Are farmers motivated to select for heat tolerance? Linking attitudinal factors, perceived climate change impacts, and social trust to farmers' breeding desires.

This study provides an understanding of dairy farmers' willingness to include heat tolerance in breeding goals and the modulating effect of sociopsychological factors and farm profile. A survey instrument including a choice experiment was designed to specifically address the trade-off between heat tolerance and milk production level. A total of 122 farmers across cattle, goat, and sheep farms were surveyed face-to-face. The results of the experiment show that most farmers perceive that heat stress and climate change are increasingly important problems, and that farming communities should invest more in generating knowledge and resources on mitigation strategies. However, we found limited initial support for selection for heat tolerance. This attitude changed when farmers were presented with objective information on the benefits and limitations of the different breeding choices, after which most farmers supported selection for heat tolerance, but only if doing so would compromise milk production gains to a small extent. Our results show that farmers' selection choices are driven by the interactions between heat stress risk perception, attitudes toward breeding tools, social trust, the species reared, and farm production level. In general, farmers willing to support selection of heat-tolerant animals are those with positive attitudes toward genetic values and genomic information and a strong perception of climate change and heat stress impacts on farms. On the contrary, negative support for selection for heat tolerance is found among farmers with high milk production levels; high trust in farming magazines, livestock farmers' associations, and veterinarians; and low trust in environmental and animalist groups.

Prediction of birth weight using body measurements of local caprine population kids raised in a low-input breeding mode under arid environment.

The aim of this study is to establish linear measurements of local goat kids at birth and their factors of variation, as well as their possible correlations with birth weight. Additionally, the study analyses statistical models and barymetric functions to predict birth weight of kids based on their morphometric data. The database includes data on 128 goat kids born to 89 goats and 9 bucks in the experimental goat herd at the El GORDHAB station of IRA. Average BW, withers height (L1), heart girth (L2), rump height (L3), and body length (L4) of all kids were 2.45kg, 32.66cm,30.56cm, 33.41cm, and 31.21cm respectively. Results show that in general, local goat kids are small in size and weight at birth, which varies depending on sex, dam age, and type of birth. Highest and positive correlation coefficient value between birth weight and heart girth were observed (r = 0.95). The coefficient of determination (R2) for heart girth (0.78) was higher than other body measurements in single trait evaluation indicating it as the best trait for the predication of birth weight. The most appropriate combination of body measurements (R2 = 0.82) was observed between height at withers and heart girth for predication of birth weight estimation. Developing a system for recording birth weight based on easily obtainable body measurements could be a useful approach for rural areas. Result join the study objective by conceiving feasible genetic improvement plans for agropastoral herds by establishing individual phenotypes estimation even when the classical animal management does not already allowed.

Assessing heat tolerance through productive vs physiological indicators. Data from dairy sheep under on-farm conditions.

The search for criteria that allow the quantification of the level of thermotolerance of an animal is a major challenge in animal production. Different criteria have been proposed to date, mainly the use of routine milk recording and weather information or the collection of physiological measures related with heat stress. This study aimed at quantifying the association between indicators of heat tolerance derived from productive and physiological traits. For this purpose, two physiological traits, rectal temperature (RT) and respiratory rate (RR), and nine productive traits (milk yield, fat, protein and lactose yields and contents, casein and urea contents) were measured from June to September of 2018 in three flocks of Manchega sheep. A total of 462 lactating ewes participated in the study. Air temperature (Ta), relative humidity (RH) and associated temperature and humidity index (THI) were recorded inside the barn and also obtained from the closest weather station from the national meteorological network, and used to produce several measurements of heat load on animals. Based on the results of fits for quadratic and cubic regressions on the alternative heat load measures, the cubic regression on Ta and THI obtained inside the barn at time of recording yielded the best fit for physiological and productive parameters. The use of weather information taken from the official weather station closest to the farm also produced similar estimates and could be considered as a good alternative when on-farm meteorological data are not available. Two-trait random regression models that involved individual intercept and slope of response to heat load were used to obtain correlations between basal levels and heat tolerance within and across traits. Estimated correlations showed that animals with smaller vs larger basal levels of RT and RR tend to be more vs less heat tolerant (correlations up to 0.46) and that slopes of increase for RR and RT under heat stress were highly correlated (0.82). Estimated correlations between tolerance criteria from production vs physiology were up to -0.5 (between milk yield and RT), indicating that animals that show less increase in body temperature also tend to show a smaller decrease in production under heat stress. However, because of the non-unity correlation between the two types of indicators of heat tolerance, both sources of information, productive and physiological ought to be taken into account to ensure the long-term sustainability of selection programmes aiming at improving productive levels when heat stress is a concerning issue.

