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Home / Equine Research Bank / J Anim Breed Genet / Bayesian Recursive and Structural Equation Models to Infer C...
Journal of animal breeding and genetics = Zeitschrift fur Tierzuchtung und Zuchtungsbiologie2024; doi: 10.1111/jbg.12919

Bayesian Recursive and Structural Equation Models to Infer Causal Links Among Gait Visual Scores on Campolina Horses.

Abstract: Gait visual scores are widely applied to horse breeding because they are a fast and easy phenotyping strategy, allowing the numeric interpretation of a complex biological process such as gait quality. However, they may suffer from subjectivity or high environmental influence. We aimed to investigate potential causal relationships among six visual gait scores in Campolina horses. The data included 5475 horses with records for at least one of the following traits: Dissociation (Di), Comfort (C), Style (S), Regularity (R), Development (De), and Gait total Scores (GtS). The pedigree comprised three generations with 14,079 horses in the additive relationship matrix. Under a Bayesian framework, (co)variance components were estimated through a multitrait animal model (MTM). Then, the inductive causation algorithm (IC) was applied to the residual (co)variance matrix samples. The resulting undirected graph from IC was directed in 6 possible causal structures, each fitted by a structural equation model. The final causal structure was chosen based on deviance information criteria (DIC). It was found that S significantly impacts the causal network of gait, directly and indirectly affecting C. The indirect causal effect of S on C was through the direct effect of S on De, then the direct effect of De on R, and finally, the direct effect of R on C. Di was caused by S, which is the reason for the genetic correlation between Di and GtS, due to causal effects being added to the model, they absorb the genetic correlation between Di and GtS. Those paths have biological meaning to horse movements and can help breeders and researchers better understand horses' complex causal network of gait.
© 2024 The Author(s). Journal of Animal Breeding and Genetics published by John Wiley & Sons Ltd.
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Publication Date: 2024-12-19 PubMed ID: 39698947DOI: 10.1111/jbg.12919Google Scholar: Lookup
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  • Journal Article

Summary

This research summary has been generated with artificial intelligence and may contain errors and omissions. Refer to the original study to confirm details provided. Submit correction.

This study investigates the causal relationships among six behaviour traits related to horse gait using a Bayesian framework in Campolina horses, with the intent to help breeders make better decisions and understand the complexity of horse movement.

Objective and Methods

  • The research aimed to study the possible causal relationships among six visual gait scores: Dissociation (Di), Comfort (C), Style (S), Regularity (R), Development (De), and Gait total Scores (GtS) in Campolina horses which are important indicators in horse breeding.
  • The data for this study included 5475 horses that had records for at least one of the mentioned traits. The pedigree comprised three generations with 14,079 horses in the additive relationship matrix.
  • The researchers applied a Bayesian framework and used a multitrait animal model to estimate the (co)variance components. After this, they applied the inductive causation algorithm to the residual (co)variance matrix samples.
  • Then, the undirected graph resulting from the Inductive causation algorithm was directed into 6 possible causal structures. Each of these structures was fitted into a structural equation model.
  • The final causal structure was chosen based on the deviance information criteria (DIC).

Findings

  • Among the many findings, one key discovery was that the “Style” trait significantly impacted the horse’s gait network, both directly and indirectly impacting the “Comfort” trait.
  • The indirect effect of “Style” on “Comfort” was through its direct impact on “Development”, which directly affected “Regularity”, which in turn had a direct impact on “Comfort”.
  • It was discovered that “Dissociation” was caused by “Style”, which explained why a genetic correlation was found between “Dissociation” and “Gait total Scores”.
  • The addition of causal effects to the model effectively absorbed the genetic correlation between “Dissociation” and “Gait total Scores”.
  • The research deduced that the paths established through the study gave a biological context to horse movements and would assist breeders and researchers in better understanding the causal network of horse gait.

Implications

  • These findings offer valuable insights into horse breeding strategies as they allow numeric interpretation of complex processes like the quality of gait. In turn, this could lead to more informed decisions in the breeding process, helping improve different aspects of horse gait.
  • The results also provide a better understanding of horse gait from a biological perspective, which could be instrumental for veterinary studies and animal research.
  • The Bayesian framework and the associated methodologies used in the study could be utilized for similar research in other animal species, making it valuable for the wider animal research and breeding community.

