Animal Permanent Environmental Effects Research Articles

Elucidating genotype by environment interaction over the growth trajectory of Malpura sheep in the semi-arid region of India through Random regression model

The Presence of genotype by environment (GxE) interaction over different ages across growth trajectory in different environments leads to alteration in sires ranking, it may cause problem in any breeding program by affecting efficiency of selection. The objective of the present study was to compare the random regression models (RRM) and conventional animal models and also to plot the trajectory of the growth curve using Legendre polynomial (LP) function of the RRM for better genetic evaluation for growth traits of the Malpura sheep. The data was collected from 8299 animals descended from 2529 dams and 525 sires for growth traits of Malpura sheep, selected over 45 years (1975–2019) maintained at the Animal Genetics and Breeding Division, ICAR-Central Sheep and Wool Research Institute (CSWRI), Avikanagar, Rajasthan, India. The Legendre polynomial based random regression models (LP-RRM) was more robust as compared to conventional animal model and it included direct genetic, direct maternal, maternal permanent environmental and animal permanent environmental effects as a random effects in different orders of fit. The estimates for the additive direct heritability (h2) using best LP-RRM (4444) were 0.176 ± 0.022, 0.367 ± 0.024, 0.314 ± 0.021, 0.323 ± 0.023 and 0.314 ± 0.023, respectively for live body weight at birth (BWT), three-month (WWT), six-month (6WT), nine-month (9WT) and twelve-month (12WT). The comparable trends of variances were found in LP-RRM with trends obtained from the inclusive univariate animal model that included the direct genetic, direct maternal and maternal permanent environmental components. The h2 estimates indicated the further scope of genetic improvement through selection. The maternal proportion of variance was accounting for 1–15 % variance across growth trajectory indicating the low influence of maternal effects that reduced significantly post-weaning. However, we observed that the animal permanent environment accounted for 42–58 % of variance across growth trajectory. The estimates of genetic correlation in LP-RRM were positive and higher (mostly >0.80) between most of the time points as compared to the estimates obtained from animal model, indicating less GxE when RRM is used. Currently selection of Malpura sheep is carried out at the age of six month for growth traits. The presence of genotype by environment (GxE) interaction resulted in to significant re-ranking of sires at 12WT on the basis of breeding values using animal model. However, more consistency in sires ranking were found in the reaction norms plotted for breeding values at 6WT and 12WT using LP-RRM. The RRM have property for accounting (GxE) interaction across growth trajectories more precisely. Therefore, it is recommended that the RRM approach should be used for genetic evaluation of Malpura sheep at 6-month age for unbiased, accurate, and consistent prediction of breeding values for growth traits.

Evaluation of body weight and hip height in Nellore cows in a tropical environment

The aim of this study was to evaluate random regression models to estimate genetic parameters for body weight and hip height in Nellore females and identify the best time to select these characteristics for adult size control. The dataset comprised 33,569 body weight and 31,804 height records from 3,860 and 3,487 females, respectively. Contemporary group and physiological state (for body weight analysis) were modeled as fixed effects, whereas age at birth (both linear and quadratic effects) and Legendre polynomials of age at (k = 4) as covariates. Random effects, including the additive genetic effects, and the animal permanent environment effect and the dam (for body weight analysis), were also included in the model. Random effects were modeled by Legendre polynomials of degree k in [3, 6], while residues were considered to be homogeneous or heterogeneous. The best model for body weight included heterogeneous residual variance with 21 classes and Legendre polynomials of degree k = 3, k = 6 and k = 1 for the additive genetic effects, animal and maternal permanent environment effects, respectively. The best model for hip height included homogeneous residual variance and Legendre polynomials of degree k = 4 and k = 3 for the additive genetic effects and animal permanent environment effect, respectively. Heritability estimates were moderate to high and suggest the studied characteristics could be used for maintaining cow size, being the selection at 3 years sufficient to get the desired size.

