Searching for causal networks involving latent variables in complex traits: Application to growth, carcass, and meat quality traits in pigs

Applying recursive modelling to assess the role of the host genome and the gut microbiome on feed efficiency in pigs

The gut microbiome plays an important role in the performance and health of swine by providing essential nutrients and supporting the immune system. Recent studies have demonstrated that the gut microbiome can explain part of the variation observed in growth, health, and meat quality. Feed efficiency is crucial in swine production, as feed cost account for more than 60% of total production costs. This study aimed to assess the relationships between the host genome, gut microbiome, and feed efficiency in Iberian pigs raised under intensive conditions. The specific objectives were to assess the mediating effects of the gut microbiome on feed efficiency and to estimate the direct and total heritability of feed efficiency. The data set included the feed conversion ratio (FCR) and residual feed intake (RFI) from 587 Iberian pigs, as well as the 16S rRNA gut microbial abundance from 151 of those pigs raised in a nucleus of selection. We reparametrised variance components from standard bivariate mixed models into recursive models to disentangle the microbiome's mediating effect on feed efficiency. In our models, the host genome has direct effects on both the phenotype (G→P) and the gut microbiome (G→M). Additionally, there is an indirect effect of the host genome on the phenotype mediated by the microbiome (G→M→P). We identified a total of 14 taxa with relevant effects on FCR and 16 taxa with relevant effects on RFI. We categorised the gut microbiome into groups for potential practical application in pig farming. The gut microbes with relevant causal effects and low heritability can be manipulated through management interventions, while those microbes with relevant causal effects and moderate heritability can be targeted through selective breeding. Our findings indicate that incorporating microbiome data leads to a reduction in total heritability for both FCR and RFI. This study provides new insights into the link between the gut microbiome and feed efficiency, presenting practical methods to target microbes that can be influenced through selective breeding or management interventions.

Inferring Causal Relationships for Lifetime Reproductive Traits and Modelling Latent Reproductive Performance Variable in Murciano-Granadina Goats

The current study investigated the application of structural equation models for genetic analysis of lifetime reproductive traits and latent variable modelling in the Murciano-Granadina goat breed. In the current investigation, data collected between 2016 and 2023 in a private dairy farm of the Murciano-Granadina goat breed in Ghale-Ganj city, located in the southern area of Kerman Iranian province were used. The investigated lifetime reproductive traits included overall litter size at birth (OLSB), overall litter size at weaning (OLSW), overall litter weight at birth (OLWB), and overall litter weight at weaning (OLWW). Four multivariate animal models, including standard (SMM), Inductive Causation algorithm-based structural equation (ICM), ICM with biological modification (ICM-BM), and fully recursive (FRM) models were fitted on the data and compared in terms of predictive ability measures including mean squared prediction error (MSE) and Pearson's correlation coefficient between the observed and predicted values (r(y,y ̂ $$ \hat{\mathrm{y}} $$ )) of records. ICM-BM performed better than other models in terms of the lowest MSE and the highest r(y,y ̂ $$ \hat{\mathrm{y}} $$ ). Under ICM-BM, heritability estimates were low values of 0.08, 0.08, 0.11, and 0.10 for OLSB, OLSW, OLWB, and OLWW, respectively. Genetic correlations among lifetime reproductive traits were positive and varied from 0.72 (OLSB-OLWW) to 0.95 (OLSB-OLWB). The confirmatory factor analysis technique was used to construct a latent variable named reproductive performance (RP) from the investigated lifetime reproductive traits. The posterior mean for heritability of RP was estimated at 0.06. The genetic correlations between RP and the investigated lifetime reproductive traits were high and positive, ranging from 0.92 (RP-OLSB) to 0.99 (RP-OLSW). The corresponding phenotypic correlations were also high and positive, ranging from 0.81 (RP-OLWB) to 0.95 (RP-OLSW). Considering causal structure among the traits detected via ICM-BM had more advantages for genetic evaluation of the lifetime reproductive traits in the Murciano-Granadina goat compared with SMM. The low heritability estimates implied that the studied lifetime reproductive traits and RP were mainly controlled by non-additive genetic and environmental effects which limits the efficiency of direct genetic selection for improving these traits. Furthermore, positive genetic and phenotypic correlations favoured using RP latent variable for breeding purposes.