Cite This Article

APA
Bussiman F, Richter J, Hidalgo J, Silva FFE, Ventura RV, Carvalho RSB, Mattos EC, Ferraz JBS, Eler JP, de Carvalho Balieiro JC. (2024). Bayesian Recursive and Structural Equation Models to Infer Causal Links Among Gait Visual Scores on Campolina Horses. J Anim Breed Genet. https://doi.org/10.1111/jbg.12919

Publication

Journal of animal breeding and genetics = Zeitschrift fur Tierzuchtung und Zuchtungsbiologie
ISSN: 1439-0388
NlmUniqueID: 100955807
Country: Germany
Language: English

Researcher Affiliations

Bussiman, Fernando
  • Animal Nutrition and Production Department, University of São Paulo, Pirassununga, São Paulo, Brazil.
  • Animal and Dairy Science Department, University of Georgia, Athens, Georgia, USA.
Richter, Jennifer
  • Animal and Dairy Science Department, University of Georgia, Athens, Georgia, USA.
Hidalgo, Jorge
  • Animal and Dairy Science Department, University of Georgia, Athens, Georgia, USA.
Silva, Fabyano Fonseca E
  • Animal Science Department, Federal University of Viçosa, Viçosa, Minas Gerais, Brazil.
Ventura, Ricardo Vieira
  • Animal Nutrition and Production Department, University of São Paulo, Pirassununga, São Paulo, Brazil.
Carvalho, Rachel Santos Bueno
  • Basic Sciences Department, University of São Paulo, Pirassununga, São Paulo, Brazil.
Mattos, Elisângela Chicaroni
  • Veterinary Medicine Department, University of São Paulo, Pirassununga, São Paulo, Brazil.
Ferraz, José Bento Sterman
  • Veterinary Medicine Department, University of São Paulo, Pirassununga, São Paulo, Brazil.
Eler, Joanir Pereira
  • Veterinary Medicine Department, University of São Paulo, Pirassununga, São Paulo, Brazil.
de Carvalho Balieiro, Júlio Cesar
  • Animal Nutrition and Production Department, University of São Paulo, Pirassununga, São Paulo, Brazil.

Grant Funding

  • 2018/26465-3 / Fundau00e7u00e3o de Amparo u00e0 Pesquisa do Estado de Su00e3o Paulo
  • 001 / Coordenau00e7u00e3o de Aperfeiu00e7oamento de Pessoal de Nu00edvel Superior

