Genetic (co)variances between milk mineral concentration and chemical composition in lactating Holstein-Friesian dairy cows

Milk mineral concentration is important from both the perspective of processing milk into dairy products and its nutritive value for human consumption. Precise estimates of genetic parameters for milk mineral concentration are lacking because of the considerable resources required to collect vast phenotypes quantities. The milk concentration of calcium (Ca), potassium (K), magnesium (Mg), sodium (Na) and phosphorus (P) in the present study was quantified from mid-IR spectroscopy on 12 223 test-day records from 1717 Holstein-Friesian cows. (Co)variance components were estimated using random regressions to model both the additive genetic and within-lactation permanent environmental variances of each trait. The coefficient of genetic variation averaged across days-in-milk (DIM) was 6.93%, 3.46%, 6.55%, 5.20% and 6.68% for Ca, K, Mg, Na and P concentration, respectively; heritability estimates varied across lactation from 0.31±0.05 (5 DIM) to 0.67±0.04 (181 DIM) for Ca, from 0.18±0.03 (60 DIM) to 0.24±0.05 (305 DIM) for K, from 0.08±0.03 (15 DIM) to 0.37±0.03 (223 DIM) for Mg, from 0.16±0.03 (30 DIM) to 0.37±0.04 (305 DIM) for Na and from 0.21±0.04 (12 DIM) to 0.57±0.04 (211 DIM) for P. Genetic correlations within the same trait across different DIM were almost unity between adjacent DIM but weakened as the time interval between pairwise compared DIM lengthened; genetic correlations were weaker than 0.80 only when comparing both peripheries of the lactation. The analysis of the geometry of the additive genetic covariance matrix revealed that almost 90% of the additive genetic variation was accounted by the intercept term of the covariance functions for each trait. Milk protein concentration and mineral concentration were, in general, positively genetically correlated with each other across DIM, whereas milk fat concentration was positively genetically correlated throughout the entire lactation with Ca, K and Mg; the genetic correlation with fat concentration changed from negative to positive with Na and P at 243 DIM and 50 DIM, respectively. Genetic correlations between somatic cell score and Na ranged from 0.38±0.21 (5 DIM) to 0.79±0.18 (305 DIM). Exploitable genetic variation existed for all milk minerals, although many national breeding objectives are probably contributing to an indirect positive response to selection in milk mineral concentration.     

Partitioning of genomic variance reveals biological pathways associated with udder health and milk production traits in dairy cattle

Background

We have used a linear mixed model (LMM) approach to examine the joint contribution of genetic markers associated with a biological pathway. However, with these markers being scattered throughout the genome, we are faced with the challenge of modelling the contribution from several, sometimes even all, chromosomes at once. Due to linkage disequilibrium (LD), all markers may be assumed to account for some genomic variance; but the question is whether random sets of markers account for the same genomic variance as markers associated with a biological pathway?

Results

We applied the LMM approach to identify biological pathways associated with udder health and milk production traits in dairy cattle. A random gene sampling procedure was applied to assess the biological pathways in a dataset that has an inherently complex genetic correlation pattern due to the population structure of dairy cattle, and to linkage disequilibrium within the bovine genome and within the genes associated to the biological pathway.

Conclusions

Several biological pathways that were significantly associated with health and production traits were identified in dairy cattle; i.e. the markers linked to these pathways explained more of the genomic variance and provided a better model fit than 95 % of the randomly sampled gene groups. Our results show that immune related pathways are associated with production traits, and that pathways that include a causal marker for production traits are identified with our procedure.We are confident that the LMM approach provides a general framework to exploit and integrate prior biological information and could potentially lead to improved understanding of the genetic architecture of complex traits and diseases.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-015-0132-6) contains supplementary material, which is available to authorized users.     

