Breeding value accuracy estimates for growth traits using random regression and multi-trait models in Nelore cattle

We quantified the potential increase in accuracy of expected breeding value for weights of Nelore cattle, from birth to mature age, using multi-trait and random regression models on Legendre polynomials and B-spline functions. A total of 87,712 weight records from 8144 females were used, recorded every three months from birth to mature age from the Nelore Brazil Program. For random regression analyses, all female weight records from birth to eight years of age (data set I) were considered. From this general data set, a subset was created (data set II), which included only nine weight records: at birth, weaning, 365 and 550 days of age, and 2, 3, 4, 5, and 6 years of age. Data set II was analyzed using random regression and multi-trait models. The model of analysis included the contemporary group as fixed effects and age of dam as a linear and quadratic covariable. In the random regression analyses, average growth trends were modeled using a cubic regression on orthogonal polynomials of age. Residual variances were modeled by a step function with five classes. Legendre polynomials of fourth and sixth order were utilized to model the direct genetic and animal permanent environmental effects, respectively, while third-order Legendre polynomials were considered for maternal genetic and maternal permanent environmental effects. Quadratic polynomials were applied to model all random effects in random regression models on B-spline functions. Direct genetic and animal permanent environmental effects were modeled using three segments or five coefficients, and genetic maternal and maternal permanent environmental effects were modeled with one segment or three coefficients in the random regression models on B-spline functions. For both data sets (I and II), animals ranked differently according to expected breeding value obtained by random regression or multi-trait models. With random regression models, the highest gains in accuracy were obtained at ages with a low number of weight records. The results indicate that random regression models provide more accurate expected breeding values than the traditionally finite multi-trait models. Thus, higher genetic responses are expected for beef cattle growth traits by replacing a multi-trait model with random regression models for genetic evaluation. B-spline functions could be applied as an alternative to Legendre polynomials to model covariance functions for weights from birth to mature age.     

Random regression analyses using B-spline functions to model growth of Nellore cattle

The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.     

Random regression models using different functions to model test-day milk yield of Brazilian Holstein cows

We analyzed 152,145 test-day records from 7317 first lactations of Holstein cows recorded from 1995 to 2003. Our objective was to model variations in test-day milk yield during the first lactation of Holstein cows by random regression model (RRM), using various functions in order to obtain adequate and parsimonious models for the estimation of genetic parameters. Test-day milk yields were grouped into weekly classes of days in milk, ranging from 1 to 44 weeks. The contemporary groups were defined as herd-test-day. The analyses were performed using a single-trait RRM, including the direct additive, permanent environmental and residual random effects. In addition, contemporary group and linear and quadratic effects of the age of cow at calving were included as fixed effects. The mean trend of milk yield was modeled with a fourth-order orthogonal Legendre polynomial. The additive genetic and permanent environmental covariance functions were estimated by random regression on two parametric functions, Ali and Schaeffer and Wilmink, and on B-spline functions of days in milk. The covariance components and the genetic parameters were estimated by the restricted maximum likelihood method. Results from RRM parametric and B-spline functions were compared to RRM on Legendre polynomials and with a multi-trait analysis, using the same data set. Heritability estimates presented similar trends during mid-lactation (13 to 31 weeks) and between week 37 and the end of lactation, for all RRM. Heritabilities obtained by multi-trait analysis were of a lower magnitude than those estimated by RRM. The RRMs with a higher number of parameters were more useful to describe the genetic variation of test-day milk yield throughout the lactation. RRM using B-spline and Legendre polynomials as base functions appears to be the most adequate to describe the covariance structure of the data.     

