Optimizing selection based on BLUPs or BLUEs in multiple sets of genotypes differing in their population parameters.

KEY MESSAGE: Selection response in truncation selection across multiple sets of candidates hinges on their post-selection proportions, which can deviate grossly from their initial proportions. For BLUPs, using a uniform threshold for all candidates maximizes the selection response, irrespective of differences in population parameters. Plant breeding programs typically involve multiple families from either the same or different populations, varying in means, genetic variances and prediction accuracy of BLUPs or BLUEs for true genetic values (TGVs) of candidates. We extend the classical breeder's equation for truncation selection from single to multiple sets of genotypes, indicating that the expected overall selection response ( Δ G Tot ) for TGVs depends on the selection response within individual sets and their post-selection proportions. For BLUEs, we show that maximizing Δ G Tot requires thresholds optimally tailored for each set, contingent on their population parameters. For BLUPs, we prove that Δ G Tot is maximized by applying a uniform threshold across all candidates from all sets. We provide explicit formulas for the origin of the selected candidates from different sets and show that their proportions before and after selection can differ substantially, especially for sets with inferior properties and low proportion. We discuss implications of these results for (a) optimum allocation of resources to training and prediction sets and (b) the need to counteract narrowing the genetic variation under genomic selection. For genomic selection of hybrids based on BLUPs of GCA of their parent lines, selecting distinct proportions in the two parent populations can be advantageous, if these differ substantially in the variance and/or prediction accuracy of GCA. Our study sheds light on the complex interplay of selection thresholds and population parameters for the selection response in plant breeding programs, offering insights into the effective resource management and prudent application of genomic selection for improved crop development.

Phylogenetic network classes through the lens of expanding covers.

It was recently shown that a large class of phylogenetic networks, the 'labellable' networks, is in bijection with the set of 'expanding' covers of finite sets. In this paper, we show how several prominent classes of phylogenetic networks can be characterised purely in terms of properties of their associated covers. These classes include the tree-based, tree-child, orchard, tree-sibling, and normal networks. In the opposite direction, we give an example of how a restriction on the set of expanding covers can define a new class of networks, which we call 'spinal' phylogenetic networks.

Accuracy of Genomic prediction for fleece traits in Inner Mongolia Cashmere goats.

The fleece traits are important economic traits of goats. With the reduction of sequencing and genotyping cost and the improvement of related technologies, genomic selection for goats has become possible. The research collect pedigree, phenotype and genotype information of 2299 Inner Mongolia Cashmere goats (IMCGs) individuals. We estimate fixed effects, and compare the estimates of variance components, heritability and genomic predictive ability of fleece traits in IMCGs when using the pedigree based Best Linear Unbiased Prediction (ABLUP), Genomic BLUP (GBLUP) or single-step GBLUP (ssGBLUP). The fleece traits considered are cashmere production (CP), cashmere diameter (CD), cashmere length (CL) and fiber length (FL). It was found that year of production, sex, herd and individual ages had highly significant effects on the four fleece traits (P < 0.01). All of these factors should be considered when the genetic parameters of fleece traits in IMCGs are evaluated. The heritabilities of FL, CL, CP and CD with ABLUP, GBLUP and ssGBLUP methods were 0.26 ~ 0.31, 0.05 ~ 0.08, 0.15 ~ 0.20 and 0.22 ~ 0.28, respectively. Therefore, it can be inferred that the genetic progress of CL is relatively slow. The predictive ability of fleece traits in IMCGs with GBLUP (56.18% to 69.06%) and ssGBLUP methods (66.82% to 73.70%) was significantly higher than that of ABLUP (36.73% to 41.25%). For the ssGBLUP method is significantly (29% ~ 33%) higher than that with ABLUP, and which is slightly (4% ~ 14%) higher than that of GBLUP. The ssGBLUP will be as an superiors method for using genomic selection of fleece traits in Inner Mongolia Cashmere goats.

Statistical sampling of missing environmental variables improves biophysical genomic prediction in wheat.

