Effects of reference population size and structure on genomic prediction of maternal traits in two pig lines using whole-genome sequence-, high-density- and combined annotation-dependent depletion genotypes.

The aim of this study was to investigate the reference population size required to obtain substantial prediction accuracy within- and across-lines and the effect of using a multi-line reference population for genomic predictions of maternal traits in pigs. The data consisted of two nucleus pig populations, one pure-bred Landrace (L) and one Synthetic (S) Yorkshire/Large White line. All animals were genotyped with up to 30 K animals in each line, and all had records on maternal traits. Prediction accuracy was tested with three different marker data sets: High-density SNP (HD), whole genome sequence (WGS), and markers derived from WGS based on pig combined annotation dependent depletion-score (pCADD). Also, two different genomic prediction methods (GBLUP and Bayes GC) were compared for four maternal traits; total number piglets born (TNB), total number of stillborn piglets (STB), Shoulder Lesion Score and Body Condition Score. The main results from this study showed that a reference population of 3 K-6 K animals for within-line prediction generally was sufficient to achieve high prediction accuracy. However, when the number of animals in the reference population was increased to 30 K, the prediction accuracy significantly increased for the traits TNB and STB. For multi-line prediction accuracy, the accuracy was most dependent on the number of within-line animals in the reference data. The S-line provided a generally higher prediction accuracy compared to the L-line. Using pCADD scores to reduce the number of markers from WGS data in combination with the GBLUP method generally reduced prediction accuracies relative to GBLUP using HD genotypes. The BayesGC method benefited from a large reference population and was less dependent on the different genotype marker datasets to achieve a high prediction accuracy.

GWABLUP: genome-wide association assisted best linear unbiased prediction of genetic values.

BACKGROUND: Since the very beginning of genomic selection, researchers investigated methods that improved upon SNP-BLUP (single nucleotide polymorphism best linear unbiased prediction). SNP-BLUP gives equal weight to all SNPs, whereas it is expected that many SNPs are not near causal variants and thus do not have substantial effects. A recent approach to remedy this is to use genome-wide association study (GWAS) findings and increase the weights of GWAS-top-SNPs in genomic predictions. Here, we employ a genome-wide approach to integrate GWAS results into genomic prediction, called GWABLUP. RESULTS: GWABLUP consists of the following steps: (1) performing a GWAS in the training data which results in likelihood ratios; (2) smoothing the likelihood ratios over the SNPs; (3) combining the smoothed likelihood ratio with the prior probability of SNPs having non-zero effects, which yields the posterior probability of the SNPs; (4) calculating a weighted genomic relationship matrix using the posterior probabilities as weights; and (5) performing genomic prediction using the weighted genomic relationship matrix. Using high-density genotypes and milk, fat, protein and somatic cell count phenotypes on dairy cows, GWABLUP was compared to GBLUP, GBLUP (topSNPs) with extra weights for GWAS top-SNPs, and BayesGC, i.e. a Bayesian variable selection model. The GWAS resulted in six, five, four, and three genome-wide significant peaks for milk, fat and protein yield and somatic cell count, respectively. GWABLUP genomic predictions were 10, 6, 7 and 1% more reliable than those of GBLUP for milk, fat and protein yield and somatic cell count, respectively. It was also more reliable than GBLUP (topSNPs) for all four traits, and more reliable than BayesGC for three of the traits. Although GWABLUP showed a tendency towards inflation bias for three of the traits, this was not statistically significant. In a multitrait analysis, GWABLUP yielded the highest accuracy for two of the traits. However, for SCC, which was relatively unrelated to the yield traits, including yield trait GWAS-results reduced the reliability compared to a single trait analysis. CONCLUSIONS: GWABLUP uses GWAS results to differentially weigh all the SNPs in a weighted GBLUP genomic prediction analysis. GWABLUP yielded up to 10% and 13% more reliable genomic predictions than GBLUP for single and multitrait analyses, respectively. Extension of GWABLUP to single-step analyses is straightforward.

Genetically controlled mtDNA deletions prevent ROS damage by arresting oxidative phosphorylation.