Polynomials to model the growth of young bulls in performance tests

The use of polynomial functions to describe the average growth trajectory and covariance functions of Nellore and MA (21/32 Charolais+11/32 Nellore) young bulls in performance tests was studied. The average growth trajectories and additive genetic and permanent environmental covariance functions were fit with Legendre (linear through quintic) and quadratic B-spline (with two to four intervals) polynomials. In general, the Legendre and quadratic B-spline models that included more covariance parameters provided a better fit with the data. When comparing models with the same number of parameters, the quadratic B-spline provided a better fit than the Legendre polynomials. The quadratic B-spline with four intervals provided the best fit for the Nellore and MA groups. The fitting of random regression models with different types of polynomials (Legendre polynomials or B-spline) affected neither the genetic parameters estimates nor the ranking of the Nellore young bulls. However, fitting different type of polynomials affected the genetic parameters estimates and the ranking of the MA young bulls. Parsimonious Legendre or quadratic B-spline models could be used for genetic evaluation of body weight of Nellore young bulls in performance tests, whereas these parsimonious models were less efficient for animals of the MA genetic group owing to limited data at the extreme ages.     

Genetic parameters of body weight in sheep estimated via random regression and multi-trait animal models

Variance components for five consecutive measurements of body weight in Polish sheep were estimated using random regression and multi-trait animal models. The data included between 7856 and 31694 body weight records at 5 age classes from birth to 150 days of age. The random additive genetic, maternal environmental and individual permanent environmental effects were fitted. All variance components were increasing over time (not at equal rates), which reflects increasing phenotypic mean and variance with age. Direct heritability tended to increase with age, whereas the effect of dam was reduced for older ages, and the proportion of permanent environmental component was relatively stable. Generally, similar tendencies were registered for estimates obtained via multi-trait animal model. The results confirm that there is a scope for genetic improvement in growth pattern in Polish sheep.     

Genetic parameter estimates for pre-weaning performance and reproduction traits in Markhoz goats

Genetic parameters for growth, mortality and reproductive performances of Markhoz goats were estimated from data collected during 1993–2010 at Markhoz goat Performance Testing Station in Sanandaj, Iran. For kid performance traits 3763 records were available for birth weight (BW), 2931 for weaning weight (WW), average daily gain (ADG) and Kleiber ratio (KR) (approximated as ADW/WW^0.75) and 3032 for pre-weaning mortality (PWM). For doe reproductive performance traits there were 2920 records available for litter size at birth (LSB), litter size at weaning (LSW), total litter weight at birth (TLWB) and litter mean weight per kid born (LMWKB), and 2182 for total litter weight at weaned (TLWW) and litter mean weight per kid weaned (LMWKW). Genetic parameters were estimated with univariate and bivariate models using restricted maximum likelihood (REML) procedures. Random effects were explored by fitting additive direct genetic effects, maternal additive genetic effects, maternal permanent environmental effects, the covariance between direct and maternal genetic effects, and common litter effects in different models for pre-weaning traits of kids. Also, in addition to an animal model, sire and threshold models, using a logit link function, were used for analyses of PWM. Models for LSB, LSW, TLWB, TLWW, LMWKB, and LMWKW included direct additive genetic effects, permanent environmental effects due to the animal as well as service sire effects. Estimated direct heritabilities were moderate for pre-weaning traits (0.22 for BW, 0.16 for WW, 0.21 for ADG, and 0.27 for KR and 0.29 for PWM), and low for reproduction traits (0.01 for LSB, 0.01 for LSW, 0.02 for TLWB, 0.03 for TLWW, 0.07 for LMWKB, and 0.06 for LMWKW). The estimates for the maternal additive genetic variance ratios were lower than direct heritability for BW (0.07) and KR (0.04). The estimate for the maternal permanent environmental variance ratios (c²) varied from 0.01 for KR to 0.07 for WW and ADG. The magnitude of common litter variance ratios (l²) was more substantial for BW (0.46) than the PWM (0.19) and KR (0.16). The estimate for the permanent environmental variance due to the animal (c²) ranged from 0.03 for LMWKB to 0.07 for TLWB and LMWKW, whereas service sire effects (s²) ranged from 0.02 to 0.04. The correlation between direct and maternal genetic effects were negative and high for BW (?0.51) and KR (?0.62). The genetic correlations between pre-weaning growth traits were positive and moderate to strong, as were genetic correlations between reproductive traits. Between BW and PWM the correlation was ?0.35. Phenotypic and environmental correlations for all traits were generally lower than genetic correlations.     