BREEDING AND GENETICS SYMPOSIUM: Breeding for resilience to heat stress effects in dairy ruminants. A comprehensive review.

Selection for heat tolerant (HT) animals in dairy production has been so far linked to estimation of declines in production using milk recording and meteorological information on the day of control using reaction norms. Results from these models show that there is a reasonable amount of genetic variability in the individual response to high heat loads, which makes feasible selection of HT animals at low costs. However, the antagonistic relationship between level of production and response to heat stress (HS) implies that selection for HT animals under this approach must be done with caution so that productivity is not damaged. Decomposition of the genetic variability in principal components (PC) can provide selection criteria independent of milk production level although biological interpretation of PC is difficult. Moreover, given that response to heat stress for each animal is estimated with very sparse information collected under different physiological and management circumstances, biased (normally underestimation) and lack of accuracy may be expected. Alternative phenotypic characterization of HT can come from the use of physiological traits, which have also shown moderate heritability. However, costs of a large scale implementation based on physiological characteristics has precluded its use. Another alternative is the use of biomarkers that define heat tolerance. A review of biomarkers of HS from more recent studies is provided. Of particular interest are milk biomarkers, which together with infrared spectra prediction equations can provide useful tools for genetic selection. In the 'omics' era, genomics, transcriptomics, proteomics and metabolomics have been already used to detect genes affecting HT. A review of findings in these areas is also provided. Except for the slick hair gene, there are no other genes for which variants have been clearly associated with HT. However, integration of omics information could help in pointing at knots of the HS control network and, in the end, to a panel of markers to be used in the selection of HT animals. Overall, HT is a complex phenomenon that requires integration of fine phenotypes and omics information to provide accurate tools for selection without damaging productivity. Technological developments to make on-farm implementation feasible and with greater insight into the key biomarkers and genes involved in HT are needed.

Linkage disequilibrium, persistence of phase, and effective population size in Spanish local beef cattle breeds assessed through a high-density single nucleotide polymorphism chip.

Linkage disequilibrium (LD) and persistence of phase are fundamental approaches for exploring the genetic basis of economically important traits in cattle, including the identification of QTL for genomic selection and the estimation of effective population size () to determine the size of the training populations. In this study, we have used the Illumina BovineHD chip in 168 trios of 7 Spanish beef cattle breeds to obtain an overview of the magnitude of LD and the persistence of LD phase through the physical distance between markers. Also, we estimated the time of divergence based on the persistence of the LD phase and calculated past from LD estimates using different alternatives to define the recombination rate. Estimates of average (as a measure of LD) for adjacent markers were close to 0.52 in the 7 breeds and decreased with the distance between markers, although in long distances, some LD still remained (0.07 and 0.05 for markers 200 kb and 1 Mb apart, respectively). A panel with a lower boundary of 38,000 SNP would be necessary to launch a successful within-breed genomic selection program. Persistence of phase, measured as the pairwise correlations between estimates of in 2 breeds at short distances (10 kb), was in the 0.89 to 0.94 range and decreased from 0.33 to 0.52 to a range of 0.01 to 0.08 when marker distance increased from 200 kb to 1 Mb, respectively. The magnitude of the persistence of phase between the Spanish beef breeds was similar to those found in dairy breeds. For across-breed genomic selection, the size of the SNP panels must be in the range of 50,000 to 83,000 SNP. Estimates of past showed values ranging from 26 to 31 for 1 generation ago in all breeds. The divergence among breeds occurred between 129 and 207 generations ago. The results of this study are relevant for the future implementation of within- and across-breed genomic selection programs in the Spanish beef cattle populations. Our results suggest that a reduced subset of the SNP panel would be enough to achieve an adequate precision of the genomic predictions.