Identification of genomic regions associated with inbreeding depression in Holstein and Jersey dairy cattle

Background

Inbreeding reduces the fitness of individuals by increasing the frequency of homozygous deleterious recessive alleles. Some insight into the genetic architecture of fitness, and other complex traits, can be gained by using single nucleotide polymorphism (SNP) data to identify regions of the genome which lead to reduction in performance when identical by descent (IBD). Here, we compared the effect of genome-wide and location-specific homozygosity on fertility and milk production traits in dairy cattle.

Methods

Genotype data from more than 43 000 SNPs were available for 8853 Holstein and 4138 Jersey dairy cows that were part of a much larger dataset that had pedigree records (338 696 Holstein and 64 049 Jersey animals). Measures of inbreeding were based on: (1) pedigree data; (2) genotypes to determine the realised proportion of the genome that is IBD; (3) the proportion of the total genome that is homozygous and (4) runs of homozygosity (ROH) which are stretches of the genome that are homozygous.

Results

A 1% increase in inbreeding based either on pedigree or genomic data was associated with a decrease in milk, fat and protein yields of around 0.4 to 0.6% of the phenotypic mean, and an increase in calving interval (i.e. a deterioration in fertility) of 0.02 to 0.05% of the phenotypic mean. A genome-wide association study using ROH of more than 50 SNPs revealed genomic regions that resulted in depression of up to 12.5 d and 260 L for calving interval and milk yield, respectively, when completely homozygous.

Conclusions

Genomic measures can be used instead of pedigree-based inbreeding to estimate inbreeding depression. Both the diagonal elements of the genomic relationship matrix and the proportion of homozygous SNPs can be used to measure inbreeding. Longer ROH (>3 Mb) were found to be associated with a reduction in milk yield and captured recent inbreeding independently and in addition to overall homozygosity. Inbreeding depression can be reduced by minimizing overall inbreeding but maybe also by avoiding the production of offspring that are homozygous for deleterious alleles at specific genomic regions that are associated with inbreeding depression.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-014-0071-7) contains supplementary material, which is available to authorized users.     

Review: How to improve genomic predictions in small dairy cattle populations

This paper reviews strategies and methods to improve accuracies of genomic predictions from the perspective of a numerically small population. Improvements are realized by influencing one or both of the main factors: (1) improve or increase genomic connections to phenotypic records in training data. (2) Models and strategies to focus genomic predictions on markers closer to the causative variants. Combining populations into a joint reference population results in high improvements when combining populations of the same breed and diminishes as the genetic distance between populations increases. For distantly related breeds sophisticated Bayesian variable selection models in combination with denser markers sets or functional subsets of markers is needed. This is expected to be further improved by the efficient use of sequence information. In addition predictions can be improved by the use of phenotypes of genotyped and non-genotyped cows directly. For a small population the optimal approach will combine the above components.     

An evolutionary quantitative genetics model for phenotypic (co)variances under limited dispersal,with an application to socially synergistic traits

Darwinian evolution consists of the gradual transformation of heritable traits due to natural selection and the input of random variation by mutation. Here, we use a quantitative genetics approach to investigate the coevolution of multiple quantitative traits under selection, mutation, and limited dispersal. We track the dynamics of trait means and of variance–covariances between traits that experience frequency‐dependent selection. Assuming a multivariate‐normal trait distribution, we recover classical dynamics of quantitative genetics, as well as stability and evolutionary branching conditions of invasion analyses, except that due to limited dispersal, selection depends on indirect fitness effects and relatedness. In particular, correlational selection that associates different traits within‐individuals depends on the fitness effects of such associations between‐individuals. We find that these kin selection effects can be as relevant as pleiotropy for the evolution of correlation between traits. We illustrate this with an example of the coevolution of two social traits whose association within‐individuals is costly but synergistically beneficial between‐individuals. As dispersal becomes limited and relatedness increases, associations between‐traits between‐individuals become increasingly targeted by correlational selection. Consequently, the trait distribution goes from being bimodal with a negative correlation under panmixia to unimodal with a positive correlation under limited dispersal.     