References

This article includes 86 references
  1. ABCCCampolina. Regulamento do Serviço de Registro Genealógico do cavalo Campolina—SRGCC 212028.006084/2017–11 No. 39/2018/SMA. p 1–28.
  2. Alexander RM. The Gaits of Bipedal and Quadrupedal Animals. International Journal of Robotics Research 3, no. 2: 49–59.
    doi: 10.1177/027836498400300205google scholar: lookup
  3. Árnason T. Breeding in horses. Sustainable Food Production 401–416.
  4. Árnason T, Van Vleck LD. Genetic Improvement of the Horse. The Genetics of the Horse 473–498.
  5. Bartolomé E, Menéndez‐Buxadera A, Molina A, Valera M. Plasticity Effect of Rider‐Horse Interaction on Genetic Evaluations for Show Jumping Discipline in Sport Horses. Journal of Animal Breeding and Genetics 135, no. 2: 138–148.
    doi: 10.1111/jbg.12315google scholar: lookup
  6. Bello NM, Renter DG. Invited Review: Reproducible Research From Noisy Data: Revisiting Key Statistical Principles for the Animal Sciences. Journal of Dairy Science 101, no. 7: 5679–5701.
    doi: 10.3168/jds.2017‐13978google scholar: lookup
  7. Boligon AA, Albuquerque LG, Mercadante MEZ, Lôbo RB. Herdabilidades e correlações entre pesos do nascimento à idade adulta em rebanhos da raça Nelore. Revista Brasileira de Zootecnia 38, no. 12: 2320–2326.
    doi: 10.1590/s1516‐35982009001200005google scholar: lookup
  8. Bouwman AC, Valente BD, Janss LLG, Bovenhuis H, Rosa GJM. Exploring Causal Networks of Bovine Milk Fatty Acids in a Multivariate Mixed Model Context. Genetics, Selection, Evolution 46, no. 1: 2.
    doi: 10.1186/1297‐9686‐46‐2google scholar: lookup
  9. Brown TA. Confirmatory Factor Analysis for Applied Research. 2nd ed.
  10. Bussiman FDO, Carvalho RSB, Silva FFE. Reduced Rank Analysis of Morphometric and Functional Traits in Campolina Horses. Journal of Animal Breeding and Genetics 139, no. 2: 231–246.
    doi: 10.1111/jbg.12658google scholar: lookup
  11. Bussiman FDO, Santos BAD, Abreu Silva BDC. Genome‐Wide Association Study: Understanding the Genetic Basis of the Gait Type in Brazilian Mangalarga Marchador Horses, a Preliminary Study. Livestock Science 231: 103867.
    doi: 10.1016/j.livsci.2019.103867google scholar: lookup
  12. Bussiman FO, Ferraz JBS, Eler JP, Mattos EC, Ventura RV, Balieiro JCC. Análise de Componentes Principais e Resposta à Seleção em características de andamento em cavalos Campolina. In: XIV Simpósio de Pós‐Graduação e Pesquisa em Nutrição e Produção Animal, Pirassununga.
  13. Bussiman FO, Perez BC, Ventura RV. Genetic Analysis of Morphological and Functional Traits in Campolina Horses Using Bayesian Multi‐Trait Model. Livestock Science 216: 119–129.
    doi: 10.1016/j.livsci.2018.08.002google scholar: lookup
  14. Cavani L, Lopes FB, Giglioti R. Inferring Phenotypic Causal Networks for Tick Infestation, Babesia Bovis Infection, and Weight Gain in Hereford and Braford Cattle Using Structural Equation Models. Livestock Science 238: 104032.
    doi: 10.1016/j.livsci.2020.104032google scholar: lookup
  15. Cervantes I, Gutiérrez JP, García‐Ballesteros S, Varona L. Combining Threshold, Thurstonian and Classical Linear Models in Horse Genetic Evaluations for Endurance Competitions. Animals 10, no. 6: 1075.
    doi: 10.3390/ani10061075google scholar: lookup
  16. Chitakasempornkul K, Meneget MB, Rosa GJM. Investigating Causal Biological Relationships Between Reproductive Performance Traits in High‐Performing Gilts and Sows. Journal of Animal Science 97, no. 6: 2385–2401.
    doi: 10.1093/jas/skz115google scholar: lookup
  17. Chitakasempornkul K, Rosa GJM, Jager A, Bello NM. Hierarchical Modeling of Structural Coefficients for Heterogeneous Networks With an Application to Animal Production Systems. Journal of Agricultural, Biological and Environmental Statistics 25, no. 4: 1–22.
    doi: 10.1007/s13253‐020‐00389‐0google scholar: lookup
