The genetics of phenotypic plasticity. II. Response to selection

We selected on phenotypic plasticity of thorax size in response to temperature in Drosophila melanogaster using a family selection scheme. The results were compared to those of lines selected directly on thorax size. We found that the plasticity of a character does respond to selection and this response is partially independent of the response to selection on the mean of the character. One puzzling result was that a selection limit of zero plasticity was reached in the lines selected for decreased plasticity yet additive genetic variation for plasticity still existed in the lines. We tested the predictions of three models of the genetic basis of phenotypic plasticity: overdominance, pleiotropy, and epistasis. The results mostly support the epistasis model, that the plasticity of a character is determined by separate loci from those determining the mean of the character.     

The effect of selection on genetic balance when the population size is varying

It is known that a reformulation for variable population size of the classical Sewall Wright model for balance between two genotypes can lead, under some circumstances, to a situation of balanced polymorphism when there is no selection present. In this note it is shown that the presence of selection prohibits the possibility of balance and assures ultimate homozygosity with probability one.     

Response to mass selection when the genotype by environment interaction is modelled as a linear reaction norm

A breeding goal accounting for the effects of genotype by environment interaction (G × E) has to define not only traits but also the environment in which those traits are to be improved. The aim of this study was to predict the selection response in the coefficients of a linear reaction norm, and response in average phenotypic value in any environment, when mass selection is applied to a trait where G × E is modelled as a linear reaction norm. The optimum environment in which to test the selection candidates for a given breeding objective was derived. Optimisation of the selection environment can be used as a means to either maximise genetic progress in a certain response environment, to keep the change in environmental sensitivity at a desired rate, or to reduce the proportion of animals performing below an acceptance level. The results showed that the optimum selection environment is not always equal to the environment in which the response is to be realised, but depends on the degree of G × E (determined by the ratio of variances in slope and level of a linear reaction norm), the correlation between level and slope, and the heritability of the trait.     

Genomic selection in soybean: accuracy and time gain in relation to phenotypic selection

Genomic selection (GS) can potentially accelerate genetic improvement of soybean [Glycine max L. (Merrill)] by reducing the time to complete breeding cycles. The objectives of this study were to (1) explore the accuracy of GS in soybean, (2) evaluate the contribution of intrapopulational structure to the accuracy of GS, and (3) compare the efficiencies of phenotypic selection and GS in soybean. For this, phenotypic and genotypic data were collected from 324 soybean genotypes (243 recombinant inbred lines and 81 cultivars) and GS was performed for five yield related traits. BayesB methodology with a 10-fold cross-validation was used to compute accuracies. The GS accuracies were evaluated for grain yield, plant height, insertion of first pod, days to maturity, and 1000-grain weight at eight locations. We found that GS can reduce the time required to complete a selection cycle in soybean, which can lead to increased production of this commercially important crop. Furthermore, genotypic accuracy was similar regardless of population structure correction.     

Genomic assisted selection for enhancing line breeding: merging genomic and phenotypic selection in winter wheat breeding programs with preliminary yield trials

Key message

Early generation genomic selection is superior to conventional phenotypic selection in line breeding and can be strongly improved by including additional information from preliminary yield trials.

Abstract

The selection of lines that enter resource-demanding multi-environment trials is a crucial decision in every line breeding program as a large amount of resources are allocated for thoroughly testing these potential varietal candidates. We compared conventional phenotypic selection with various genomic selection approaches across multiple years as well as the merit of integrating phenotypic information from preliminary yield trials into the genomic selection framework. The prediction accuracy using only phenotypic data was rather low (r = 0.21) for grain yield but could be improved by modeling genetic relationships in unreplicated preliminary yield trials (r = 0.33). Genomic selection models were nevertheless found to be superior to conventional phenotypic selection for predicting grain yield performance of lines across years (r = 0.39). We subsequently simplified the problem of predicting untested lines in untested years to predicting tested lines in untested years by combining breeding values from preliminary yield trials and predictions from genomic selection models by a heritability index. This genomic assisted selection led to a 20% increase in prediction accuracy, which could be further enhanced by an appropriate marker selection for both grain yield (r = 0.48) and protein content (r = 0.63). The easy to implement and robust genomic assisted selection gave thus a higher prediction accuracy than either conventional phenotypic or genomic selection alone. The proposed method took the complex inheritance of both low and high heritable traits into account and appears capable to support breeders in their selection decisions to develop enhanced varieties more efficiently.