Partitioning additive genetic variance into genomic and remaining polygenic components for complex traits in dairy cattle

ABSTRACT: BACKGROUND: Low cost genotyping of individuals using high density genomic markers were recently introduced as genomic selection in genetic improvement programs in dairy cattle. Most implementations of genomic selection only use marker information, in the models used for prediction of genetic merit. However, in other species it has been shown that only a fraction of the total genetic variance can be explained by markers. Using 5217 bulls in the Nordic Holstein population that were genotyped and had genetic evaluations based on progeny, we partitioned the total additive genetic variance into a genomic component explained by markers and a remaining component explained by familial relationships. The traits analyzed were production and fitness related traits in dairy cattle. Furthermore, we estimated the genomic variance that can be attributed to individual chromosomes and we illustrate methods that can predict the amount of additive genetic variance that can be explained by sets of markers with different density. RESULTS: The amount of additive genetic variance that can be explained by markers was estimated by an analysis of the matrix of genomic relationships. For the traits in the analysis, most of the additive genetic variance can be explained by 44 K informative SNP markers. The same amount of variance can be attributed to individual chromosomes but surprisingly the relation between chromosomal variance and chromosome length was weak. In models including both genomic (marker) and familial (pedigree) effects most (on average 77.2%) of total additive genetic variance was explained by genomic effects while the remaining was explained by familial relationships. CONCLUSIONS: Most of the additive genetic variance for the traits in the Nordic Holstein population can be explained using 44 K informative SNP markers. By analyzing the genomic relationship matrix it is possible to predict the amount of additive genetic variance that can be explained by a reduced (or increased) set of markers. For the population analyzed the improvement of genomic prediction by increasing marker density beyond 44 K is limited.     

Genetic parameters for serial, automatically recorded milkability and its relationship to udder health in dairy cattle

Serial measurements of three milkability traits from two commercial dairy farms in Germany were used to estimate heritabilities and breeding values (BVs). Overall, 6352 cows in first, second and third lactations supplied 2 188 810 records based on daily values recorded from 1998 to 2003. Only the records between day 8 and day 305 after calving were considered. The estimated genetic correlations between different parities within the three milkability traits ranged from rg = 0.88 to 0.98, i.e. they were sufficiently high to warrant a repeatability model. The resulting estimated heritability coefficients were h2 = 0.42 for average milk flow, h2 = 0.56 for maximum milk flow and h2 = 0.38 for milking time. We analysed the genetic correlation between milkability and somatic cell score (SCS) and between milkability and the liability to mastitis, respectively, as the optimum milk flow for udder health is not well defined. There were 66 146 records with information on somatic cell count. Furthermore, 23 488 days of medical treatment for udder diseases were available, resulting in 2 600 302 days of observation in total. Heritabilities for the liability to mastitis, estimated with a test-day threshold model, were h2 = 0.19 and h2 = 0.13, depending on the data-recording period (first 50 days of lactation and first 305 days of lactation, respectively). With respect to the relationship between milkability and udder health, the results indicated a slight and linear correlation insofar as one can assume: the higher the milk flow, the worse the udder health. For this reason, bulls and cows with high BVs for milk flow should be excluded from breeding to avoid a deterioration of udder health. The establishment of a special data-recording scheme for functional traits such as milkability and mastitis on commercial dairy farms may be possible according to these results.     

Predicted accuracy of and response to genomic selection for new traits in dairy cattle