Impact of inbreeding on milk fatty acids of a Brazilian Holstein cattle

Context Reproductive technologies may either contribute to the increase of genetic gains or inbreeding levels in dairy cattle breeding programs and herds. In general, studies have evaluated the impacts of inbreeding on traditional traits, such as production and reproduction. However, studies on novel traits, such as milk fatty acids profile, are scarce in the literature. Aim We aimed to evaluate the impact of inbreeding levels on milk fatty acids profile measured in a Brazilian Holstein cattle population. Methods Monthly records of the percentages (%) of palmitic, stearic, oleic, total saturated, unsaturated, monounsaturated and polyunsaturated fatty acids in milk were collected from 2047 Holstein cows between May and December 2012. The pedigree file contained 7963 animals over seven generations. The inbreeding trend was evaluated by linear regression of inbreeding coefficients on generations. The inbreeding impacts on breeding and phenotypic values were evaluated by linear regression of breeding values and phenotypic values on generations respectively. Breeding values were obtained by a Bayesian approach based on an animal model that included the systematic effect of contemporary group, cubic effect of days in milk as a covariate, and the random direct additive genetic and animal permanent environmental effects. Key results The average inbreeding coefficient was 0.28% for all animals, and 1.39% for inbred animals. Inbreeding tended to increase 0.24% per generation (P-value <0.0001). The regression coefficients of phenotypic values on inbreeding were not significant for saturated, unsaturated, monounsaturated, palmitic, stearic and oleic fatty acids (P-values >0.18, 0.10, 0.16, 0.26, 0.51 and 0.09 respectively); whereas for polyunsaturated fatty acids, they were significant (P-value <0.04), with an increase of –0.000978% on phenotypic values for each 1% increase in inbreeding. The regression coefficients of breeding values on inbreeding were not significant for unsaturated, monounsaturated, polyunsaturated, stearic and oleic fatty acids (P-values >0.33, 0.78, 0.48, 0.32 and 0.07 respectively). However, they were significant for saturated and palmitic fatty acids (P-values <0.03 and 0.0001 respectively), presenting an increase of 0.000689% and 0.000283% respectively on breeding values for each 1% increase in inbreeding. Conclusions There was a significant increase in inbreeding coefficients over the studied generations; however, the impacts on both breeding and phenotypic values were small, when significant. Implications Our study may contribute to the understanding of how inbreeding levels may affect the fatty acids profile in a Brazilian Holstein cattle population, as well as encourage future research on this subject.

Time class for racing performance of the Quarter Horse: Genetic parameters and trends using Bayesian and multivariate threshold models

The aim of this study was to evaluate racing performance in the Quarter Horse breed in Brazil using genetic parameter estimates, breeding values, and genetic trends for a differentiated trait, time class (TC), at four different distances. The speed records comprising races that occurred between 1981 and 2011 were obtained from hippodromes in the states of São Paulo, Ceará, Brasília, and Mato Grosso do Sul. The final archive analysed contained 4263 horses born to 431 stallions and 1716 dams. These animals participated in 3904 races, providing 17,342 records of final racing time. The four TC traits were defined by 5 scores based on the final times (in seconds) of each animal in each race. The scores for formation of the classes were attributed within each race based on the percent difference from winner's time. Time class was evaluated at distances of 301, 320, 365 and 402 m, generating four phenotypic measures: TC301, TC320, TC365 and TC402, respectively. The genetic parameters were estimated by Bayesian inference in multivariate analysis using a threshold animal model. The model included the fixed effects of race, sex and age class of animal in the race, in addition to additive genetic, animal permanent environmental and residual random effects. The mean heritability estimates were of high magnitude and ranged from 0.45 ± 0.06 (TC402) to 0.56 ± 0.04 (TC365). Repeatability estimates ranged from 0.78 ± 0.06 (TC402) to 0.97 ± 0.01 (TC320). The additive genetic and animal permanent environmental correlations were positive, with mean correlations ranging from 0.33 ± 0.06 between TC301 and TC320 to 0.62 ± 0.06 between TC365 and TC402 and from 0.44 ± 0.08 between TC301 and TC320 to 0.58 ± 0.06 between TC365 and TC402, respectively. The mean breeding values transformed by the cumulative distribution function of the standard normal distribution ranged from 54.6 ± 25.3 (TC365) to 57.8 ± 28.5 (TC320) in the group of animals included in the pedigree and born after 1980. The genetic trends observed indicated that TC301 (301 m) exhibited the greatest evolution between 1981 and 2008. The results suggest the possible use of TC traits as selection criteria since they respond positively to selection, permitting genetic gains in breeding programs of racehorses.