Deletion of mitochondrial DNA in eukaryotes is currently attributed to rare accidental events associated with mitochondrial replication or repair of double-strand breaks. We report the discovery that yeast cells arrest harmful intramitochondrial superoxide production by shutting down respiration through genetically controlled deletion of mitochondrial oxidative phosphorylation genes. We show that this process critically involves the antioxidant enzyme superoxide dismutase 2 and two-way mitochondrial-nuclear communication through Rtg2 and Rtg3. While mitochondrial DNA homeostasis is rapidly restored after cessation of a short-term superoxide stress, long-term stress causes maladaptive persistence of the deletion process, leading to complete annihilation of the cellular pool of intact mitochondrial genomes and irrevocable loss of respiratory ability. This shows that oxidative stress-induced mitochondrial impairment may be under strict regulatory control. If the results extend to human cells, the results may prove to be of etiological as well as therapeutic importance with regard to age-related mitochondrial impairment and disease.

A high-throughput study of visceral organs in CT-scanned pigs.

It has been debated whether intensive selection for growth and carcass yield in pig breeding programmes can affect the size of internal organs, and thereby reduce the animal's ability to handle stress and increase the risk of sudden deaths. To explore the respiratory and circulatory system in pigs, a deep learning based computational pipeline was built to extract the size of lungs and hearts from CT-scan images. This pipeline was applied on CT images from 11,000 boar selection candidates acquired during the last decade. Further, heart and lung volumes were analysed genetically and correlated with production traits. Both heart and lung volumes were heritable, with h2 estimated to 0.35 and 0.34, respectively, in Landrace, and 0.28 and 0.4 in Duroc. Both volumes were positively correlated with lean meat percentage, and lung volume was negatively genetically correlated with growth (rg = - 0.48 ± 0.07 for Landrace and rg = - 0.44 ± 0.07 for Duroc). The main findings suggest that the current pig breeding programs could, as an indirect response to selection, affect the size of hearts- and lungs. The presented methods can be used to monitor the development of internal organs in the future.

Fine Mapping of a Major Backfat QTL Reveals a Causal Regulatory Variant Affecting the CCND2 Gene.

Backfat is an important trait in pork production, and it has been included in the breeding objectives of genetic companies for decades. Although adipose tissue is a good energy storage, excessive fat results in reduced efficiency and economical losses. A large QTL for backfat thickness on chromosome 5 is still segregating in different commercial pig breeds. We fine mapped this QTL region using a genome-wide association analysis (GWAS) with 133,358 genotyped animals from five commercial populations (Landrace, Pietrain, Large White, Synthetic, and Duroc) imputed to the porcine 660K SNP chip. The lead SNP was located at 5:66103958 (G/A) within the third intron of the CCND2 gene, with the G allele associated with more backfat, while the A allele is associated with less backfat. We further phased the QTL region to discover a core haplotype of five SNPs associated with low backfat across three breeds. Linkage disequilibrium analysis using whole-genome sequence data revealed three candidate causal variants within intronic regions and downstream of the CCND2 gene, including the lead SNP. We evaluated the association of the lead SNP with the expression of the genes in the QTL region (including CCND2) in a large cohort of 100 crossbred samples, sequenced in four different tissues (lung, spleen, liver, muscle). Results show that the A allele increases the expression of CCND2 in an additive way in three out of four tissues. Our findings indicate that the causal variant for this QTL region is a regulatory variant within the third intron of the CCND2 gene affecting the expression of CCND2.

SALARECON connects the Atlantic salmon genome to growth and feed efficiency.