Genetic analysis of body weights of individually fed beef bulls in South Africa using random regression models

The aim of this study was to estimate genetic parameters for body weights of individually fed beef bulls measured at centralized testing stations in South Africa using random regression models. Weekly body weights of Bonsmara bulls (N = 2919) tested between 1999 and 2003 were available for the analyses. The model included a fixed regression of the body weights on fourth-order orthogonal Legendre polynomials of the actual days on test (7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, and 84) for starting age and contemporary group effects. Random regressions on fourth-order orthogonal Legendre polynomials of the actual days on test were included for additive genetic effects and additional uncorrelated random effects of the weaning-herd-year and the permanent environment of the animal. Residual effects were assumed to be independently distributed with heterogeneous variance for each test day. Variance ratios for additive genetic, permanent environment and weaning-herd-year for weekly body weights at different test days ranged from 0.26 to 0.29, 0.37 to 0.44 and 0.26 to 0.34, respectively. The weaning-herd-year was found to have a significant effect on the variation of body weights of bulls despite a 28-day adjustment period. Genetic correlations amongst body weights at different test days were high, ranging from 0.89 to 1.00. Heritability estimates were comparable to literature using multivariate models. Therefore, random regression model could be applied in the genetic evaluation of body weight of individually fed beef bulls in South Africa.     

(Co)Variance components and genetic parameter estimates for growth traits in Moghani sheep

Genetic parameters were estimated for birth weight (BW), weaning weight (WW), yearling weight (YW), average daily gain from birth to weaning (ADG1) and average daily gain from weaning to yearling (ADG2) in Moghani sheep. Maximum number of data was 4237 at birth, but only 1389 records at yearling were investigated. The data was collected from 1995 to 2007 at the Breeding Station of Moghani sheep in Jafarabad, Moghan, Iran. (Co)Variance components and genetic parameters were estimated with different models which including direct effects, with and without maternal additive genetic effects as well as maternal permanent environmental effects using restricted maximum likelihood (REML) method. The most appropriate model for each trait was determined based on likelihood ratio tests and Akaike's Information Criterion (AIC). Maternal effects were important only for pre-weaning traits. Direct heritability estimates for BW, ADG1, WW, ADG2 and YW were 0.07, 0.08, 0.09, 0.09 and 0.17, respectively. Fractions of variance due to maternal permanent environmental effects on phenotypic variance were 0.08 for ADG1. Maternal heritability estimates for BW and WW were 0.18 and 0.06, respectively. Multivariate analysis was performed using the most appropriate models obtained in univariate analysis. Direct genetic correlations among studied traits were positive and ranged from 0.37 for BW–ADG2 to 0.85 for ADG1–YW. Maternal genetic correlation estimate between BW and WW was 0.33. Phenotypic and environmental correlation estimates were generally lower than those of genetic correlation. Low direct heritability estimates imply that mass selection for these traits results in slow genetic gain.     

Milk yield persistency in Brazilian Gyr cattle based on a random regression model