Estimates of covariance functions for growth of Kordi sheep in Iran using random regression models

In the current paper, restricted maximum likelihood estimates of covariance functions for growth records from birth to 360 days of age in Kordi sheep population were estimated using random regression models (RRM). Kordi sheep is an important breed known for adaptability and resistance to unfavorable climatic conditions and suitable feed efficiency in mountainous regions of Iran. Data included 23,720 body weight records of 6730 Kordi lambs collected from 1989 to 2012 at Hossein Abad Kordi sheep Breeding Station in Shirvan city, North Khorasan province, Iran. Fixed effects in the model were lamb sex, birth type, and birth year as well as dam age. Legendre polynomials (LP) of order 3 was used for age to illustrate the average growth curve. In the random part, the functions with different orders were included to model variances associated to direct and maternal effects. Results showed that a model with LP of order 4,3,4,3 for direct additive genetic effects, animal permanent environmental effects, maternal additive genetic and maternal permanent environmental effects was sufficient to model changes in (co)variances with age, according to Akaike’s Information Criterion (AIC) and Bayesian information criterion (BIC). Direct additive genetic and animal permanent environment variances increased with age. Direct heritability (h2a) increased with age from 0.133 ± 0.021 at birth to 0.391 ± 0.034 at 360 days of age. The ratio of animal permanent environmental variances to phenotypic variance (pe2) was 0.047 ± 0.083 at birth, increased with age and reached 0.537 ± 0.034 at the end of the growth trajectory. Maternal heritability (h2m) was 0.152 ± 0.025 at birth decreased to 0.067 ± 0.016 until weaning and then fluctuated between 0.06 and 0.10. The ratio of maternal permanent environmental variances to phenotypic variance (mpe2) was 0.082 ± 0.02 at birth; however, it gradually decreased until the end of trajectory. The first eigenvalues of the coefficient matrices explained 69% and 91% of the total direct additive variance and maternal genetic variance, respectively. Direct genetic correlations ranged from low and negative to positively high, and generally decreased as the distance between tests increased. Current study has demonstrated that RRM have potential for modeling growth of Kordi sheep and a greater response to selection would be expected, if selection focuses on body weights from 30 days of age to 120 days of age.

Use of Random Regression Test-Day Model to Estimate Genetic Parameters of Milk Yield in Holstein Cows

(Co) variance components and genetic parameters were estimated for milk yield of Iranian Holstein cows. A total number of 68,945 milk test-day records of first, second and third lactations of 8515 animals from 100 sires and 7743 dams originated from 34 herds collected during 2007 to 2009 by Iranian animal breeding center were used. The ASReml computer program was used to analyze the milk test-day records using the random regression procedure. Herd test date (HTD), milking times per day (milking frequency), number of lactations, year of birth, year of calving, age of animal at calving and days in milk (DIM) considered as fixed effects and additive genetic effects and animal permanent environmental effects were considered as the random effects. Additive genetic variance, animal permanent environment variance, residual variance, phenotypic variance, heritability and repeatability were estimated during different months of lactation between 5.7 - 19.6, 15.3 - 27.1, 31.4 - 17.2, 45.8 - 64.83, 0.1 - 0.32 and 0.4 - 0.6, respectively. Genetic correlation and phenotypic correlation were also estimated between months of lactation in range of -0.35 - 0.98 and 0.03 - 0.67, respectively. Genetic correlation and phenotypic correlation both showed the same changing pattern and they decreased as the interval between months of lactation increased.

Random regression models to estimate genetic parameters for weights in Murrah buffaloes.