Effect of exposure to adverse climatic conditions on production in Manchega dairy sheep.

The present study aimed to examine the effects of exposure to adverse weather conditions on milk production to assess the thermotolerance capability of the Manchega breed, a dairy sheep reared in the Mediterranean area, and the extent of decline in production outside the thermal comfort zone. To achieve this purpose, we merged data from the official milk recording of the breed with weather information and used to describe the cold and heat stress response for production traits. Production data consisted of 1,094,804 test-day records from the first 3 lactations of 177,605 ewes gathered between years 2000 to 2010. For each production trait and climate variable, the thermal load production response was characterized by the estimation of cold and heat stress thresholds that define a thermoneutral zone and the slopes of production decay outside this thermoneutral zone. Overall, we observed a comfort region between 10 and 22°C for daily average temperature, 18 and 30°C for daily maximum temperature, and from 9 to 18 units for a temperature-humidity index (THI) for all traits. Decline in production due to cold stress effects was of a greater magnitude than heat stress effects, especially for milk yield. Production losses ranged between 7 and 16 and from 0.2 to 0.6g/d per °C (or THI unit) for milk and for fat and protein yields, respectively. For heat stress, the observed decline in production was of 1 to 5 and 0.1 to 0.3g/d per °C (or THI unit) above the threshold for milk yield and for fat and protein yields, respectively. Highly productive animals showed a narrower comfort zone and higher slopes of decay. The study of lagged effects of thermal load showed how consequences of cold and heat stress are already visible in the first hours after exposure. Thus, production losses were due mainly to climate conditions on the day of control and the day before, with conditions on the previous days having a smaller effect. Annual economic losses due to thermal (cold and heat) stress ranged from 0.1 up to 4% of total profit depending on which climate variable was considered. Although of small magnitude, the effect of adverse climatic conditions on total annual farm profit is not negligible; thus, we consider the implementation of strategies aimed at reducing these losses to be important. These strategies could be target improving the mitigation strategies as well as obtaining more thermotolerant animals through selection.

Modeling heat stress under different environmental conditions.

Renewed interest in heat stress effects on livestock productivity derives from climate change, which is expected to increase temperatures and the frequency of extreme weather events. This study aimed at evaluating the effect of temperature and humidity on milk production in highly selected dairy cattle populations across 3 European regions differing in climate and production systems to detect differences and similarities that can be used to optimize heat stress (HS) effect modeling. Milk, fat, and protein test day data from official milk recording for 1999 to 2010 in 4 Holstein populations located in the Walloon Region of Belgium (BEL), Luxembourg (LUX), Slovenia (SLO), and southern Spain (SPA) were merged with temperature and humidity data provided by the state meteorological agencies. After merging, the number of test day records/cows per trait ranged from 686,726/49,655 in SLO to 1,982,047/136,746 in BEL. Values for the daily average and maximum temperature-humidity index (THIavg and THImax) ranges for THIavg/THImax were largest in SLO (22-74/28-84) and shortest in SPA (39-76/46-83). Change point techniques were used to determine comfort thresholds, which differed across traits and climatic regions. Milk yield showed an inverted U-shaped pattern of response across the THI scale with a HS threshold around 73 THImax units. For fat and protein, thresholds were lower than for milk yield and were shifted around 6 THI units toward larger values in SPA compared with the other countries. Fat showed lower HS thresholds than protein traits in all countries. The traditional broken line model was compared with quadratic and cubic fits of the pattern of response in production to increasing heat loads. A cubic polynomial model allowing for individual variation in patterns of response and THIavg as heat load measure showed the best statistical features. Higher/lower producing animals showed less/more persistent production (quantity and quality) across the THI scale. The estimated correlations between comfort and THIavg values of 70 (which represents the upper end of the THIavg scale in BEL-LUX) were lower for BEL-LUX (0.70-0.80) than for SPA (0.83-0.85). Overall, animals producing in the more temperate climates and semi-extensive grazing systems of BEL and LUX showed HS at lower heat loads and more re-ranking across the THI scale than animals producing in the warmer climate and intensive indoor system of SPA.