Atlantic salmon (Salmo salar) is the most valuable farmed fish globally and there is much interest in optimizing its genetics and rearing conditions for growth and feed efficiency. Marine feed ingredients must be replaced to meet global demand, with challenges for fish health and sustainability. Metabolic models can address this by connecting genomes to metabolism, which converts nutrients in the feed to energy and biomass, but such models are currently not available for major aquaculture species such as salmon. We present SALARECON, a model focusing on energy, amino acid, and nucleotide metabolism that links the Atlantic salmon genome to metabolic fluxes and growth. It performs well in standardized tests and captures expected metabolic (in)capabilities. We show that it can explain observed hypoxic growth in terms of metabolic fluxes and apply it to aquaculture by simulating growth with commercial feed ingredients. Predicted limiting amino acids and feed efficiencies agree with data, and the model suggests that marine feed efficiency can be achieved by supplementing a few amino acids to plant- and insect-based feeds. SALARECON is a high-quality model that makes it possible to simulate Atlantic salmon metabolism and growth. It can be used to explain Atlantic salmon physiology and address key challenges in aquaculture such as development of sustainable feeds.

Accuracy of genomic prediction of maternal traits in pigs using Bayesian variable selection methods.

The aim of this study was to compare three methods of genomic prediction: GBLUP, BayesC and BayesGC for genomic prediction of six maternal traits in Landrace sows using a panel of 660 K SNPs. The effects of different priors for the Bayesian methods were also investigated. GBLUP does not take the genetic architecture into account as all SNPs are assumed to have equally sized effects and relies heavily on the relationships between the animals for accurate predictions. Bayesian approaches rely on both fitting SNPs that describe relationships between animals in addition to fitting single SNP effects directly. Both the relationship between the animals and single SNP effects are important for accurate predictions. Maternal traits in sows are often more difficult to record and have lower heritabilities. BayesGC was generally the method with the higher accuracy, although its accuracy was for some traits matched by that of GBLUP and for others by that of BayesC. For piglet mortality within 3 weeks, BayesGC achieved up to 9.2% higher accuracy. For many of the traits, however, the methods did not show significant differences in accuracies.

Correcting for base-population differences and unknown parent groups in single-step genomic predictions of Norwegian Red cattle.

Bias and inflation in genomic evaluation with the single-step methods have been reported in several studies. Incompatibility between the base-populations of the pedigree-based and the genomic relationship matrix (G) could be a reason for these biases. Inappropriate ways of accounting for missing parents could be another reason for biases in genetic evaluations with or without genomic information. To handle these problems, we fitted and evaluated a fixed covariate (J) that contains ones for genotyped animals and zeros for unrelated non-genotyped animals, or pedigree-based regression coefficients for related non-genotyped animals. We also evaluated alternative ways of fitting the J covariate together with genetic groups on biases and stability of breeding value estimates, and of including it into G as a random effect. In a whole vs. partial data set comparison, four scenarios were investigated for the partial data: genotypes missing, phenotypes missing, both genotypes and phenotypes missing, and pedigree missing. Fitting J either as fixed or random reduced level-bias and inflation and increased stability of genomic predictions as compared to the basic model where neither J nor genetic groups were fitted. In most models, genomic predictions were largely biased for scenarios with missing genotype and phenotype information. The biases were reduced for models which combined group and J effects. Models with these corrected group covariates performed better than the recently published model where genetic groups were encapsulated and fitted as random via the Quaas and Pollak transformation. In our Norwegian Red cattle data, a model which combined group and J regression coefficients was preferred because it showed least bias and highest stability of genomic predictions across the scenarios.

Our study dealt with strategies on how to reduce biases (inflation and level-bias) and improve a parameter related to accuracy (stability) of genomic predictions of breeding values that combine genotyped and non-genotyped animals, which are denoted as single-step genomic predictions. We tried to remedy incompatibilities between the pedigree- and the genomics-based relationships matrices by fitting a covariate (J) that corrects for base-population differences that may occur between both relationship matrices. We also evaluated alternative ways to combine the J covariate and genetic group effects to account for missing parental information, which often occurs in practical breeding schemes. We found that fitting J either as fixed or random reduced level-bias and inflation and increased stability of genomic predictions as compared to the basic model where neither J nor genetic groups were fitted. Level-biases and inflation of breeding value estimates were reduced, and stability of genomic predictions improved for models which combined group and J effects. A model which fits group regression coefficients minus the part that could be explained from pedigree was recommended because it showed least bias and highest stability across the scenarios and has theoretical justification.