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.

Genetic correlations and causal effects of fighting ability on fitness traits in cattle reveal antagonistic trade-offs

Complex genetic and phenotypic relationships are theorized to link different fitness components but revealing the correlations occurring among disparate traits requires large datasets of pedigreed populations. In particular, the association between traits beneficial to social dominance with health and fitness could be antagonistic, because of trade-offs, or positive, because of greater resource acquisition by dominant individuals. Studies investigating these relationships found some empirical evidence in support of both theories, mainly using multiple trait models (MTM). However, if a trait giving a social advantage is suspected to affect the expression of other traits, MTM could provide some bias, that structural equation models (SEM) could highlight. We used Aosta Chestnut-Black Pied cattle to investigate whether the fighting ability of cows (the capability of winning social dominance interactions) is genetically correlated with health and fitness traits. We ran both MTM and SEM using a Gibbs sampling algorithm to disentangle the possible causal effects of fighting ability from the genetic correlations that this trait shares with other traits: individual milk yield, somatic cells (representing mammary health), fertility, and longevity. We found antagonistic genetic correlations, similar under both approaches, for fighting ability vs. milk, somatic cells, and fertility, Accordingly, we found only a slight causal effects of fighting ability on these traits (–0.012 to 0.059 in standardized value). However, we found genetic correlations opposite in sign between fighting ability and longevity under MTM (0.237) and SEM (–0.183), suggesting a strong causal effect (0.386 standardized) of fighting ability on longevity. In other words, MTM found a positive correlation between longevity and fighting ability, while SEM found a negative correlation. The explanation could be that for economic reasons dominant cows are kept in this population for longer, thus attaining greater longevity: using MTM, the economic importance of competitions probably covers the true genetic correlation among traits. This artificially simulates a natural situation where an antagonistic genetic correlation between longevity and fighting ability appears positive under MTM due to a non-genetic advantage obtained by the best fighters. The use of SEM to properly assess the relationships among traits is suggested in both evolutionary studies and animal breeding.

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.

Modeling multiple phenotypes in wheat using data-driven genomic exploratory factor analysis and Bayesian network learning

Inferring trait networks from a large volume of genetically correlated diverse phenotypes such as yield, architecture, and disease resistance can provide information on the manner in which complex phenotypes are interrelated. However, studies on statistical methods tailored to multidimensional phenotypes are limited, whereas numerous methods are available for evaluating the massive number of genetic markers. Factor analysis operates at the level of latent variables predicted to generate observed responses. The objectives of this study were to illustrate the manner in which data-driven exploratory factor analysis can map observed phenotypes into a smaller number of latent variables and infer a genomic latent factor network using 45 agro-morphological, disease, and grain mineral phenotypes measured in synthetic hexaploid wheat lines (Triticum aestivum L.). In total, eight latent factors including grain yield, architecture, flag leaf-related traits, grain minerals, yellow rust, two types of stem rust, and leaf rust were identified as common sources of the observed phenotypes. The genetic component of the factor scores for each latent variable was fed into a Bayesian network to obtain a trait structure reflecting the genetic interdependency among traits. Three directed paths were consistently identified by two Bayesian network algorithms. Flag leaf-related traits influenced leaf rust, and yellow rust and stem rust influenced grain yield. Additional paths that were identified included flag leaf-related traits to minerals and minerals to architecture. This study shows that data-driven exploratory factor analysis can reveal smaller dimensional common latent phenotypes that are likely to give rise to numerous observed field phenotypes without relying on prior biological knowledge. The inferred genomic latent factor structure from the Bayesian network provides insights for plant breeding to simultaneously improve multiple traits, as an intervention on one trait will affect the values of focal phenotypes in an interrelated complex trait system.