Modeling heat stress effect on Holstein cows under hot and dry conditions: selection tools.

Data from milk recording of Holstein-Friesian cows together with weather information from 2 regions in Southern Spain were used to define the models that can better describe heat stress response for production traits and somatic cell score (SCS). Two sets of analyses were performed, one aimed at defining the population phenotypic response and the other at studying the genetic components. The first involved 2,514,762 test-day records from up to 5 lactations of 128,112 cows. Two models, one fitting a comfort threshold for temperature and a slope of decay after the threshold, and the other a cubic Legendre polynomial (LP) model were tested. Average (TAVE) and maximum daily temperatures were alternatively considered as covariates. The LP model using TAVE as covariate showed the best goodness of fit for all traits. Estimated rates of decay from this model for production at 25 and 34°C were 36 and 170, 3.8 and 3.0, and 3.9 and 8.2g/d per degree Celsius for milk, fat, and protein yield, respectively. In the second set of analyses, a sample of 280,958 test-day records from first lactations of 29,114 cows was used. Random regression models including quadratic or cubic LP regressions (TEM_) on TAVE or a fixed threshold and an unknown slope (DUMMY), including or not cubic regressions on days in milk (DIM3_), were tested. For milk and SCS, the best models were the DIM3_ models. In contrast, for fat and protein yield, the best model was TEM3. The DIM3DUMMY models showed similar performance to DIM3TEM3. The estimated genetic correlations between the same trait under cold and hot temperatures (ρ) indicated the existence of a large genotype by environment interaction for fat (ρ=0.53 for model TEM3) and protein yield (ρ around 0.6 for DIM3TEM3) and for SCS (ρ=0.64 for model DIM3TEM3), and a small genotype by environment interaction for milk (ρ over 0.8). The eigendecomposition of the additive genetic covariance matrix from model TEM3 showed the existence of a dominant component, a constant term that is not affected by temperature, representing from 64% of the variation for SCS to 91% of the variation for milk. The second component, showing a flat pattern at intermediate temperatures and increasing or decreasing slopes for the extremes, gathered 15, 11, and 24% of the variation for fat and protein yield and SCS, respectively. This component could be further evaluated as a selection criterion for heat tolerance independently of the production level.

Determination of non-market values to inform conservation strategies for the threatened Alistana-Sanabresa cattle breed.

Livestock breed-related public good functions are often used to justify support for endangered breed conservation despite the fact that little is known about such non-market values. We show how stated preference techniques can be used to assess the non-market values that people place on livestock breeds. Through the application of a case study choice experiment survey in Zamora province, Spain, the total economic value (TEV) of the threatened Alistana-Sanabresa (AS) cattle breed was investigated. An analysis of the relative importance of the non-market components of its TEV and an assessment of the socio-economic variables that influence people's valuation of such components is used to inform conservation strategy design. Overall, the findings reveal that the AS breed had significant non-market values associated with it and that the value that respondents placed on each specific public good function also varied significantly. Functions related with indirect use cultural and existence values were much more highly valued than landscape maintenance values. These high cultural and existence values (totalling over 80% of TEV) suggest that an AS in situ conservation strategy will be required to secure such values. As part of such a strategy, incentive mechanisms will be needed to permit farmers to capture some of these public good values and thus be able to afford to maintain breed population numbers at socially desirable levels. One such mechanism could be related to the development of breed-related agritourism initiatives, with a view to enhancing private good values and providing an important addition to continued direct support. Where linked with cultural dimensions, niche product market development, including through improving AS breed-related product quality and brand recognition may also have a role to play as part of such an overall conservation and use strategy. We conclude that livestock breed conservation strategies with the highest potential to maximise societal welfare would be those that secure the breed-related functions that people value most, with appropriate in situ conservation interventions and strategies being identified accordingly.

