Breeding and Genetics Symposium: inferring causal effects from observational data in livestock

Equivalence of variance components between standard and recursive genetic models using LDL' transformations

BACKGROUND

Recursive models are a category of structural equation models that propose a causal relationship between traits. These models are more parameterized than multiple trait models, and they require imposing restrictions on the parameter space to ensure statistical identification. Nevertheless, in certain situations, the likelihood of recursive models and multiple trait models are equivalent. Consequently, the estimates of variance components derived from the multiple trait mixed model can be converted into estimates under several recursive models through LDL' or block-LDL' transformations.

RESULTS

The procedure was employed on a dataset comprising five traits (birth weight-BW, weight at 90 days-W90, weight at 210 days-W210, cold carcass weight-CCW and conformation-CON) from the Pirenaica beef cattle breed. These phenotypic records were unequally distributed among 149,029 individuals and had a high percentage of missing data. The pedigree used consisted of 343,753 individuals. A Bayesian approach involving a multiple-trait mixed model was applied using a Gibbs sampler. The variance components obtained at each iteration of the Gibbs sampler were subsequently used to estimate the variance components within three distinct recursive models.

CONCLUSIONS

The LDL' or block-LDL' transformations applied to the variance component estimates achieved from a multiple trait mixed model enabled inference across multiple sets of recursive models, with the sole prerequisite of being likelihood equivalent. Furthermore, the aforementioned transformations simplify the handling of missing data when conducting inference within the realm of recursive models.

Effects of a mastitis J5 bacterin vaccination on the productive performance of dairy cows: An observational study using propensity score matching techniques

Inferring causal effects between variables when utilizing observational data is challenging due to confounding factors not controlled through a randomized experiment. Propensity score matching can decrease confounding in observational studies and offers insights about potential causal effects of prophylactic management interventions such as vaccinations. The objective of this study was to determine potential causality and impact of vaccination with an Escherichia coli J5 bacterin on the productive performance of dairy cows applying propensity score matching techniques to farm-recorded (e.g., observational) data. Traits of interest included 305-d milk yield (MY305), 305-d fat yield (FY305), 305-d protein yield (PY305), and somatic cell score (SCS). Records from 6,418 lactations generated by 5,121 animals were available for the analysis. Vaccination status of each animal was obtained from producer-recorded information. Confounding variables considered were herd-year-season groups (56 levels), parity (5 levels: 1, 2, 3, 4, and ≥5), and genetic quartile groups (4 levels: top 25% through bottom 25%) derived from genetic predictions for MY305, FY305, PY305, and SCS, as well as for the genetic susceptibility to mastitis. A logistic regression model was applied to estimate the propensity score (PS) for each cow. Subsequently, PS values were used to form pairs of animals (1 vaccinated with 1 unvaccinated control), depending on their PS similarities (difference in PS values of cows within a match required to be <20% of 1 standard deviation of the logit of PS). After the matching process, 2,091 pairs of animals (4,182 records) remained available to infer the causal effects of vaccinating dairy cows with the E. coli J5 bacterin. Causal effects estimation was performed using 2 approaches: simple matching and a bias-corrected matching. According to the PS methodology, causal effects of vaccinating dairy cows with a J5 bacterin on their productive performance were identified for MY305. The simple matched estimator suggested that vaccinated cows produced 163.89 kg more milk over an entire lactation when compared with nonvaccinated counterparts, whereas the bias-corrected estimator suggested that such increment in milk production was of 150.48 kg. Conversely, no causal effects of immunizing dairy cows with a J5 bacterin were identified for FY305, PY305, or SCS. In conclusion, the utilization of PS matching techniques applied to farm-recorded data was feasible and allowed us to identify that vaccination with an E. coli J5 bacterin relates to an overall milk production increment without compromising milk quality.

