applies to a two-population scenario and demonstrates that allelic turnover alone may explain a substantial percentage of the reduced accuracy observed in cross-population predictions, akin to those performed in human genetics. Finally, we use simulations to explore the effects of recent directional selection, a bias-inducing process, on the statistics of interest. We find that even in the presence of bias, weak selection induces minimal deviations from our neutral expectations for the decay of polygenic score accuracy. By quantifying the limitations of polygenic scores in an explicit evolutionary context, our work lays the foundation for the development of more sophisticated statistical procedures to analyze both temporally and geographically resolved polygenic scores.     

Linkage Analysis with an Alternative Formulation for the Mixed Model of Inheritance: The Finite Polygenic Mixed Model

This paper presents an extension of the finite polygenic mixed model of FERNANDO et al. (1994) to linkage analysis. The finite polygenic mixed model, extended for linkage analysis, leads to a likelihood that can be calculated using efficient algorithms developed for oligogenic models. For comparison, linkage analysis of 5 simulated 4021-member pedigrees was performed using the usual mixed model of inheritance, approximated by HASSTEDT (1982), and the finite polygenic mixed model extended for linkage analysis presented here. Maximum likelihood estimates of the finite polygenic mixed model could be inferred to be closer to the simulated values in these pedigrees.     

Population dynamics of the additive polygenic system under truncation selection]

Common features of the equations describing dynamics of the additive polygenic system under truncation selection are summarized. A combination of parameters playing the role of the effective selective pressure on the ith polygenic locus was revealed. The product of mean relative fitnesses of the individual polygenic loci, [formula: see text], was shown to play the role of relative mean fitness of the polygenic population. This value depends on the measurable parameters of the character distribution in the population: [formula: see text]. It was shown that under the constant population number during truncation selection, the characteristic of the best genotype increases, [formula: see text]; which is also a product of the frequencies of preferable genotypes at individual polygenic loci. This value plays the role of the proportion of the number of the best ("champion") genotype in the population. In fact, this is the champion genotype polygene consensus pattern frequency, which a priori indicates the possibility of the champion pattern fixation. The analogue of Haldane's dilemma for the polygenic system which restrict the number of polygenes simultaneously subjected to adaptive evolution [formula: see text] was obtained for the case of constant effective population number (Ne = const).