     

Assessment of diagnostic tests when disease verification is subject to selection bias

In the assessment of the statistical properties of a diagnostic test, for example the sensitivity and specificity of the test, it is common to derive estimates from a sample limited to those cases for whom subsequent definitive disease verification is obtained. Omission of nonverified cases can seriously bias the estimates. In order to adjust the estimates it is necessary to make assumptions about the mechanism for selecting cases for verification. Methods for making the necessary adjustments can then be derived.     

The impact of epistatic selection on the genomic traces of selection

The rapid accumulation of genomic data has led to an explosion of studies searching for signals of past selection left within DNA sequences. Yet the majority of theoretical studies investigating the traces of selection have assumed a simple form of selection, without interactions among selectively fixed sites. Fitness interactions—‘epistasis’—are commonplace, however, and take on a myriad of forms ( Whitlock et al. 1995 ; Segrèet al. 2005 ; Phillips 2008 ). It is thus important to determine how such epistasis would influence selective sweeps. On p. 5018 of this issue, Takahasi (2009) explores the effect of epistasis on genetic variation neighbouring two sites that interact in determining fitness, finding that such epistasis has a dramatic impact on the genetic variability in regions surrounding the interacting sites.     

On selection criteria and estimation of parameters when the variance is heterogeneous

Summary Procedures for ranking candidates for selection and for estimating genetic and environmental parameters when variances are heterogeneous are discussed. The best linear unbiased predictor (BLUP) accounts automatically for heterogeneous variance provided that the covariance structure is known and that the assumptions of the model hold. Under multivariate normality BLUP allowing for heterogeneous variance maximizes expected genetic progress. Examples of application of BLUP to selection when residual or genetic variances are heterogeneous are given. Restricted maximum likelihood estimation of heterogeneous variances and covariances via the expectation-maximization algorithm is presented.     

Copy number variants and genetic traits: closer to the resolution of phenotypic to genotypic variability

A considerable and unanticipated plasticity of the human genome, manifested as inter-individual copy number variation, has been discovered. These structural changes constitute a major source of inter-individual genetic variation that could explain variable penetrance of inherited (Mendelian and polygenic) diseases and variation in the phenotypic expression of aneuploidies and sporadic traits, and might represent a major factor in the aetiology of complex, multifactorial traits. For these reasons, an effort should be made to discover all common and rare copy number variants (CNVs) in the human population. This will also enable systematic exploration of both SNPs and CNVs in association studies to identify the genomic contributors to the common disorders and complex traits.     

The kappa coefficient of agreement for multiple observers when the number of subjects is small

Published results on the use of the kappa coefficient of agreement have traditionally been concerned with situations where a large number of subjects is classified by a small group of raters. The coefficient is then used to assess the degree of agreement among the raters through hypothesis testing or confidence intervals. A modified kappa coefficient of agreement for multiple categories is proposed and a parameter-free distribution for testing null agreement is provided, for use when the number of raters is large relative to the number of categories and subjects. The large-sample distribution of kappa is shown to be normal in the nonnull case, and confidence intervals for kappa are provided. The results are extended to allow for an unequal number of raters per subject.     

Bounds on the distribution of the number of gaps when circles and lines are covered by fragments: Theory and practical application to genomic and metagenomic projects

Background  

The question of how a circle or line segment becomes covered when random arcs are marked off has arisen repeatedly in bioinformatics. The number of uncovered gaps is of particular interest. Approximate distributions for the number of gaps have been given in the literature, one motivation being ease of computation. Error bounds for these approximate distributions have not been given.     

The effect of genomic information on optimal contribution selection in livestock breeding programs

Background

Long-term benefits in animal breeding programs require that increases in genetic merit be balanced with the need to maintain diversity (lost due to inbreeding). This can be achieved by using optimal contribution selection. The availability of high-density DNA marker information enables the incorporation of genomic data into optimal contribution selection but this raises the question about how this information affects the balance between genetic merit and diversity.

Methods

The effect of using genomic information in optimal contribution selection was examined based on simulated and real data on dairy bulls. We compared the genetic merit of selected animals at various levels of co-ancestry restrictions when using estimated breeding values based on parent average, genomic or progeny test information. Furthermore, we estimated the proportion of variation in estimated breeding values that is due to within-family differences.