  18. Clayton HM, Hobbs SJ. An Exploration of Strategies Used by Dressage Horses to Control Moments Around the Center of Mass When Performing Passage. PeerJ 5: e3866.
    doi: 10.7717/peerj.3866google scholar: lookup
  19. Clayton HM, Hobbs SJ. A Review of Biomechanical Gait Classification With Reference to Collected Trot, Passage and Piaffe in Dressage Horses. Animals 9, no. 10: 763.
    doi: 10.3390/ani9100763google scholar: lookup
  20. Cruz AM, Vidondo B, Ramseyer AA, Maninchedda UE. Effect of Trotting Speed on Kinematic Variables Measured by Use of Extremity‐Mounted Inertial Measurement Units in Nonlame Horses Performing Controlled Treadmill Exercise. American Journal of Veterinary Research 79, no. 2: 211–218.
    doi: 10.2460/ajvr.79.2.211google scholar: lookup
  21. de los Campos G, Gianola D, Boettcher P, Moroni P. A Structural Equation Model for Describing Relationships Between Somatic Cell Score and Milk Yield in Dairy goats1. Journal of Animal Science 84, no. 11: 2934–2941.
    doi: 10.2527/jas.2006‐016google scholar: lookup
  22. de los Campos G, Gianola D, Heringstad B. A Structural Equation Model for Describing Relationships Between Somatic Cell Score and Milk Yield in First‐Lactation Dairy Cows. Journal of Dairy Science 89, no. 11: 4445–4455.
    doi: 10.3168/jds.s0022‐0302(06)72493‐6google scholar: lookup
  23. de Maturana EL, Wu XL, Gianola D, Weigel KA, Rosa GJM. Exploring Biological Relationships Between Calving Traits in Primiparous Cattle With a Bayesian Recursive Model. Genetics 181, no. 1: 277–287.
    doi: 10.1534/genetics.108.094888google scholar: lookup
  24. Dunbar DC, Macpherson JM, Simmons RW, Zarcades A. Stabilization and Mobility of the Head, Neck and Trunk in Horses During Overground Locomotion: Comparisons With Humans and Other Primates. Journal of Experimental Biology 211, no. 24: 3889–3907.
    doi: 10.1242/jeb.020578google scholar: lookup
  25. Fonseca MG, Ferraz GC, Lage J, Pereira GL, Curi RA. A Genome‐Wide Association Study Reveals Differences in the Genetic Mechanism of Control of the Two Gait Patterns of the Brazilian Mangalarga Marchador Breed. Journal of Equine Veterinary Science 53: 64–67.
    doi: 10.1016/j.jevs.2016.01.015google scholar: lookup
  26. Geweke J. Evaluating the Accuracy of Sampling‐Based Approaches to the Calculation of Posterior Moments. Bayesian Statistics 4: 169–193.
  27. Gianola D, Sorensen D. Quantitative Genetic Models for Describing Simultaneous and Recursive Relationships Between Phenotypes. Genetics 167, no. 3: 1407–1424.
    doi: 10.1534/genetics.103.025734google scholar: lookup
  28. Haavelmo T. The Statistical Implications of a System of Simultaneous Equations. Econometrica 11, no. 1: 1.
    doi: 10.2307/1905714google scholar: lookup
  29. Heidelberger P, Welch PD. Simulation Run Length Control in the Presence of an Initial Transient. Operations Research 31, no. 6: 1109–1144.
    doi: 10.1287/opre.31.6.1109google scholar: lookup
  30. Henderson CR. Rapid Method for Computing the Inverse of a Relationship Matrix. Journal of Dairy Science 58, no. 11: 1727–1730.
    doi: 10.3168/jds.s0022‐0302(75)84776‐xgoogle scholar: lookup
  31. Heringstad B, Wu XL, Gianola D. Inferring Relationships Between Health and Fertility in Norwegian Red Cows Using Recursive Models. Journal of Dairy Science 92, no. 4: 1778–1784.
    doi: 10.3168/jds.2008‐1535google scholar: lookup
  32. Hobbs SJ, Bertram JEA, Clayton HM. An Exploration of the Influence of Diagonal Dissociation and Moderate Changes in Speed on Locomotor Parameters in Trotting Horses. PeerJ 4: e2190.
    doi: 10.7717/peerj.2190google scholar: lookup
  33. Hobbs SJ, Richards J, Clayton HM. The Effect of Centre of Mass Location on Sagittal Plane Moments Around the Centre of Mass in Trotting Horses. Journal of Biomechanics 47, no. 6: 1278–1286.