KEY MESSAGE: The integration of genomic prediction with crop growth models enabled the estimation of missing environmental variables which improved the prediction accuracy of grain yield. Since the invention of whole-genome prediction (WGP) more than two decades ago, breeding programmes have established extensive reference populations that are cultivated under diverse environmental conditions. The introduction of the CGM-WGP model, which integrates crop growth models (CGM) with WGP, has expanded the applications of WGP to the prediction of unphenotyped traits in untested environments, including future climates. However, CGMs require multiple seasonal environmental records, unlike WGP, which makes CGM-WGP less accurate when applied to historical reference populations that lack crucial environmental inputs. Here, we investigated the ability of CGM-WGP to approximate missing environmental variables to improve prediction accuracy. Two environmental variables in a wheat CGM, initial soil water content (InitlSoilWCont) and initial nitrate profile, were sampled from different normal distributions separately or jointly in each iteration within the CGM-WGP algorithm. Our results showed that sampling InitlSoilWCont alone gave the best results and improved the prediction accuracy of grain number by 0.07, yield by 0.06 and protein content by 0.03. When using the sampled InitlSoilWCont values as an input for the traditional CGM, the average narrow-sense heritability of the genotype-specific parameters (GSPs) improved by 0.05, with GNSlope, PreAnthRes, and VernSen showing the greatest improvements. Moreover, the root mean square of errors for grain number and yield was reduced by about 7% for CGM and 31% for CGM-WGP when using the sampled InitlSoilWCont values. Our results demonstrate the advantage of sampling missing environmental variables in CGM-WGP to improve prediction accuracy and increase the size of the reference population by enabling the utilisation of historical data that are missing environmental records.

GbyE: an integrated tool for genome widely association study and genome selection based on genetic by environmental interaction.

BACKGROUND: The growth and development of organism were dependent on the effect of genetic, environment, and their interaction. In recent decades, lots of candidate additive genetic markers and genes had been detected by using genome-widely association study (GWAS). However, restricted to computing power and practical tool, the interactive effect of markers and genes were not revealed clearly. And utilization of these interactive markers is difficult in the breeding and prediction, such as genome selection (GS). RESULTS: Through the Power-FDR curve, the GbyE algorithm can detect more significant genetic loci at different levels of genetic correlation and heritability, especially at low heritability levels. The additive effect of GbyE exhibits high significance on certain chromosomes, while the interactive effect detects more significant sites on other chromosomes, which were not detected in the first two parts. In prediction accuracy testing, in most cases of heritability and genetic correlation, the majority of prediction accuracy of GbyE is significantly higher than that of the mean method, regardless of whether the rrBLUP model or BGLR model is used for statistics. The GbyE algorithm improves the prediction accuracy of the three Bayesian models BRR, BayesA, and BayesLASSO using information from genetic by environmental interaction (G × E) and increases the prediction accuracy by 9.4%, 9.1%, and 11%, respectively, relative to the Mean value method. The GbyE algorithm is significantly superior to the mean method in the absence of a single environment, regardless of the combination of heritability and genetic correlation, especially in the case of high genetic correlation and heritability. CONCLUSIONS: Therefore, this study constructed a new genotype design model program (GbyE) for GWAS and GS using Kronecker product. which was able to clearly estimate the additive and interactive effects separately. The results showed that GbyE can provide higher statistical power for the GWAS and more prediction accuracy of the GS models. In addition, GbyE gives varying degrees of improvement of prediction accuracy in three Bayesian models (BRR, BayesA, and BayesCpi). Whatever the phenotype were missed in the single environment or multiple environments, the GbyE also makes better prediction for inference population set. This study helps us understand the interactive relationship between genomic and environment in the complex traits. The GbyE source code is available at the GitHub website ( https://github.com/liu-xinrui/GbyE ).

Biologically meaningful regulatory logic enhances the convergence rate in Boolean networks and bushiness of their state transition graph.