Results

Optimal selection on genomic estimated breeding values increased genetic gain. Genetic merit was further increased using genomic rather than pedigree-based measures of co-ancestry under an inbreeding restriction policy. Using genomic instead of pedigree relationships to restrict inbreeding had a significant effect only when the population consisted of many large full-sib families; with a half-sib family structure, no difference was observed. In real data from dairy bulls, optimal contribution selection based on genomic estimated breeding values allowed for additional improvements in genetic merit at low to moderate inbreeding levels. Genomic estimated breeding values were more accurate and showed more within-family variation than parent average breeding values; for genomic estimated breeding values, 30 to 40% of the variation was due to within-family differences. Finally, there was no difference between constraining inbreeding via pedigree or genomic relationships in the real data.

Conclusions

The use of genomic estimated breeding values increased genetic gain in optimal contribution selection. Genomic estimated breeding values were more accurate and showed more within-family variation, which led to higher genetic gains for the same restriction on inbreeding. Using genomic relationships to restrict inbreeding provided no additional gain, except in the case of very large full-sib families.     

Simultaneous improvement of grain yield and protein content in durum wheat by different phenotypic indices and genomic selection

Key message

Simultaneous improvement of protein content and grain yield by index selection is possible but its efficiency largely depends on the weighting of the single traits. The genetic architecture of these indices is similar to that of the primary traits.

Abstract

Grain yield and protein content are of major importance in durum wheat breeding, but their negative correlation has hampered their simultaneous improvement. To account for this in wheat breeding, the grain protein deviation (GPD) and the protein yield were proposed as targets for selection. The aim of this work was to investigate the potential of different indices to simultaneously improve grain yield and protein content in durum wheat and to evaluate their genetic architecture towards genomics-assisted breeding. To this end, we investigated two different durum wheat panels comprising 159 and 189 genotypes, which were tested in multiple field locations across Europe and genotyped by a genotyping-by-sequencing approach. The phenotypic analyses revealed significant genetic variances for all traits and heritabilities of the phenotypic indices that were in a similar range as those of grain yield and protein content. The GPD showed a high and positive correlation with protein content, whereas protein yield was highly and positively correlated with grain yield. Thus, selecting for a high GPD would mainly increase the protein content whereas a selection based on protein yield would mainly improve grain yield, but a combination of both indices allows to balance this selection. The genome-wide association mapping revealed a complex genetic architecture for all traits with most QTL having small effects and being detected only in one germplasm set, thus limiting the potential of marker-assisted selection for trait improvement. By contrast, genome-wide prediction appeared promising but its performance strongly depends on the relatedness between training and prediction sets.

     

Spectrum of large copy number variations in 26 diverse Indian populations: potential involvement in phenotypic diversity

Copy number variations (CNVs) have provided a dynamic aspect to the apparently static human genome. We have analyzed CNVs larger than 100 kb in 477 healthy individuals from 26 diverse Indian populations of different linguistic, ethnic and geographic backgrounds. These CNVRs were identified using the Affymetrix 50K Xba 240 Array. We observed 1,425 and 1,337 CNVRs in the deletion and amplification sets, respectively, after pooling data from all the populations. More than 50% of the genes encompassed entirely in CNVs had both deletions and amplifications. There was wide variability across populations not only with respect to CNV extent (ranging from 0.04–1.14% of genome under deletion and 0.11–0.86% under amplification) but also in terms of functional enrichments of processes like keratinization, serine proteases and their inhibitors, cadherins, homeobox, olfactory receptors etc. These did not correlate with linguistic, ethnic, geographic backgrounds and size of populations. Certain processes were near exclusive to deletion (serine proteases, keratinization, olfactory receptors, GPCRs) or duplication (homeobox, serine protease inhibitors, embryonic limb morphogenesis) datasets. Populations having same enriched processes were observed to contain genes from different genomic loci. Comparison of polymorphic CNVRs (5% or more) with those cataloged in Database of Genomic Variants revealed that 78% (2473) of the genes in CNVRs in Indian populations are novel. Validation of CNVs using Sequenom MassARRAY revealed extensive heterogeneity in CNV boundaries. Exploration of CNV profiles in such diverse populations would provide a widely valuable resource for understanding diversity in phenotypes and disease.     

Bayesian optimization for genomic selection: a method for discovering the best genotype among a large number of candidates

Key message

A new pre-breeding strategy based on an optimization algorithm is proposed and evaluated via simulations. This strategy can find superior genotypes with less phenotyping effort.

