Novel interpretation of sperm stress test and morphology for maturity assessment of young Norwegian Red bulls.

The use of genomic selection significantly reduces the age of dairy bulls entering semen production compared to progeny testing. The study aimed to identify early indicators that could be used for screening bulls during their performance testing period and could give us insight into their future semen production performance, acceptance for the AI station, and prediction of their future fertility. The study population consisted of 142 young Norwegian Red bulls enrolled at the performance test station, followed until we received semen production data, semen doses, and, subsequently, non-return rates (NR56) from the AI station. A range of semen quality parameters were measured with computer-assisted sperm analysis and flow cytometry from ejaculates collected from 65 bulls (9-13 months). The population morphometry of normal spermatozoa was examined, showing that Norwegian Red bulls at 10 months of age have homogenous sperm morphometry. Norwegian Red bulls could be separated into 3 clusters according to their sperm's reaction patterns to stress test and cryopreservation. Results of semi-automated morphology assessment of young Norwegian Red bulls showed that 42% of bulls rejected for the AI station and 18% of bulls accepted had ejaculates with abnormal morphology scores. For the youngest age group at 10 months, the mean (SD) proportion of spermatozoa with normal morphology was 77.5% (10.6). Using novel interpretation of sperm stress test combined with sperm morphology analysis and consecutive cryopreservation at a young age allowed identification of the candidate's sperm quality status. This could help breeding companies introduce young bulls earlier to the AI stations.

Associations between insulin-like factor 3, scrotal circumference and semen characteristics in young Norwegian Red bulls.

With the integration of genomic selection in the cattle artificial insemination (AI) industry, bulls are selected for their semen production capacity and fertility at a younger age than previously. Norwegian Red bull calves selected as candidates to become future AI bulls based on their genomic breeding value are kept in a performance testing station from around the age of 3-12 months, allowing for sample collection and analysis of different parameters during their pre- and peripubertal period. Insulin-like factor 3 (INSL3) is a small peptide hormone specifically secreted by the mature Leydig cells of the testes. In the foetus, it induces the first phase of testicular descent and is considered to reflect Leydig cell development during puberty; it could therefore be an interesting early indicator of future semen production capacity. The main objective of our study was to evaluate the relationship between INSL3, scrotal circumference (SC), and semen characteristics. This is the first time INSL3 was measured in the Norwegian Red population. We collected blood samples for analysis of INSL3 from 142 Norwegian Red bulls at the performance testing station and measured their SC on the same day. Altogether, measurements were made at four time points: upon arrival at the performance testing station (quarantine (Q): 2-5 months) and later at approximately 6, 9 and 12 months of age. Information on season and place of birth were made available from the database of the breeding company Geno, together with data on semen characteristics from the test station and the AI station. The median SCs for age groups Q, 6, 9, and 12 were 15, 21.5, 29, and 34 cm, respectively. INSL3 was shown to be positively correlated with SC (R = 0.4) but not with any of the semen characteristics. Similarly, we found no correlation between SC and sperm characteristics from data on ejaculates analysed at the performance testing station and AI station. The mean sperm volume for the 31 selected bulls with at least 10 ejaculates produced in the AI station increased from 2.3 ml at the performance testing station to 6.4 ml at the AI station. The corresponding increase in mean sperm concentration was from 497 million/ml to 1 049 million/ml. We conclude that INSL3 exhibits high inter-individual variability in the Norwegian Red bull population, which cannot be explained by the parameters measured in this study. At present, INSL3 cannot be used as a biomarker of sperm production in this breed.

Sperm chromatin integrity and DNA methylation in Norwegian Red bulls of contrasting fertility.