With the objective of evaluating measures of milk yield persistency, 27,000 test-day milk yield records from 3362 first lactations of Brazilian Gyr cows that calved between 1990 and 2007 were analyzed with a random regression model. Random, additive genetic and permanent environmental effects were modeled using Legendre polynomials of order 4 and 5, respectively. Residual variance was modeled using five classes. The average lactation curve was modeled using a fourth-order Legendre polynomial. Heritability estimates for measures of persistency ranged from 0.10 to 0.25. Genetic correlations between measures of persistency and 305-day milk yield (Y305) ranged from -0.52 to 0.03. At high selection intensities for persistency measures and Y305, few animals were selected in common. As the selection intensity for the two traits decreased, a higher percentage of animals were selected in common. The average predicted breeding values for Y305 according to year of birth of the cows had a substantial annual genetic gain. In contrast, no improvement in the average persistency breeding value was observed. We conclude that selection for total milk yield during lactation does not identify bulls or cows that are genetically superior in terms of milk yield persistency. A measure of persistency represented by the sum of deviations of estimated breeding value for days 31 to 280 in relation to estimated breeding value for day 30 should be preferred in genetic evaluations of this trait in the Gyr breed, since this measure showed a medium heritability and a genetic correlation with 305-day milk yield close to zero. In addition, this measure is more adequate at the time of peak lactation, which occurs between days 25 and 30 after calving in this breed.     

Estimates of direct and maternal covariance functions for growth of Australian beef calves from birth to weaning

Records for birth and subsequent, monthly weights until weaning on beef calves of two breeds in a selection experiment were analysed fitting random regression models. Independent variables were orthogonal (Legendre) polynomials of age at weighing in days. Orders of polynomial fit up to 6 were considered. Analyses were carried out fitting sets of random regression coefficients due to animals'' direct and maternal, additive genetic and permanent environmental effects, with changes in variances due to temporary environmental effects modelled through a variance function, estimating up to 67 parameters. Results identified similar patterns of variation for both breeds, with maternal effects considerably more important in purebred Polled Herefords than a four-breed synthetic, the so-called Wokalups. Conversely, repeatabilities were higher for the latter. For both breeds, heritabilities decreased after birth, being lowest when maternal effects were most important around 100 days of age. Estimates at birth and weaning were consistent with previous, univariate results.     

Genetic modelling of test day records in dairy sheep using orthogonal Legendre polynomials

Test day milk yields of three lactations in Sfakia sheep were analyzed fitting a random regression (RR) model, regressing on orthogonal polynomials of the stage of the lactation period, i.e. days in milk. Univariate (UV) and multivariate (MV) analyses were also performed for four stages of the lactation period, represented by average days in milk, i.e. 15, 45, 70 and 105 days, to compare estimates obtained from RR models with estimates from UV and MV analyses. The total number of test day records were 790, 1314 and 1041 obtained from 214, 342 and 303 ewes in the first, second and third lactation, respectively. Error variances and covariances between regression coefficients were estimated by restricted maximum likelihood. Models were compared using likelihood ratio tests (LRTs). Log likelihoods were not significantly reduced when the rank of the orthogonal Legendre polynomials (LPs) of lactation stage was reduced from 4 to 2 and homogenous variances for lactation stages within lactations were considered. Mean weighted heritability estimates with RR models were 0.19, 0.09 and 0.08 for first, second and third lactation, respectively. The respective estimates obtained from UV analyses were 0.14, 0.12 and 0.08, respectively. Mean permanent environmental variance, as a proportion of the total, was high at all stages and lactations ranging from 0.54 to 0.71. Within lactations, genetic and permanent environmental correlations between lactation stages were in the range from 0.36 to 0.99 and 0.76 to 0.99, respectively. Genetic parameters for additive genetic and permanent environmental effects obtained from RR models were different from those obtained from UV and MV analyses.     

Estimation of genetic parameters for monthly egg production in laying hens based on random regression models

Heritability and genetic correlations of monthly egg production under random regression models were estimated. Three layer lines (A22, A88, K66) in six consecutive generations were analysed. A22 (13, 770 recorded hens) and A88 (13, 950 recorded hens) are maternal lines of Rhode Island White birds selected on egg production and shell colour; K66 (9, 351 recorded birds) is a paternal line of Rhode Island Red birds selected on egg weight. Eight models with different orders of Legendre polynomials were applied. Adequacy of the models was checked by the Akaike Information Criterion. According to the most adequate model including second order Legendre polynomials for fixed effects and third order for additive genetic and permanent environmental effects, relatively high heritabilities were estimated in the first (h²=0.3) and final (h² above 0.3) periods of production with a substantial decrease in heritability during the egg production peak. Methodology based on random regression animal models can be recommended for genetic evaluation of laying hens.     