Reaction norm of fertility traits adjusted for protein and fat production level across lactations in Holstein cattle.

A total of 304,001 artificial insemination outcomes in up to 7 lactations from 142,389 Holstein cows, daughters of 5,349 sires and 101,433 dams, calving between January 1995 and December 2007 in 1,347 herds were studied by a reaction norm model. The (co)variance components for days to first service (DFS), days open, nonreturn rate in the first service (NRFS), and number of services per conception were estimated by 6 models: 3 Legendre polynomial degrees for the genetic effects and adjustment or not for the level of fat plus protein (FP) production recorded at day closest to DFS. For all traits and type of FP adjustment, a second degree polynomial showed the best fit. The use of the adjusted FP model did not increase the level of genetic (co)variance components except for DFS. The heritability for each of the traits was low in general (0.03-0.10) and increased from the first to fourth calving; nevertheless, very important variability was found for the estimated breeding value (EBV) of the sires. The genetic correlations (rg) were close to unity between adjacent calvings, but decreased for most distant parities, ranging from rg=0.36 (for DFS) to rg=0.63 (for NRFS), confirming the existence of heterogeneous genetic (co)variance components and EBV across lactations. The results of the eigen decomposition of rg shows that the first eigenvalue explained between 82 to 92% and the second between 8 to 14% of the genetic variance for all traits; therefore, a deformation of the overall mean trajectory for reproductive performance across the trajectory of the different calving could be expected if selection favored these eigenfunctions. The results of EBV for the 50 best sires showed a substantial reranking and variation in the shape of response across lactations. The more important aspect to highlight, however, is the difference between the EBV of the same sires in different calvings, a characteristic known as plasticity, which is particularly important for DFS and NRFS. This component of fertility adds another dimension to selection for fertility that can be used to change the negative genetic progress of reproductive performance presented in this population of Holstein cows. The use of a reaction norm model should allow producers to obtain more robust cows for maintenance of fertility levels along the whole productive life of the cows.

Is sperm DNA fragmentation a good marker for field AI bull fertility?

This paper aimed at investigating the potential use of sperm DNA fragmentation (SDF) to improve the routine screening of infertility of Holstein bulls. Cryopreserved sperm samples from 201 Holstein bulls provided by an AI center were used in the analyses of SDF at 0 (SDF_0) and 6 (SDF_6) h of incubation at 37°C. A refinement of the sperm chromatin dispersion test implemented in the Sperm-Halomax kit was employed to measure SDF. Records on routinely collected semen traits (volume, concentration, mass and individual motility evaluated in the fresh ejaculate, and individual motility in post-thawed semen straws) were provided by the AI center. Artificial insemination bull fertility was obtained from official field recording as successful or failed insemination. The results show that the average SDF was low (around 3.5%) at 0 and 6 h of incubation. A moderate effect of inbreeding depression was found. Estimated heritability for SDF traits were moderately high (0.41 and 0.29 for SDF_0 and SDF_6, respectively) and estimated repeatability of SDF measures in the same animal were high (0.73 and 0.70 for SDF_0 and SDF_6, respectively). An overall estimated service bull value (ESBV) obtained through statistical modeling that allowed for adjustment of systematic environmental effects not specific to a bull and of the female contribution to fertility, and the estimated genetic values (EGV) were obtained from field-recorded AI information. The ESBV and EGV were also obtained for all semen traits. Moderately large and negative Pearson correlation coefficients were observed between SDF traits and male fertility ranging from (-0.43 to -0.50; P <0.001). Results of stepwise regression analyses showed that SDF_6 had the largest partial r(2) (0.15 to 0.26) among all semen characteristics. Overall, the selected semen traits explained 25% and 31% of the observed variability in bull fertility measured as EGV and ESBV, respectively. When looking at the predictive ability of bull fertility categories, the results of discriminant and logistic regression analyses showed that low-fertility bulls (those in the 10th or lower percentile in the fertility distribution) can be accurately identified by using measures of SDF alone or in combination with sperm motility. Values of SDF around 7% to 10% could be used as indicators of low AI success.

Product versus additive model for studying artificial insemination results in several livestock populations.

