Mixed effects structural equation models and phenotypic causal networks

Analysis of the causal structure of traits involved in sow lactation feed efficiency

BACKGROUND

Feed efficiency during lactation involves a set of phenotypic traits that form a complex system, with some traits exerting causal effects on the others. Information regarding such interrelationships can be used to predict the effect of external interventions on the system, and ultimately to optimize management practices and multi-trait selection strategies. Structural equation models can be used to infer the magnitude of the different causes of such interrelationships. The causal network necessary to fit structural equation models can be inferred using the inductive causation (IC) algorithm. By implementing these statistical tools, we inferred the causal association between the main energy sources and sinks involved in sow lactation feed efficiency for the first time, i.e., daily lactation feed intake (dLFI) in kg/day, daily sow weight balance (dSWB) in kg/day, daily litter weight gain (dLWG) in kg/day, daily back fat thickness balance (dBFTB) in mm/day, and sow metabolic body weight (SMBW) in kg0.75. Then, we tested several selection strategies based on selection indices, with or without dLFI records, to improve sow efficiency during lactation.

RESULTS

The IC algorithm using 95% highest posterior density (HPD95%) intervals resulted in a fully directed acyclic graph, in which dLFI and dLWG affected dSWB, the posterior mean of the corresponding structural coefficients (PMλ) being 0.12 and - 0.03, respectively. In turn, dSWB influenced dBFTB and SMBW, with PMλ equal to 0.70 and - 1.22, respectively. Multiple indirect effects contributed to the variances and covariances among the analyzed traits, with the most relevant indirect effects being those involved in the association between dSWB and dBFTB and between dSWB and SMBW. Selection strategies with or without phenotypic information on dLFI, or that hold this trait constant, led to the same pattern and similar responses in dLFI, dSWB, and dLWG.

CONCLUSIONS

Selection based on an index including only dBFTB and dLWG records can reduce dLFI, keep dSWB constant or increase it, and increase dLWG. However, a favorable response for all three traits is probably not achievable. Holding the amount of feed provided to the sows constant did not offer an advantage in terms of response over the other strategies.

Searching for causal relationships among latent variables concerning performance, carcass, and meat quality traits in broilers

In causal relationship studies, the latent variables may summarize the phenotypes in theoretical traits according to their phenotypic correlations, improving the understanding of causal relationships between broilers phenotypes. In this study, we aimed to investigate potential causal relationships among latent variables in broilers using a structural equation model in the context of genetic analysis. The data used in this study comprised 14 traits in broilers with 2,017 records each, and 104,154 animals in pedigree. Four latent variables (WEIGHT, LOSSES, COLOUR, and VISCERA) were defined and validated using Bayesian Confirmatory Factor Analysis. Subsequently, a search for causal linkage structures was performed, obtaining a single causal link structure between the latent variables. Then, this information was used to fit the structural equation model (SEM). The results from the SEM indicated positive causal effects of the variables WEIGHT and LOSSES on the variables VISCERA and COLOUR, respectively, with structural coefficient estimates of 1.006 and 0.040, respectively. On the other hand, an antagonist causal effect of the variable WEIGHT on the variable LOSSES was verified, with a structural coefficient estimate of -4.333. These results highlight the causal relationship between performance and meat quality traits, which may be associated with the natural processes involved in the conversion of muscle into meat and the structural changes in muscle tissues due to intense selection for high growth rates in broilers.

Accuracy of breeding values for production traits in turkeys (Meleagris gallopavo) using recursive models with or without genomics

Background

Knowledge about potential functional relationships among traits of interest offers a unique opportunity to understand causal mechanisms and to optimize breeding goals, management practices, and prediction accuracy. In this study, we inferred the phenotypic causal networks among five traits in a turkey population and assessed the effect of the use of such causal structures on the accuracy of predictions of breeding values.

Methods

Phenotypic data on feed conversion ratio, residual feed intake, body weight, breast meat yield, and walking score in addition to genotype data from a commercial breeding population were used. Causal links between the traits were detected using the inductive causation algorithm based on the joint distribution of genetic effects obtained from a standard Bayesian multiple trait model. Then, a structural equation model was implemented to infer the magnitude of causal structure coefficients among the phenotypes. Accuracies of predictions of breeding values derived using pedigree- and blending-based multiple trait models were compared to those obtained with the pedigree- and blending-based structural equation models.

Results

In contrast to the two unconditioned traits (i.e., feed conversion ratio and breast meat yield) in the causal structures, the three conditioned traits (i.e., residual feed intake, body weight, and walking score) showed noticeable changes in estimates of genetic and residual variances between the structural equation model and the multiple trait model. The analysis revealed interesting functional associations and indirect genetic effects. For example, the structural coefficient for the path from body weight to walking score indicated that a 1-unit genetic improvement in body weight is expected to result in a 0.27-unit decline in walking score. Both structural equation models outperformed their counterpart multiple trait models for the conditioned traits. Applying the causal structures led to an increase in accuracy of estimated breeding values of approximately 7, 6, and 20% for residual feed intake, body weight, and walking score, respectively, and different rankings of selection candidates for the conditioned traits.