Genetic analysis of sexual dimorphism of body weight in broilers

Variation in sexual dimorphism (SD) is particularly marked in meat-type chickens. This paper investigates the genetic basis of SD in an important economic trait, i.e. body weight (BW) at 35 days of age, in broilers by applying quantitative genetic analysis. A large dataset comprising 203,323 BW records of a commercial line of broiler chicken was used. First, a bivariate approach was employed treating BW as a sex-specific trait. During this approach, seven bivariate models were applied and variances due to direct additive genetic, maternal genetic and maternal environmental effects were estimated via the restricted maximum likelihood method. The best-fitting model included direct additive genetic, maternal genetic and maternal environmental effects with a direct–maternal genetic covariance. Differences between male and female direct heritabilities were non-significant (0.28 vs. 0.29 for males and females, respectively), implying no need for sex-specific selection strategies. The direct–maternal genetic correlation was more strongly negative in males than in females (?0.72 vs. ?0.56), implying a more profound antagonism between direct additive and maternal genetic effects in this particular gender. The direct genetic correlation of BW between the two sexes was as high as 0.91, i.e. only slightly lower than unity. Second, variance components and genetic parameters of two measures of SD, i.e. the weight difference (Δ) and the weight ratio (R), between the genders were estimated. Direct heritabilities for both measures were significantly different to 0 but of low magnitude (0.04). Apart from the additive–maternal covariance, no other random effects were found to be of importance for Δ and R. The results of the present study suggest that only minimal selection responses due to the selection of Δ and/or R and a small capacity for amplifying or reducing the BW differences between the sexes are to be expected in this specific population. Furthermore, selection pressure on BW is expected to amplify SD.     

Genetic variability of body weight in two goose strains under long-term selection

Body weight is one of the most important traits in any genetic improvement program in geese for at least 2 reasons. First, measurements of the trait are very easy. Second, body weight is correlated with a number of other meat performance traits. However, the genetic background of body weight shows considerable complexity. Three genetic models (with direct, maternal genetic and permanent maternal environmental effects) were employed in this study. Records of 3076 individuals of maternal strain W11 and 2656 individuals of paternal strain W33 over 6 consecutive generations, kept in the pedigree farm of Ko?uda Wielka, were analysed. Body weight (in kilograms) was measured in weeks 8 (BW8) and 11 (BW11). The inbreeding levels in both populations were relatively low (0.14% and 0.02% for W11 and W33, respectively), therefore these effects were not included in the linear models to estimate genetic parameters. Three fixed effects (hatch period, sex and year) were included in each linear model. Two criteria (AIC, BIC) were used to check the goodness of fit of the models. The computations were performed by WOMBAT software. In general, the genetic parameter estimates varied across the traits, models and strains studied. Direct additive heritability estimates ranged from 0.0001 (for BW11 of W33) to 0.55 (for BW11 of W33). Maternal and total heritabilities were also variable. Estimates of ratios of direct-maternal effect covariance in phenotypic variance were both positive and negative, but they were negligible, whereas ratios of the permanent environmental maternal variance to phenotypic variance were close to zero. Both of the applied criteria of model adequacy indicate that the model with maternal genetic and environmental effects should be considered as optimal. Genetic trends were close to zero. It seems that they were influenced by long-term selection. Similar tendencies have been observed for phenotypic trends, as well.     