Field Implementation of Forecasting Models for Predicting Nursery Mortality in a Midwestern US Swine Production System

The performance of five forecasting models was investigated for predicting nursery mortality using the master table built for 3242 groups of pigs (~13 million animals) and 42 variables, which concerned the pre-weaning phase of production and conditions at placement in growing sites. After training and testing each model's performance through cross-validation, the model with the best overall prediction results was the Support Vector Machine model in terms of Root Mean Squared Error (RMSE = 0.406), Mean Absolute Error (MAE = 0.284), and Coefficient of Determination (R2 = 0.731). Subsequently, the forecasting performance of the SVM model was tested on a new dataset containing 72 new groups, simulating ongoing and near real-time forecasting analysis. Despite a decrease in R2 values on the new dataset (R2 = 0.554), the model demonstrated high accuracy (77.78%) for predicting groups with high (>5%) or low (<5%) nursery mortality. This study demonstrated the capability of forecasting models to predict the nursery mortality of commercial groups of pigs using pre-weaning information and stocking condition variables collected post-placement in nursery sites.

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.

Feeding behaviors collected from automated milk feeders were associated with disease in group-housed dairy calves in the Upper Midwest United States

Automated milk feeders (AMF) are an attractive option for producers interested in adopting practices that offer greater behavioral freedom for calves and can potentially improve labor management. These feeders give farmers the opportunity to have a more flexible labor schedule and more efficiently feed group-housed calves. However, housing calves in group systems can pose challenges for monitoring calf health on an individual basis, potentially leading to increased morbidity and mortality. Feeding behavior recorded by AMF software could potentially be used as an indicator of disease. Therefore, the objective of this observational study was to investigate the association between feeding behaviors and disease in preweaning group-housed dairy calves fed with AMF. The study was conducted at a dairy farm located in the Upper Midwest United States and included a final data set of 599 Holstein heifer calves. The farm was visited on a weekly basis from May 2018, to May 2019, when calves were visually health scored and AMF data were collected. Calf health scores included calf attitude, ear position, ocular discharge, nasal discharge, hide dirtiness, cough score, and rectal temperatures. Generalized additive mixed models (GAMM) were used to identify associations between feeding behavior and disease. The final quasibinomial GAMM included the fixed (main and interactions) effects of feeding behavior at calf visit-level including milk intake (mL/d), drinking speed (mL/min), visit duration (min), rewarded (with milk being offered) and unrewarded (without milk) visits (number per day), and interval between visits (min), as well as the random effects of calf age in regard to their relationship with calf health status. Total milk intake (mL/d), drinking speed (mL/min), interval between visits (min) to the AMF, calf age (d), and rewarded visits were significantly associated with dairy calf health status. These results indicate that as total milk intake and drinking speed increased, the risk of calves being sick decreased. In contrast, as the interval between visits and age increased, the risk of calves being sick also increased. This study suggests that AMF data may be a useful screening tool for detecting disease in dairy calves. In addition, GAMM were shown to be a simple and flexible approach to modeling calf health status, as they can cope with non-normal data distribution of the response variable, capture nonlinear relationships between explanatory and response variables and accommodate random effects.

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.

The Effects of Prenatal Diet on Calf Performance and Perspectives for Fetal Programming Studies: A Meta-Analytical Investigation

This meta-analysis aimed to identify knowledge gaps in the scientific literature on future fetal-programming studies and to investigate the factors that determine the performance of beef cows and their offspring. A dataset composed of 35 publications was used. The prenatal diet, body weight (BW), average daily gain (ADG) during pregnancy, and calf sex were elicited as possible modulators of the beef cows and their offspring performance. Then, the correlations between these variables and the outcomes of interest were investigated. A mixed multiple linear regression procedure was used to evaluate the relationships between the responses and all the possible explanatory variables. A knowledge gap was observed in studies focused on zebu animals, with respect to the offspring sex and the consequences of prenatal nutrition in early pregnancy. The absence of studies considering the possible effects promoted by the interactions between the different stressors' sources during pregnancy was also detected. A regression analysis showed that prenatal diets with higher levels of protein improved the ADG of pregnant beef cows and that heavier cows give birth to heavier calves. Variations in the BW at weaning were related to the BW at birth and calf sex. Therefore, this research reinforces the importance of monitoring the prenatal nutrition of beef cows.