Recombination rates in pigs differ between breeds, sexes and individuals, and are associated with the RNF212, SYCP2, PRDM7, MEI1 and MSH4 loci.

BACKGROUND: Recombination is a fundamental part of mammalian meiosis that leads to the exchange of large segments of DNA between homologous chromosomes and is therefore an important driver of genetic diversity in populations. In breeding populations, understanding recombination is of particular interest because it can break up unfavourable linkage phases between alleles and produce novel combinations of alleles that could be exploited in selection. In this study, we used dense single nucleotide polymorphism (SNP) genotype data and pedigree information to analyse individual and sex-specific variation and genetic architecture of recombination rates within and between five commercially selected pig breeds. RESULTS: In agreement with previous studies, recombination rates were higher in females than in males for all breeds and for all chromosomes, except 1 and 13, for which male rates were slightly higher. Total recombination rate differed between breeds but the pattern of recombination along the chromosomes was well conserved across breeds for the same sex. The autosomal linkage maps spanned a total length of 1731 to 1887 cM for males and of 2231 to 2515 cM for females. Estimates of heritability for individual autosomal crossover count ranged from 0.04 to 0.07 for males and from 0.08 to 0.11 for females. Fourteen genomic regions were found to be associated with individual autosomal crossover count. Of these, four were close to or within candidate genes that have previously been associated with individual recombination rates in pigs and other mammals, namely RNF212, SYCP2 and MSH4. Two of the identified regions included the PRDM7 and MEI1 genes, which are known to be involved in meiosis but have not been previously associated with variation in individual recombination rates. CONCLUSIONS: This study shows that genetic variation in autosomal recombination rate persists in domesticated species under strong selection, with differences between closely-related breeds and marked differences between the sexes. Our findings support results from other studies, i.e., that individual crossover counts are associated with the RNF212, SYCP2 and MSH4 genes in pig. In addition, we have found two novel candidate genes associated with the trait, namely PRDM7 and MEI1.

Accelerated discovery of functional genomic variation in pigs.

The genotype-phenotype link is a major research topic in the life sciences but remains highly complex to disentangle. Part of the complexity arises from the number of genes contributing to the observed phenotype. Despite the vast increase of molecular data, pinpointing the causal variant underlying a phenotype of interest is still challenging. In this study, we present an approach to map causal variation and molecular pathways underlying important phenotypes in pigs. We prioritize variation by utilizing and integrating predicted variant impact scores (pCADD), functional genomic information, and associated phenotypes in other mammalian species. We demonstrate the efficacy of our approach by reporting known and novel causal variants, of which many affect non-coding sequences. Our approach allows the disentangling of the biology behind important phenotypes by accelerating the discovery of novel causal variants and molecular mechanisms affecting important phenotypes in pigs. This information on molecular mechanisms could be applicable in other mammalian species, including humans.

Meta-analysis for milk fat and protein percentage using imputed sequence variant genotypes in 94,321 cattle from eight cattle breeds.

BACKGROUND: Sequence-based genome-wide association studies (GWAS) provide high statistical power to identify candidate causal mutations when a large number of individuals with both sequence variant genotypes and phenotypes is available. A meta-analysis combines summary statistics from multiple GWAS and increases the power to detect trait-associated variants without requiring access to data at the individual level of the GWAS mapping cohorts. Because linkage disequilibrium between adjacent markers is conserved only over short distances across breeds, a multi-breed meta-analysis can improve mapping precision. RESULTS: To maximise the power to identify quantitative trait loci (QTL), we combined the results of nine within-population GWAS that used imputed sequence variant genotypes of 94,321 cattle from eight breeds, to perform a large-scale meta-analysis for fat and protein percentage in cattle. The meta-analysis detected (p ≤ 10-8) 138 QTL for fat percentage and 176 QTL for protein percentage. This was more than the number of QTL detected in all within-population GWAS together (124 QTL for fat percentage and 104 QTL for protein percentage). Among all the lead variants, 100 QTL for fat percentage and 114 QTL for protein percentage had the same direction of effect in all within-population GWAS. This indicates either persistence of the linkage phase between the causal variant and the lead variant across breeds or that some of the lead variants might indeed be causal or tightly linked with causal variants. The percentage of intergenic variants was substantially lower for significant variants than for non-significant variants, and significant variants had mostly moderate to high minor allele frequencies. Significant variants were also clustered in genes that are known to be relevant for fat and protein percentages in milk. CONCLUSIONS: Our study identified a large number of QTL associated with fat and protein percentage in dairy cattle. We demonstrated that large-scale multi-breed meta-analysis reveals more QTL at the nucleotide resolution than within-population GWAS. Significant variants were more often located in genic regions than non-significant variants and a large part of them was located in potentially regulatory regions.