In this study, the complexity of chromatin integrity was investigated in frozen-thawed semen samples from 37 sires with contrasting fertility, expressed as 56-day non-return rates (NR56). Protamine deficiency, thiols, and disulfide bonds were assessed and compared with previously published data for DNA fragmentation index (DFI) and high DNA stainability (HDS). In addition, in vitro embryo development and sperm DNA methylation were assessed using semen samples from 16 of these bulls. The percentages of DFI and HDS were negatively associated with NR56 and cleavage rate and positively associated with sperm protamine deficiency (p < 0.05). Significant differences in cleavage and blastocyst rates were observed between bulls of high and low NR56. However, once fertilization occurred, further development into blastocysts was not associated with NR56. The differential methylation analysis showed that spermatozoa from bulls of low NR56 were hypermethylated compared to bulls of high NR56. Pathway analysis showed that genes annotated to differentially methylated cytosines could participate in different biological pathways and have important biological roles related to bull fertility. In conclusion, sperm cells from Norwegian Red bulls of inferior fertility have less compact chromatin structure, higher levels of DNA damage, and are hypermethylated compared with bulls of superior fertility.

Differences in sperm functionality and intracellular metabolites in Norwegian Red bulls of contrasting fertility.

In the dairy breeding industry, prediction of bull fertility in artificial insemination (AI) is important for efficient and economically sustainable production. However, it is challenging to identify bulls with superior fertility applying conventional in vitro sperm assays. In the present study, sperm functionality was investigated to identify a multivariate model that could predict fertility. Two groups of young Norwegian Red bulls were selected, one with inferior fertility (18 bulls) and one with superior fertility (19 bulls) based on non-return rate after 56 days (NR56). Frozen-thawed semen doses were analysed for sperm chromatin integrity, viability, acrosome integrity, motility, and ATP content. A targeted approach was used to study intracellular concentrations of amino acids and trace elements in viable sperm cells. Significant differences between the two groups of bulls were observed, both for sperm functional attributes and intracellular concentrations of metabolites. Pearson correlation analyses indicated a negative relationship between NR56 and chromatin integrity parameters, DNA fragmentation index (DFI) and high DNA stainability (HDS). Several motility parameters correlated positively with NR56. The concentrations of cysteine and glutamic acid in sperm cells correlated negatively with NR56, while the concentrations of aspartic acid, leucine and serine showed a positive NR56-correlation. The sperm intracellular concentrations of the trace elements Fe, Al and Zn, correlated negatively with NR56. Correlations were observed between several sperm parameters and metabolites. Stepwise multiple regression analysis indicated that the best predictor of NR56 was a model containing %DFI, together with the intracellular sperm concentration of aspartic acid, Fe and Zn. This model explained 59% of the variability in NR56.

Ovarian follicular response to oestrous synchronisation and induction of ovulation in Norwegian Red cattle.

BACKGROUND: Oestrous synchronisation of cattle has been widely applied to accomplish simultaneous ovulation in animals and facilitate timed artificial insemination. The main aim of this study was to investigate the ovarian follicular growth and ovulatory response to oestrus and ovulation synchronisation in Norwegian Red heifers and cows. Oestrous cycles in 34 heifers and 10 cows from 4 herds were synchronised with two PGF2α analogue treatments 11 days apart, followed by GnRH analogue treatment for induction of ovulation. Thereafter, the ovaries were examined by ultrasonography at 3 h intervals until ovulation. RESULTS: The luteolytic effect of the PGF2α analogue was verified in 9 of 10 cows by progesterone contents in milk. Maximum physical activity of the cows occurred on average 69 h after PGF2α analogue treatment. An ovulatory response was recorded in 95.5% (42/44) of the animals. A significant difference in follicle size at ovulation was found between 2 of the herds. Animals with medium sized and large follicles and heifers aged > 16 months ovulated earlier than other animals. CONCLUSIONS: The applied sequence of treatments in the study was shown to be effective in synchronizing and inducing ovulation within a relatively narrow time interval in the Norwegian Red heifers and cows, consistent with findings in other cattle breeds.

Studies of gel with immobilized semen by intrauterine endoscopy post-artificial insemination.

An extended lifespan of spermatozoa following artificial insemination (AI) can make the timing of insemination less critical, as previously demonstrated with immobilized spermatozoa that are gradually released from an alginate gel. The purpose was to examine the in vivo dissolution of SpermVital (SV) alginate gel over time by endoscopy and secondly to assess spermatozoa quality after incubation of the gel. In vivo endoscopy showed SV gel in the uterus 3, 6, 20 and 24 hr after AI, demonstrating the potential release of spermatozoa to the uterus during this period. In utero ex vivo incubation of the semen demonstrated that high motility and viability of sperm cells was sustained following overnight incubation.