This article reports genetic analysis of the weight at different ages of Murrah water buffaloes, using random regression models (RRM). Models ranging from third to sixth order polynomial were used to describe direct genetic and animal permanent environmental effects. Contemporary group was included as a fixed effect, and a cubic polynomial was used to model the mean curve of the population. The residual was modeled considering a log-linear function. Two models were selected for study of genetic parameters. The first model included third and sixth order polynomials for direct genetic and animal permanent environmental effects (M36). The second model included sixth order polynomials for all random effects (M66). The estimates of heritability varied from 0.16+0.04 (44days) to 0.38+0.04 (568days) for model M36 and from 0.16+0.05 (33days) to 0.42+0.05 (600days) for model M66. Regarding estimates of the correlation for all effects, the magnitude tended to decline with the increase of the time span between measurements. These results indicate that the species has potential for genetic selection based on weight at different ages, since we found favorable genetic variability within the herd, with selection likely to be more efficient at ages near 600days.

Random regression model with heterogeneous residual variance reduces polynomial order fitted for permanent environmental effect but does not affect genetic parameters for milk production in Sahiwal cattle

The random regression test-day models can accelerate the genetic improvement of Sahiwal cattle as test-day milk yield models offer a faster, accurate and economical approach of genetic evaluation. First three lactation monthly test-day records of Sahiwal cows calved between 1961 and 2012 at ICAR-National Dairy Research Institute, Karnal were used to fit random regression model (RRM) with various order of legendre polynomial, and a constant (RRM-HOM) or heterogeneous residual variance (RRM-HET). For both RRM-HOM and RRM-HET third order legendre polynomial for modelling additive genetic effects were found best. There was reduction in order of fit for modelling permanent environmental effects due to assumption of heterogeneous residual variance, as legendre polynomial of sixth order for RRM-HOM and fourth or fifth order for RRM-HET was found to be best, for modelling the permanent environmental effect. First two eigenvalues of additive genetic random regression coefficient matrix explained more than 99% of the additive genetic variation, whereas four eigenvalues explained ~98% of the permanent environment variations. First eigenfunction from both the models did not show any large change along lactation, suggesting most variation can be explained by genes that act in same way during lactation. The heritability estimates were generally low but moderate for some test-day milk yields, and it ranged from 0.007 to 0.088 for first, 0.044 to 0.279 for second, and 0.089 to 0.129 for third lactation from RRM-HOM. The values of genetic correlation between test-day milk yields ranged from 0.06 to 0.99 for first, 0.77 to 0.99 for second, and 0.07 to 0.99 for third lactation, from RRM-HOM. The value of permanent environment correlation ranged from 0.30 to 0.98 for first, 0.07 to 0.99 for second, and 0.16 to 0.98 for third lactation. The genetic correlations between two adjacent test-days were high (≥0.90). RRM-HET also gave similar heritability and correlation estimates. The rank correlation between sire breeding values for first, second, and third lactation, estimated using two models were 0.98, 1.00, and 0.99, respectively, indicating there was no difference in the ranking of animals using two models. Thus the random regression model with lower order of polynomial for modelling additive genetic effect and higher order polynomial for modelling animal permanent environmental effect was found suitable for genetic evaluation and both RRM-HOM and RRM-HET can be used for modelling test-day milk yield and breeding value prediction in Sahiwal cattle.

Estimation of genetic parameters for test-day milk yield in Khuzestan buffalo

Abstract: The objective of this work was to estimate covariance functions for additive genetic and permanent environmental effects, as well as to obtain genetic parameters for buffalo test-day milk yield using random regression models on Legendre polynomials (LPs). A total of 2,538 test-day milk yield (TDMY) records from 516 first lactation records of Khuzestan buffalo, calving from 1993 to 2009 and belonging to 150 herds located in the state of Khuzestan, Iran, were analyzed. The residual variances were modeled through a step function with 1, 5, 6, 9, and 19 classes. The additive genetic and permanent environmental random effects were modeled by LPs of days in milk using quadratic to septic polynomial functions. The model with additive genetic and animal permanent environmental effects adjusted by cubic and third order LP, respectively, and with the residual variance modeled through a step function with nine classes was the most adequate one to describe the covariance structure. The model with the highest significant log-likelihood ratio test (LRT) and with the lowest Akaike information criterion (AIC) and Bayesian information criterion (BIC) was considered to be the most appropriate one. Unexpected negative genetic correlation estimates were obtained between TDMY records of the twenty-fifth and thirty-seventh week (-0.03). Genetic correlation estimates were generally higher, close to unity, between adjacent weeks during the middle of lactation. Random regression models can be used for routine genetic evaluation of milk yield in Khuzestan buffalo.