Translating insights from the seed metabolome into improved prediction for lipid-composition traits in oat (Avena sativa L.)

Oat (Avena sativa L.) seed is a rich resource of beneficial lipids, soluble fiber, protein, and antioxidants, and is considered a healthful food for humans. Little is known regarding the genetic controllers of variation for these compounds in oat seed. We characterized natural variation in the mature seed metabolome using untargeted metabolomics on 367 diverse lines and leveraged this information to improve prediction for seed quality traits. We used a latent factor approach to define unobserved variables that may drive covariance among metabolites. One hundred latent factors were identified, of which 21% were enriched for compounds associated with lipid metabolism. Through a combination of whole-genome regression and association mapping, we show that latent factors that generate covariance for many metabolites tend to have a complex genetic architecture. Nonetheless, we recovered significant associations for 23% of the latent factors. These associations were used to inform a multi-kernel genomic prediction model, which was used to predict seed lipid and protein traits in two independent studies. Predictions for 8 of the 12 traits were significantly improved compared to genomic best linear unbiased prediction when this prediction model was informed using associations from lipid-enriched factors. This study provides new insights into variation in the oat seed metabolome and provides genomic resources for breeders to improve selection for health-promoting seed quality traits. More broadly, we outline an approach to distill high-dimensional "omics" data to a set of biologically meaningful variables and translate inferences on these data into improved breeding decisions.

Structural equation modeling for unraveling the multivariate genomic architecture of milk proteins in dairy cattle

The aims of this study were to investigate potential functional relationships among milk protein fractions in dairy cattle and to carry out a structural equation model (SEM) GWAS to provide a decomposition of total SNP effects into direct effects and effects mediated by traits that are upstream in a phenotypic network. To achieve these aims, we first fitted a mixed Bayesian multitrait genomic model to infer the genomic correlations among 6 milk nitrogen fractions [4 caseins (CN), namely κ-, β-, α_S1-, and α_S2-CN, and 2 whey proteins, namely β-lactoglobulin (β-LG) and α-lactalbumin (α-LA)], in a population of 989 Italian Brown Swiss cows. Animals were genotyped with the Illumina BovineSNP50 Bead Chip v.2 (Illumina Inc.). A Bayesian network approach using the max-min hill-climbing (MMHC) algorithm was implemented to model the dependencies or independence among traits. Strong and negative genomic correlations were found between β-CN and α_S1-CN (-0.706) and between β-CN and κ-CN (-0.735). The application of the MMHC algorithm revealed that κ-CN and β-CN seemed to directly or indirectly influence all other milk protein fractions. By integrating multitrait model GWAS and SEM-GWAS, we identified a total of 127 significant SNP for κ-CN, 89 SNP for β-CN, 30 SNP for α_S1-CN, and 14 SNP for α_S2-CN (mostly shared among CN and located on Bos taurus autosome 6) and 15 SNP for β-LG (mostly located on Bos taurus autosome 11), whereas no SNP passed the significance threshold for α-LA. For the significant SNP, we assessed and quantified the contribution of direct and indirect paths to total marker effect. Pathway analyses confirmed that common regulatory mechanisms (e.g., energy metabolism and hormonal and neural signals) are involved in the control of milk protein synthesis and metabolism. The information acquired might be leveraged for setting up optimal management and selection strategies aimed at improving milk quality and technological characteristics in dairy cattle.

