Inductive Causation Research Articles

Investigating functional relationships among health and fertility traits in dairy cows

The association between health and pregnancy per artificial insemination, maintenance of pregnancy, and interval to pregnancy in dairy cattle is well documented. However, the understanding of the causal relationships among health and fertility traits is limited. Although information on heritabilities and genetic correlations between traits is key for the development of multiple-trait selection strategies, only knowledge about functional and causal relationships among them allow the prediction of the consequences of external interventions such as management decisions. Thus, this research was carried out to investigate potential causal relationships among multiple health events (retained fetal membranes [RFM], metritis [MET], clinical endometritis [CE], lameness [LS]) and fertility indicators including resumption of ovarian cyclicity (CY) by 50 days in milk and pregnancy on day 60 (P60) after the first artificial insemination in Holstein cows. Mixed-effects structural equation models (SEM) were fitted conditionally on a causal structure among traits, represented by a directed acyclic graph, inferred from the data using the inductive causation (IC) algorithm. The posterior mean and standard deviation of heritability for RFM, MET, CE, LS, CY and P60 were 0.20 ± 0.07, 0.09 ± 0.02, 0.10 ± 0.04, 0.35 ± 0.04, 0.15 ± 0.03, and 0.10 ± 0.03, respectively. The moderate estimates of heritability found for CY and P60 suggest that selective breeding could be effective for the genetic improvement of these traits. The estimates of genetic correlation among traits ranged from -0.82 ± 0.07 (MET and CY) to 0.70 ± 0.13 (RFM and MET). Biological considerations and results from the inductive causation algorithm analysis retrieved six potential causal connections between traits: RFM→MET; RFM→CE; LS→CE; CE→P60; CY→P60; and CY→CE. In addition to the data-driven network recovered, some additional connections or variations on their directions were also considered on the SEM analyses based on biological and chronological knowledge. Overall, the SEM results were very similar to those obtained from the traditional multi-trait mixed model analysis. The advantage of the SEM analysis is that it sheds some light onto the potential causal relationships between traits, which can aid better decisions to manage events occurring during the postpartum of dairy cattle.

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

BackgroundFeed 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.ResultsThe 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.ConclusionsSelection 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.

Application of structural equation models for genetic evaluation of lifetime reproductive traits and age at first lambing in Moghani sheep

The present study aimed to investigate the advantages of structural equation modeling for genetic evaluation of lifetime reproduction traits and age at first lambing in Moghani sheep. Data collected between 1988 and 2011 were retrieved from the Jafarabad Breeding Station of Moghani sheep, located in the north-west of Iran. The investigated traits were age at first lambing (AFL) and lifetime reproductive traits, including 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). Two multivariate animal models, including standard (SMM) and Inductive Causation algorithm-based structural equation models (IC-SEM), were compared in terms of deviance information criterion (DIC) and predictive ability measures, including the mean square of error (MSE) and Pearson's correlation coefficient between the observed and predicted values (r(y,yˆ)) of records. In general, IC-SEM performed better than SMM in terms of DIC, MSE, and r(y,yˆ) in such a way that the lowest DIC and MSE, and the highest r(y,yˆ) were obtained under IC-SEM. All the structural coefficients estimated by IC-SEM were statistically significant. Heritability estimates for the traits studied were low values of 0.11, 0.03, 0.07, 0.03, and 0.09 for AFL, OLSB, OLSW, OLWB, and OLWW, respectively, implying that the studied traits were mainly controlled by non-additive genetic and environmental effects. AFL had negative and statistically significant (95% highest posterior density (HPD) intervals did not include zero) genetic correlations with other traits studied, ranging from − 0.45 for AFL-OLSB to − 0.69 for AFL-OLWW; meaning that a fast-growing ewe lamb can achieve higher reproductive performance. Genetic correlations among lifetime reproductive traits were positive and statistically significant (99% HPD did not include zero), and varied from 0.36 (OLSB-OLWW) to 0.81 (OLSB-OLSW). According to the causal structure detected by the inductive causation (IC) algorithm, it can be concluded that OLSB, as a parent trait, had indirect causal effects on OLWW, as a composite reproductive trait, mediated via both OLSW and OLWB. AFL had no phenotypic causal impact on the lifetime reproductive traits of Moghani ewes but was negatively associated with these traits in terms of additive genetic effects.