Abstract

Genomic prediction is a promising approach to search for superior genotypes among a large number of accessions in germplasm collections preserved in gene banks. When some accessions are phenotyped and genotyped, a prediction model can be built, and the genotypic values of the remaining accessions can be predicted from their marker genotypes. In this study, we focused on the application of genomic prediction to pre-breeding, and propose a novel strategy that would reduce the cost of phenotyping needed to discover better accessions. We regarded the exploration of superior genotypes with genomic prediction as an optimization problem, and introduced Bayesian optimization to solve it. Bayesian optimization, that samples unobserved inputs according to the expected improvement (EI) as a selection criterion, seemed to be beneficial in pre-breeding. The EI depends on the predicted distribution of genotypic values, whereas usual selection depends only on the point estimate. We simulated a search for the best genotype among candidate genotypes and showed that the EI-based strategy required fewer genotypes to identify the best genotype than the usual and random selection strategy. Therefore, Bayesian optimization can be useful for applying genomic prediction to pre-breeding and would reduce the number of phenotyped accessions needed to find the best accession among a large number of candidates.

     

Comparisons of single-stage and two-stage approaches to genomic selection

Genomic selection (GS) is a method for predicting breeding values of plants or animals using many molecular markers that is commonly implemented in two stages. In plant breeding the first stage usually involves computation of adjusted means for genotypes which are then used to predict genomic breeding values in the second stage. We compared two classical stage-wise approaches, which either ignore or approximate correlations among the means by a diagonal matrix, and a new method, to a single-stage analysis for GS using ridge regression best linear unbiased prediction (RR-BLUP). The new stage-wise method rotates (orthogonalizes) the adjusted means from the first stage before submitting them to the second stage. This makes the errors approximately independently and identically normally distributed, which is a prerequisite for many procedures that are potentially useful for GS such as machine learning methods (e.g. boosting) and regularized regression methods (e.g. lasso). This is illustrated in this paper using componentwise boosting. The componentwise boosting method minimizes squared error loss using least squares and iteratively and automatically selects markers that are most predictive of genomic breeding values. Results are compared with those of RR-BLUP using fivefold cross-validation. The new stage-wise approach with rotated means was slightly more similar to the single-stage analysis than the classical two-stage approaches based on non-rotated means for two unbalanced datasets. This suggests that rotation is a worthwhile pre-processing step in GS for the two-stage approaches for unbalanced datasets. Moreover, the predictive accuracy of stage-wise RR-BLUP was higher (5.0–6.1 %) than that of componentwise boosting.     

Microhabitat selection when detection is imperfect: the case of an endemic Atlantic forest mammal

Studies on habitat selection based on the presence and absence of individuals still rarely include the uncertainty of absence. With it, one can model the probability of detection, which is a parameter of interest especially when dealing with species where non-detection is common. Here, we performed an analysis of microhabitat selection of a New World marsupial (Marmosa paraguayana, Tate 1931)??an arboreal species endemic to the Brazilian Atlantic forest??accounting for false absence. We found empirical evidence supporting one of our hypotheses: the angle of the terrain??s inclination at a site positively affects detection probability. This is probably due to the fact that, at an inclined site, the area available to the animals tends to be larger and the probability of detection of M. paraguayana would be higher, due either to greater local abundance or increased frequency of moving. The probability of resource use was heterogeneous, or rather, not constant in space, but constant in time. We found weak evidence for the correlation between the canopy volume and the probability of resource use. However, we observed a tendency in the estimates of site-specific probability of resource use: the highest values of the probability of resource use appeared in the upper part of the study grid, where the canopies were denser as well as more closed. Thus, this specie??s probability of resource use possibly diminishes in habitats such as early secondary forest with tiny canopies.     

The evolution of the phenotypic covariance matrix: evidence for selection and drift in Melanoplus

Phenotypic variation in trait means is a common observation for geographically separated populations. Such variation is typically retained under common garden conditions, indicating that there has been evolutionary change in the populations, as a result of selection and/or drift. Much less frequently studied is variation in the phenotypic covariance matrix (hereafter, P matrix), although this is an important component of evolutionary change. In this paper, we examine variation in the phenotypic means and P matrices in two species of grasshopper, Melanoplus sanguinipes and M. devastator. Using the P matrices estimated for 14 populations of M. sanguinipes and three populations of M. devastator we find that (1) significant differences between the sexes can be attributed to scaling effects; (2) there is no significant difference between the two species; (3) there are highly significant differences among populations that cannot be accounted for by scaling effects; (4) these differences are a consequence of statistically significant patterns of covariation with geographic and environmental factors, phenotypic variances and covariances increasing with increased temperature but decreasing with increased latitude and altitude. This covariation suggests that selection has been important in the evolution of the P matrix in these populations Finally, we find a significant positive correlation between the average difference between matrices and the genetic distance between the populations, indicating that drift has caused some of the variation in the P matrices.