Genomic selection relaxes the requirement of traditional selection tools to have phenotypic measurements on close relatives of all selection candidates. This opens up possibilities to select for traits that are difficult or expensive to measure. The objectives of this paper were to predict accuracy of and response to genomic selection for a new trait, considering that only a cow reference population of moderate size was available for the new trait, and that selection simultaneously targeted an index and this new trait. Accuracy for and response to selection were deterministically evaluated for three different breeding goals. Single trait selection for the new trait based only on a limited cow reference population of up to 10 000 cows, showed that maximum genetic responses of 0.20 and 0.28 genetic standard deviation (s.d.) per year can be achieved for traits with a heritability of 0.05 and 0.30, respectively. Adding information from the index based on a reference population of 5000 bulls, and assuming a genetic correlation of 0.5, increased genetic response for both heritability levels by up to 0.14 genetic s.d. per year. The scenario with simultaneous selection for the new trait and the index, yielded a substantially lower response for the new trait, especially when the genetic correlation with the index was negative. Despite the lower response for the index, whenever the new trait had considerable economic value, including the cow reference population considerably improved the genetic response for the new trait. For scenarios with a zero or negative genetic correlation with the index and equal economic value for the index and the new trait, a reference population of 2000 cows increased genetic response for the new trait with at least 0.10 and 0.20 genetic s.d. per year, for heritability levels of 0.05 and 0.30, respectively. We conclude that for new traits with a very small or positive genetic correlation with the index, and a high positive economic value, considerable genetic response can already be achieved based on a cow reference population with only 2000 records, even when the reliability of individual genomic breeding values is much lower than currently accepted in dairy cattle breeding programs. New traits may generally have a negative genetic correlation with the index and a small positive economic value. For such new traits, cow reference populations of at least 10 000 cows may be required to achieve acceptable levels of genetic response for the new trait and for the whole breeding goal.     

ChromoScan: a scan statistic application for identifying chromosomal regions in genomic studies

ChromoScan is an implementation of a genome-based scan statistic that detects genomic regions, which are statistically significant for targeted measurements, such as genetic associations with disease, gene expression profiles, DNA copy number variations, as well as other genome-based measurements. A Java graphic user interface (GUI) is provided to allow users to select appropriate data transformations and thresholds for defining the significant events. AVAILABILITY: ChromoScan is freely available from http://www.epidkardia.sph.umich.edu/software/chromoscan/     

Accuracy of genomic predictions in Bos indicus (Nellore) cattle

Background

Nellore cattle play an important role in beef production in tropical systems and there is great interest in determining if genomic selection can contribute to accelerate genetic improvement of production and fertility in this breed. We present the first results of the implementation of genomic prediction in a Bos indicus (Nellore) population.

Methods

Influential bulls were genotyped with the Illumina Bovine HD chip in order to assess genomic predictive ability for weight and carcass traits, gestation length, scrotal circumference and two selection indices. 685 samples and 320 238 single nucleotide polymorphisms (SNPs) were used in the analyses. A forward-prediction scheme was adopted to predict the genomic breeding values (DGV). In the training step, the estimated breeding values (EBV) of bulls were deregressed (dEBV) and used as pseudo-phenotypes to estimate marker effects using four methods: genomic BLUP with or without a residual polygenic effect (GBLUP20 and GBLUP0, respectively), a mixture model (Bayes C) and Bayesian LASSO (BLASSO). Empirical accuracies of the resulting genomic predictions were assessed based on the correlation between DGV and dEBV for the testing group.

Results

Accuracies of genomic predictions ranged from 0.17 (navel at weaning) to 0.74 (finishing precocity). Across traits, Bayesian regression models (Bayes C and BLASSO) were more accurate than GBLUP. The average empirical accuracies were 0.39 (GBLUP0), 0.40 (GBLUP20) and 0.44 (Bayes C and BLASSO). Bayes C and BLASSO tended to produce deflated predictions (i.e. slope of the regression of dEBV on DGV greater than 1). Further analyses suggested that higher-than-expected accuracies were observed for traits for which EBV means differed significantly between two breeding subgroups that were identified in a principal component analysis based on genomic relationships.

Conclusions

Bayesian regression models are of interest for future applications of genomic selection in this population, but further improvements are needed to reduce deflation of their predictions. Recurrent updates of the training population would be required to enable accurate prediction of the genetic merit of young animals. The technical feasibility of applying genomic prediction in a Bos indicus (Nellore) population was demonstrated. Further research is needed to permit cost-effective selection decisions using genomic information.     