Two models can be used for studying binary results of AI. The additive threshold model proposes an underlying variable as summing the environmental and genetic effects from the 2 individuals involved in the mating, and the product threshold model assumes that the conditional probability of AI success is the product of the probabilities of success of 2 unobserved binary phenotypes (one is the male fertility; the other is the female fertility). The purpose of this paper is to compare the predictive ability of the product and the additive threshold models for studying AI results and to compare results obtained with the 2 models in 3 different species: cattle, sheep, and rabbits. Results showed that the predictive ability of the product model is similar to the additive model in sheep and rabbits but worst in cattle (percentage of wrong prediction = 42, 27, and 35% in the additive model; 43, 28, and 47% in the product model in sheep, rabbits, and cattle, respectively). Even when the 2 models have similar performance, they differed in their EBV (for instance, Pearson correlation between EBV predicted with the 2 models = 0.46 in sheep for male fertility). The product model can determine which sex is responsible for an AI failure. In sheep, the female was the responsible in 94% of the cases and male in 2% of them; in rabbits, the female was the responsible in 54% of the cases and the male in 39% of them. Different estimates of probabilities for male and female fertility success obtained with the product model in the 3 species suggest that male and female fertilities behave differently depending on the species and the uniqueness of the data sets. Although product model seems to provide additional information in the fertility process, further research is needed to understand the worst performance of the product model in cattle.

Bacteria in bovine semen can increase sperm DNA fragmentation rates: a kinetic experimental approach.

Cryopreserved straws of semen (n=228) from Holstein bulls (n=47) were examined for bacterial presence and sperm DNA fragmentation (SDF) dynamics. Commercial semen doses (representing six ejaculates per individual) were randomly selected from a bull stud in Spain. The dynamics of SDF were assessed after thawing (T0) and at 4, 24, 48, 72 and 96h of incubation at 37°C, using the commercial variant of the sperm chromatin dispersion test for Bovine (Halomax®). One group of bulls showed a bacterial presence in semen samples between 0 and 96h of incubation (n=23, group A) while the other did not (n=24, group B). Immediate post-thaw differences in SDF were not observed when both groups were compared. However, the rate of increase in SDF (rSDF) over time, considered as an estimate of the kinetic behaviour of sperm DNA survival, was significantly higher (P<0.05) in semen samples from group A (0.7% per hour) versus group B (0.05% per hour). Polymerase Chain Reaction (PCR) assay was used for DNA amplification using primers designed for specific regions of the bacterial gene that codifies for 16S rRNA. Different species within the phyla Bacteroidetes, Firmicutes, Proteobacteria, Cyanobacteria, Fusobacteria and Actinobacteria were identified. The results show that (1) SDF at baseline (T0) may not be affected by the presence of bacteria but the rSDF can increase due to bacterial growth during incubation, (2) the increase in the rSDF is characteristic of some bulls but not for others, and (3) certain bacterial strains are repeatedly found in separate ejaculates from the same bull.

Model selection in a global analysis of a microarray experiment.

Analysis of data from complementary DNA microarray experiments is an area of intense research. Options include models at the gene level or at the global level, the latter combining information from all of the profiled genes. In general, a joint analysis is expected to be more powerful than gene-specific analyses. Global analysis of microarray data requires fitting a model that jointly performs data normalization and analyses. The objective of this study was to assess the optimality of alternative models for data normalization and analysis in an experiment to identify differentially expressed genes between 2 muscles in Avileña Negra Ibérica calves. Three major groups of models were explored according to several aspects including spatial arrangement of spots, other technical sources of variation such as dye effects, assumptions related to effects included in the model, and gene-specific effects. In addition, 3 sources of heterogeneity of residual variance were investigated. All models were compared by Bayes factors and cross-validation predictive densities. The model that included array-block, dye, muscle, and array-dye as systematic effects and all gene-related components as random effects was the best model for normalization and analysis of these data under heterogeneity of residual variances. Furthermore, level of intensity seemed to be the major source of heteroscedasticity for all models investigated. Such models rendered the best goodness of fit without compromising the predictive ability. The best model also provided the best performance to detect genes differentially expressed with the lowest false discovery rate. The large differences found for the model comparison criteria across models indicate the importance of defining the factors that more accurately account for experiment-wide variability to ensure correct inference on differential expression of genes. Our results also illustrate the importance of the experimental setup to account for possible sources of bias in the detection of differentially expressed genes.