Conclusions

Our results suggest that structural equation models can improve genetic selection decisions and increase the prediction accuracy of breeding values of selection candidates. The identified causal relationships between the studied traits should be carefully considered in future turkey breeding programs.

Inferring phenotypic causal structure among farrowing and weaning traits in pigs

Direct selection for litter size or weight at weaning in pigs is often hindered by external interventions such as cross-fostering. The objective of this study was to infer the causal structure among phenotypes of reproductive traits in pigs to enable subsequent direct selection for these traits. Examined traits included: number born alive (NBA), litter size on day 21 (LS21), and litter weight on day 21 (LW21). The study included 6,240 litters from 1,673 Landrace dams and 5,393 litters from 1,484 Large White dams. The inductive causation (IC) algorithm was used to infer the causal structure, which was then fitted to a structural equation model (SEM) to estimate causal coefficients and genetic parameters. Based on the IC algorithm and temporal and biological information, the causal structure among traits was identified as: NBA → LS21 → LW21 and NBA → LW21. Owing to the causal effect of NBA on LS21 and LW21, the genetic, permanent environmental, and residual variances of LS21 and LW21were much lower in the SEM than in the multiple-trait model for both breeds. Given the strong effect of NBA on LS21 and LW21, the SEM and causal information might assist with selective breeding for LS21 and LW21 when cross-fostering occurs.

Application of Bayesian causal inference and structural equation model to animal breeding

Optimized breeding goals and management practices for the improvement of target traits requires knowledge regarding any potential functional relationships between them. Fitting a structural equation model (SEM) allows for inferences about the magnitude of causal effects between traits to be made. In recent years, an adaptation of SEM was proposed in the context of quantitative genetics and mixed models. Several studies have since applied the SEM in the context of animal breeding. However, fitting the SEM requires choosing a causal structure with prior biological or temporal knowledge. The inductive causation (IC) algorithm can be used to recover an underlying causal structure from observed associations between traits. The results of the papers, which are introduced in this review, showed that using the IC algorithm to infer a causal structure is a helpful tool for detecting a causal structure without proper prior knowledge or with uncertain relationships between traits. The reports also presented that fitting the SEM could infer the effects of interventions, which are not given by correlations. Hence, information from the SEM provides more insights into and suggestions on breeding strategy than that from a multiple-trait model, which is the conventional model used for multitrait analysis.

Inferring phenotypic causal structures among meat quality traits and the application of a structural equation model in Japanese Black cattle

Meat quality is one of the most important traits determining carcass price in the Japanese beef market. Optimized breeding goals and management practices for the improvement of meat quality traits requires knowledge regarding any potential functional relationships between them. In this context, the objective of this research was to infer phenotypic causal networks involving beef marbling score (BMS), beef color score (BCL), firmness of beef (FIR), texture of beef (TEX), beef fat color score (BFS), and the ratio of MUFA to SFA (MUS) from 11,855 Japanese Black cattle. The inductive causation (IC) algorithm was implemented to search for causal links among these traits and was conditionally applied to their joint distribution on genetic effects. This information was obtained from the posterior distribution of the residual (co)variance matrix of a standard Bayesian multiple trait model (MTM). Apart from BFS, the IC algorithm implemented with 95% highest posterior density (HPD) intervals detected only undirected links among the traits. However, as a result of the application of 80% HPD intervals, more links were recovered and the undirected links were changed into directed ones, except between FIR and TEX. Therefore, 2 competing causal networks resulting from the IC algorithm, with either the arrow FIR → TEX or the arrow FIR ← TEX, were fitted using a structural equation model () to infer causal structure coefficients between the selected traits. Results indicated similar genetic and residual variances as well as genetic correlation estimates from both structural equation models. The genetic variances in BMS, FIR, and TEX from the structural equation models were smaller than those obtained from the MTM. In contrast, the variances in BCL, BFS, and MUS, which were not conditioned on any of the other traits in the causal structures, had no significant differences between the structural equation model and MTM. The structural coefficient for the path from MUS (BCL) to BMS showed that a 1-unit improvement in MUS (BCL) resulted in an increase of 0.85 or 1.45 (an decrease of 0.52 or 0.54) in BMS in the causal structures. The analysis revealed some interesting functional relationships, direct genetic effects, and the magnitude of the causal effects between these traits, for example, indicating that BMS would be affected by interventions on MUS and BCL. In addition, if interventions existed in this scenario, a breeding strategy based only on the MTM would lead to a mistaken selection for BMS.