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

Invited review: Recursive models in animal breeding: Interpretation, limitations, and extensions

Structural equation models allow causal effects between 2 or more variables to be considered and can postulate unidirectional (recursive models; RM) or bidirectional (simultaneous models) causality between variables. This review evaluated the properties of RM in animal breeding and how to interpret the genetic parameters and the corresponding estimated breeding values. In many cases, RM and mixed multitrait models (MTM) are statistically equivalent, although subject to the assumption of variance-covariance matrices and restrictions imposed for achieving model identification. Inference under RM requires imposing some restrictions on the (co)variance matrix or on the location parameters. The estimates of the variance components and the breeding values can be transformed from RM to MTM, although the biological interpretation differs. In the MTM, the breeding values predict the full influence of the additive genetic effects on the traits and should be used for breeding purposes. In contrast, the RM breeding values express the additive genetic effect while holding the causal traits constant. The differences between the additive genetic effect in RM and MTM can be used to identify the genomic regions that affect the additive genetic variation of traits directly or causally mediated for another trait or traits. Furthermore, we presented some extensions of the RM that are useful for modeling quantitative traits with alternative assumptions. The equivalence of RM and MTM can be used to infer causal effects on sequentially expressed traits by manipulating the residual (co)variance matrix under the MTM. Further, RM can be implemented to analyze causality between traits that might differ among subgroups or within the parametric space of the independent traits. In addition, RM can be expanded to create models that introduce some degree of regularization in the recursive structure that aims to estimate a large number of recursive parameters. Finally, RM can be used in some cases for operational reasons, although there is no causality between traits.

Genetical analysis of mastitis and reproductive traits in first-parity Holstein cows using standard and structural equation modelling

The present study aimed to investigate the causal relationships between clinical mastitis and some reproductive traits, including success at first insemination (SFI), the number of inseminations to pregnancy (INS), the interval from calving to first service (CTFS), first and last service interval (IFL), and open days (OD) in first-parity Holstein cows. For this purpose, the records of 58 281 first parity Holstein cows were analysed. These data sets were collected from 17 large dairy herds from 2008 to 2017. Recursive Mixed Models (RMMs) were applied and compared with the estimations under Standard Mixed Models. Then, one trivariate and three bivariate Gaussian-threshold models were used for the analyses. Recursive models were applied, considering that clinical mastitis can influence fertility traits. Mastitis is considered a covariate for the reproductive traits to determine their causal relationship. The results of this study indicated that causal effects of mastitis on SFI (on the observed scale, %), CTFS, IFL, OD, and INS were -5.7%, 3.3 days, 12.27 days, seven days, and 0.26 services, respectively. The estimated structural coefficients of the recursive models in the first parity imply that mastitis significantly lengthened the fertility interval and decreased the conception rate. In addition, genetic, residual, and phenotypic correlations between mastitis and the reproductive traits under both models were statistically significant. Results of genetic correlations between mastitis and fertility traits suggest that more incidence of mastitis during lactation is related to the delays in the heat show and pregnancy rate after insemination. In summary, considering the causal effects under RMMs may be advantageous to comprehend complicated relationships between complex traits better.

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.

Inferring phenotypic causal structures among body weight traits via structural equation modeling in Kurdi sheep

Data collected on 2550 Kurdi lambs originated from 1505 dams and 149 sires during 1991 to 2015 in Hossein Abad Kurdi Sheep Breeding Station, located in Shirvan city, North Khorasan province, North-eastern area of Iran, were used for inferring causal relationship among the body weights at birth (BW), at weaning (WW), at six-month age (6MW), at nine-month age (9MW) and yearling age (YW). The inductive causation (IC) algorithm was employed to search for causal structure among these traits. This algorithm was applied to the posterior distribution of the residual (co)variance matrix of a standard multivariate model (SMM). The causal structure detected by the IC algorithm coupling with biological prior knowledge provides a temporal recursive causal network among the studied traits. The studied traits were analyzed under three multivariate models including SMM, fully recursive multivariate model (FRM) and IC-based multivariate model (ICM) via a Bayesian approach by 100,000 iterations, thinning interval of 10 and the first 10,000 iterations as burn-in. The three considered multivariate models (SMM, FRM and ICM) were compared using deviance information criterion (DIC) and predictive ability measures including mean square of error (MSE) and Pearson's correlation coefficient between the observed and predicted values (r(y, )) of records. In general, structural equation based models (FRM and ICM) performed better than SMM in terms of lower DIC and MSE and also higher r(y, ). Among the tested models ICM had the lowest (36678.551) and SMM had the highest (36744.107)DIC values. In each case of the traits studied, the lowest MSE and the highest r(y, ) were obtained under ICM. The causal effects of BW on WW, WW on 6MW, 6MW on 9MW and 9MW on YW were statistically significant values of 1.478, 0.737, 0.776 and 0.929 kg, respectively (99% highest posterior density intervals did not include zero).

Structural equation modeling for investigating multi-trait genetic architecture of udder health in dairy cattle

Mastitis is one of the most prevalent and costly diseases in dairy cattle. It results in changes in milk composition and quality which are indicators of udder inflammation in absence of clinical signs. We applied structural equation modeling (SEM) - GWAS aiming to explore interrelated dependency relationships among phenotypes related to udder health, including milk yield (MY), somatic cell score (SCS), lactose (%, LACT), pH and non-casein N (NCN, % of total milk N), in a cohort of 1,158 Brown Swiss cows. The phenotypic network inferred via the Hill-Climbing algorithm was used to estimate SEM parameters. Integration of multi-trait models-GWAS and SEM-GWAS identified six significant SNPs for SCS, and quantified the contribution of MY and LACT acting as mediator traits to total SNP effects. Functional analyses revealed that overrepresented pathways were often shared among traits and were consistent with biological knowledge (e.g., membrane transport activity for pH and MY or Wnt signaling for SCS and NCN). In summary, SEM-GWAS offered new insights on the relationships among udder health phenotypes and on the path of SNP effects, providing useful information for genetic improvement and management strategies in dairy cattle.