Modelos de regressão aleatória para características de crescimento de bovinos da raça Nelore do estado de Mato Groso

Foram utilizados 138.976 registros de informações de pesos corporais variando de 60 a 610 dias de idade, provenientes de 27.327 animais da raça Nelore, oriundos de rebanhos do estado do Mato Grosso, com o objetivo de descrever a variabilidade genética e estimar parâmetros genéticos para o peso corporal em diferentes idades, utilizando-se modelos de regressão aleatória. O modelo empregado incluiu efeitos fixos de grupo de contemporâneos e idade da vaca ao parto como covariáveis, além de efeitos aleatórios genético aditivo direto, genético materno, ambiente permanente de animal, ambiente permanente materno e efeito de ambiente temporário. O modelo de regressão aleatória mais adequado foi o que empregou função de covariância com polinômios de quarta ordem para descrição da variabilidade de todos os efeitos e duas classes de variância residual. As estimativas de variância genética aditiva direta e de ambiente permanente de animal aumentaram com a idade dos animais. As variâncias genética materna e de ambiente permanente materno exibiram comportamento semelhante, com maiores valores na fase de aleitamento. Os coeficientes de herdabilidade estimados variam de 0,25 a 0,43, com maiores valores nas idades mais avançadas na trajetória de crescimento dos animais. Esses resultados indicaram presença de variabilidade genética suficiente para obtenção de ganho genético expressivo por meio da seleção, principalmente após desmama. Os resultados encontrados para a correlação genética aditiva direta exibiram baixas correlações entre pesos nas idades iniciais e finais, porém pesos altamente correlacionados entre idades mais próximas. As correlações genéticas estimadas entre os pesos da desmama com os pesos até 610 dias de idade foram altas e positivas e indicam que os genes responsáveis por maiores pesos nesse período, em sua maioria, são os mesmos.

Variance Components and Genetic Parameters Estimated for Fat and Protein Content in Individual Months of Lactation: The Case of Tsigai Sheep.

The objective of this study was to assess variance components and genetic parameters for fat and protein content in Tsigai sheep using multivariate animal models in which fat and protein content in individual months of lactation were treated as different traits, and univariate models in which fat and protein content were treated as repeated measures of the same traits. Test day measurements were taken between the second and the seventh month of lactation. The fixed effects were lactation number, litter size and days in milk. The random effects were animal genetic effect and permanent environmental effect of ewe. The effect of flock-year-month of test day measurement was fitted either as a fixed (FYM) or random (fym) effect. Heritabilities for fat content were estimated between 0.06 and 0.17 (FYM fitted) and between 0.06 and 0.11 (fym fitted). Heritabilities for protein content were estimated between 0.15 and 0.23 (FYM fitted) and between 0.10 and 0.18 (fym fitted). For fat content, variance ratios of permanent environmental effect of ewe were estimated between 0.04 and 0.11 (FYM fitted) and between 0.02 and 0.06 (fym fitted). For protein content, variance ratios of permanent environmental effect of ewe were estimated between 0.13 and 0.20 (FYM fitted) and between 0.08 and 0.12 (fym fitted). The proportion of phenotypic variance explained by fym effect ranged from 0.39 to 0.43 for fat content and from 0.25 to 0.36 for protein content. Genetic correlations between individual months of lactation ranged from 0.74 to 0.99 (fat content) and from 0.64 to 0.99 (protein content). Fat content heritabilities estimated with univariate animal models roughly corresponded with heritability estimates from multivariate models: 0.13 (FYM fitted) and 0.07 (fym fitted). Protein content heritabilities estimated with univariate animal models also corresponded with heritability estimates from multivariate models: 0.18 (FYM fitted) and 0.13 (fym fitted).