Identifying genomic regions for fine-mapping using genome scan meta-analysis (GSMA) to identify the minimum regions of maximum significance (MRMS) across populations

In order to detect linkage of the simulated complex disease Kofendrerd Personality Disorder across studies from multiple populations, we performed a genome scan meta-analysis (GSMA). Using the 7-cM microsatellite map, nonparametric multipoint linkage analyses were performed separately on each of the four simulated populations independently to determine p-values. The genome of each population was divided into 20-cM bin regions, and each bin was rank-ordered based on the most significant linkage p-value for that population in that region. The bin ranks were then averaged across all four studies to determine the most significant 20-cM regions over all studies. Statistical significance of the averaged bin ranks was determined from a normal distribution of randomly assigned rank averages. To narrow the region of interest for fine-mapping, the meta-analysis was repeated two additional times, with each of the 20-cM bins offset by 7 cM and 13 cM, respectively, creating regions of overlap with the original method. The 6-7 cM shared regions, where the highest averaged 20-cM bins from each of the three offsets overlap, designated the minimum region of maximum significance (MRMS). Application of the GSMA-MRMS method revealed genome wide significance (p-values refer to the average rank assigned to the bin) at regions including or adjacent to all of the simulated disease loci: chromosome 1 (p < 0.0001 for 160-167 cM, including D1), chromosome 3 (p-value < 0.0000001 for 287-294 cM, including D2), chromosome 5 (p-value < 0.001 for 0-7 cM, including D3), and chromosome 9 (p-value < 0.05 for 7-14 cM, the region adjacent to D4). This GSMA analysis approach demonstrates the power of linkage meta-analysis to detect multiple genes simultaneously for a complex disorder. The MRMS method enhances this powerful tool to focus on more localized regions of linkage.     

Estimation by simulation of the efficiency of the French marker-assisted selection program in dairy cattle (Open Access publication)

The efficiency of the French marker-assisted selection (MAS) was estimated by a simulation study. The data files of two different time periods were used: April 2004 and 2006. The simulation method used the structure of the existing French MAS: same pedigree, same marker genotypes and same animals with records. The program simulated breeding values and new records based on this existing structure and knowledge on the QTL used in MAS (variance and frequency). Reliabilities of genetic values of young animals (less than one year old) obtained with and without marker information were compared to assess the efficiency of MAS for evaluation of milk, fat and protein yields and fat and protein contents. Mean gains of reliability ranged from 0.015 to 0.094 and from 0.038 to 0.114 in 2004 and 2006, respectively. The larger number of animals genotyped and the use of a new set of genetic markers can explain the improvement of MAS reliability from 2004 to 2006. This improvement was also observed by analysis of information content for young candidates. The gain of MAS reliability with respect to classical selection was larger for sons of sires with genotyped progeny daughters with records. Finally, it was shown that when superiority of MAS over classical selection was estimated with daughter yield deviations obtained after progeny test instead of true breeding values, the gain was underestimated.     

Invited review: The evolution of cattle bioacoustics and application for advanced dairy systems

Vocalisations are commonly expressed by gregarious animals, including cattle, as a form of short- and long-distance communication. They can provide conspecifics with meaningful information about the physiology, affective state and physical attributes of the caller. In cattle, calls are individually distinct meaning they assist animals to identify specific individuals in the herd. Consequently, there is potential for these vocalisations to be acoustically analysed to make inferences about how individual animals or herds are coping with their external surroundings, and then act on these signals to improve feed conversion efficiency, reproductive efficiency and welfare. In the case of dairy farming, where herd sizes are expanding and farmers are becoming more reliant on technologies to assist in the monitoring of cattle, the study of vocal behaviour could provide an objective, cost effective and non-invasive alternative to traditional measures of welfare. The vocalisations of cattle in response to calf separation, social isolation and painful husbandry procedures, alongside changes to feeding and oestrous activity are here reviewed. For future application of sound technology, research is first necessary to analyse the acoustic structure of cattle vocalisations and determine the specific information they encode. This review draws together the latest research in field of cattle bioacoustics highlighting how the source–filter theory and affective state dimensional approach can be adopted to decode this information and improve on-farm management.     