Boolean models of gene regulatory networks (GRNs) have gained widespread traction as they can easily recapitulate cellular phenotypes via their attractor states. Their overall dynamics are embodied in a state transition graph (STG). Indeed, two Boolean networks (BNs) with the same network structure and attractors can have drastically different STGs depending on the type of Boolean functions (BFs) employed. Our objective here is to systematically delineate the effects of different classes of BFs on the structural features of the STG of reconstructed Boolean GRNs while keeping network structure and biological attractors fixed, and explore the characteristics of BFs that drive those features. Using $10$ reconstructed Boolean GRNs, we generate ensembles that differ in BFs and compute from their STGs the dynamics' rate of contraction or 'bushiness' and rate of 'convergence', quantified with measures inspired from cellular automata (CA) that are based on the garden-of-Eden (GoE) states. We find that biologically meaningful BFs lead to higher STG 'bushiness' and 'convergence' than random ones. Obtaining such 'global' measures gets computationally expensive with larger network sizes, stressing the need for feasible proxies. So we adapt Wuensche's $Z$-parameter in CA to BFs in BNs and provide four natural variants, which, along with the average sensitivity of BFs computed at the network level, comprise our descriptors of local dynamics and we find some of them to be good proxies for bushiness. Finally, we provide an excellent proxy for the 'convergence' based on computing transient lengths originating at random states rather than GoE states.

Effects of mRNA conformational switching on translational noise in gene circuits.

Intragenic translational heterogeneity describes the variation in translation at the level of transcripts for an individual gene. A factor that contributes to this source of variation is the mRNA structure. Both the composition of the thermodynamic ensemble, i.e., the stationary distribution of mRNA structures, and the switching dynamics between those play a role. The effect of the switching dynamics on intragenic translational heterogeneity remains poorly understood. We present a stochastic translation model that accounts for mRNA structure switching and is derived from a Markov model via approximate stochastic filtering. We assess the approximation on various timescales and provide a method to quantify how mRNA structure dynamics contributes to translational heterogeneity. With our approach, we allow quantitative information on mRNA switching from biophysical experiments or coarse-grain molecular dynamics simulations of mRNA structures to be included in gene regulatory chemical reaction network models without an increase in the number of species. Thereby, our model bridges a gap between mRNA structure kinetics and gene expression models, which we hope will further improve our understanding of gene regulatory networks and facilitate genetic circuit design.

Multiple phenotype association tests based on sliced inverse regression.

BACKGROUND: Joint analysis of multiple phenotypes in studies of biological systems such as Genome-Wide Association Studies is critical to revealing the functional interactions between various traits and genetic variants, but growth of data in dimensionality has become a very challenging problem in the widespread use of joint analysis. To handle the excessiveness of variables, we consider the sliced inverse regression (SIR) method. Specifically, we propose a novel SIR-based association test that is robust and powerful in testing the association between multiple predictors and multiple outcomes. RESULTS: We conduct simulation studies in both low- and high-dimensional settings with various numbers of Single-Nucleotide Polymorphisms and consider the correlation structure of traits. Simulation results show that the proposed method outperforms the existing methods. We also successfully apply our method to the genetic association study of ADNI dataset. Both the simulation studies and real data analysis show that the SIR-based association test is valid and achieves a higher efficiency compared with its competitors. CONCLUSION: Several scenarios with low- and high-dimensional responses and genotypes are considered in this paper. Our SIR-based method controls the estimated type I error at the pre-specified level α .

Exact results for gene-expression models with general waiting-time distributions.

Complex molecular details of transcriptional regulation can be coarse-grained by assuming that reaction waiting times for promoter-state transitions, the mRNA synthesis, and the mRNA degradation follow general distributions. However, how such a generalized two-state model is analytically solved is a long-standing issue. Here we first present analytical formulas of burst-size distributions for this model. Then, we derive an iterative equation for the mRNA moment-generating function, by which mRNA raw and binomial moments of any order can be conveniently calculated. The analytical results obtained in the special cases of phase-type waiting-time distributions not only provide insights into the mechanisms of complex transcriptional regulations but also bring conveniences for experimental data-based statistical inferences.

Preponderance of generalized chain functions in reconstructed Boolean models of biological networks.

Boolean networks (BNs) have been extensively used to model gene regulatory networks (GRNs). The dynamics of BNs depend on the network architecture and regulatory logic rules (Boolean functions (BFs)) associated with nodes. Nested canalyzing functions (NCFs) have been shown to be enriched among the BFs in the large-scale studies of reconstructed Boolean models. The central question we address here is whether that enrichment is due to certain sub-types of NCFs. We build on one sub-type of NCFs, the chain functions (or chain-0 functions) proposed by Gat-Viks and Shamir. First, we propose two other sub-types of NCFs, namely, the class of chain-1 functions and generalized chain functions, the union of the chain-0 and chain-1 types. Next, we find that the fraction of NCFs that are chain-0 (also holds for chain-1) functions decreases exponentially with the number of inputs. We provide analytical treatment for this and other observations on BFs. Then, by analyzing three different datasets of reconstructed Boolean models we find that generalized chain functions are significantly enriched within the NCFs. Lastly we illustrate that upon imposing the constraints of generalized chain functions on three different GRNs we are able to obtain biologically viable Boolean models.

