Biology is characterized by complex interactions between phenotypes, such as recursive and simultaneous relationships between substrates and enzymes in biochemical systems. Structural equation models (SEMs) can be used to study such relationships in multivariate analyses, e.g., with multiple traits in a quantitative genetics context. Nonetheless, the number of different recursive causal structures that can be used for fitting a SEM to multivariate data can be huge, even when only a few traits are considered. In recent applications of SEMs in mixed-model quantitative genetics settings, causal structures were preselected on the basis of prior biological knowledge alone. Therefore, the wide range of possible causal structures has not been properly explored. Alternatively, causal structure spaces can be explored using algorithms that, using data-driven evidence, can search for structures that are compatible with the joint distribution of the variables under study. However, the search cannot be performed directly on the joint distribution of the phenotypes as it is possibly confounded by genetic covariance among traits. In this article we propose to search for recursive causal structures among phenotypes using the inductive causation (IC) algorithm after adjusting the data for genetic effects. A standard multiple-trait model is fitted using Bayesian methods to obtain a posterior covariance matrix of phenotypes conditional to unobservable additive genetic effects, which is then used as input for the IC algorithm. As an illustrative example, the proposed methodology was applied to simulated data related to multiple traits measured on a set of inbred lines.

Phenotypic traits may exert causal effects between them. For example, on the one hand, high yield in dairy cows may increase the liability to certain diseases and, on the other hand, the incidence of a disease may affect yield negatively. Likewise, the transcriptome may be a function of the reproductive status in mammals and the latter may depend on other physiological variables. Knowledge of phenotype networks describing such interrelationships can be used to predict the behavior of complex systems, e.g. biological pathways underlying complex traits such as diseases, growth and reproduction. Structural Equation Models (SEM) can be used to study recursive and simultaneous relationships among phenotypes in multivariate systems such as genetical genomics, system biology, and multiple trait models in quantitative genetics. Hence, SEM can produce an interpretation of relationships among traits which differs from that obtained with traditional multiple trait models, in which all relationships are represented by symmetric linear associations among random variables, such as covariances and correlations. In this review, we discuss the application of SEM and related techniques for the study of multiple phenotypes. Two basic scenarios are considered, one pertaining to genetical genomics studies, in which QTL or molecular marker information is used to facilitate causal inference, and another related to quantitative genetic analysis in livestock, in which only phenotypic and pedigree information is available. Advantages and limitations of SEM compared to traditional approaches commonly used for the analysis of multiple traits, as well as some indication of future research in this area are presented in a concluding section.

The prediction of total egg production (TEP) potential in poultry is an important task to aid optimized management decisions in commercial enterprises. The objective of the present study was to compare different modeling approaches for prediction of TEP in meat type quails (Coturnix coturnix coturnix) using phenotypes such as weight, weight gain, egg production and egg quality measurements. Phenotypic data on 30 traits from two lines (L1, n=180; and L2, n=205) of quail were modeled to predict TEP. Prediction models included multiple linear regression and artificial neural network (ANN). Moreover, Bayesian network (BN) and a stepwise approach were used as variable selection methods. BN results showed that TEP is independent from other earlier expressed traits when conditioned on egg production from 35 to 80 days of age (EP1). In addition, the prediction accuracy was much lower when EP1 was not included in the model. The best predictive model was ANN, after feature selection, showing prediction correlations of r=0.792 and r=0.714 for L1 and L2, respectively. In conclusion, machine learning methods may be useful, but reasonable prediction accuracies are obtained only when partial egg production measurements are included in the model.

BackgroundStructural 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.MethodsHere, 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.ResultsAs 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.ConclusionsCoupling 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.

BackgroundGenotype imputation is an important tool for whole-genome prediction as it allows cost reduction of individual genotyping. However, benefits of genotype imputation have been evaluated mostly for linear additive genetic models. In this study we investigated the impact of employing imputed genotypes when using more elaborated models of phenotype prediction. Our hypothesis was that such models would be able to track genetic signals using the observed genotypes only, with no additional information to be gained from imputed genotypes.ResultsFor the present study, an outbred mice population containing 1,904 individuals and genotypes for 1,809 pre-selected markers was used. The effect of imputation was evaluated for a linear model (the Bayesian LASSO - BL) and for semi and non-parametric models (Reproducing Kernel Hilbert spaces regressions – RKHS, and Bayesian Regularized Artificial Neural Networks – BRANN, respectively). The RKHS method had the best predictive accuracy. Genotype imputation had a similar impact on the effectiveness of BL and RKHS. BRANN predictions were, apparently, more sensitive to imputation errors. In scenarios where the masking rates were 75% and 50%, the genotype imputation was not beneficial. However, genotype imputation incorporated information about important markers and improved predictive ability, especially for body mass index (BMI), when genotype information was sparse (90% masking), and for body weight (BW) when the reference sample for imputation was weakly related to the target population.ConclusionsIn conclusion, genotype imputation is not always helpful for phenotype prediction, and so it should be considered in a case-by-case basis. In summary, factors that can affect the usefulness of genotype imputation for prediction of yet-to-be observed traits are: the imputation accuracy itself, the structure of the population, the genetic architecture of the target trait and also the model used for phenotype prediction.