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.

Conceptual framework for investigating causal effects from observational data in livestock

Understanding causal mechanisms among variables is critical to efficient management of complex biological systems such as animal agriculture production. The increasing availability of data from commercial livestock operations offers unique opportunities for attaining causal insight, despite the inherently observational nature of these data. Causal claims based on observational data are substantiated by recent theoretical and methodological developments in the rapidly evolving field of causal inference. Thus, the objectives of this review are as follows: 1) to introduce a unifying conceptual framework for investigating causal effects from observational data in livestock, 2) to illustrate its implementation in the context of the animal sciences, and 3) to discuss opportunities and challenges associated with this framework. Foundational to the proposed conceptual framework are graphical objects known as directed acyclic graphs (DAGs). As mathematical constructs and practical tools, DAGs encode putative structural mechanisms underlying causal models together with their probabilistic implications. The process of DAG elicitation and causal identification is central to any causal claims based on observational data. We further discuss necessary causal assumptions and associated limitations to causal inference. Last, we provide practical recommendations to facilitate implementation of causal inference from observational data in the context of the animal sciences.

Implementing structural equation models to observational data from feedlot production systems

The objective of this study was to illustrate the implementation of a mixed-model-based structural equation modeling (SEM) approach to observational data in the context of feedlot production systems. Different from traditional multiple-trait models, SEMs allow assessment of potential causal interrelationships between outcomes and can effectively discriminate between direct and indirect effects. For illustration, we focused on feedlot performance and its relationship to health outcomes related to Bovine Respiratory Disease (BRD), which accounts for approximately 75% of morbidity and 50-80% of deaths in feedlots. Our data consisted of 1430 lots representing 178,983 cattle from 9 feedlot operations located across the US Great Plains. We explored functional links between arrival weight (AW; i = 1), BRD-related treatment costs (Trt$; as a proxy for health; i = 2) and average daily weight gain (ADG; as an indicator of productive performance i = 3), accounting for the fixed effect of sex and correlation patterns due to the clustering of lots within feedlots. We proposed competing plausible causal models based on expert knowledge. The best fitting model selected for inference supported direct effects of AW on ADG as well as indirect effects of AW on ADG mediated by Trt$. Direct effects from outcome i' to outcome i are quantified by the structural coefficient λ_ii', such that every unit increase in kg/head of AW had a direct effect of increasing ADG by approximately (estimate ± standard error) λˆ₃₁=0.002±0.0001 kg/head/day and also a direct effect of reducing Trt$ by an estimated λˆ₂₁=$0.08±0.006 USD per head. In addition, every $1 USD spent on Trt$ directly decreased ADG by an estimated λˆ₃₂=0.004±0.0006 kg/head/day. From these estimates, we show how to compute the indirect, Trt$-mediated, effect of AW on ADG, as well as the overall effect of AW on ADG, including both direct and indirect effects. We further compared estimates of SEM-based effects with those obtained from standard linear regression mixed models and demonstrated the additional advantage of explicitly distinguishing direct and indirect components of an overall regression effect using SEMs. Understanding the direct and indirect mechanisms of interplay between health and performance outcomes may provide valuable insight into production systems.

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.

Iron and hepcidin as risk factors in atherosclerosis: what do the genes say?

Background

Previous reports suggested a role for iron and hepcidin in atherosclerosis. Here, we evaluated the causality of these associations from a genetic perspective via (i) a Mendelian randomization (MR) approach, (ii) study of association of atherosclerosis-related single nucleotide polymorphisms (SNPs) with iron and hepcidin, and (iii) estimation of genomic correlations between hepcidin, iron and atherosclerosis.

Results

Analyses were performed in a general population sample. Iron parameters (serum iron, serum ferritin, total iron-binding capacity and transferrin saturation), serum hepcidin and genome-wide SNP data were available for N = 1,819; non-invasive measurements of atherosclerosis (NIMA), i.e., presence of plaque, intima media thickness and ankle-brachial index (ABI), for N = 549. For the MR, we used 12 iron-related SNPs that were previously identified in a genome-wide association meta-analysis on iron status, and assessed associations of individual SNPs and quartiles of a multi-SNP score with NIMA. Quartile 4 versus quartile 1 of the multi-SNP score showed directionally consistent associations with the hypothesized direction of effect for all NIMA in women, indicating that increased body iron status is a risk factor for atherosclerosis in women. We observed no single SNP associations that fit the hypothesized directions of effect between iron and NIMA, except for rs651007, associated with decreased ferritin concentration and decreased atherosclerosis risk. Two of six NIMA-related SNPs showed association with the ratio hepcidin/ferritin, suggesting that an increased hepcidin/ferritin ratio increases atherosclerosis risk. Genomic correlations were close to zero, except for hepcidin and ferritin with ABI at rest [−0.27 (SE 0.34) and −0.22 (SE 0.35), respectively] and ABI after exercise [−0.29 (SE 0.34) and −0.30 (0.35), respectively]. The negative sign indicates an increased atherosclerosis risk with increased hepcidin and ferritin concentrations.

Conclusions

Our results suggest a potential causal role for hepcidin and ferritin in atherosclerosis, and may indicate that iron status is causally related to atherosclerosis in women.

Electronic supplementary material

The online version of this article (doi:10.1186/s12863-015-0246-4) contains supplementary material, which is available to authorized users.