Background Selection From Unlinked Sites Causes Nonindependent Evolution of Deleterious Mutations.

Background selection describes the reduction in neutral diversity caused by selection against deleterious alleles at other loci. It is typically assumed that the purging of deleterious alleles affects linked neutral variants, and indeed simulations typically only treat a genomic window. However, background selection at unlinked loci also depresses neutral diversity. In agreement with previous analytical approximations, in our simulations of a human-like genome with a realistically high genome-wide deleterious mutation rate, the effects of unlinked background selection exceed those of linked background selection. Background selection reduces neutral genetic diversity by a factor that is independent of census population size. Outside of genic regions, the strength of background selection increases with the mean selection coefficient, contradicting the linked theory but in agreement with the unlinked theory. Neutral diversity within genic regions is fairly independent of the strength of selection. Deleterious genetic load among haploid individuals is underdispersed, indicating nonindependent evolution of deleterious mutations. Empirical evidence for underdispersion was previously interpreted as evidence for global epistasis, but we recover it from a non-epistatic model.

Prediction accuracy of genomic estimated breeding values for fruit traits in cultivated tomato (Solanum lycopersicum L.).

BACKGROUND: Genomic selection (GS) is an efficient breeding strategy to improve quantitative traits. It is necessary to calculate genomic estimated breeding values (GEBVs) for GS. This study investigated the prediction accuracy of GEBVs for five fruit traits including fruit weight, fruit width, fruit height, pericarp thickness, and Brix. Two tomato germplasm collections (TGC1 and TGC2) were used as training populations, consisting of 162 and 191 accessions, respectively. RESULTS: Large phenotypic variations for the fruit traits were found in these collections and the 51K Axiom™ SNP array generated confident 31,142 SNPs. Prediction accuracy was evaluated using different cross-validation methods, GS models, and marker sets in three training populations (TGC1, TGC2, and combined). For cross-validation, LOOCV was effective as k-fold across traits and training populations. The parametric (RR-BLUP, Bayes A, and Bayesian LASSO) and non-parametric (RKHS, SVM, and random forest) models showed different prediction accuracies (0.594-0.870) between traits and training populations. Of these, random forest was the best model for fruit weight (0.780-0.835), fruit width (0.791-0.865), and pericarp thickness (0.643-0.866). The effect of marker density was trait-dependent and reached a plateau for each trait with 768-12,288 SNPs. Two additional sets of 192 and 96 SNPs from GWAS revealed higher prediction accuracies for the fruit traits compared to the 31,142 SNPs and eight subsets. CONCLUSION: Our study explored several factors to increase the prediction accuracy of GEBVs for fruit traits in tomato. The results can facilitate development of advanced GS strategies with cost-effective marker sets for improving fruit traits as well as other traits. Consequently, GS will be successfully applied to accelerate the tomato breeding process for developing elite cultivars.

A quantitative genetic model of background selection in humans.

Across the human genome, there are large-scale fluctuations in genetic diversity caused by the indirect effects of selection. This "linked selection signal" reflects the impact of selection according to the physical placement of functional regions and recombination rates along chromosomes. Previous work has shown that purifying selection acting against the steady influx of new deleterious mutations at functional portions of the genome shapes patterns of genomic variation. To date, statistical efforts to estimate purifying selection parameters from linked selection models have relied on classic Background Selection theory, which is only applicable when new mutations are so deleterious that they cannot fix in the population. Here, we develop a statistical method based on a quantitative genetics view of linked selection, that models how polygenic additive fitness variance distributed along the genome increases the rate of stochastic allele frequency change. By jointly predicting the equilibrium fitness variance and substitution rate due to both strong and weakly deleterious mutations, we estimate the distribution of fitness effects (DFE) and mutation rate across three geographically distinct human samples. While our model can accommodate weaker selection, we find evidence of strong selection operating similarly across all human samples. Although our quantitative genetic model of linked selection fits better than previous models, substitution rates of the most constrained sites disagree with observed divergence levels. We find that a model incorporating selective interference better predicts observed divergence in conserved regions, but overall our results suggest uncertainty remains about the processes generating fitness variation in humans.

