Exploring causal networks of bovine milk fatty acids in a multivariate mixed model context

Background

Knowledge regarding causal relationships among traits is important to understand complex biological systems. Structural equation models (SEM) can be used to quantify the causal relations between traits, which allow prediction of outcomes to interventions applied to such a network. Such models are fitted conditionally on a causal structure among traits, represented by a directed acyclic graph and an Inductive Causation (IC) algorithm can be used to search for causal structures. The aim of this study was to explore the space of causal structures involving bovine milk fatty acids and to select a network supported by data as the structure of a SEM.

Results

The IC algorithm adapted to mixed models settings was applied to study 14 correlated bovine milk fatty acids, resulting in an undirected network. The undirected pathway from C4:0 to C12:0 resembled the de novo synthesis pathway of short and medium chain saturated fatty acids. By using prior knowledge, directions were assigned to that part of the network and the resulting structure was used to fit a SEM that led to structural coefficients ranging from 0.85 to 1.05. The deviance information criterion indicated that the SEM was more plausible than the multi-trait model.

Conclusions

The IC algorithm output pointed towards causal relations between the studied traits. This changed the focus from marginal associations between traits to direct relationships, thus towards relationships that may result in changes when external interventions are applied. The causal structure can give more insight into underlying mechanisms and the SEM can predict conditional changes due to such interventions.     

Exploring biological relationships between calving traits in primiparous cattle with a Bayesian recursive model

Structural equation models (SEMs) of a recursive type with heterogeneous structural coefficients were used to explore biological relationships between gestation length (GL), calving difficulty (CD), and perinatal mortality, also known as stillbirth (SB), in cattle, with the last two traits having categorical expression. An acyclic model was assumed, where recursive effects existed from the GL phenotype to the liabilities (latent variables) to CD and SB and from the liability to CD to that of SB considering four periods regarding GL. The data contained GL, CD, and SB records from 90,393 primiparous cows, sired by 1122 bulls, distributed over 935 herd-calving year classes. Low genetic correlations between GL and the other calving traits were found, whereas the liabilities to CD and SB were high and positively correlated, genetically. The model indicated that gestations of approximately 274 days of length (3 days shorter than the average) would lead to the lowest CD and SB and confirmed the existence of an intermediate optimum of GL with respect to these traits.     

Searching for phenotypic causal networks involving complex traits: an application to European quail

Background

Structural equation models (SEM) are used to model multiple traits and the casual links among them. The number of different causal structures that can be used to fit a SEM is typically very large, even when only a few traits are studied. In recent applications of SEM in quantitative genetics mixed model settings, causal structures were pre-selected based on prior beliefs alone. Alternatively, there are algorithms that search for structures that are compatible with the joint distribution of the data. However, such a search cannot be performed directly on the joint distribution of the phenotypes since causal relationships are possibly masked by genetic covariances. In this context, the application of the Inductive Causation (IC) algorithm to the joint distribution of phenotypes conditional to unobservable genetic effects has been proposed.

Methods

Here, we applied this approach to five traits in European quail: birth weight (BW), weight at 35 days of age (W35), age at first egg (AFE), average egg weight from 77 to 110 days of age (AEW), and number of eggs laid in the same period (NE). We have focused the discussion on the challenges and difficulties resulting from applying this method to field data. Statistical decisions regarding partial correlations were based on different Highest Posterior Density (HPD) interval contents and models based on the selected causal structures were compared using the Deviance Information Criterion (DIC). In addition, we used temporal information to perform additional edge orienting, overriding the algorithm output when necessary.

Results

As a result, the final causal structure consisted of two separated substructures: BW→AEW and W35→AFE→NE, where an arrow represents a direct effect. Comparison between a SEM with the selected structure and a Multiple Trait Animal Model using DIC indicated that the SEM is more plausible.

Conclusions

Coupling prior knowledge with the output provided by the IC algorithm allowed further learning regarding phenotypic causal structures when compared to standard mixed effects SEM applications.     

Modeling relationships between calving traits: a comparison between standard and recursive mixed models

Background

The use of structural equation models for the analysis of recursive and simultaneous relationships between phenotypes has become more popular recently. The aim of this paper is to illustrate how these models can be applied in animal breeding to achieve parameterizations of different levels of complexity and, more specifically, to model phenotypic recursion between three calving traits: gestation length (GL), calving difficulty (CD) and stillbirth (SB). All recursive models considered here postulate heterogeneous recursive relationships between GL and liabilities to CD and SB, and between liability to CD and liability to SB, depending on categories of GL phenotype.