Factors associated with milking-to-milking variability in somatic cell counts from healthy cows in an automatic milking system.

Fully automated on-line analysis equipment is available for analysis of somatic cell count (SCC) at every milking in automatic milking systems. In addition to results from on-line cell counters (OCC), an array of additional cow-level and quarter-level factors considered important for udder health are recorded in these systems. However, the amount of variability in SCC that can be explained by available data is unknown, and so is the proportion of the variability that may be due to physiological or normal variability. Our aim was to increase our knowledge on OCC as an indicator for disturbances in udder health by assessing the variability in OCC in cows free from clinical mastitis. The first objective was to evaluate how much of the variability in OCC could be explained by different potential sources of variability, including intramammary infection (IMI) status (assessed by bacterial culture of quarter milk samples). The second objective was to evaluate the repeatability of the OCC sensor used in our study and the agreement between OCC values and SCC measured in a dairy herd improvement (DHI) laboratory. A longitudinal study was performed in the research herd of the Norwegian University of Life Sciences from January 5th 2016 to May 22nd 2017. Data from 62,471 milkings from 173 lactations in 129 cows were analyzed. We used ln-transformed OCC values (in 1000 cells/ml) as the outcome (lnOCC) in linear mixed models, with random intercepts at cow-level and lactation-level within cow. We were able to explain 15.0% of the variability in lnOCC with the following fixed effects: lactation stage, parity, milk yield, OCC in residual milk from the previous milking, inter-quarter difference between the highest and lowest conductivity, season, IMI status, and genetic lineage. When including the random intercepts, the degree of explanation was 55.2%. The individual variables explained only a small part of the total variability in lnOCC. We concluded that physiological or normal variability is probably responsible for a large part of the overall variability in OCC in cows without clinical mastitis. This is important to consider when using OCC data for research purposes or in decision-support tools. Sensor repeatability was evaluated by analyzing milk from the same sample multiple times. The coefficient of variation was 0.11 at an OCC level relevant for detection of subclinical mastitis. The agreement study showed a concordance correlation coefficient of 0.82 when comparing results from the OCC with results from a DHI laboratory.

Transcription Profiling of Monocyte-Derived Macrophages Infected In Vitro With Two Strains of Streptococcus agalactiae Reveals Candidate Pathways Affecting Subclinical Mastitis in Cattle.

Macrophages are key cells of innate immune response and serve as the first line of defense against bacteria. Transcription profiling of bacteria-infected macrophages could provide important insights on the pathogenicity and host defense mechanisms during infection. We have examined transcription profiles of bovine monocyte-derived macrophages (bMDMs) isolated from the blood of 12 animals and infected in vitro with two strains of Streptococcus agalactiae. Illumina sequencing of RNA from 36 bMDMs cultures exposed in vitro to either one of two sequence types of S. agalactiae (ST103 or ST12) for 6 h and unchallenged controls was performed. Analyses of over 1,656 million high-quality paired-end sequence reads revealed 5,936 and 6,443 differentially expressed genes (p < 0.05) in bMDMs infected with ST103 and ST12, respectively, versus unchallenged controls. Moreover, 588 genes differentially expressed between bMDMs infected with ST103 versus ST12 were identified. Ingenuity pathway analysis of the differentially up-regulated genes in the bMDMs infected with ST103 revealed significant enrichment for granulocyte adhesion and diapedesis, while significant enrichment for the phagosome formation pathway was found among down-regulated genes. Moreover, Ingenuity pathway analysis of the differentially up-regulated genes in the bMDMs infected with ST12 showed significant enrichment for type 1/type 2 T helper cell activation, while the complement activation pathway was overrepresented in the down-regulated genes. Our study identified pathogen-induced regulation of key genes and pathways involved in the immune response of macrophages against infection but also likely involved in bacterial evasion of the host immune system. These results may contribute to better understanding of the mechanisms underlying subclinical infection such as bovine streptococcal mastitis.