The cliff edge model of the evolution of schizophrenia: Mathematical, epidemiological, and genetic evidence.

How has schizophrenia, a condition that significantly reduces an individual's evolutionary fitness, remained common across generations and cultures? Numerous theories about the evolution of schizophrenia have been proposed, most of which are not consistent with modern epidemiological and genetic evidence. Here, we briefly review this evidence and explore the cliff edge model of schizophrenia. It suggests that schizophrenia is the extreme manifestation of a polygenic trait or a combination of traits that, within a normal range of variation, confer cognitive, linguistic, and/or social advantages. Only beyond a certain threshold, these traits precipitate the onset of schizophrenia and reduce fitness. We provide the first mathematical model of this qualitative concept and show that it requires only very weak positive selection of the underlying trait(s) to explain today's schizophrenia prevalence. This prediction, along with expectations about the effect size of schizophrenia risk alleles, are surprisingly well matched by empirical evidence. The cliff edge model predicts a dynamic change of selection of risk alleles, which explains the contradictory findings of evolutionary genetic studies.

Dominance and multi-locus interaction.

Dominance is usually considered a constant value that describes the relative difference in fitness or phenotype between heterozygotes and the average of homozygotes at a focal polymorphic locus. However, the observed dominance can vary with the genetic background of the focal locus. Here, alleles at other loci modify the observed phenotype through position effects or dominance modifiers that are sometimes associated with pathogen resistance, lineage, sex, or mating type. Theoretical models have illustrated how variable dominance appears in the context of multi-locus interaction (epistasis). Here, we review empirical evidence for variable dominance and how the observed patterns may be captured by proposed epistatic models. We highlight how integrating epistasis and dominance is crucial for comprehensively understanding adaptation and speciation.

The pseudoentropy of allele frequency trajectories, the persistence of variation, and the effective population size.

To concisely describe how genetic variation, at individual loci or across whole genomes, changes over time, and to follow transitory allelic changes, we introduce a quantity related to entropy, that we term pseudoentropy. This quantity emerges in a diffusion analysis of the mean time a mutation segregates in a population. For a neutral locus with an arbitrary number of alleles, the mean time of segregation is generally proportional to the pseudoentropy of initial allele frequencies. After the initial time point, pseudoentropy generally decreases, but other behaviours are possible, depending on the genetic diversity and selective forces present. For a biallelic locus, pseudoentropy and entropy coincide, but they are distinct quantities with more than two alleles. Thus for populations with multiple biallelic loci, the language of entropy suffices. Then entropy, combined across loci, serves as a concise description of genetic variation. We used individual based simulations to explore how this entropy behaves under different evolutionary scenarios. In agreement with predictions, the entropy associated with unlinked neutral loci decreases over time. However, deviations from free recombination and neutrality have clear and informative effects on the entropy's behaviour over time. Analysis of publicly available data of a natural D. melanogaster population, that had been sampled over seven years, using a sliding-window approach, yielded considerable variation in entropy trajectories of different genomic regions. These mostly follow a pattern that suggests a substantial effective population size and a limited effect of positive selection on genome-wide diversity over short time scales.

Indirect genetic effects should make group size more evolvable than expected.

Group size is an important trait for many ecological and evolutionary processes. However, it is not a trait possessed by individuals but by social groups, and as many genomes contribute to group size understanding its genetic underpinnings and so predicting its evolution is a conceptual challenge. Here I suggest how group size can be modelled as a joint phenotype of multiple individuals, and so how models for evolution accounting for indirect genetic effects are essential for understanding the genetic variance of group size. This approach makes it clear that (a) group size should have a larger genetic variance than initially expected as indirect genetic effects always contribute exactly as much as direct genetic effects and (b) the response to selection of group size should be faster than expected based on direct genetic variance alone as the correlation between direct and indirect effects is always at the maximum positive limit of 1. Group size should therefore show relatively rapid evolved increases and decreases, the consequences of which and evidence for I discuss.