Level-biases in estimated breeding values due to the use of different SNP panels over time in ssGBLUP.

BACKGROUND: The main aim of single-step genomic predictions was to facilitate optimal selection in populations consisting of both genotyped and non-genotyped individuals. However, in spite of intensive research, biases still occur, which make it difficult to perform optimal selection across groups of animals. The objective of this study was to investigate whether incomplete genotype datasets with errors could be a potential source of level-bias between genotyped and non-genotyped animals and between animals genotyped on different single nucleotide polymorphism (SNP) panels in single-step genomic predictions. RESULTS: Incomplete and erroneous genotypes of young animals caused biases in breeding values between groups of animals. Systematic noise or missing data for less than 1% of the SNPs in the genotype data had substantial effects on the differences in breeding values between genotyped and non-genotyped animals, and between animals genotyped on different chips. The breeding values of young genotyped individuals were biased upward, and the magnitude was up to 0.8 genetic standard deviations, compared with breeding values of non-genotyped individuals. Similarly, the magnitude of a small value added to the diagonal of the genomic relationship matrix affected the level of average breeding values between groups of genotyped and non-genotyped animals. Cross-validation accuracies and regression coefficients were not sensitive to these factors. CONCLUSIONS: Because, historically, different SNP chips have been used for genotyping different parts of a population, fine-tuning of imputation within and across SNP chips and handling of missing genotypes are crucial for reducing bias. Although all the SNPs used for estimating breeding values are present on the chip used for genotyping young animals, incompleteness and some genotype errors might lead to level-biases in breeding values.

Loss of function mutations in essential genes cause embryonic lethality in pigs.

Lethal recessive alleles cause pre- or postnatal death in homozygous affected individuals, reducing fertility. Especially in small size domestic and wild populations, those alleles might be exposed by inbreeding, caused by matings between related parents that inherited the same recessive lethal allele from a common ancestor. In this study we report five relatively common (up to 13.4% carrier frequency) recessive lethal haplotypes in two commercial pig populations. The lethal haplotypes have a large effect on carrier-by-carrier matings, decreasing litter sizes by 15.1 to 21.6%. The causal mutations are of different type including two splice-site variants (affecting POLR1B and TADA2A genes), one frameshift (URB1), and one missense (PNKP) variant, resulting in a complete loss-of-function of these essential genes. The recessive lethal alleles affect up to 2.9% of the litters within a single population and are responsible for the death of 0.52% of the total population of embryos. Moreover, we provide compelling evidence that the identified embryonic lethal alleles contribute to the observed heterosis effect for fertility (i.e. larger litters in crossbred offspring). Together, this work marks specific recessive lethal variation describing its functional consequences at the molecular, phenotypic, and population level, providing a unique model to better understand fertility and heterosis in livestock.

Disentangling genetic and epigenetic determinants of ultrafast adaptation.