Phenotypic causal networks between boar taint compounds measured in biopsies and carcasses

Context Boar taint compounds (androstenone, skatole and indole) can be measured in pig carcasses, after slaughter or, alternatively, in biopsies of subcutaneous adipose tissue from selected living pigs. Measuring these compounds via biopsy enables data collection in selected animals and high standardisation regarding tissue-collection procedures for phenotyping. Because different analytical methods can be used to measure boar taint compounds, it is important to better understand the relationship between boar taint compounds measured in biopsies and in carcasses. Aims This research aimed to identify the causal relationship and causal effects among boar taint compounds (androstenone, skatole and indole) measured in pig adipose tissue from carcasses and biopsies. Methods The concentrations of androstenone (AC), skatole (SC) and indole (IC) measured in adipose tissue from pig carcasses and the concentrations of androstenone (AB), skatole (SB) and indole (IB) measured in biopsies were used to fit a multi-trait Structural Equation Model (SEM) considering causal network graphs obtained via inductive causation algorithm with or without a priori information. Models were compared using the deviance information criterion (DIC). Key results The best DIC was obtained in a model with a causal structure built using a priori information; however, this model was considered inappropriate, because it returned several null genetic correlations among traits described as positively correlated. The best structure returned using only inductive causation algorithm was IB → SC ← AB ← AC ← SB: SC → IC, which was obtained with an 80–70% high-probability distribution interval. This model returned positive genetic correlations and improved goodness-of-fit compared with the multi-trait model in all cases. Several causal relationships among boar taint compounds in carcasses and biopsies were identified. Conclusion Boar taint compounds measured in biopsies have direct effects on boar taint compounds measured in carcasses. Implications Knowledge concerning the causal structure of boar taint compounds may be used in breeding programs, helping in the formulation of selection indexes and improving the ability for prediction and selection of this complex trait (boar taint).

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

BackgroundKnowledge 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.MethodsPhenotypic 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.ResultsIn 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.ConclusionsOur 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 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).

Inferring phenotypic causal networks for tick infestation, Babesia bovis infection, and weight gain in Hereford and Braford cattle using structural equation models

Tick infestation and associated diseases (i.e., babesiosis) constitute major drawbacks for improvement of beef cattle productivity in the tropics, mainly when purebred and crossbred taurine animals are used. Host-parasite-pathogen interactions form complex biological systems that are poorly understood and which significantly affect production and quality traits in ways yet to be dissected and described. This research was carried out to investigate potential causal relationships, through the use of structural equation modeling (SEM), among tick counts (TC), Babesia bovis infection level (IB) and the gains in weight: from birth to adjusted weaning age (WG), and from weaning to yearling (YG). Statistical analyses were conducted in three steps: 1) Partition of (co)variances into genetic and residual components using Bayesian multiple-trait modeling (MTM); of 2) Search for plausible causal structures by applying the inductive causation (IC) algorithm to the residual (co)variances obtained in the first step; and 3) Final analysis using SEM, which was based on the causal network learned from the IC algorithm. The most plausible results comprised three direct links between traits: WG→YG, TC→WG, and WG→IB with structural coefficients posterior means equal to -0.3026, 6.3620, and 0.0004, respectively. The final inferred directed acyclic graph (DAG) suggests that interventions on TC would directly affect WG, which would then affected YG; moreover, WG could also present a small positive effect on IB.

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.

Actionable knowledge discovery from social networks using causal structures of structural features

Knowledge discovery and data mining provide an array of solutions for real-world problems. When facing business requirements, the ultimate goal of knowledge discovery is not the knowledge itself but rather making the gained knowledge practical. Consequently, the models and patterns found by the mining methods often require post-processing. To this end, actionable knowledge discovery has been introduced which is developed to extract actionable knowledge from data. The output of actionable knowledge discovery is a set of actions that help the domain expert to gain the desired outcome. Such a process where a set of actions are extracted is called action extraction. One of the challenges of action extraction is to incorporate causal dependencies among the variables to find actions with higher effectiveness compared to when no such dependencies are used. The goal of this paper is to dive into the lesser studied subject of “action discovery in social networks” and intends to extract actions by utilizing the casual structures discovered from such data. Furthermore, in order to capture the underlying information within a social network, we extract the corresponding structural features. We propose a method called SF-ICE-CREAM (Social Features included Inductive Causation Enabled Causal Relationship-based Economical Action Mining) to overcome the challenges introduced above. This method uses structural features to find the underlying causal structures within a social network and incorporates them into the action extraction process.

Including Phenotypic Causal Networks in Genome-Wide Association Studies Using Mixed Effects Structural Equation Models.