Genetic parameters for stayability to consecutive calvings in Zebu cattle

Longer-lived cows tend to be more profitable and the stayability trait is a selection criterion correlated to longevity. An alternative to the traditional approach to evaluate stayability is its definition based on consecutive calvings, whose main advantage is the more accurate evaluation of young bulls. However, no study using this alternative approach has been conducted for Zebu breeds. Therefore, the objective of this study was to compare linear random regression models to fit stayability to consecutive calvings of Guzerá, Nelore and Tabapuã cows and to estimate genetic parameters for this trait in the respective breeds. Data up to the eighth calving were used. The models included the fixed effects of age at first calving and year-season of birth of the cow and the random effects of contemporary group, additive genetic, permanent environmental and residual. Random regressions were modeled by orthogonal Legendre polynomials of order 1 to 4 (2 to 5 coefficients) for contemporary group, additive genetic and permanent environmental effects. Using Deviance Information Criterion as the selection criterion, the model with 4 regression coefficients for each effect was the most adequate for the Nelore and Tabapuã breeds and the model with 5 coefficients is recommended for the Guzerá breed. For Guzerá, heritabilities ranged from 0.05 to 0.08, showing a quadratic trend with a peak between the fourth and sixth calving. For the Nelore and Tabapuã breeds, the estimates ranged from 0.03 to 0.07 and from 0.03 to 0.08, respectively, and increased with increasing calving number. The additive genetic correlations exhibited a similar trend among breeds and were higher for stayability between closer calvings. Even between more distant calvings (second v. eighth), stayability showed a moderate to high genetic correlation, which was 0.77, 0.57 and 0.79 for the Guzerá, Nelore and Tabapuã breeds, respectively. For Guzerá, when the models with 4 or 5 regression coefficients were compared, the rank correlations between predicted breeding values for the intercept were always higher than 0.99, indicating the possibility of practical application of the least parameterized model. In conclusion, the model with 4 random regression coefficients is recommended for the genetic evaluation of stayability to consecutive calvings in Zebu cattle.     

Genetic (co)variance for sire fertility estimated by additive,non-additive and longitudinal models in Holstein–Zebu cross-bred cows

For this study, we used the results of sire fertility (SF) measured on a monthly basis by the ratio between the number of pregnant cows and the number of inseminations, from a total of 905 140 inseminations carried out in Cuba between 1994 and 2003. These artificial inseminations were made using 815 sires in 3249 herds throughout the country, and were analysed using additive, non-additive linear models and a random regression model (RRM). The additive genetic (add), heterosis (het) and recombination loss (rec) coefficients were estimated according to the proportion of Zebu (Z) and Holstein (H) blood from the paternal and maternal origin of each cow. The mean level of SF was 48.8%, whereas het and rec were 9.6% and −8.4%, respectively. The heritability (h²) of a single insemination ranged from h² = 0.011 to h² = 0.030 for females from 0% to 100% of H genes. The additive multi-trait and RRM analyses showed the existence of heterogeneous genetic (co)variance components, as the proportion of Holstein genes in the inseminated cow increased. We found low genetic correlations for SF recorded in pure-bred and cross-bred females, with over 50% of breed differences in their additive genetic composition. The use of a RRM allows us to identify the changes in genetic (co)variance and estimated breeding values in the whole trajectory of the different proportions of Bos taurus × Bos indicus blood.     

Simultaneous estimation of daily weight and feed intake curves for growing pigs by random regression

In this study, random regression models were used to estimate covariance functions between feed intake and BW in boars from the two breeds: the Norwegian Landrace and the Norwegian Duroc. In total, 1476 animals of the Norwegian Landrace breed and 1300 animals of the Norwegian Duroc breed had registrations on daily feed intake and growth from 54 to 180 days of age. Random regressions on the Legendre polynomials of age were used to describe genetic and permanent environmental curves in BW (up to the second order) and feed intake (up to the first order) for both the breeds. Heritabilities on BW increased over time for the Landrace (0.18 to 0.24), but were approximately constant for the Duroc (0.33 to 0.35). Average heritabilities for feed intake were approximately the same in both the breeds (0.09 to 0.11), and the estimates decreased over time, most pronounced in Duroc. On the basis of the current data, daily feed intake was seemingly controlled by the same genetic factors throughout the test period for Duroc; however, for Landrace, genetic correlations between test days decreased with increasing distance in time. For BW, the genetic correlations between test days were in general high, and did not go below 0.8 for any of the two breeds in this study. For both feed intake and BW, permanent environmental correlations between start and end of the test were reduced with increasing difference in days, most pronounced in Duroc. This study indicates that weight of the animal at the end of the test was more closely genetically correlated to feed intake of earlier periods compared with later periods of growth for both the breeds. This may be explained by the fact that BW is the cumulative growth of an individual, which is likely to be heavily affected by the feed intake during the most intense growth period.     