Forecasting beef production and quality using large-scale integrated data from Brazil

With agriculture rapidly becoming a data-driven field, it is imperative to extract useful information from large data collections to optimize the production systems. We compared the efficacy of regression (linear regression or generalized linear regression [GLR] for continuous or categorical outcomes, respectively), random forests (RF) and multilayer neural networks (NN) to predict beef carcass weight (CW), age when finished (AS), fat deposition (FD), and carcass quality (CQ). The data analyzed contained information on over 4 million beef cattle from 5,204 farms, corresponding to 4.3% of Brazil's national production between 2014 and 2016. Explanatory variables were integrated from different data sources and encompassed animal traits, participation in a technical advising program, nutritional products sold to farms, economic variables related to beef production, month when finished, soil fertility, and climate in the location in which animals were raised. The training set was composed of information collected in 2014 and 2015, while the testing set had information recorded in 2016. After parameter tuning for each algorithm, models were used to predict the testing set. The best model to predict CW and AS was RF (CW: predicted root mean square error = 0.65, R2 = 0.61, and mean absolute error = 0.49; AS: accuracy = 28.7%, Cohen's kappa coefficient [Kappa] = 0.08). While the best approach for FD and CQ was GLR (accuracy = 45.7%, Kappa = 0.05, and accuracy = 58.7%, Kappa = 0.09, respectively). Across all models, there was a tendency for better performance with RF and regression and worse with NN. Animal category, nutritional plan, cattle sales price, participation in a technical advising program, and climate and soil in which animals were raised were deemed important for prediction of meat production and quality with regression and RF. The development of strategies for prediction of livestock production using real-world large-scale data will be core to projecting future trends and optimizing the allocation of resources at all levels of the production chain, rendering animal production more sustainable. Despite beef cattle production being a complex system, this analysis shows that by integrating different sources of data it is possible to forecast meat production and quality at the national level with moderate-high levels of accuracy.

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.

Generalized additive mixed model on the analysis of total transport losses of market-weight pigs1

Transportation losses of market-weight pigs are an animal welfare concern, and result in direct economic impact for producers and abattoirs. Such losses are related to multiple factors including pig genetics, human handling, management, and weather conditions. Understanding the factors associated with total transport losses (TTL) is important to the swine industry because it can aid decision-making, and help in the development of transportation strategies to minimize the risk of losses. Hence, the objective of this study was to investigate factors associated with TTL on market-weight pigs in typically field conditions for Midwestern United States using a generalized additive mixed model (GAMM). The final quasi-binomial GAMM included the fixed (main and interactions) effects of abattoir of destination, type of driver, average market weight, distance traveled, wind speed, precipitation, and temperature-humidity index (THI), as well as the random effects of truck companies and the combination of site of origin and period of the year. Results indicate significant associations between TTL and the main effect of all explanatory variables (P < 0.05), except for wind speed and precipitation. Interactions of average market weight × abattoir, and wind speed × precipitation were also significant. A complex nonlinear relationship between TTL and model covariates were observed for distance traveled, THI, and interaction terms. This study showed that TTL of market-weight pigs are caused by a complex system involving multiple interacting factors, which can be potentially managed to mitigate the risk of losses. In addition, the GAMM showed to be a simple and flexible approach to model TTL because it can capture nonlinear relationships, handle non-normal data, and can potentially accommodate data structure.

Revealing the structure of the associations between housing system, facilities, management and welfare of commercial laying hens using Additive Bayesian Networks

After the ban of battery cages in 1988, a welfare control programme for laying hens was developed in Sweden. Its goal was to monitor and ensure that animal welfare was not negatively affected by the new housing systems. The present observational study provides an overview of the current welfare status of commercial layer flocks in Sweden and explores the complexity of welfare aspects by investigating and interpreting the inter-relationships between housing system, production type (i.e. organic or conventional), facilities, management and animal welfare indicators. For this purpose, a machine learning procedure referred to as structure discovery was applied to data collected through the welfare programme during 2010-2014 in 397 flocks housed in 193 different farms. Seventeen variables were fitted to an Additive Bayesian Network model. The optimal model was identified by an exhaustive search of the data iterated across incremental parent limits, accounting for prior knowledge about causality, potential over-dispersion and clustering. The resulting Directed Acyclic Graph shows the inter-relationships among the variables. The animal-based welfare indicators included in this study - flock mortality, feather condition and mite infestation - were indirectly associated with each other. Of these, severe mite infestations were rare (4% of inspected flocks) and mortality was below the acceptable threshold (< 0.6%). Feather condition scored unsatisfactory in 21% of the inspected flocks; however, it seemed to be only associated to the age of the flock, ruling out any direct connection with managerial and housing variables. The environment-based welfare indicators - lighting and air quality - were an issue in 5 and 8% of the flocks, respectively, and showed a complex inter-relationship with several managerial and housing variables leaving room for several options for intervention. Additive Bayesian Network modelling outlined graphically the underlying process that generated the observed data. In contrast to ordinary regression, it aimed at accounting for conditional independency among variables, facilitating causal interpretation.