Indirect effects of FRIGIDA: floral trait (co)variances are altered by seasonally variable abiotic factors associated with flowering time

Reproductive timing is a critical life‐history event that could influence the (co)variation of traits developing later in ontogeny by regulating exposure to seasonally variable factors. In a field experiment with Arabidopsis thaliana, we explore whether allelic variation at a flowering‐time gene of major effect (FRIGIDA) affects (co)variation of floral traits by regulating exposure to photoperiod, temperature, and moisture levels. We detect a positive latitudinal cline in floral organ size among plants with putatively functional FRI alleles. Statistically controlling for bolting day removes the cline, suggesting that seasonal abiotic variation affects floral morphology. Both photoperiod and precipitation at bolting correlate positively with the length of petals, stamens, and pistils. Additionally, floral (co)variances differ significantly across FRI backgrounds, such that the sign of some floral‐trait correlations reverses. Subsequent experimental manipulations of photoperiod and water availability demonstrate direct effects of these abiotic factors on floral traits. In sum, these results highlight how the timing of life‐history events can affect the expression of traits developing later in ontogeny, and provide some of the first empirical evidence for the effects of major genes on evolutionary potential.     

Genome sizes for 71 species of Zamia (Cycadales: Zamiaceae) correspond with three different biogeographic regions

Nuclear DNA contents (2C‐value) are reported for 71 out of 76 accepted species of Zamia (Zamiaceae) using flow cytometry with propidium iodide. Nuclear DNA content in Zamia ranges between 33.7 and 45.7 pg. Despite this small range, the largest genome contains roughly 10¹⁰ more base pairs than the smallest genome. The results for Zamia point to two centers of biogeographic distribution: Mexico and Colombia. Nicaragua seems to be the biogeographic boundary for these two centres for Zamia. To the north, genome sizes of 33.7–38.0 pg (average 35.6 pg) are found and to the south (Costa Rica, Panama and South America) 41.2–45.7 pg (average 42.9 pg). Plants from the Caribbean islands (including Florida) have intermediate genome sizes with 37.3–40.9 pg (average 38.7 pg). Costa Rica and Panama are in a transition zone and its species can be divided into three subsections: four species with ‘Caribbean’ values of 38.4–39.5 pg (average 39.0 pg), six species with ‘South American’ values with 42.7–43.6 pg, (average 42.9 pg, and six species with intermediate values ranging between 40.1–41.0 pg (average 40.4 pg). The latter values are nearly absent in other areas, suggesting that they could be the products of (introgressive) hybridization. This study represents the first, nearly complete overview of the genome sizes of the genus Zamia and their relationship with biogeography.     

Population genomics in Sardinia: a novel approach to hunt for genomic combinations underlying complex traits and diseases.