Comparison of sperm adenosine triphosphate content, motility and fertility of immobilized and conventionally cryopreserved Norwegian Red bull semen.

Estrus detection and timing of AI remains a challenge in cattle breeding. Prolonging spermatozoa lifespan after AI, making sperm cells available over an extended period, could make timing of AI relative to ovulation less crucial and improve fertility. Immobilization of sperm cells by the patented SpermVital technology in an alginate gel will provide a gradual release of spermatozoa after AI. The first aim of this study was to examine fertility, measured as non-return rate after 56 days (NR56), of SpermVital (SV) processed semen with reduced sperm cell number per dose compared to earlier studies, and compare with conventionally processed semen in Biladyl, a proprietary version of the egg yolk Tris semen extender. The second aim was to examine in vitro sperm quality post-thaw and after thermal stress. The third aim was to examine potential correlations between in vitro sperm parameters and NR56. Ejaculates from 16 Norwegian Red young bulls were split in three, processed and cryopreserved as Biladyl semen (B15; 15 million spermatozoa/dose) or by SpermVital technology (SV25; 25 million spermatozoa/dose or SV15; 15 million spermatozoa/dose). 1400 semen doses were produced per bull and distributed throughout Norway for a blinded field trial. Fertility was recorded as NR56 after first AI (N = 7155). Two ejaculates from each bull were randomly selected for in vitro experiments. B15 and SV15 semen samples were analyzed for motility by computer-assisted sperm analysis, viability and acrosome integrity by flow cytometry and ATP content by bioluminescence assay, post-thaw and after thermal stress. The AI trial detected no differences in NR56; least square means being 75.5% (B15), 75.6% (SV25) and 74.8% (SV15) (p > 0.05). There were no differences in total motility and progressive motility post-thaw, however, after three hours incubation at 38 °C, SV sperm motility and progressivity were higher for SV15 than for B15 spermatozoa (p < 0.05). The percentage of acrosome intact live sperm cells was higher for SV15 than B15 spermatozoa at all timepoints analyzed (0 h, 3 h, 24 h, p < 0.05). B15 semen showed a higher ATP level than SV15 at 0 h (p < 0.05), while SV15 sperm cells had higher ATP levels after 3 and 24 h (p < 0.05). No association was detected between in vitro sperm parameters and NR56. In conclusion, SV15, SV25 and B15 semen yielded equal fertility after AI. However, there were differences in sperm quality, as SV15 spermatozoa displayed higher motility, viability and ATP levels after thermal stress than B15 spermatozoa (p < 0.05).

MicroRNA expression profiles of bovine monocyte-derived macrophages infected in vitro with two strains of Streptococcus agalactiae.

BACKGROUND: MicroRNAs (miRNAs) are short, non-coding RNAs that regulate gene expression at the post-transcriptional level and play a key role in the control of innate and adaptive immune responses. For a subclinical infection such as bovine streptococcal mastitis, early detection is a great challenge, and miRNA profiling could potentially assist in the diagnosis and contribute to the understanding of the pathogenicity and defense mechanisms. We have examined the miRNA repertoire and the transcript level of six key immune genes [tumor necrosis factor alpha (TNFα), interleukin-1 beta (IL-1ß), interleukin-6 (IL-6), interleukin-8 (IL-8), interleukin-10 (IL-10) and transforming growth factor beta 1 (TGFß1)] during the early phase response of bovine immature macrophages to in vitro infection with live Streptococcus agalactiae. Next generation sequencing of small RNA libraries from 20 cultures of blood monocyte-derived macrophages exposed to either one of two sequence types of S. agalactiae (ST103 or ST12) for 6 h in vitro and unchallenged controls was performed. RESULTS: Analyzes of over 356 million high quality sequence reads, revealed differential expression of 17 and 44 miRNAs (P < 0.05) in macrophages infected with ST103 and ST12, respectively, versus unchallenged control cultures. We also identified the expression of 31 potentially novel bovine miRNAs. Pathway analysis of the differentially regulated miRNAs and their predicted target genes in the macrophages infected with ST12 revealed significant enrichment for inflammatory response and apoptosis, while significant enrichment for integrin and GABA signaling were found in ST103 infected macrophages. Furthermore, both bacterial strains regulated miRNAs involved in the alternative activation of macrophages. The transcript levels of TNF-α, IL-1ß, IL-6, IL-8 and IL-10 were significantly up-regulated by both bacterial strains, however the expression of TGFß1 was significantly down-regulated only by ST12. CONCLUSIONS: Our study identified pathogen-induced differential regulation of miRNAs controlling inflammation and polarization in bovine macrophages. This implies that miRNAs have potential to serve as biomarkers for early detection of bacterial infection.

