The action of stabilizing selection, mutation, and drift on epistatic quantitative traits

Opportunities and limits of combining microbiome and genome data for complex trait prediction

Background

Analysis and prediction of complex traits using microbiome data combined with host genomic information is a topic of utmost interest. However, numerous questions remain to be answered: how useful can the microbiome be for complex trait prediction? Are estimates of microbiability reliable? Can the underlying biological links between the host’s genome, microbiome, and phenome be recovered?

Methods

Here, we address these issues by (i) developing a novel simulation strategy that uses real microbiome and genotype data as inputs, and (ii) using variance-component approaches (Bayesian Reproducing Kernel Hilbert Space (RKHS) and Bayesian variable selection methods (Bayes C)) to quantify the proportion of phenotypic variance explained by the genome and the microbiome. The proposed simulation approach can mimic genetic links between the microbiome and genotype data by a permutation procedure that retains the distributional properties of the data.

Results

Using real genotype and rumen microbiota abundances from dairy cattle, simulation results suggest that microbiome data can significantly improve the accuracy of phenotype predictions, regardless of whether some microbiota abundances are under direct genetic control by the host or not. This improvement depends logically on the microbiome being stable over time. Overall, random-effects linear methods appear robust for variance components estimation, in spite of the typically highly leptokurtic distribution of microbiota abundances. The predictive performance of Bayes C was higher but more sensitive to the number of causative effects than RKHS. Accuracy with Bayes C depended, in part, on the number of microorganisms’ taxa that influence the phenotype.

Conclusions

While we conclude that, overall, genome-microbiome-links can be characterized using variance component estimates, we are less optimistic about the possibility of identifying the causative host genetic effects that affect microbiota abundances, which would require much larger sample sizes than are typically available for genome-microbiome-phenome studies. The R code to replicate the analyses is in https://github.com/miguelperezenciso/simubiome.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12711-021-00658-7.

Accelerated inbreeding depression suggests synergistic epistasis for deleterious mutations in Drosophila melanogaster

Epistasis may have important consequences for a number of issues in quantitative genetics and evolutionary biology. In particular, synergistic epistasis for deleterious alleles is relevant to the mutation load paradox and the evolution of sex and recombination. Some studies have shown evidence of synergistic epistasis for spontaneous or induced deleterious mutations appearing in mutation-accumulation experiments. However, many newly arising mutations may not actually be segregating in natural populations because of the erasing action of natural selection. A demonstration of synergistic epistasis for naturally segregating alleles can be achieved by means of inbreeding depression studies, as deleterious recessive allelic effects are exposed in inbred lines. Nevertheless, evidence of epistasis from these studies is scarce and controversial. In this paper, we report the results of two independent inbreeding experiments carried out with two different populations of Drosophila melanogaster. The results show a consistent accelerated inbreeding depression for fitness, suggesting synergistic epistasis among deleterious alleles. We also performed computer simulations assuming different possible models of epistasis and mutational parameters for fitness, finding some of them to be compatible with the results observed. Our results suggest that synergistic epistasis for deleterious mutations not only occurs among newly arisen spontaneous or induced mutations, but also among segregating alleles in natural populations.

A population genetic interpretation of GWAS findings for human quantitative traits

Human genome-wide association studies (GWASs) are revealing the genetic architecture of anthropomorphic and biomedical 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 because genetic variation that affects one trait often affects many others, we model the genetic architecture of a focal trait that arises under stabilizing selection in a multidimensional trait space. We solve the model for the phenotypic distribution and allelic dynamics at steady state and derive robust, closed-form solutions for summary statistics of the genetic architecture. Our results provide a simple interpretation for missing heritability and why it varies among traits. They predict that the distribution of variances contributed by loci identified in GWASs is well approximated by a simple functional form that depends on a single parameter: the expected contribution to genetic variance of a strongly selected site affecting the trait. We test this prediction against the results of GWASs for height and body mass index (BMI) and find that it fits the data well, allowing us to make inferences about the degree of pleiotropy and mutational target size for these traits. Our findings help to explain why the GWAS for height explains more of the heritable variance than the similarly sized GWAS for BMI and to predict the increase in explained heritability with study sample size. Considering the demographic history of European populations, in which these GWASs were performed, we further find that most of the associations they identified likely involve mutations that arose shortly before or during the Out-of-Africa bottleneck at sites with selection coefficients around s = 10-3.