The availability of highly polymorphic markers permits testing whether complex traits and diseases result from genomic interactions between nonallelic normal variants at separate loci. Such variants may be identified by deviations from the expected distributions of alleles at a high number of polymorphic loci, when individuals with the phenotype of interest are compared to normal controls of the same breeding unit, provided that both groups share the same remote ancestry and had no ancestors in common for the last three to four generations. The circumstances needed for such studies are ideally met on the island of Sardinia. The recurrent finding of the same type of association in separate breeding units between the phenotype of interest and a given genotype should allow a distinction between true genetic identity by descent and randomly occurring identities, as these will be obviously different in separate breeding units. The availability of several breeding units located in sharply different ecological environments will permit assessment of the role of nature/nurture factors in the degree of manifestation of each newly discovered genotype/phenotype association. A pilot study to evaluate the proposed strategy has been carried out in the Sardinian village of Carloforte, a community of about 8,000 individuals who have remained genetically homogeneous. Fifty-five control samples have been genotyped with six tetranucleotide microsatellites and with a subset of the 400 markers contained in the ABI PRISM linkage mapping panel, version 2. The allele frequencies for these microsatellite markers have been determined for these 55 individuals and compared to those from a random sampling of subsets of these 55 persons. For the six tetranucleotide microsatellites, a subset of as few as 20 people displayed the same allele frequency distributions as observed with the original 55 unrelated individuals. In conclusion, when samples are chosen from the same breeding unit, the number of individuals sufficient to draw the genomic profile of an isolated population can be relatively small. Likewise, the number of probands with the phenotype of interest can be even smaller when they are ascertained with the same genealogical criteria as the normal controls. By comparing the genomic profile of the probands to a fraction of the control samples within each of several separate breeding units of common remote ancestry, the search for genotype/phenotype association for mono- and multifactorial traits and diseases should be simplified and yield unequivocal results.     

Associations of the bovine major histocompatibility complex DRB3 (BoLA-DRB3) with production traits in Canadian dairy cattle

Associations of two alleles of the bovine major histocompatibility complex DRB3 gene (BoLA-DRB3) with lowered somatic cell score (SCS) and occurrence of disease (BoLA-DRB3.2* 16 and *23, respectively) have previously been documented. The objective of this study was to evaluate potential relationships between BoLA-DRB3 alleles with production traits, namely 305-day milk, milk fat and milk protein yield, in a population of Canadian dairy cattle (Holstein, n = 835 and Jersey, n = 66) over the course of two lactations. No significant associations were detected between BoLA alleles and production traits in Jerseys. In Holsteins, alleles *16 and *23 also did not show associations with production traits but allele *8 was significantly associated with increased 305-day milk, fat and protein yields in the previous lactation (the lactation prior to immunization with a gram negative core antigen vaccine), and with increased protein production in the subsequent (with reference to the time of immunization) lactation. Allele *22 was associated with decreased milk and protein yield in both previous and subsequent lactations. Therefore, it can be concluded that increasing or decreasing the frequency of BoLA alleles *16 and *23 to reduce SCS or increase resistance to mastitis in this population would not have adverse effects on production in this population, and that certain BoLA alleles (*8 and *22) are associated with altered production traits in Canadian Holsteins.     

Longitudinal random effects models for genetic analysis of binary data with application to mastitis in dairy cattle

A Bayesian analysis of longitudinal mastitis records obtained in the course of lactation was undertaken. Data were 3341 test-day binary records from 329 first lactation Holstein cows scored for mastitis at 14 and 30 days of lactation and every 30 days thereafter. First, the conditional probability of a sequence for a given cow was the product of the probabilities at each test-day. The probability of infection at time t for a cow was a normal integral, with its argument being a function of "fixed" and "random" effects and of time. Models for the latent normal variable included effects of: (1) year-month of test + a five-parameter linear regression function ("fixed", within age-season of calving) + genetic value of the cow + environmental effect peculiar to all records of the same cow + residual. (2) As in (1), but with five parameter random genetic regressions for each cow. (3) A hierarchical structure, where each of three parameters of the regression function for each cow followed a mixed effects linear model. Model 1 posterior mean of heritability was 0.05. Model 2 heritabilities were: 0.27, 0.05, 0.03 and 0.07 at days 14, 60, 120 and 305, respectively. Model 3 heritabilities were 0.57, 0.16, 0.06 and 0.18 at days 14, 60, 120 and 305, respectively. Bayes factors were: 0.011 (Model 1/Model 2), 0.017 (Model 1/Model 3) and 1.535 (Model 2/Model 3). The probability of mastitis for an "average" cow, using Model 2, was: 0.06, 0.05, 0.06 and 0.07 at days 14, 60, 120 and 305, respectively. Relaxing the conditional independence assumption via an autoregressive process (Model 2) improved the results slightly.