Fine mapping of a QTL on bovine chromosome 6 using imputed full sequence data suggests a key role for the group-specific component (GC) gene in clinical mastitis and milk production.

BACKGROUND: Clinical mastitis is an inflammation of the mammary gland and causes significant costs to dairy production. It is unfavourably genetically correlated to milk production, and, thus, knowledge of the mechanisms that underlie these traits would be valuable to improve both of them simultaneously through breeding. A quantitative trait locus (QTL) that affects both clinical mastitis and milk production has recently been fine-mapped to around 89 Mb on bovine chromosome 6 (BTA6), but identification of the gene that underlies this QTL was not possible due to the strong linkage disequilibrium between single nucleotide polymorphisms (SNPs) within this region. Our aim was to identify the gene and, if possible, the causal polymorphism(s) responsible for this QTL through association analysis of high-density SNPs and imputed full sequence data in combination with analyses of transcript and protein levels of the identified candidate gene. RESULTS: Associations between SNPs and the studied traits were strongest for SNPs that were located within and immediately upstream of the group-specific component (GC) gene. This gene encodes the vitamin D-binding protein (DBP) and has multiple roles in immune defense and milk production. A 12-kb duplication that was identified downstream of this gene covered its last exon and segregated with the QTL allele that is associated with increased mastitis susceptibility and milk production. However, analyses of GC mRNA levels on the available samples revealed no differences in expression between animals having or lacking this duplication. Moreover, we detected no differences in the concentrations of DBP and its ligand vitamin D between the animals with different GC genotypes that were available for this study. CONCLUSIONS: Our results suggest GC as the gene that underlies the QTL for clinical mastitis and milk production. However, since only healthy animals were sampled for transcription and expression analyses, we could not draw any final conclusion on the absence of quantitative differences between animals with different genotypes. Future studies should investigate GC RNA expression and protein levels in cows with different genotypes during an infection.

Information from later lactations improves accuracy of genomic predictions of fertility-related disorders in Norwegian Red.

Our aim was to investigate whether including information from later lactations improves accuracy of genomic breeding values for 4 fertility-related disorders: cystic ovaries, retained placenta, metritis, and silent heat. Data consisted of health records from 6,015,245 lactations from 2,480,976 Norwegian Red cows, recorded from 1979 to 2012. These were daughters of 3,675 artificial insemination bulls. The mean frequency of these disorders for cows in lactation 1 to 5 ranged from 0.6 to 2.4% for cystic ovaries, 1.0 to 1.5% for metritis, 1.9 to 4.1% for retained placenta, and 2.4 to 3.8% for silent heat. Genomic information was available for all sires, and the 312 youngest bulls were used for validation. After standard editing of a 25K/54K single nucleotide polymorphism data set that was imputed both ways, a total of 48,249 single nucleotide polymorphism loci were available for genomic predictions. Genomic breeding values were predicted using univariate genomic BLUP for the first lactation only and for the first 5 lactations and multivariate genomic BLUP with 5 lactations for each disorder was also used for genomic predictions. Correlations between estimated breeding values for the 4 traits in 5 lactations with predicted genomic breeding values were compared. Accuracy ranged from 0.47 and 0.51 for cystic ovaries, 0.50 to 0.74 for retained placenta, 0.21 to 0.47 for metritis, and 0.22 to 0.60 for silent heat. Including later lactations in a multitrait genomic BLUP improved accuracy of genomic estimated breeding values for cystic ovaries, retained placenta, and silent heat, whereas for metritis no obvious advantage in accuracy was found.

Short communication: genetic parameters for fertility-related disorders in Norwegian Red.