    doi: 10.1016/j.jbiomech.2014.02.024google scholar: lookup
  34. Ibáñez‐Escriche N, López de Maturana E, Noguera JL, Varona L. An Application of Change‐Point Recursive Models to the Relationship Between Litter Size and Number of Stillborns in Pigs. Journal of Animal Science 88, no. 11: 3493–3503.
    doi: 10.2527/jas.2009‐2557google scholar: lookup
  35. Inoue K. Application of Bayesian Causal Inference and Structural Equation Model to Animal Breeding. Animal Science Journal 91: e13359.
    doi: 10.1111/asj.13359google scholar: lookup
  36. Inoue K, Valente BD, Shoji N, Honda T, Oyama K, Rosa GJM. Inferring Phenotypic Causal Structures Among Meat Quality Traits and the Application of a Structural Equation Model in Japanese Black Cattle1. Journal of Animal Science 94, no. 10: 4133–4142.
    doi: 10.2527/jas.2016‐0554google scholar: lookup
  37. Jamrozik J, Schaeffer LR. Recursive Relationships Between Milk Yield and Somatic Cell Score of Canadian Holsteins From Finite Mixture Random Regression Models. Journal of Dairy Science 93, no. 11: 5474–5486.
    doi: 10.3168/jds.2010‐3470google scholar: lookup
  38. Legarra A, Reverter A. Semi‐Parametric Estimates of Population Accuracy and Bias of Predictions of Breeding Values and Future Phenotypes Using the LR Method. Genetics, Selection, Evolution 50, no. 1: 53.
    doi: 10.1186/s12711‐018‐0426‐6google scholar: lookup
  39. McGhee R, Frank A. On the Stability Properties of Quadruped Creeping Gaits. Bellman Prize in Mathematical Biosciences 3: 331–351.
  40. Meyer K. Estimates of Genetic Parameters for Mature Weight of Australian Beef Cows and Its Relationship to Early Growth and Skeletal Measures. Livestock Production Science 44, no. 2: 125–137.
    doi: 10.1016/0301‐6226(95)00067‐4google scholar: lookup
  41. Meyer K. Genetic Principal Components for Live Ultrasound Scan Traits of Angus Cattle. Animal Science 81, no. 3: 337–345.
    doi: 10.1079/asc50850337google scholar: lookup
  42. Misztal I, Tsuruta S, Strabel T, Auvray B, Druet T, Lee DH. BLUPF90 and Related Programs (BGF90). In: Proceedings of the 7th World Congress on Genetics Applied to Livestock Production. p 21‐22.
  43. Molina A, Valera M, Dos Santos R, Rodero A. Genetic Parameters of Morphofunctional Traits in Andalusian Horse. Livestock Production Science 60, no. 2–3: 295–303.
    doi: 10.1016/s0301‐6226(99)00101‐3google scholar: lookup
  44. Molina A, Valera M, Galisteo AMM. Genetic Parameters of Biokinematic Variables at Walk in the Spanish Purebred (Andalusian) Horse Using Experimental Treadmill Records. Livestock Science 116, no. 1–3: 137–145.
    doi: 10.1016/j.livsci.2007.09.021google scholar: lookup
  45. Momen M, Ayatollahi Mehrgardi A, Amiri Roudbar M. Including Phenotypic Causal Networks in Genome‐Wide Association Studies Using Mixed Effects Structural Equation Models. Frontiers in Genetics 9, no. 455: 1–11.
    doi: 10.3389/fgene.2018.00455google scholar: lookup
  46. Nascimento CAMS, Gonzaga IVF, Santiago JM. Participation Frequency and Performance of Horses in National Shows of Campolina and Mangalarga Marchador Breeds. Revista Brasileira de Zootecnia 48, no. e20190078: 1–9.
    doi: 10.1590/rbz4820190078google scholar: lookup
  47. Nicodemus MC, Clayton HM. Temporal Variables of Four‐Beat, Stepping Gaits of Gaited Horses. Applied Animal Behaviour Science 80, no. 1: 133–142.
  48. Pearl J. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. 2nd ed.
  49. Pearl J. Causality: Models, Reasoning and Inference. 2nd ed.
  50. Peñagaricano F, Valente BD, Steibel JP. Searching for Causal Networks Involving Latent Variables in Complex Traits: Application to Growth, Carcass, and Meat Quality Traits in Pigs. Journal of Animal Science 93, no. 10: 4617–4623.
    doi: 10.2527/jas.2015‐9213google scholar: lookup