Methods

Four models were compared in terms of goodness of fit and predictive ability: 1) standard mixed model (SMM), a model with unstructured (co)variance matrices; 2) recursive mixed model 1 (RMM1), assuming that residual correlations are due to the recursive relationships between phenotypes; 3) RMM2, assuming that correlations between residuals and contemporary groups are due to recursive relationships between phenotypes; and 4) RMM3, postulating that the correlations between genetic effects, contemporary groups and residuals are due to recursive relationships between phenotypes.

Results

For all the RMM considered, the estimates of the structural coefficients were similar. Results revealed a nonlinear relationship between GL and the liabilities both to CD and to SB, and a linear relationship between the liabilities to CD and SB.Differences in terms of goodness of fit and predictive ability of the models considered were negligible, suggesting that RMM3 is plausible.

Conclusions

The applications examined in this study suggest the plausibility of a nonlinear recursive effect from GL onto CD and SB. Also, the fact that the most restrictive model RMM3, which assumes that the only cause of correlation is phenotypic recursion, performs as well as the others indicates that the phenotypic recursion may be an important cause of the observed patterns of genetic and environmental correlations.     

Robust inference of bi-directional causal relationships in presence of correlated pleiotropy with GWAS summary data

To infer a causal relationship between two traits, several correlation-based causal direction (CD) methods have been proposed with the use of SNPs as instrumental variables (IVs) based on GWAS summary data for the two traits; however, none of the existing CD methods can deal with SNPs with correlated pleiotropy. Alternatively, reciprocal Mendelian randomization (MR) can be applied, which however may perform poorly in the presence of (unknown) invalid IVs, especially for bi-directional causal relationships. In this paper, first, we propose a CD method that performs better than existing CD methods regardless of the presence of correlated pleiotropy. Second, along with a simple but yet effective IV screening rule, we propose applying a closely related and state-of-the-art MR method in reciprocal MR, showing its almost identical performance to that of the new CD method when their model assumptions hold; however, if the modeling assumptions are violated, the new CD method is expected to better control type I errors. Notably bi-directional causal relationships impose some unique challenges beyond those for uni-directional ones, and thus requiring special treatments. For example, we point out for the first time several scenarios where a bi-directional relationship, but not a uni-directional one, can unexpectedly cause the violation of some weak modeling assumptions commonly required by many robust MR methods. We also offer some numerical support and a modeling justification for the application of our new methods (and more generally MR) to binary traits. Finally we applied the proposed methods to 12 risk factors and 4 common diseases, confirming mostly well-known uni-directional causal relationships, while identifying some novel and plausible bi-directional ones such as between body mass index and type 2 diabetes (T2D), and between diastolic blood pressure and stroke.     

Genetic parameters estimation for preweaning traits and their relationship with reproductive,productive and morphological traits in alpaca

The aim of this study was to estimate the genetic parameters for preweaning traits and their relationship with reproductive, productive and morphological traits in alpacas. The data were collected from 2001 to 2015 in the Pacomarca experimental farm. The data set contained data from 4330 females and 3788 males corresponding to 6396 and 1722 animals for Huacaya and Suri variants, respectively. The number of records for Huacaya and Suri variants were 5494 and 1461 for birth weight (BW), 5429 and 1431 for birth withers height (BH), 3320 and 896 for both weaning weight (WW) and average daily gain (DG) from birth to weaning, 3317 and 896 for weaning withers height (WH), and 5514 and 1474 for survival to weaning. The reproductive traits analyzed were age at first calving and calving interval. The fiber traits were fiber diameter (FD), standard deviation of FD (SD), comfort factor and coefficient of variation of FD and the morphological traits studied were density, crimp in Huacaya and lock structure in Suri, head, coverage and balance. Regarding preweaning traits, model of analysis included additive, maternal and residual random effects for all traits, with sex, coat color, number of calving, month–year and contemporary group as systematic effects, and age at weaning as linear covariate for WW and WH. The most relevant direct heritabilities for Huacaya and Suri were 0.50 and 0.34 for WW, 0.36 and 0.66 for WH, 0.45 and 0.20 for DG, respectively. Maternal heritabilities were 0.25 and 0.38 for BW, 0.18 and 0.32 for BH, 0.29 and 0.39 for WW, 0.19 and 0.26 for WH, 0.27 and 0.36 for DG, respectively. Direct genetic correlations within preweaning traits were high and favorable and lower between direct and maternal genetic effects. The genetic correlations of preweaning traits with fiber traits were moderate and unfavorable. With morphological traits they were high and positive for Suri but not for Huacaya and favorable for direct genetic effect but unfavorable for maternal genetic effect with reproductive traits. If the selection objective was meat production, the selection would have to be based on the direct genetic effect for WW but not on the maternal genetic effect that has been shown to have less relevance. Other weaning traits such as WH or DG would be indirectly selected.     