Heritabilities and genetic correlations were estimated for the 4 most common fertility-related disorders in Norwegian Red: retained placenta, cystic ovaries, silent heat, and metritis. Data on 1,747,500 lactations from 780,114 cows calving from January 2001 through December 2011 were analyzed using multivariate threshold sire models to estimate variance components for the 4 disorders in the first 5 lactations. The traits were defined as binary within lactation (0=unaffected, 1=affected), and each fertility-related disorder was analyzed separately with the 5 lactations as correlated traits. The mean frequency of affected cows ranged from 0.5 to 1.7% for cystic ovaries, 0.7 to 1.1% for metritis, 1.3 to 3.4% for retained placenta, and 1.7 to 2.7% for silent heat. Posterior means (standard deviations) of heritability of liability ranged from 0.02 (0.01) to 0.12 (0.01), and were lowest for silent heat and highest for cystic ovaries. Genetic correlations across lactation within disorder were positive and moderate to high, ranging from 0.79 to 0.95 for cystic ovaries, 0.40 to 0.75 for metritis, 0.53 to 0.94 for retained placenta, and 0.39 to 0.83 for silent heat.

A comparison of principal component regression and genomic REML for genomic prediction across populations.

BACKGROUND: Genomic prediction faces two main statistical problems: multicollinearity and n ≪ p (many fewer observations than predictor variables). Principal component (PC) analysis is a multivariate statistical method that is often used to address these problems. The objective of this study was to compare the performance of PC regression (PCR) for genomic prediction with that of a commonly used REML model with a genomic relationship matrix (GREML) and to investigate the full potential of PCR for genomic prediction. METHODS: The PCR model used either a common or a semi-supervised approach, where PC were selected based either on their eigenvalues (i.e. proportion of variance explained by SNP (single nucleotide polymorphism) genotypes) or on their association with phenotypic variance in the reference population (i.e. the regression sum of squares contribution). Cross-validation within the reference population was used to select the optimum PCR model that minimizes mean squared error. Pre-corrected average daily milk, fat and protein yields of 1609 first lactation Holstein heifers, from Ireland, UK, the Netherlands and Sweden, which were genotyped with 50 k SNPs, were analysed. Each testing subset included animals from only one country, or from only one selection line for the UK. RESULTS: In general, accuracies of GREML and PCR were similar but GREML slightly outperformed PCR. Inclusion of genotyping information of validation animals into model training (semi-supervised PCR), did not result in more accurate genomic predictions. The highest achievable PCR accuracies were obtained across a wide range of numbers of PC fitted in the regression (from one to more than 1000), across test populations and traits. Using cross-validation within the reference population to derive the number of PC, yielded substantially lower accuracies than the highest achievable accuracies obtained across all possible numbers of PC. CONCLUSIONS: On average, PCR performed only slightly less well than GREML. When the optimal number of PC was determined based on realized accuracy in the testing population, PCR showed a higher potential in terms of achievable accuracy that was not capitalized when PC selection was based on cross-validation. A standard approach for selecting the optimal set of PC in PCR remains a challenge.

A simple algorithm to estimate genetic variance in an animal threshold model using Bayesian inference.

BACKGROUND: In the genetic analysis of binary traits with one observation per animal, animal threshold models frequently give biased heritability estimates. In some cases, this problem can be circumvented by fitting sire- or sire-dam models. However, these models are not appropriate in cases where individual records exist on parents. Therefore, the aim of our study was to develop a new Gibbs sampling algorithm for a proper estimation of genetic (co)variance components within an animal threshold model framework. METHODS: In the proposed algorithm, individuals are classified as either "informative" or "non-informative" with respect to genetic (co)variance components. The "non-informative" individuals are characterized by their Mendelian sampling deviations (deviance from the mid-parent mean) being completely confounded with a single residual on the underlying liability scale. For threshold models, residual variance on the underlying scale is not identifiable. Hence, variance of fully confounded Mendelian sampling deviations cannot be identified either, but can be inferred from the between-family variation. In the new algorithm, breeding values are sampled as in a standard animal model using the full relationship matrix, but genetic (co)variance components are inferred from the sampled breeding values and relationships between "informative" individuals (usually parents) only. The latter is analogous to a sire-dam model (in cases with no individual records on the parents). RESULTS: When applied to simulated data sets, the standard animal threshold model failed to produce useful results since samples of genetic variance always drifted towards infinity, while the new algorithm produced proper parameter estimates essentially identical to the results from a sire-dam model (given the fact that no individual records exist for the parents). Furthermore, the new algorithm showed much faster Markov chain mixing properties for genetic parameters (similar to the sire-dam model). CONCLUSIONS: The new algorithm to estimate genetic parameters via Gibbs sampling solves the bias problems typically occurring in animal threshold model analysis of binary traits with one observation per animal. Furthermore, the method considerably speeds up mixing properties of the Gibbs sampler with respect to genetic parameters, which would be an advantage of any linear or non-linear animal model.