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.

Invited review: Reproducible research from noisy data: Revisiting key statistical principles for the animal sciences

Reproducible results define the very core of scientific integrity in modern research. Yet, legitimate concerns have been raised about the reproducibility of research findings, with important implications for the advancement of science and for public support. With statistical practice increasingly becoming an essential component of research efforts across the sciences, this review article highlights the compelling role of statistics in ensuring that research findings in the animal sciences are reproducible-in other words, able to withstand close interrogation and independent validation. Statistics set a formal framework and a practical toolbox that, when properly implemented, can recover signal from noisy data. Yet, misconceptions and misuse of statistics are recognized as top contributing factors to the reproducibility crisis. In this article, we revisit foundational statistical concepts relevant to reproducible research in the context of the animal sciences, raise awareness on common statistical misuse undermining it, and outline recommendations for statistical practice. Specifically, we emphasize a keen understanding of the data generation process throughout the research endeavor, from thoughtful experimental design and randomization, through rigorous data analysis and inference, to careful wording in communicating research results to peer scientists and society in general. We provide a detailed discussion of core concepts in experimental design, including data architecture, experimental replication, and subsampling, and elaborate on practical implications for proper elicitation of the scope of reach of research findings. For data analysis, we emphasize proper implementation of mixed models, in terms of both distributional assumptions and specification of fixed and random effects to explicitly recognize multilevel data architecture. This is critical to ensure that experimental error for treatments of interest is properly recognized and inference is correctly calibrated. Inferential misinterpretations associated with use of P-values, both significant and not, are clarified, and problems associated with error inflation due to multiple comparisons and selective reporting are illustrated. Overall, we advocate for a responsible practice of statistics in the animal sciences, with an emphasis on continuing quantitative education and interdisciplinary collaboration between animal scientists and statisticians to maximize reproducibility of research findings.

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.

Causal effect of prolificacy on milk yield in dairy sheep using propensity score

In animal production, it is often important to investigate causal relationships among variables. The gold standard tool for such investigation is randomized experiments. However, randomized experiments may not always be feasible, possible, or cost effective or reflect real-world farm conditions. Sometimes it is necessary to infer effects from farm-recorded data. Inferring causal effects between variables from field data is challenging because the association between them may arise not only from the effect of one on another but also from confounding background factors. Propensity score (PS) methods address this issue by correcting for confounding in different levels of the causal variable, which allows unbiased inference of causal effects. Here the objective was to estimate the causal effect of prolificacy on milk yield (MY) in dairy sheep using PS based on matched samples. Data consisted of 4,319 records from 1,534 crossbred ewes. Confounders were lactation number (first, second, and third through sixth) and dairy breed composition (<0.5, 0.5-0.75, and >0.75 of East Friesian or Lacaune). The causal variable prolificacy was considered as 2 levels (single or multiple lambs at birth). The outcome MY represented the volume of milk produced in the whole lactation. Pairs of single- and multiple-birth ewes (1,166) with similar PS were formed. The matching process diminished major discrepancies in the distribution of prolificacy for each confounder variable indicating bias reduction (cutoff standardized bias = 20%). The causal effect was estimated as the average difference within pairs. The effect of prolificacy on MY per lactation was 20.52 L of milk with a simple matching estimator and 12.62 L after correcting for remaining biases. A core advantage of causal over probabilistic approaches is that they allow inference of how variables would react as a result of external interventions (e.g., changes in the production system). Therefore, results imply that management and decision-making practices increasing prolificacy would positively affect MY, which is important knowledge at the farm level. Farm-recorded data can be a valuable source of information given its low cost, and it reflects real-world herd conditions. In this context, PS methods can be extremely useful as an inference tool for investigating causal effects. In addition, PS analysis can be implemented as a preliminary evaluation or a hypothesis generator for future randomized trials (if the trait analyzed allows randomization).