"Conversion" of epistatic into additive genetic variance in finite populations and possible impact on long-term selection response

The role of epistasis in understanding the genetic architecture and variation of quantitative traits and its role, if any, in artificial selection and livestock improvement more generally has a long and sometimes controversial history. Its presence has been clearly demonstrated in, for example, laboratory experiments, but the amount of variation it contributes is likely to be small in outbred populations. In a finite population, although additive x additive epistatic variance is lost by genetic drift, it also contributes by conversion to additive variance through drift sampling and therefore has a potential indirect role in medium and long-term selection response, with superficial similarity to and hard to distinguish from mutation. Whilst predictions of response require knowledge of genetic parameters, an infinitesimal model provides some analytic results. Otherwise there is little quantitative information relevant to animal populations on which to judge this potential role of epistasis and reach firm conclusions.

Epistasis × environment interactions among Arabidopsis thaliana glucosinolate genes impact complex traits and fitness in the field

Despite the growing number of studies showing that genotype × environment and epistatic interactions control fitness, the influences of epistasis × environment interactions on adaptive trait evolution remain largely uncharacterized. Across three field trials, we quantified aliphatic glucosinolate (GSL) defense chemistry, leaf damage, and relative fitness using mutant lines of Arabidopsis thaliana varying at pairs of causal aliphatic GSL defense genes to test the impact of epistatic and epistasis × environment interactions on adaptive trait variation. We found that aliphatic GSL accumulation was primarily influenced by additive and epistatic genetic variation, leaf damage was primarily influenced by environmental variation and relative fitness was primarily influenced by epistasis and epistasis × environment interactions. Epistasis × environment interactions accounted for up to 48% of the relative fitness variation in the field. At a single field site, the impact of epistasis on relative fitness varied significantly over 2 yr, showing that epistasis × environment interactions within a location can be temporally dynamic. These results suggest that the environmental dependency of epistasis can profoundly influence the response to selection, shaping the adaptive trajectories of natural populations in complex ways, and deserves further consideration in future evolutionary studies.

The effect of gene interactions on the long-term response to selection

The role of gene interactions in the evolutionary process has long been controversial. Although some argue that they are not of importance, because most variation is additive, others claim that their effect in the long term can be substantial. Here, we focus on the long-term effects of genetic interactions under directional selection assuming no mutation or dominance, and that epistasis is symmetrical overall. We ask by how much the mean of a complex trait can be increased by selection and analyze two extreme regimes, in which either drift or selection dominate the dynamics of allele frequencies. In both scenarios, epistatic interactions affect the long-term response to selection by modulating the additive genetic variance. When drift dominates, we extend Robertson's [Robertson A (1960)Proc R Soc Lond B Biol Sci153(951):234-249] argument to show that, for any form of epistasis, the total response of a haploid population is proportional to the initial total genotypic variance. In contrast, the total response of a diploid population is increased by epistasis, for a given initial genotypic variance. When selection dominates, we show that the total selection response can only be increased by epistasis when some initially deleterious alleles become favored as the genetic background changes. We find a simple approximation for this effect and show that, in this regime, it is the structure of the genotype-phenotype map that matters and not the variance components of the population.

Influence of gene interaction on complex trait variation with multilocus models

Although research effort is being expended into determining the importance of epistasis and epistatic variance for complex traits, there is considerable controversy about their importance. Here we undertake an analysis for quantitative traits utilizing a range of multilocus quantitative genetic models and gene frequency distributions, focusing on the potential magnitude of the epistatic variance. All the epistatic terms involving a particular locus appear in its average effect, with the number of two-locus interaction terms increasing in proportion to the square of the number of loci and that of third order as the cube and so on. Hence multilocus epistasis makes substantial contributions to the additive variance and does not, per se, lead to large increases in the nonadditive part of the genotypic variance. Even though this proportion can be high where epistasis is antagonistic to direct effects, it reduces with multiple loci. As the magnitude of the epistatic variance depends critically on the heterozygosity, for models where frequencies are widely dispersed, such as for selectively neutral mutations, contributions of epistatic variance are always small. Epistasis may be important in understanding the genetic architecture, for example, of function or human disease, but that does not imply that loci exhibiting it will contribute much genetic variance. Overall we conclude that theoretical predictions and experimental observations of low amounts of epistatic variance in outbred populations are concordant. It is not a likely source of missing heritability, for example, or major influence on predictions of rates of evolution.