Network based statistical models accounting for putative causal relationships among multiple phenotypes can be used to infer single-nucleotide polymorphism (SNP) effect which transmitting through a given causal path in genome-wide association studies (GWAS). In GWAS with multiple phenotypes, reconstructing underlying causal structures among traits and SNPs using a single statistical framework is essential for understanding the entirety of genotype-phenotype maps. A structural equation model (SEM) can be used for such purposes. We applied SEM to GWAS (SEM-GWAS) in chickens, taking into account putative causal relationships among breast meat (BM), body weight (BW), hen-house production (HHP), and SNPs. We assessed the performance of SEM-GWAS by comparing the model results with those obtained from traditional multi-trait association analyses (MTM-GWAS). Three different putative causal path diagrams were inferred from highest posterior density (HPD) intervals of 0.75, 0.85, and 0.95 using the inductive causation algorithm. A positive path coefficient was estimated for BM → BW, and negative values were obtained for BM → HHP and BW → HHP in all implemented scenarios. Further, the application of SEM-GWAS enabled the decomposition of SNP effects into direct, indirect, and total effects, identifying whether a SNP effect is acting directly or indirectly on a given trait. In contrast, MTM-GWAS only captured overall genetic effects on traits, which is equivalent to combining the direct and indirect SNP effects from SEM-GWAS. Although MTM-GWAS and SEM-GWAS use the similar probabilistic models, we provide evidence that SEM-GWAS captures complex relationships in terms of causal meaning and mediation and delivers a more comprehensive understanding of SNP effects compared to MTM-GWAS. Our results showed that SEM-GWAS provides important insight regarding the mechanism by which identified SNPs control traits by partitioning them into direct, indirect, and total SNP effects.

On the changing structure among Chinese equity markets: Hong Kong, Shanghai, and Shenzhen

This study investigates information discovery among five Chinese equity markets measured daily over the period 1995–2014. We employ time series methods for finding structural breaks (if any) and uncovering both short-run and long-run fluctuations. We apply a new algorithm of inductive causation for use with non-Gaussian data to study the information flows in contemporaneous time. The empirical results show that there are four break dates and that the underlying causal models changed over our study period. The Shanghai A-share market dominates the other markets in the most recent period.

Inferring causal structures and comparing the causal effects among calving difficulty, gestation length and calf size in Japanese Black cattle

The objectives of this study were to infer phenotypic causal networks involving gestation length (GL) and calving difficulty (CD) for the primiparity of 1850 Japanese Black heifers, and the birth weight (BWT), withers height (WH) and chest girth (CHG) of their full blood calves, and to compare the causal effects among them. The inductive causation (IC) algorithm was employed to search for causal links among these traits; it was applied to the posterior distribution of the residual (co)variance matrix of a multiple-trait sire-maternal grand sire (MGS) model. The IC algorithm implemented with 95% and 90% highest posterior density intervals detected only one structure with links between GL and BWT (WH or CHG) and between BWT (WH or CHG) and CD, although their directions were not resolved. Therefore, a possible causal structure based on the networks obtained from the IC algorithm [GL→BWT (WH or CHG)→CD] was fitted using a structural equation model to infer causal structure coefficients between the traits. The structural coefficients of GL on BWT and of BWT on GL on the observable scale showed that an extra day of GL led to a 270-g gain in BWT, and a 1-kg increase in BWT increased the risk for dystocia by 1.1%, in the causal structure. Similarly, an increase in GL by 1 day resulted in a 2.1 (2.0)-mm growth in WH (CHG), and a 1-cm increase in WH (CHG) increased the risk of dystocia by 1.2% (0.9%). The structural equation model was also fitted to alternative causal structures, which involved the addition of a directed link from GL to CD, or GL→CD to the structures described above. The inferred structural coefficients with the alternative structures were almost the same as the corresponding ones that had GL→BWT (WH or CHG)→CD. However, the direct causal effect of the extra link from GL on CD was similar to the indirect causal effect of GL through the mediating effect of BWT (WH or CHG) on CD and significant (P<0.05). This suggest that maternal genetic effects might not be removed completely from the residual variance components in the sire-MGS model, and the application of the IC algorithm to the variances from the model could detect an incorrect structure. Nonetheless, fitting the structural equation model to the causal structure provided useful information such as the magnitude of the causal effects between the traits.

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.

Algorithms of causal inference for the analysis of effective connectivity among brain regions.

In recent years, powerful general algorithms of causal inference have been developed. In particular, in the framework of Pearl’s causality, algorithms of inductive causation (IC and IC*) provide a procedure to determine which causal connections among nodes in a network can be inferred from empirical observations even in the presence of latent variables, indicating the limits of what can be learned without active manipulation of the system. These algorithms can in principle become important complements to established techniques such as Granger causality and Dynamic Causal Modeling (DCM) to analyze causal influences (effective connectivity) among brain regions. However, their application to dynamic processes has not been yet examined. Here we study how to apply these algorithms to time-varying signals such as electrophysiological or neuroimaging signals. We propose a new algorithm which combines the basic principles of the previous algorithms with Granger causality to obtain a representation of the causal relations suited to dynamic processes. Furthermore, we use graphical criteria to predict dynamic statistical dependencies between the signals from the causal structure. We show how some problems for causal inference from neural signals (e.g., measurement noise, hemodynamic responses, and time aggregation) can be understood in a general graphical approach. Focusing on the effect of spatial aggregation, we show that when causal inference is performed at a coarser scale than the one at which the neural sources interact, results strongly depend on the degree of integration of the neural sources aggregated in the signals, and thus characterize more the intra-areal properties than the interactions among regions. We finally discuss how the explicit consideration of latent processes contributes to understand Granger causality and DCM as well as to distinguish functional and effective connectivity.