Genetic parameters for body weight,longissimus muscle depth and fat depth for Suffolk sheep in the Czech Republic

In this study, heritabilities and (co)variance components for body weight at 100 days (BW), muscle depth (MD) and fat depth (FD) were estimated for Suffolk, the most common sheep breed in the Czech Republic. Data from 1996 to 2004 were extracted from the sheep recording database of the Czech Sheep and Goat Breeding Association. Genetic parameters were estimated using multivariate animal models, including both direct and maternal genetic effects and permanent environmental effects. Average values for BW, MD and FD were 27.91 kg, 25.5 mm and 3.3 mm, respectively. Direct and maternal heritability for BW were 0.17 and 0.08, respectively, and direct heritabilities were 0.16 for MD and 0.08 for FD. Maternal heritability estimates for ultrasonic measurements were generally low. Direct genetic correlations between BW and MD and maternal genetic correlations between BW and MD were positive and favourable. Both direct genetic correlations between BW and FD and maternal genetic correlations between BW and FD were negative, but not significantly different from zero. The favourable genetic correlations between BW and MD make ultrasound measurements a valuable tool in breeding programs focusing on growth and carcass characteristics.     

Model comparison for genetic evaluation of milk yield in crossbred Holsteins in the tropics

The objective of this study was to compare models for appropriate genetic parameter estimation for milk yield (305-day) in crossbred Holsteins in the tropics, where only records from crossbred cows were available. Eleven models with different effects of contemporary group (CG) at calving (herd-year-season or herd-year-month as fixed, and herd-year-month as random), age at calving (as linear or quadratic covariates, age-class, and age-class x lactation), and dominance were considered. On-farm records from small herds (n < 50) were included or excluded to validate the parameter estimates. Average Information Restricted Maximum Likelihood (AIREML) and Best Linear Unbiased Prediction (BLUP) were used to estimate variance components and breeding values. R-square (R2) and standard error of heritability (h2) were used to determine the appropriate model. The estimates of heritability from most models ranged from 0.18 to 0.22. CG formation of herd-year-month as a random effect slightly lowered the additive genetic variance but considerably decreased the permanent environmental variance. The model with age-class x lactation gave better R2 than other age adjustments. The models including records from smallholders gave similar estimates of heritability and a lower standard error than the models excluding them. The estimate of dominance variance as a proportion of total variance was close to zero. The low ratio of dominance to additive genetic variance suggested that the inclusion of dominance effects in the model was unjustified. In conclusion, the model including the effects of herd-year-month, age-class x lactation, as well as additive genetic, permanent environmental and residual effects, was the most appropriate for genetic evaluation in crossbred Holsteins, where records from smallholders could be included.     

Misspecification in Mixed-Model-Based Association Analysis

Additive genetic variance in natural populations is commonly estimated using mixed models, in which the covariance of the genetic effects is modeled by a genetic similarity matrix derived from a dense set of markers. An important but usually implicit assumption is that the presence of any nonadditive genetic effect increases only the residual variance and does not affect estimates of additive genetic variance. Here we show that this is true only for panels of unrelated individuals. In the case that there is genetic relatedness, the combination of population structure and epistatic interactions can lead to inflated estimates of additive genetic variance.