Exploring the use of random regression models with legendre polynomials to analyze measures of volume of ejaculate in Holstein bulls.

Artificial insemination centers routinely collect records of quantity and quality of semen of bulls throughout the animals' productive period. The goal of this paper was to explore the use of random regression models with orthogonal polynomials to analyze repeated measures of semen production of Spanish Holstein bulls. A total of 8,773 records of volume of first ejaculate (VFE) collected between 12 and 30 mo of age from 213 Spanish Holstein bulls was analyzed under alternative random regression models. Legendre polynomial functions of increasing order (0 to 6) were fitted to the average trajectory, additive genetic and permanent environmental effects. Age at collection and days in production were used as time variables. Heterogeneous and homogeneous residual variances were alternatively assumed. Analyses were carried out within a Bayesian framework. The logarithm of the marginal density and the cross-validation predictive ability of the data were used as model comparison criteria. Based on both criteria, age at collection as a time variable and heterogeneous residuals models are recommended to analyze changes of VFE over time. Both criteria indicated that fitting random curves for genetic and permanent environmental components as well as for the average trajector improved the quality of models. Furthermore, models with a higher order polynomial for the permanent environmental (5 to 6) than for the genetic components (4 to 5) and the average trajectory (2 to 3) tended to perform best. High-order polynomials were needed to accommodate the highly oscillating nature of the phenotypic values. Heritability and repeatability estimates, disregarding the extremes of the studied period, ranged from 0.15 to 0.35 and from 0.20 to 0.50, respectively, indicating that selection for VFE may be effective at any stage. Small differences among models were observed. Apart from the extremes, estimated correlations between ages decreased steadily from 0.9 and 0.4 for measures 1 mo apart to 0.4 and 0.2 for most distant measures for additive genetic and phenotypic components, respectively. Further investigation to account for environmental factors that may be responsible for the oscillating observations of VFE is needed.

Comparing alternative definitions of the contemporary group effect in Avilena Negra Iberica beef cattle using classical and Bayesian criteria.

Data on weaning weight from 12,740 animals were used to compare different definitions of contemporary groups (CG) for the genetic evaluation of the Avilena Negra Iberica beef cattle breed. Six alternative definitions for the CG effect were considered: herd-year-season of calving (HYS), with seasons defined according to the four natural seasons; herd-year-month of calving (HYM); herd clusters of 30 d (HC30-30) or 90 d (HC90-90); and adaptive herd clusters with two time limits, 30 and 90 d (HC30-90), and 30 and 180 d (HC30-180). A minimum of five observations in each CG class was required. This rendered substantial differences in loss of information, ranging from 0.7% of the total number of records for HC30-180 to 14% for HYM. Several classical statistics and Bayesian criteria for statistical model comparison were used. The use of classical criteria, such as the between- and within-CG variation and the accuracy of prediction, can be controversial because of their dependency on the unknown variance components. Residual variance decreased with the decrease in time span associated with the definition of CG. This was expected in this population because environmental conditions are highly variable throughout the year. However, estimates of the additive genetic variance for direct effects, which should not be affected by the definition of CG, were substantially larger for definitions involving larger time periods (HYS, HC90-90). When parameters used in the current evaluation procedure were used with all data sets, CG involving 30 d (HYM and HC30-30) were optimal in terms of providing the lowest/largest within-/between-CG variation. On the other hand, CG involving 90 d (HYS and HC90-90) yielded the poorest within-/between CG variation, with only a slight improvement of accuracy of prediction of direct genetic values over the other definitions. Bayes factors and cross-validation predictive densities allowed for improved discrimination among models. Models including CG spanning 30 d were more plausible and showed better predicting ability than models spanning 90 d. Adaptive CG showed intermediate results. Overall, it seems that average time span rendered by the different definitions had a major effect on the ranking of models. However, from the breeder's point of view, the loss of information associated with definitions involving shorter periods of time, such as HYM or HC30-30, might be unacceptable.