Estimates of genetic parameters for growth traits in Brahman cattle using random regression and multitrait models.

Random regression models (RRM) and multitrait models (MTM) were used to estimate genetic parameters for growth traits in Brazilian Brahman cattle and to compare the estimated breeding values obtained by these 2 methodologies. For RRM, 78,641 weight records taken between 60 and 550 d of age from 16,204 cattle were analyzed, and for MTM, the analysis consisted of 17,385 weight records taken at the same ages from 12,925 cattle. All models included the fixed effects of contemporary group and the additive genetic, maternal genetic, and animal permanent environmental effects and the quadratic effect of age at calving (AAC) as covariate. For RRM, the AAC was nested in the animal's age class. The best RRM considered cubic polynomials and the residual variance heterogeneity (5 levels). For MTM, the weights were adjusted for standard ages. For RRM, additive heritability estimates ranged from 0.42 to 0.75, and for MTM, the estimates ranged from 0.44 to 0.72 for both models at 60, 120, 205, 365, and 550 d of age. The maximum maternal heritability estimate (0.08) was at 140 d for RRM, but for MTM, it was highest at weaning (0.09). The magnitude of the genetic correlations was generally from moderate to high. The RRM adequately modeled changes in variance or covariance with age, and provided there was sufficient number of samples, increased accuracy in the estimation of the genetic parameters can be expected. Correlation of bull classifications were different in both methods and at all the ages evaluated, especially at high selection intensities, which could affect the response to selection.

<b>Effect of age of dam on weight of calf in the genetic assessment of Zebu cattle in random regression models

Current analysis estimated co-variance components and genetic parameters for growth traits by random regression models taking into consideration the cow's age on the weight of calves. Genealogical data and records on weights of male and female Zebu cattle, born between 1993 and 2011, were provided by the National Association of Breeders and Researchers (ANCP). Different models were compared by Akaike and Bayesian criteria. Legendre's orthogonal polynomials were used to model the direct and maternal genetic effects of maternal and animal permanent environmental effects. Joint modeling of cow age at the moment their progenies were weighed resulted in more accurate estimates of co-variance components and genetics parameters. Co-variance functions of the cow age retrieved the dam effect on real performance of the progenies, reduced biases, improved parameter estimates and predicted breeding rates.

An exploratory analysis to determine the impact of fixed effects and to establish genetic parameters across six types of ostrich feathers

After a decline in value, ostrich feathers have again become an important part of the income of ostrich producers. Between 22586 and 22753 feather weights, as well as length and width measurements, were obtained from feathers harvested annually during the resting period from a pair-bred ostrich flock maintained at Oudtshoorn Research Farm from 2001 to 2012. The flock consisted mostly of the South African Black (SAB) genotype, but birds from the Zimbabwean Blue (ZB) and Kenyan Redneck (KR) strains were also introduced to study strain effects, as well as the effect of crossbreeding between these genotypes (ZB x SAB; SAB x ZB; KR x SAB; SAB x KR). The feathers were sorted into six feather-type categories, namely floss, short hard body feathers, long hard body feathers, tail feathers, white plumes and short body floss. White plumes had the highest average feather length (AFL), average feather width (AFWD) and square-root-transformed feather weight (SRFW) at 66.2 ± 0.38 cm, 21.2 ± 0.23 cm and 13.66 ± 0.17 g, respectively. A significant decline in AFL took place from 2001 and 2012 (40.0 ± 0.25 cm and 38.7 ± 0.56 cm, respectively), while AFWD stayed fairly constant. Feather weights were higher for males than females resulting in a 24% higher geometric mean for backtransformed feather weights (GMFW) for males relative to females. SAB birds outperformed ZB and KR birds for AFL, AFWD and SRFW. Crosses were intermediate and sometimes comparable with the SAB genotype. Except for long hard body plumes, the weights for all the feather types were higher for the purebred SAB breeders compared with purebred ZB and KR breeders. Heritability estimates of AFL, AFWD and SRFW across the six feather categories were low to moderate at 0.080 ± 0.012, 0.044 ± 0.009 and 0.116 ± 0.017, respectively. The animal permanent environmental effect for the feather traits was lower in magnitude and ranged between 0.025 ± 0.008 for AFL and 0.041 ± 0.012 cm for SRFW. Direct genetic correlations of feather dimensions with SRFW were moderate to high at 0.287 ± 0.117 with AFL and 0.614 ± 0.072 with AFWD. The present results indicate that feather quantity can be improved by genetic selection in ostriches, and further studies should be conducted.Keywords: Age, feather length, feather weight, feather width, genotype, sex