GIS-FA: an approach to integrating thematic maps, factor-analytic, and envirotyping for cultivar targeting.

KEY MESSAGE: We propose an "enviromics" prediction model for recommending cultivars based on thematic maps aimed at decision-makers. Parsimonious methods that capture genotype-by-environment interaction (GEI) in multi-environment trials (MET) are important in breeding programs. Understanding the causes and factors of GEI allows the utilization of genotype adaptations in the target population of environments through environmental features and factor-analytic (FA) models. Here, we present a novel predictive breeding approach called GIS-FA, which integrates geographic information systems (GIS) techniques, FA models, partial least squares (PLS) regression, and enviromics to predict phenotypic performance in untested environments. The GIS-FA approach enables: (i) the prediction of the phenotypic performance of tested genotypes in untested environments, (ii) the selection of the best-ranking genotypes based on their overall performance and stability using the FA selection tools, and (iii) the creation of thematic maps showing overall or pairwise performance and stability for decision-making. We exemplify the usage of the GIS-FA approach using two datasets of rice [Oryza sativa (L.)] and soybean [Glycine max (L.) Merr.] in MET spread over tropical areas. In summary, our novel predictive method allows the identification of new breeding scenarios by pinpointing groups of environments where genotypes demonstrate superior predicted performance. It also facilitates and optimizes cultivar recommendations by utilizing thematic maps.

Dominance reversals: the resolution of genetic conflict and maintenance of genetic variation.

Beneficial reversals of dominance reduce the costs of genetic trade-offs and can enable selection to maintain genetic variation for fitness. Beneficial dominance reversals are characterized by the beneficial allele for a given context (e.g. habitat, developmental stage, trait or sex) being dominant in that context but recessive where deleterious. This context dependence at least partially mitigates the fitness consequence of heterozygotes carrying one non-beneficial allele for their context and can result in balancing selection that maintains alternative alleles. Dominance reversals are theoretically plausible and are supported by mounting empirical evidence. Here, we highlight the importance of beneficial dominance reversals as a mechanism for the mitigation of genetic conflict and review the theory and empirical evidence for them. We identify some areas in need of further research and development and outline three methods that could facilitate the identification of antagonistic genetic variation (dominance ordination, allele-specific expression and allele-specific ATAC-Seq (assay for transposase-accessible chromatin with sequencing)). There is ample scope for the development of new empirical methods as well as reanalysis of existing data through the lens of dominance reversals. A greater focus on this topic will expand our understanding of the mechanisms that resolve genetic conflict and whether they maintain genetic variation.

Benchmarking machine learning and parametric methods for genomic prediction of feed efficiency-related traits in Nellore cattle.

Genomic selection (GS) offers a promising opportunity for selecting more efficient animals to use consumed energy for maintenance and growth functions, impacting profitability and environmental sustainability. Here, we compared the prediction accuracy of multi-layer neural network (MLNN) and support vector regression (SVR) against single-trait (STGBLUP), multi-trait genomic best linear unbiased prediction (MTGBLUP), and Bayesian regression (BayesA, BayesB, BayesC, BRR, and BLasso) for feed efficiency (FE) traits. FE-related traits were measured in 1156 Nellore cattle from an experimental breeding program genotyped for ~ 300 K markers after quality control. Prediction accuracy (Acc) was evaluated using a forward validation splitting the dataset based on birth year, considering the phenotypes adjusted for the fixed effects and covariates as pseudo-phenotypes. The MLNN and SVR approaches were trained by randomly splitting the training population into fivefold to select the best hyperparameters. The results show that the machine learning methods (MLNN and SVR) and MTGBLUP outperformed STGBLUP and the Bayesian regression approaches, increasing the Acc by approximately 8.9%, 14.6%, and 13.7% using MLNN, SVR, and MTGBLUP, respectively. Acc for SVR and MTGBLUP were slightly different, ranging from 0.62 to 0.69 and 0.62 to 0.68, respectively, with empirically unbiased for both models (0.97 and 1.09). Our results indicated that SVR and MTGBLUBP approaches were more accurate in predicting FE-related traits than Bayesian regression and STGBLUP and seemed competitive for GS of complex phenotypes with various degrees of inheritance.