A major rationale for the advocacy of epigenetically mediated adaptive responses is that they facilitate faster adaptation to environmental challenges. This motivated us to develop a theoretical-experimental framework for disclosing the presence of such adaptation-speeding mechanisms in an experimental evolution setting circumventing the need for pursuing costly mutation-accumulation experiments. To this end, we exposed clonal populations of budding yeast to a whole range of stressors. By growth phenotyping, we found that almost complete adaptation to arsenic emerged after a few mitotic cell divisions without involving any phenotypic plasticity. Causative mutations were identified by deep sequencing of the arsenic-adapted populations and reconstructed for validation. Mutation effects on growth phenotypes, and the associated mutational target sizes were quantified and embedded in data-driven individual-based evolutionary population models. We found that the experimentally observed homogeneity of adaptation speed and heterogeneity of molecular solutions could only be accounted for if the mutation rate had been near estimates of the basal mutation rate. The ultrafast adaptation could be fully explained by extensive positive pleiotropy such that all beneficial mutations dramatically enhanced multiple fitness components in concert. As our approach can be exploited across a range of model organisms exposed to a variety of environmental challenges, it may be used for determining the importance of epigenetic adaptation-speeding mechanisms in general.

Towards causally cohesive genotype-phenotype modelling for characterization of the soft-tissue mechanics of the heart in normal and pathological geometries.

A scientific understanding of individual variation is key to personalized medicine, integrating genotypic and phenotypic information via computational physiology. Genetic effects are often context-dependent, differing between genetic backgrounds or physiological states such as disease. Here, we analyse in silico genotype-phenotype maps (GP map) for a soft-tissue mechanics model of the passive inflation phase of the heartbeat, contrasting the effects of microstructural and other low-level parameters assumed to be genetically influenced, under normal, concentrically hypertrophic and eccentrically hypertrophic geometries. For a large number of parameter scenarios, representing mock genetic variation in low-level parameters, we computed phenotypes describing the deformation of the heart during inflation. The GP map was characterized by variance decompositions for each phenotype with respect to each parameter. As hypothesized, the concentric geometry allowed more low-level parameters to contribute to variation in shape phenotypes. In addition, the relative importance of overall stiffness and fibre stiffness differed between geometries. Otherwise, the GP map was largely similar for the different heart geometries, with little genetic interaction between the parameters included in this study. We argue that personalized medicine can benefit from a combination of causally cohesive genotype-phenotype modelling, and strategic phenotyping that captures effect modifiers not explicitly included in the mechanistic model.

Concerted evolution of life stage performances signals recent selection on yeast nitrogen use.

Exposing natural selection driving phenotypic and genotypic adaptive differentiation is an extraordinary challenge. Given that an organism's life stages are exposed to the same environmental variations, we reasoned that fitness components, such as the lag, rate, and efficiency of growth, directly reflecting performance in these life stages, should often be selected in concert. We therefore conjectured that correlations between fitness components over natural isolates, in a particular environmental context, would constitute a robust signal of recent selection. Critically, this test for selection requires fitness components to be determined by different genetic loci. To explore our conjecture, we exhaustively evaluated the lag, rate, and efficiency of asexual population growth of natural isolates of the model yeast Saccharomyces cerevisiae in a large variety of nitrogen-limited environments. Overall, fitness components were well correlated under nitrogen restriction. Yeast isolates were further crossed in all pairwise combinations and coinheritance of each fitness component and genetic markers were traced. Trait variations tended to map to quantitative trait loci (QTL) that were private to a single fitness component. We further traced QTLs down to single-nucleotide resolution and uncovered loss-of-function mutations in RIM15, PUT4, DAL1, and DAL4 as the genetic basis for nitrogen source use variations. Effects of SNPs were unique for a single fitness component, strongly arguing against pleiotropy between lag, rate, and efficiency of reproduction under nitrogen restriction. The strong correlations between life stage performances that cannot be explained by pleiotropy compellingly support adaptive differentiation of yeast nitrogen source use and suggest a generic approach for detecting selection.

A computational pipeline for quantification of mouse myocardial stiffness parameters.