Gut microbiome mediates host genomic effects on phenotypes: a case study with fat deposition in pigs

A large number of studies have highlighted the importance of gut microbiome composition in shaping fat deposition in mammals. Several studies have also highlighted how host genome controls the abundance of certain species that make up the gut microbiota. We propose a systematic approach to infer how the host genome can control the gut microbiome, which in turn contributes to the host phenotype determination. We implemented a mediation test that can be applied to measured and latent dependent variables to describe fat deposition in swine (Sus scrofa). In this study, we identify several host genomic features having a microbiome-mediated effects on fat deposition. This demonstrates how the host genome can affect the phenotypic trait by inducing a change in gut microbiome composition that leads to a change in the phenotype. Host genomic variants identified through our analysis are different than the ones detected in a traditional genome-wide association study. In addition, the use of latent dependent variables allows for the discovery of additional host genomic features that do not show a significant effect on the measured variables. Microbiome-mediated host genomic effects can help understand the genetic determination of fat deposition. Since their contribution to the overall genetic variance is usually not included in association studies, they can contribute to filling the missing heritability gap and provide further insights into the host genome – gut microbiome interplay. Further studies should focus on the portability of these effects to other populations as well as their preservation when pro-/pre-/anti-biotics are used (i.e. remediation).

Deciphering Cattle Temperament Measures Derived From a Four-Platform Standing Scale Using Genetic Factor Analytic Modeling

The animal's reaction to human handling (i.e., temperament) is critical for work safety, productivity, and welfare. Subjective phenotyping methods have been traditionally used in beef cattle production. Even so, subjective scales rely on the evaluator's knowledge and interpretation of temperament, which may require substantial experience. Selection based on such subjective scores may not precisely change temperament preferences in cattle. The objectives of this study were to investigate the underlying genetic interrelationships among temperament measurements using genetic factor analytic modeling and validate a movement-based objective method (four-platform standing scale, FPSS) as a measure of temperament. Relationships among subjective methods of docility score (DS), temperament score (TS), 12 qualitative behavior assessment (QBA) attributes and objective FPSS including the standard deviation of total weight on FPSS over time (SSD) and coefficient of variation of SSD (CVSSD) were investigated using 1,528 calves at weaning age. An exploratory factor analysis (EFA) identified two latent variables account for TS and 12 QBA attributes, termed difficult and easy from their characteristics. Inclusion of DS in EFA was not a good fit because it was evaluated under restraint and other measures were not. A Bayesian confirmatory factor analysis inferred the difficult and easy scores discovered in EFA. This was followed by fitting a pedigree-based Bayesian multi-trait model to characterize the genetic interrelationships among difficult, easy, DS, SSD, and CVSSD. Estimates of heritability ranged from 0.18 to 0.4 with the posterior standard deviation averaging 0.06. The factors of difficult and easy exhibited a large negative genetic correlation of -0.92. Moderate genetic correlation was found between DS and difficult (0.36), easy (-0.31), SSD (0.42), and CVSSD (0.34) as well as FPSS with difficult (CVSSD: 0.35; SSD: 0.42) and easy (CVSSD: -0.35; SSD: -0.4). Correlation coefficients indicate selection could be performed with either and have similar outcomes. We contend that genetic factor analytic modeling provided a new approach to unravel the complexity of animal behaviors and FPSS-like measures could increase the efficiency of genetic selection by providing automatic, objective, and consistent phenotyping measures that could be an alternative of DS, which has been widely used in beef production.

Genomic Bayesian Confirmatory Factor Analysis and Bayesian Network To Characterize a Wide Spectrum of Rice Phenotypes