Bayesian structural equation models for inferring relationships between phenotypes: a review of methodology, identifiability, and applications.

Structural equation models provide a general statistical modelling technique for estimating and testing relationships among variables. Such relationships are often not revealed by standard linear models, but are of importance for understanding mechanisms underlying e.g., production-related diseases, such as mastitis. This paper gives a review of Bayesian structural equation models concerning methodology and identifiability, focused on animal breeding and genetics modelling. Applications of this type of methods in animal breeding are also reviewed critically, with discussion on advantages and disadvantages of these approaches.

Exploration of lagged relationships between mastitis and milk yield in dairy cows using a Bayesian structural equation Gaussian-threshold model.

A Gaussian-threshold model is described under the general framework of structural equation models for inferring simultaneous and recursive relationships between binary and Gaussian characters, and estimating genetic parameters. Relationships between clinical mastitis (CM) and test-day milk yield (MY) in first-lactation Norwegian Red cows were examined using a recursive Gaussian-threshold model. For comparison, the data were also analyzed using a standard Gaussian-threshold, a multivariate linear model, and a recursive multivariate linear model. The first 180 days of lactation were arbitrarily divided into three periods of equal length, in order to investigate how these relationships evolve in the course of lactation. The recursive model showed negative within-period effects from (liability to) CM to test-day MY in all three lactation periods, and positive between-period effects from test-day MY to (liability to) CM in the following period. Estimates of recursive effects and of genetic parameters were time-dependent. The results suggested unfavorable effects of production on liability to mastitis, and dynamic relationships between mastitis and test-day MY in the course of lactation. Fitting recursive effects had little influence on the estimation of genetic parameters. However, some differences were found in the estimates of heritability, genetic, and residual correlations, using different types of models (Gaussian-threshold vs. multivariate linear).

A periodic analysis of longitudinal binary responses: a case study of clinical mastitis in Norwegian Red cows.

A Bayesian procedure for analyzing longitudinal binary responses using a periodic cosine function was developed. It was assumed that, after adjustment for "seasonal" effects, the oscillation of the underlying latent variables for longitudinal binary responses was a stationary series. Based on this assumption, a single dimension sinusoidal analysis of longitudinal binary responses using the Gibbs sampling and Metropolis algorithms was implemented in a study of clinical mastitis records of Norwegian Red cows taken over five lactations.

On the quantitative genetics of mixture characters.

Finite mixture models are helpful for uncovering heterogeneity due to hidden structure. Quantitative genetics issues of continuous characters having a finite mixture of Gaussian components as statistical distribution are explored in this article. The partition of variance in a mixture, the covariance between relatives under the supposition of an additive genetic model, and the offspring-parent regression are derived. Formulas for assessing the effect of mass selection operating on a mixture are given. Expressions for the genetic and phenotypic correlations between mixture and Gaussian traits and between two mixture traits are presented. It is found that, if there is heterogeneity in a population at the genetic or environmental level, then genetic parameters based on theory treating distributions as homogeneous can lead to misleading interpretations. Some peculiarities of mixture characters are: heritability depends on the mean values of the component distributions, the offspring-parent regression is nonlinear, and genetic or phenotypic correlations cannot be interpreted devoid of the mixture proportions and of the parameters of the distributions mixed.