  51. Procópio AM, Bergmann JAG, Costa MD. Formação e demografia da raça Campolina. Arquivo Brasileiro de Medicina Veterinária e Zootecnia 55, no. 3: 361–365.
    doi: 10.1590/s0102‐09352003000300018google scholar: lookup
  52. R Core Team. R: A Language and Environment for Statistical Computing R Foundation for Statistical Computing. Vol. 1, 409.
  53. Raftery AE, Lewis S. How Many Iterations in the Gibbs Sampler?. Bayesian Statistics 763–773.
  54. Raftery AE, Madigan D, Hoeting JA. Bayesian Model Averaging for Linear Regression Models. Journal of the American Statistical Association 92, no. 437: 179–191.
    doi: 10.1080/01621459.1997.10473615google scholar: lookup
  55. Ricard A, Legarra A. Validation of Models for Analysis of Ranks in Horse Breeding Evaluation. Genetics, Selection, Evolution 42, no. 1: 3.
    doi: 10.1186/1297‐9686‐42‐3google scholar: lookup
  56. Robert C, Valette JP, Pourcelot P, Audigié F, Denoix JM. Effects of Trotting Speed on Muscle Activity and Kinematics in Saddlehorses. Equine Veterinary Journal 34, no. S34: 295–301.
    doi: 10.1111/j.2042‐3306.2002.tb05436.xgoogle scholar: lookup
  57. Robilliard JJ, Pfau T, Wilson AM. Gait Characterisation and Classification in Horses. Journal of Experimental Biology 210, no. 2: 187–197.
    doi: 10.1242/jeb.02611google scholar: lookup
  58. Rosa GJM, Valente BD. Structural Equation Models for Studying Causal Phenotype Networks in Quantitative Genetics. In Probabilistic Graphical Models for Genetics, Genomics, and Postgenomics.
  59. Rosa GJM, Valente BD, de los Campos G, Wu XL, Gianola D, Silva MA. Inferring Causal Phenotype Networks Using Structural Equation Models. Genetics, Selection, Evolution 43, no. 1: 6.
    doi: 10.1186/1297‐9686‐43‐6google scholar: lookup
  60. Ruina A, Bertram JEA, Srinivasan M. A Collisional Model of the Energetic Cost of Support Work Qualitatively Explains Leg Sequencing in Walking and Galloping, Pseudo‐Elastic Leg Behavior in Running and the Walk‐To‐Run Transition. Journal of Theoretical Biology 237, no. 2: 170–192.
    doi: 10.1016/j.jtbi.2005.04.004google scholar: lookup
  61. Rustin M, Janssens S, Buys N, Gengler N. Multi‐Trait Animal Model Estimation of Genetic Parameters for Linear Type and Gait Traits in the Belgian Warmblood Horse. Journal of Animal Breeding and Genetics 126, no. 5: 378–386.
    doi: 10.1111/j.1439‐0388.2008.00798.xgoogle scholar: lookup
  62. Schumacker RE, Lomax RG. A Beginner's Guide to Structural Equation Modeling. 4th ed.
  63. Serra Bragança FM, Broomé S, Rhodin M. Improving Gait Classification in Horses by Using Inertial Measurement Unit (IMU) Generated Data and Machine Learning. Scientific Reports 10, no. 1: 17785.
    doi: 10.1038/s41598‐020‐73215‐9google scholar: lookup
  64. Shipley B. Cause and Correlation in Biology: A User's Guide to Path Analysis, Structural Equations and Causal Inference. 1st ed.
  65. Shipley B. From Biological Hypotheses to Structural Equation Models: The Imperfection of Causal Translation. In Structural Equation Modeling, 194–211.
  66. Solé M, Santos R, Molina A, Galisteo A, Valera M. Genetic Analysis of Kinematic Traits at the Trot in Lusitano Horse Subpopulations With Different Types of Training. Animal 8, no. 2: 192–199.
    doi: 10.1017/s1751731113002036google scholar: lookup
  67. Spiegelhalter DJ, Best NG, Carlin BP, Van Der Linde A. Bayesian Measures of Model Complexity and Fit. Journal of the Royal Statistical Society, Series B: Statistical Methodology 64, no. 4: 583–616.
    doi: 10.1111/1467‐9868.00353google scholar: lookup
  68. Spiegelhalter DJ, Best NG, Carlin BP, Van der Linde A. The Deviance Information Criterion: 12 Years on. Journal of the Royal Statistical Society, Series B: Statistical Methodology 76, no. 3: 485–493.
    doi: 10.1111/rssb.12062google scholar: lookup