With the advent of high-throughput phenotyping platforms, plant breeders have a means to assess many traits for large breeding populations. However, understanding the genetic interdependencies among high-dimensional traits in a statistically robust manner remains a major challenge. Since multiple phenotypes likely share mutual relationships, elucidating the interdependencies among economically important traits can better inform breeding decisions and accelerate the genetic improvement of plants. The objective of this study was to leverage confirmatory factor analysis and graphical modeling to elucidate the genetic interdependencies among a diverse agronomic traits in rice. We used a Bayesian network to depict conditional dependencies among phenotypes, which can not be obtained by standard multi-trait analysis. We utilized Bayesian confirmatory factor analysis which hypothesized that 48 observed phenotypes resulted from six latent variables including grain morphology, morphology, flowering time, physiology, yield, and morphological salt response. This was followed by studying the genetics of each latent variable, which is also known as factor, using single nucleotide polymorphisms. Bayesian network structures involving the genomic component of six latent variables were established by fitting four algorithms (i.e., Hill Climbing, Tabu, Max-Min Hill Climbing, and General 2-Phase Restricted Maximization algorithms). Physiological components influenced the flowering time and grain morphology, and morphology and grain morphology influenced yield. In summary, we show the Bayesian network coupled with factor analysis can provide an effective approach to understand the interdependence patterns among phenotypes and to predict the potential influence of external interventions or selection related to target traits in the interrelated complex traits systems.

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.

Structural Equation Modeling and Whole-Genome Scans Uncover Chromosome Regions and Enriched Pathways for Carcass and Meat Quality in Beef

Structural equation models involving latent variables are useful tools for formulating hypothesized models defined by theoretical variables and causal links between these variables. The objectives of this study were: (1) to identify latent variables underlying carcass and meat quality traits and (2) to perform whole-genome scans for these latent variables in order to identify genomic regions and individual genes with both direct and indirect effects. A total of 726 steers from an Angus-Brahman multibreed population with records for 22 phenotypes were used. A total of 480 animals were genotyped with the GGP Bovine F-250. The single-step genomic best linear unbiased prediction method was used to estimate the amount of genetic variance explained for each latent variable by chromosome regions of 20 adjacent SNP-windows across the genome. Three types of genetic effects were considered: (1) direct effects on a single latent phenotype; (2) direct effects on two latent phenotypes simultaneously; and (3) indirect effects. The final structural model included carcass quality as an independent latent variable and meat quality as a dependent latent variable. Carcass quality was defined by quality grade, fat over the ribeye and marbling, while the meat quality was described by juiciness, tenderness and connective tissue, all of them measured through a taste panel. From 571 associated genomic regions (643 genes), each one explaining at least 0.05% of the additive variance, 159 regions (179 genes) were associated with carcass quality, 106 regions (114 genes) were associated with both carcass and meat quality, 242 regions (266 genes) were associated with meat quality, and 64 regions (84 genes) were associated with carcass quality, having an indirect effect on meat quality. Three biological mechanisms emerged from these findings: postmortem proteolysis of structural proteins and cellular compartmentalization, cellular proliferation and differentiation of adipocytes, and fat deposition.

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.

A high resolution atlas of gene expression in the domestic sheep (Ovis aries)

Sheep are a key source of meat, milk and fibre for the global livestock sector, and an important biomedical model. Global analysis of gene expression across multiple tissues has aided genome annotation and supported functional annotation of mammalian genes. We present a large-scale RNA-Seq dataset representing all the major organ systems from adult sheep and from several juvenile, neonatal and prenatal developmental time points. The Ovis aries reference genome (Oar v3.1) includes 27,504 genes (20,921 protein coding), of which 25,350 (19,921 protein coding) had detectable expression in at least one tissue in the sheep gene expression atlas dataset. Network-based cluster analysis of this dataset grouped genes according to their expression pattern. The principle of 'guilt by association' was used to infer the function of uncharacterised genes from their co-expression with genes of known function. We describe the overall transcriptional signatures present in the sheep gene expression atlas and assign those signatures, where possible, to specific cell populations or pathways. The findings are related to innate immunity by focusing on clusters with an immune signature, and to the advantages of cross-breeding by examining the patterns of genes exhibiting the greatest expression differences between purebred and crossbred animals. This high-resolution gene expression atlas for sheep is, to our knowledge, the largest transcriptomic dataset from any livestock species to date. It provides a resource to improve the annotation of the current reference genome for sheep, presenting a model transcriptome for ruminants and insight into gene, cell and tissue function at multiple developmental stages.