Causal relationships between milk quality and coagulation properties in Italian Holstein-Friesian dairy cattle

Background

Recently, selection for milk technological traits was initiated in the Italian dairy cattle industry based on direct measures of milk coagulation properties (MCP) such as rennet coagulation time (RCT) and curd firmness 30 min after rennet addition (a₃₀) and on some traditional milk quality traits that are used as predictors, such as somatic cell score (SCS) and casein percentage (CAS). The aim of this study was to shed light on the causal relationships between traditional milk quality traits and MCP. Different structural equation models that included causal effects of SCS and CAS on RCT and a₃₀ and of RCT on a₃₀ were implemented in a Bayesian framework.

Results

Our results indicate a non-zero magnitude of the causal relationships between the traits studied. Causal effects of SCS and CAS on RCT and a₃₀ were observed, which suggests that the relationship between milk coagulation ability and traditional milk quality traits depends more on phenotypic causal pathways than directly on common genetic influence. While RCT does not seem to be largely controlled by SCS and CAS, some of the variation in a₃₀ depends on the phenotypes of these traits. However, a₃₀ depends heavily on coagulation time. Our results also indicate that, when direct effects of SCS, CAS and RCT are considered simultaneously, most of the overall genetic variability of a₃₀ is mediated by other traits.

Conclusions

This study suggests that selection for RCT and a₃₀ should not be performed on correlated traits such as SCS or CAS but on direct measures because the ability of milk to coagulate is improved through the causal effect that the former play on the latter, rather than from a common source of genetic variation. Breaking the causal link (e.g. standardizing SCS or CAS before the milk is processed into cheese) would reduce the impact of the improvement due to selective breeding. Since a₃₀ depends heavily on RCT, the relative emphasis that is put on this trait should be reconsidered and weighted for the fact that the pure measure of a₃₀ almost double-counts RCT.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-015-0123-7) contains supplementary material, which is available to authorized users.

The Causal Meaning of Genomic Predictors and How It Affects Construction and Comparison of Genome-Enabled Selection Models

The term "effect" in additive genetic effect suggests a causal meaning. However, inferences of such quantities for selection purposes are typically viewed and conducted as a prediction task. Predictive ability as tested by cross-validation is currently the most acceptable criterion for comparing models and evaluating new methodologies. Nevertheless, it does not directly indicate if predictors reflect causal effects. Such evaluations would require causal inference methods that are not typical in genomic prediction for selection. This suggests that the usual approach to infer genetic effects contradicts the label of the quantity inferred. Here we investigate if genomic predictors for selection should be treated as standard predictors or if they must reflect a causal effect to be useful, requiring causal inference methods. Conducting the analysis as a prediction or as a causal inference task affects, for example, how covariates of the regression model are chosen, which may heavily affect the magnitude of genomic predictors and therefore selection decisions. We demonstrate that selection requires learning causal genetic effects. However, genomic predictors from some models might capture noncausal signal, providing good predictive ability but poorly representing true genetic effects. Simulated examples are used to show that aiming for predictive ability may lead to poor modeling decisions, while causal inference approaches may guide the construction of regression models that better infer the target genetic effect even when they underperform in cross-validation tests. In conclusion, genomic selection models should be constructed to aim primarily for identifiability of causal genetic effects, not for predictive ability.