Models for genetic evaluation of growth of Brazilian Bonsmara cattle

The purpose of this study was to demonstrate the usefulness of different multi-trait models and random regression models (RRM) using Legendre polynomials for the genetic evaluation of growth in Brazilian Bonsmara cattle. Data comprised 54,039 weight records of Bonsmara cattle, from birth to adult age (614 days of age). A standard multi-trait model (SMT); reduced rank analyses fitting the first 2 genetic principal components (PC2), reduced rank analyses fitting the first direct additive genetic and maternal principal components (PC22), reduced rank analyses fitting the first direct additive genetic, maternal, and maternal permanent environmental principal components (PC222), were carried out. For all traits, genetic additive direct and maternal, and maternal permanent environmental were considered as random effects. Furthermore, linear and quadratic effects of age of the animal at recording (except for birth weight), and dam age at calving were included as covariates. The analyses were performed using a single-trait RRM. Fourth-order Legendre polynomials to model trends in the population mean. Additive direct, animal permanent environmental effects, maternal genetic, and maternal permanent environmental effects were modeled with Legendre polynomials. In addition, contemporary group as fixed effects, dam age at calving (linear and quadratic), age at recording (linear) as covariates were included. Genetic parameters from different approaches were similar, when the optimal number of PC was fitted. The model PC222 (reduced rank analyses fitting the first direct additive genetic, maternal, and maternal permanent environmental principal components) allows a reduction of the number of parameters to be estimated, and this methods was sufficient to describe the genetic covariance structure adequately.

Estimates of genetic parameters for total milk yield over multiple ages in Brazilian Murrah buffaloes using different models.

The objective of this study was to estimate variance components and genetic parameters for accumulated 305-day milk yield (MY305) over multiple ages, from 24 to 120 months of age, applying random regression (RRM), repeatability (REP) and multi-trait (MT) models. A total of 4472 lactation records from 1882 buffaloes of the Murrah breed were utilized. The contemporary group (herd-year-calving season) and number of milkings (two levels) were considered as fixed effects in all models. For REP and RRM, additive genetic, permanent environmental and residual effects were included as random effects. MT considered the same random effects as did REP and RRM with the exception of permanent environmental effect. Residual variances were modeled by a step function with 1, 4, and 6 classes. The heritabilities estimated with RRM increased with age, ranging from 0.19 to 0.34, and were slightly higher than that obtained with the REP model. For the MT model, heritability estimates ranged from 0.20 (37 months of age) to 0.32 (94 months of age). The genetic correlation estimates for MY305 obtained by RRM (L23.res4) and MT models were very similar, and varied from 0.77 to 0.99 and from 0.77 to 0.99, respectively. The rank correlation between breeding values for MY305 at different ages predicted by REP, MT, and RRM were high. It seems that a linear and quadratic Legendre polynomial to model the additive genetic and animal permanent environmental effects, respectively, may be sufficient to explain more parsimoniously the changes in MY305 genetic variation with age.