Population intervention causal effects based on stochastic interventions

Estimating the causal effect of an intervention on a population typically involves defining parameters in a nonparametric structural equation model (Pearl, 2000, Causality: Models, Reasoning, and Inference) in which the treatment or exposure is deterministically assigned in a static or dynamic way. We define a new causal parameter that takes into account the fact that intervention policies can result in stochastically assigned exposures. The statistical parameter that identifies the causal parameter of interest is established. Inverse probability of treatment weighting (IPTW), augmented IPTW (A-IPTW), and targeted maximum likelihood estimators (TMLE) are developed. A simulation study is performed to demonstrate the properties of these estimators, which include the double robustness of the A-IPTW and the TMLE. An application example using physical activity data is presented.     

Discovering phenotypic causal structure from nonexperimental data

The evolutionary potential of organisms depends on how their parts are structured into a cohesive whole. A major obstacle for empirical studies of phenotypic organization is that observed associations among characters usually confound different causal pathways such as pleiotropic modules, interphenotypic causal relationships and environmental effects. The present article proposes causal search algorithms as a new tool to distinguish these different modes of phenotypic integration. Without assuming an a priori structure, the algorithms seek a class of causal hypotheses consistent with independence relationships holding in observational data. The technique can be applied to discover causal relationships among a set of measured traits and to distinguish genuine selection from spurious correlations. The former application is illustrated with a biological data set of rat morphological measurements previously analysed by Cheverud et al. (Evolution 1983, 37, 895).     

Identifying causal variants by fine mapping across multiple studies

Increasingly large Genome-Wide Association Studies (GWAS) have yielded numerous variants associated with many complex traits, motivating the development of “fine mapping” methods to identify which of the associated variants are causal. Additionally, GWAS of the same trait for different populations are increasingly available, raising the possibility of refining fine mapping results further by leveraging different linkage disequilibrium (LD) structures across studies. Here, we introduce multiple study causal variants identification in associated regions (MsCAVIAR), a method that extends the popular CAVIAR fine mapping framework to a multiple study setting using a random effects model. MsCAVIAR only requires summary statistics and LD as input, accounts for uncertainty in association statistics using a multivariate normal model, allows for multiple causal variants at a locus, and explicitly models the possibility of different SNP effect sizes in different populations. We demonstrate the efficacy of MsCAVIAR in both a simulation study and a trans-ethnic, trans-biobank fine mapping analysis of High Density Lipoprotein (HDL).     

A New Method to Infer Causal Phenotype Networks Using QTL and Phenotypic Information

In the context of genetics and breeding research on multiple phenotypic traits, reconstructing the directional or causal structure between phenotypic traits is a prerequisite for quantifying the effects of genetic interventions on the traits. Current approaches mainly exploit the genetic effects at quantitative trait loci (QTLs) to learn about causal relationships among phenotypic traits. A requirement for using these approaches is that at least one unique QTL has been identified for each trait studied. However, in practice, especially for molecular phenotypes such as metabolites, this prerequisite is often not met due to limited sample sizes, high noise levels and small QTL effects. Here, we present a novel heuristic search algorithm called the QTL+phenotype supervised orientation (QPSO) algorithm to infer causal directions for edges in undirected phenotype networks. The two main advantages of this algorithm are: first, it does not require QTLs for each and every trait; second, it takes into account associated phenotypic interactions in addition to detected QTLs when orienting undirected edges between traits. We evaluate and compare the performance of QPSO with another state-of-the-art approach, the QTL-directed dependency graph (QDG) algorithm. Simulation results show that our method has broader applicability and leads to more accurate overall orientations. We also illustrate our method with a real-life example involving 24 metabolites and a few major QTLs measured on an association panel of 93 tomato cultivars. Matlab source code implementing the proposed algorithm is freely available upon request.     

Critical reasoning on causal inference in genome-wide linkage and association studies

Genome-wide linkage and association studies of tens of thousands of clinical and molecular traits are currently underway, offering rich data for inferring causality between traits and genetic variation. However, the inference process is based on discovering subtle patterns in the correlation between traits and is therefore challenging and could create a flood of untrustworthy causal inferences. Here we introduce the concerns and show that they are already valid in simple scenarios of two traits linked to or associated with the same genomic region. We argue that more comprehensive analysis and Bayesian reasoning are needed and that these can overcome some of the pitfalls, although not in every conceivable case. We conclude that causal inference methods can still be of use in the iterative process of mathematical modeling and biological validation.     