Does Agriculture Really Matter for Economic Growth in Developing Countries?

This paper revisits the debate on the role of agriculture in promoting economic growth in a selection of nine developing countries. We investigated the causal linkages between agriculture and gross domestic product growth with the aid of directed acyclic graphs, a recently developed algorithm of inductive causation. The results suggest that while agriculture could be an engine of economic growth, the impact varies across countries. In some cases, we found strong evidence in support of the agriculture‐led growth hypothesis. In contrast, the results for some other countries indicate that having a vibrant aggregate economy is a prerequisite for agricultural development.

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

BackgroundKnowledge regarding causal relationships among traits is important to understand complex biological systems. Structural equation models (SEM) can be used to quantify the causal relations between traits, which allow prediction of outcomes to interventions applied to such a network. Such models are fitted conditionally on a causal structure among traits, represented by a directed acyclic graph and an Inductive Causation (IC) algorithm can be used to search for causal structures. The aim of this study was to explore the space of causal structures involving bovine milk fatty acids and to select a network supported by data as the structure of a SEM.ResultsThe IC algorithm adapted to mixed models settings was applied to study 14 correlated bovine milk fatty acids, resulting in an undirected network. The undirected pathway from C4:0 to C12:0 resembled the de novo synthesis pathway of short and medium chain saturated fatty acids. By using prior knowledge, directions were assigned to that part of the network and the resulting structure was used to fit a SEM that led to structural coefficients ranging from 0.85 to 1.05. The deviance information criterion indicated that the SEM was more plausible than the multi-trait model.ConclusionsThe IC algorithm output pointed towards causal relations between the studied traits. This changed the focus from marginal associations between traits to direct relationships, thus towards relationships that may result in changes when external interventions are applied. The causal structure can give more insight into underlying mechanisms and the SEM can predict conditional changes due to such interventions.

Searching for phenotypic causal networks involving complex traits: an application to European quail

BackgroundStructural equation models (SEM) are used to model multiple traits and the casual links among them. The number of different causal structures that can be used to fit a SEM is typically very large, even when only a few traits are studied. In recent applications of SEM in quantitative genetics mixed model settings, causal structures were pre-selected based on prior beliefs alone. Alternatively, there are algorithms that search for structures that are compatible with the joint distribution of the data. However, such a search cannot be performed directly on the joint distribution of the phenotypes since causal relationships are possibly masked by genetic covariances. In this context, the application of the Inductive Causation (IC) algorithm to the joint distribution of phenotypes conditional to unobservable genetic effects has been proposed.MethodsHere, we applied this approach to five traits in European quail: birth weight (BW), weight at 35 days of age (W35), age at first egg (AFE), average egg weight from 77 to 110 days of age (AEW), and number of eggs laid in the same period (NE). We have focused the discussion on the challenges and difficulties resulting from applying this method to field data. Statistical decisions regarding partial correlations were based on different Highest Posterior Density (HPD) interval contents and models based on the selected causal structures were compared using the Deviance Information Criterion (DIC). In addition, we used temporal information to perform additional edge orienting, overriding the algorithm output when necessary.ResultsAs a result, the final causal structure consisted of two separated substructures: BW→AEW and W35→AFE→NE, where an arrow represents a direct effect. Comparison between a SEM with the selected structure and a Multiple Trait Animal Model using DIC indicated that the SEM is more plausible.ConclusionsCoupling prior knowledge with the output provided by the IC algorithm allowed further learning regarding phenotypic causal structures when compared to standard mixed effects SEM applications.

Searching for Recursive Causal Structures in Multivariate Quantitative Genetics Mixed Models

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

Structural change and international stock market interdependence: Evidence from Asian emerging markets

This study investigates the evolving pattern of the interdependence among selected Asian emerging markets and three major stock markets (Japan, UK and US). Using rolling cointegration methods and the recently developed algorithms of inductive causation, we found that time-varying cointegration relationships exist among these stock markets. The results indicate that the wave of financial liberalization policies in the early 1990s led to a significant increase in market linkages which was later weakened during the 1997 Asian financial crisis. Furthermore, the data indicate that Japan and the US have the greatest influence on the emerging markets while the influence of Singapore and Thailand has increased since the Asian financial crisis.