  69. Spirtes P, Glymour C, Scheines R. Causation, Prediction, and Search. 2nd ed.
  70. Thompson R, Meyer K. A Review of Theoretical Aspects in the Estimation of Breeding Values for Multi‐Trait Selection. Livestock Production Science 15, no. 4: 299–313.
    doi: 10.1016/0301‐6226(86)90071‐0google scholar: lookup
  71. Valente BD, de Magalhães Rosa GJ. Mixed Effects Structural Equation Models and Phenotypic Causal Networks. In Genome‐Wide Association Studies and Genomic Prediction, 449–464.
  72. Valente BD, Rosa GJM, de los Campos G, Gianola D, Silva MA. Searching for Recursive Causal Structures in Multivariate Quantitative Genetics Mixed Models. Genetics 185, no. 2: 633–644.
    doi: 10.1534/genetics.109.112979google scholar: lookup
  73. Valente BD, Rosa GJM, Gianola D, Wu XL, Weigel K. Is Structural Equation Modeling Advantageous for the Genetic Improvement of Multiple Traits?. Genetics 194, no. 3: 561–572.
    doi: 10.1534/genetics.113.151209google scholar: lookup
  74. Valente BD, Rosa GJM, Silva MA, Teixeira RB, Torres RA. Searching for Phenotypic Causal Networks Involving Complex Traits: An Application to European Quail. Genetics, Selection, Evolution 43, no. 1: 37.
    doi: 10.1186/1297‐9686‐43‐37google scholar: lookup
  75. van der Werf JHJ, van Arendonk JAM, De Vries AG. Improving Selection of Pigs Using Correlated Characters. In Book of Abstracts of European Federation of Animal Science, Madrid.
  76. Varona L, Legarra A. GIBBSTHUR: Software for Estimating Variance Components and Predicting Breeding Values for Ranking Traits Based on a Thurstonian Model. Animals 10, no. 6: 1001.
    doi: 10.3390/ani10061001google scholar: lookup
  77. Varona L, Sorensen D, Thompson R. Analysis of Litter Size and Average Litter Weight in Pigs Using a Recursive Model. Genetics 177, no. 3: 1791–1799.
    doi: 10.1534/genetics.107.077818google scholar: lookup
  78. Velie BD, Hamilton NA, Wade CM. Heritability of Racing Performance in the Australian Thoroughbred Racing Population. Animal Genetics 46, no. 1: 23–29.
    doi: 10.1111/age.12234google scholar: lookup
  79. Verma TS, Pearl J. Equivalence and Synthesis of Causal Models. In: Proceedings of the 6th Conference on Uncertainty in Artificial Intelligence, Cambridge, pp. 220–227.
  80. Vicente AA, Carolino N, Ralão‐Duarte J, Gama LT. Selection for Morphology, Gaits and Functional Traits in Lusitano Horses: I. Genetic Parameter Estimates. Livestock Science 164, no. 1: 1–12.
    doi: 10.1016/j.livsci.2014.01.020google scholar: lookup
  81. Vicente AA, Carolino N, Ralão‐Duarte J, Gama LT. Selection for Morphology, Gaits and Functional Traits in Lusitano Horses: II. Fixed Effects, Genetic Trends and Selection in Retrospect. Livestock Science 164, no. 1: 13–25.
    doi: 10.1016/j.livsci.2014.03.017google scholar: lookup
  82. Vostry L, Vostrà‐vydrovà H, Hofmanovà B, Veselà Z, Schmidovà J, Majzlik I. Genetic Parameters for Linear Type Traits in Three Czech Draught Horse Breeds. Agriculturae Conspectus Scientificus 82, no. 2: 111–115.
  83. Wanderley EK, Manso Filho HC, Manso HECCC, Santiago TA, McKeever KH. Metabolic Changes in Four Beat Gaited Horses After Field Marcha Simulation. Equine Veterinary Journal 42, no. SUPPL. 38: 105–109.
    doi: 10.1111/j.2042‐3306.2010.00288.xgoogle scholar: lookup
  84. Wright S. Correlation and Causation. Journal of Agriculture Research 201: 557–585.
  85. Wright S. Coefficients of Inbreeding and Relationship. American Naturalist 56, no. 645: 330–338.
  86. Wu XL, Heringstad B, Gianola D. Bayesian Structural Equation Models for Inferring Relationships Between Phenotypes: A Review of Methodology, Identifiability, and Applications. Journal of Animal Breeding and Genetics 127, no. 1: 3–15.
    doi: 10.1111/j.1439‐0388.2009.00835.xgoogle scholar: lookup

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