The mouse is an important model for theoretical-experimental cardiac research, and biophysically based whole organ models of the mouse heart are now within reach. However, the passive material properties of mouse myocardium have not been much studied. We present an experimental setup and associated computational pipeline to quantify these stiffness properties. A mouse heart was excised and the left ventricle experimentally inflated from 0 to 1.44kPa in eleven steps, and the resulting deformation was estimated by echocardiography and speckle tracking. An in silico counterpart to this experiment was built using finite element methods and data on ventricular tissue microstructure from diffusion tensor MRI. This model assumed a hyperelastic, transversely isotropic material law to describe the force-deformation relationship, and was simulated for many parameter scenarios, covering the relevant range of parameter space. To identify well-fitting parameter scenarios, we compared experimental and simulated outcomes across the whole range of pressures, based partly on gross phenotypes (volume, elastic energy, and short- and long-axis diameter), and partly on node positions in the geometrical mesh. This identified a narrow region of experimentally compatible values of the material parameters. Estimation turned out to be more precise when based on changes in gross phenotypes, compared to the prevailing practice of using displacements of the material points. We conclude that the presented experimental setup and computational pipeline is a viable method that deserves wider application.

Monotonicity is a key feature of genotype-phenotype maps.

It was recently shown that monotone gene action, i.e., order-preservation between allele content and corresponding genotypic values in the mapping from genotypes to phenotypes, is a prerequisite for achieving a predictable parent-offspring relationship across the whole allele frequency spectrum. Here we test the consequential prediction that the design principles underlying gene regulatory networks are likely to generate highly monotone genotype-phenotype maps. To this end we present two measures of the monotonicity of a genotype-phenotype map, one based on allele substitution effects, and the other based on isotonic regression. We apply these measures to genotype-phenotype maps emerging from simulations of 1881 different 3-gene regulatory networks. We confirm that in general, genotype-phenotype maps are indeed highly monotonic across network types. However, regulatory motifs involving incoherent feedforward or positive feedback, as well as pleiotropy in the mapping between genotypes and gene regulatory parameters, are clearly predisposed for generating non-monotonicity. We present analytical results confirming these deep connections between molecular regulatory architecture and monotonicity properties of the genotype-phenotype map. These connections seem to be beyond reach by the classical distinction between additive and non-additive gene action.

Propagation of genetic variation in gene regulatory networks.

A future quantitative genetics theory should link genetic variation to phenotypic variation in a causally cohesive way based on how genes actually work and interact. We provide a theoretical framework for predicting and understanding the manifestation of genetic variation in haploid and diploid regulatory networks with arbitrary feedback structures and intra-locus and inter-locus functional dependencies. Using results from network and graph theory, we define propagation functions describing how genetic variation in a locus is propagated through the network, and show how their derivatives are related to the network's feedback structure. Similarly, feedback functions describe the effect of genotypic variation of a locus on itself, either directly or mediated by the network. A simple sign rule relates the sign of the derivative of the feedback function of any locus to the feedback loops involving that particular locus. We show that the sign of the phenotypically manifested interaction between alleles at a diploid locus is equal to the sign of the dominant feedback loop involving that particular locus, in accordance with recent results for a single locus system. Our results provide tools by which one can use observable equilibrium concentrations of gene products to disclose structural properties of the network architecture. Our work is a step towards a theory capable of explaining the pleiotropy and epistasis features of genetic variation in complex regulatory networks as functions of regulatory anatomy and functional location of the genetic variation.

Effect of regulatory architecture on broad versus narrow sense heritability.

Additive genetic variance (VA ) and total genetic variance (VG ) are core concepts in biomedical, evolutionary and production-biology genetics. What determines the large variation in reported VA /VG ratios from line-cross experiments is not well understood. Here we report how the VA /VG ratio, and thus the ratio between narrow and broad sense heritability (h(2) /H(2) ), varies as a function of the regulatory architecture underlying genotype-to-phenotype (GP) maps. We studied five dynamic models (of the cAMP pathway, the glycolysis, the circadian rhythms, the cell cycle, and heart cell dynamics). We assumed genetic variation to be reflected in model parameters and extracted phenotypes summarizing the system dynamics. Even when imposing purely linear genotype to parameter maps and no environmental variation, we observed quite low VA /VG ratios. In particular, systems with positive feedback and cyclic dynamics gave more non-monotone genotype-phenotype maps and much lower VA /VG ratios than those without. The results show that some regulatory architectures consistently maintain a transparent genotype-to-phenotype relationship, whereas other architectures generate more subtle patterns. Our approach can be used to elucidate these relationships across a whole range of biological systems in a systematic fashion.