Assessment of homogeneity vs. heterogeneity of residual variance in random regression test-day models in a Bayesian analysis.

Test-day first-lactation milk yields from Holstein cows were analyzed with a set of random regression models based on Legendre polynomials of varying order on additive genetic and permanent environmental effects. Homogeneity and heterogeneity of residual variance, assuming three and 30 arbitrary measurement error classes of different length were considered. Unknown parameters were estimated within a Bayesian framework. Bayes factors and a checking function for the cross-validation predictive densities of the data were the tools chosen for selecting among competing models. Residual variances obtained from 30 arbitrary intervals were nearly constant between d 70 and 300 and tended to increase towards the extremes of the lactation, especially at the onset. In early lactation, the temporary measurement errors were found to be larger and highly variable. A high order of the regression submodels employed for modeling the permanent environmental deviations tended to strongly correct the heterogeneity of the residual variance. Accordingly, the assumption of homogeneity of residual variance was the most plausible specification under both comparison criteria when the number of random regression coefficients was set to five. Otherwise, the heterogeneity assumption, using three or 30 error classes, was better supported, depending on the criterion and on the order of the submodel fitted for the permanent environmental effect.

Bayesian analysis of lactation curves of Holstein-Friesian cattle using a nonlinear model.

A Bayesian procedure was developed for fitting Wood's incomplete Gamma function to test-day milk records of Spanish Holstein Friesian cattle. Each parameter of Wood's function was considered as a dependent variable in a submodel that accounted for systematic effects and genetic relationships among animals. Marginal posterior distributions of model parameters were obtained using Gibbs sampling. Variables of economic interest, such as 305-d yield, persistency, peak yield, and days in milk at peak day were predicted as functions of Wood's function curve parameters. Heritability estimates were 0.26, 0.32, and 0.19 for parameters of Wood's function and 0.26, 0.14, 0.26, and 0.05 for 305-d yield, persistency, peak yield, and days in milk at peak yield. These estimates indicate that it is possible to modify the shape of the lactation curve through genetic selection. Genetic correlations between parameters of Wood's curve and the aforementioned functions of these parameters suggest that selection for 305-d milk yield would result in higher and later peak yield, but only a slight improvement in persistency is expected.

Assessment of heterogeneity of residual variances using changepoint techniques.

Several studies using test-day models show clear heterogeneity of residual variance along lactation. A changepoint technique to account for this heterogeneity is proposed. The data set included 100,744 test-day records of 10,869 Holstein-Friesian cows from northern Spain. A three-stage hierarchical model using the Wood lactation function was employed. Two unknown changepoints at times T1 and T2, (0

Genotype by environment interaction for Holstein milk yield in Colombia, Mexico, and Puerto Rico.

Components of (co)variance and genetic parameters were estimated by REML procedures from first lactation mature equivalent Holstein milk records from 54,604 Colombian, Mexican, and Puerto Rican cows and 198,079 US cows. The objective was to determine the cause of heterogeneous daughter response to sire selection for milk yield between the regions. Data from Latin America were partitioned by country and by herd-year SD class for milk to obtain five joint analyses between the US and Latin America, low herd-year SD, high herd-year SD, Colombia, and Mexico. Sire and residual variances for milk were 41 and 29% smaller in Latin America than in the US, 47 and 58% smaller for low than for high herd-year SD, and 31 and 49% smaller for Colombia than for Mexico. Resultant heritabilities ranged from .20 to .29. Genetic correlations for milk yield between the US and Latin America, low and high herd-year SD, Colombia, and Mexico were .91, .82, .89, .78, and .90. Expected correlated responses for milk in Latin America, low and high herd-year SD, Colombia, and Mexico were 70, 53, 79, 56, and 78% of the direct response in the US. The scaling effects of heterogeneous variance resulted in smaller daughter milk responses in Latin America compared with the US even when herd-year SD was similar.