Inferring causal phenotype networks from segregating populations

A major goal in the study of complex traits is to decipher the causal interrelationships among correlated phenotypes. Current methods mostly yield undirected networks that connect phenotypes without causal orientation. Some of these connections may be spurious due to partial correlation that is not causal. We show how to build causal direction into an undirected network of phenotypes by including causal QTL for each phenotype. We evaluate causal direction for each edge connecting two phenotypes, using a LOD score. This new approach can be applied to many different population structures, including inbred and outbred crosses as well as natural populations, and can accommodate feedback loops. We assess its performance in simulation studies and show that our method recovers network edges and infers causal direction correctly at a high rate. Finally, we illustrate our method with an example involving gene expression and metabolite traits from experimental crosses.     

Epitope Mapping and In Silico Characterization of Interactions between Der p 7 Allergen and MoAb WH9

Der p 7 is an important house dust mite allergen. However, antigenic determinants of Der p 7 are largely unknown. The purpose of this study is to analyze the determinants of Der p 7 and determine the structural basis of interactions between Der p 7 and WH9, an IgE-binding inhibition mouse monoclonal antibody (MoAb). IgE and WH9-reactive determinant(s) was identified by immunoblot using allergen mutants. A 3-D binary complex structure of Der p 7 and WH9 was simulated with homology modeling and docking methods. Our results obtained showed that among the five Der p 7 mutants (S156A, I157A, L158A, D159A, P160A), serum no. 1045 with IgE-binding against Der p 7 exhibited a reduced IgE immunoblot reactivity against Der p 7 L158A and D159A mutants. WH9 showed reduced immunoblot reactivity against S156A, L158A, D159A and P160A and the observation was confirmed by immunoblot inhibition. The WH9-binding determinant on Der p 7 containing S156, L158, D159 and P160 assumes a loop-like structure. The structural model of the Der p 7-WH9 complex suggests residues S156, I157, L158, D159 and P160 of Der p 7 contribute to WH9 binding via potential hydrogen bonds, electrostatic and hydrophobic interactions. In conclusion, MoAb WH9 interacts with critical residues L158 and D159 of Der p 7 and inhibits IgE-binding to Der p 7. Results obtained advance our understanding on molecular and structural bases of the antigenicity of Der p 7, its interactions with MoAb WH9 and facilitate the design of safer immunotherapy of human atopic disorders.     

Covariate selection strategies for causal inference: Classification and comparison

When causal effects are to be estimated from observational data, we have to adjust for confounding. A central aim of covariate selection for causal inference is therefore to determine a set that is sufficient for confounding adjustment, but other aims such as efficiency or robustness can be important as well. In this paper, we review six general approaches to covariate selection that differ in the targeted type of adjustment set. We discuss and illustrate their advantages and disadvantages using causal diagrams. Moreover, the approaches and different ways of implementing them are compared empirically in an extensive simulation study. We conclude that there are considerable differences between the approaches but none of them is uniformly best, with performance depending on the chosen adjustment method as well as the true confounding structure. Any prior structural knowledge on the causal relations is helpful to choose the most appropriate method.     

Estimates of (co)variance components and genetic parameters for body weights and first greasy fleece weight in Bharat Merino sheep

(Co)variance components and genetic parameters of weight at birth (BWT), weaning (3WT), 6, 9 and 12 months of age (6WT, 9WT and 12WT, respectively) and first greasy fleece weight (GFW) of Bharat Merino sheep, maintained at Central Sheep and Wool Research Institute, Avikanagar, Rajasthan, India, were estimated by restricted maximum likelihood, fitting six animal models with various combinations of direct and maternal effects. Data were collected over a period of 10 years (1998 to 2007). A log-likelihood ratio test was used to select the most appropriate univariate model for each trait, which was subsequently used in bivariate analysis. Heritability estimates for BWT, 3WT, 6WT, 9WT and 12WT and first GFW were 0.05 ± 0.03, 0.04 ± 0.02, 0.00, 0.03 ± 0.03, 0.09 ± 0.05 and 0.05 ± 0.03, respectively. There was no evidence for the maternal genetic effect on the traits under study. Maternal permanent environmental effect contributed 19% for BWT and 6% to 11% from 3WT to 9WT and 11% for first GFW. Maternal permanent environmental effect on the post-3WT was a carryover effect of maternal influences during pre-weaning age. A low rate of genetic progress seems possible in the flock through selection. Direct genetic correlations between body weight traits were positive and ranged from 0.36 between BWT and 6WT to 0.94 between 3WT and 6WT and between 6WT and 12WT. Genetic correlations of 3WT with 6WT, 9WT and 12WT were high and positive (0.94, 0.93 and 0.93, respectively), suggesting that genetic gain in post-3WT will be maintained if selection age is reduced to 3 months. The genetic correlations of GFW with live weights were 0.01, 0.16, 0.18, 0.40 and 0.32 for BWT, 3WT, 6WT, 9WT and 12WT, respectively. Correlations of permanent environmental effects of the dam across different traits were high and positive for all the traits (0.45 to 0.98).     