Genetic parameters for body weight in buffaloes (Bubalus bubalis) in Colombia using random regression models

The objective of this research was to estimate (co) variance functions and genetic parameters for body weight in Colombian buffalo populations using random regression models with Legendre polynomials. Data consisted of 34,738 weight records from birth to 900 days of age from 7815 buffaloes. Fixed effects in the model were contemporary group and parity order of the mother. Random effects were direct and maternal additive genetic, as well as animal and maternal permanent environmental effects. A cubic orthogonal Legendre polynomial was used to model the mean curve of the population. Eleven models with first to sixth order polynomials were used to describe additive genetic direct and maternal effects, and animal and maternal permanent environmental effects. The residual was modeled considering five variance classes. The best model included fourth and sixth order polynomials for direct additive genetic and animal permanent environmental effects, respectively, and third-order polynomials for maternal genetic and maternal permanent environmental effects. The direct heritability increased from birth until 120 days of age (0.32±0.05), decreasing thereafter until one year of age (0.18±0.04) and increased again, reaching 0.39±0.09, at the end of the evaluated period. The highest maternal heritability estimates (0.11±0.05), were obtained for weights around weaning age (weaning age range is between 8 and 9.5 months). Maternal genetic and maternal permanent environmental variances increased from birth until about one year of age, decreasing at later ages. Direct genetic correlations ranged from moderate (0.60±0.060) to high (0.99±0.001), maternal genetic correlations showed a similar range (0.41±0.401 and 0.99±0.003), and all of them decreased as time between weighings increased. Direct genetic correlations suggested that selecting buffalos for heavier weights at any age would increase weights from birth through 900 days of age. However, higher heritabilities for direct genetic weights effects after 600 days of age suggested that selection for these effects would be more effective if done during this age period. A greater response to selection for maternal ability would be expected if selection used maternal genetic predictions for weights near weaning.

Heritability estimates for weight gain in Nellore in Mato Grosso state, using model of infinite dimension

Abstract: We used 138,976 records of information of body weights ranging from 60 to 610 days of age, from 27,327 Nelore cattle of herds in the state of Mato Grosso. The random regression model with the covariance function of fourth order to describe the variability of the effects of additive genetic, animal and maternal permanent environment and maternal genetic effect and maternal, showed heritability estimates from 0.209 to 0.423 at the beginning by the end of the trajectory, respectively. There is enough genetic variability to promote genetic gain satisfactory performance for weight after weaning period the animals. Keywords : beef cattle, genetic parameters, selection.

Use of orthogonal functions in random regression models in describing genetic variance in Nellore cattle

A total of 204,912 records of birth weights up to 550 days of age, of 24,890 Nellore cattle, offspring of 375 sires and 16,917 dams from five herds in the state of Mato Grosso, Brazil, were used in order to describe the variability of the weight development by random regression models. The model evaluated as the most suitable used the covariance function of fourth order to describe the variability of the effects of additive genetic, animal permanent environmental and maternal effects of third order to describe the maternal genetic effect, with four classes of residual variance. Heritability estimates ranged from 0.18 to 0.46 from the beginning of trajectory to 210 days of age, from 0.45 to 0.48 post-weaning to 365 days of age and from 0.47 to 0.57 at later ages. The values of additive genetic correlations for different ages showed higher estimates between the closest ages, while birth weight was not very related to the weights at older ages. The body weight performance of the animals has additive genetic variation to respond to selection.

Selection of a suitable data set and model for the genetic evaluation of the linear description of conformation and type description in Old Kladruber horses

Abstract. The objective of this paper was to select a suitable data subset and statistical model for the estimation of genetic parameters for 36 traits of the linear type in 977 Old Kladruber horses. Two subsets were tested to identify a suitable subset for analysis. One subset included repeated evaluation of certain individuals, whereas the other did not. The most suitable subset included repeated evaluation (n=1 390). The selection of a suitable model was made from 4 candidate models. These models comprised a number of random effects (direct individual effect and animal permanent environmental effect of the animal) and a number of fixed effects (colour variant, stud, colour variant × stud interaction, sex, age at description, year of birth, year of description). The model was selected based on the Akaike information criterion (AIC, Akaike 1974), residual variance and heritability coefficient. The model that included colour variant, stud, colour variant × stud interaction, sex, age at description, and year of description as fixed effects and direct individual and animal permanent environment as random effects was the most suitable model for the estimation of genetic parameters and for the subsequent estimation of breeding values.