A general model of functional constraints on phenotypic evolution

A general model of the functional constraints on the rate and direction of phenotypic evolution is developed using a decomposition of the Lande-Arnold model of multivariate phenotypic evolution. The important feature of the model is the F matrix of performance coefficients reflecting the causal relationship between morphophysiological (m-p) and functional performance traits. The structure of F, which reflects the functional architecture of the organism, constrains the shape of the adaptive landscape and thus the rate and direction of m-p trait evolution. The rate of m-p trait evolution is a function of the pattern of coefficients in a row of F. The sums and variances of these rows are related to current concepts of evolvability. The direction of m-p trait evolution through m-p trait space is a function of the functional covariances among m-p traits. The functional covariance between a pair of m-p traits is a measure of how much the traits function together and is computed as the covariance between rows of F. Finally, it is shown that genetic covariances between m-p traits and performance traits are a function of the F matrix, but a G matrix that includes these covariances cannot be used to model functional constraints effectively.     

Sources of sire-specific genetic variance for birth and weaning weight in Bruna dels Pirineus beef calves

This research investigated two sources of sire-specific genetic effects on the birth weight (BWT) and weaning weight (WWT) of Bruna dels Pirineus beef calves. More specifically, we focused on the influence of genes located in the non-autosomal region of the Y chromosome and the contribution of paternal imprinting. Our analyses were performed on 8130 BWT and 1245 WWT records from 12 and 2 purebred herds, respectively, they being collected between years 1986 and 2010. All animals included in the study were registered in the Yield Recording Scheme of the Bruna dels Pirineus breed. Both BWT and WWT were analyzed using a univariate linear animal model, and the relevance of paternal imprinting and Y chromosome-linked effects were checked by the deviance information criterion (DIC). In addition to sire-specific and direct genetic effects, our model accounted for random permanent effects (dam and herd-year-season) and three systematic sources of variation, that is, sex of the calf (male or female), age of the dam at calving (six levels) and birth type (single or twin). Both weight traits evidenced remarkable effects from the Y chromosome, whereas paternal imprinting was only revealed in WWT. Note that differences in DIC between the preferred model and the remaining ones exceed 39 000 and 2 800 000 DIC units for BWT and WWT, respectively. It is important to highlight that Y chromosome accounted for ∼2% and ∼6% of the total phenotypic variance for BWT and WWT, respectively, and paternal imprinting accounted for ∼13% of the phenotypic variance for WWT. These results revealed two relevant sources of sire-specific genetic variability with potential contributions to the current breeding scheme of the Bruna dels Pirineus beef cattle breed; moreover, these sire-specific effects could be included in other beef cattle breeding programs or, at least, they must be considered and appropriately analyzed.     

秦川牛脂联素基因SNPs检测及其与胴体、肉质性状的相关性

利用PCR-SSCP结合测序技术对405头24月龄秦川牛脂联素基因SNPs位点进行检测, 运用SPSS统计程序中的GLM模型将检测到的SNPs位点与部分胴体及肉质性状的相关性进行了分析。结果检测到AA、AB、BB、CC、CD 5种基因型, 其中AB、BB型个体在脂联素基因第2外显子 64 bp处发现G→C突变, CD型个体第3外显子50 bp处发现C→T的突变, G→C导致谷氨酸(GGA)转化为谷氨酰胺(GCA), C→T导致丝氨酸(TCA)转化为亮氨酸(TTA)。方差分析结果表明: AA型个体的宰前活重、胴体重、眼肌面积显著高于BB型(P<0.05), 而在胴体腿臀围方面, AA型个体极显著高于AB型、BB型个体(P<0.01)。CD型个体的宰前活重、胴体腿臀围、皮下脂肪厚、背膘厚、嫩度都显著优于CC型个体(P<0.05)。脂联素基因该位点可能是影响秦川牛胴体及肉质性状的主效QTL或与之紧密连锁, 可作为秦川牛高档牛肉生产的候选分子标记。