A genetic investigation of various growth models to describe growth of lambs of two contrasting breeds1

Estimating genetic parameters and trends in growth curve traits of Zandi sheep using the SAEM algorithm

The objectives of this study were to evaluate the influence of environmental effects on growth curve traits of Zandi lambs and estimate their genetic parameters with the best-fit animal model. For this purpose, live body weight (BW) records (n = 10,607) of 2,519 individuals (which were progeny of 278 rams and 1,485 ewes) were used to estimate genetic effects on growth curve traits from birth to yearling age of Zandi lambs. Using the Stochastic Approximation Expectation Maximization (SAEM) algorithm the growth curve parameters of five different mixed functions (i.e., Brody, Richards, Von Bertalanffy, Gompertz and Logistic) were obtained, then for the most appropriate model the genetic parameters were estimated using a Bayesian approach fitted multivariate animal model and ignoring or including maternal genetic effect. Except Richards model, all other mixed functions used here closely fitted actual BW records (R2 > 0.96). However, the Logistic function provided the best fit in every type. So, studied growth curve traits were estimated asymptotic weight which considered as mature weight (a), rate parameter (b), rate of maturing (k), and age (Ai)/weight (Wi) at the point of inflection. Of the fixed effects studied (i.e., gender, birth type, dam age, season and year of birth), the only non-significant relationship was the effect dam age on b and Ai. Based on the best-fitted model, posterior means of heritability estimates for a, b, k, Wi and Ai were 0.142 ± 0.036, 0.094 ± 0.029, 0.143 ± 0.063, 0.149 ± 0.039 and 0.029 ± 0.013, respectively. Posterior means of genetic correlations between mentioned traits ranged from -0.018 ± 0.069 (b-k) to 0.959 ± 0.029 (a-b), whereas the phenotypic correlation varied from -0.047 ± 0.014 (b-k) to 0.836 ± 0.007 (a-b). It was concluded that the model including only direct additive effect was sufficient to explain the variation in all investigated growth traits of Zandi lambs, selection for these traits results in slow genetic gain (due to the lack of sufficient genetic variation), but it would not be difficult to improve their mature weight and rate of maturing jointly. The results indicate that although the rate of genetic change for mature weight has been small (0.008 ± 0.003 kg year-1; P < 0.05) but in the favorable direction for this breed.

Modeling the growth curve in ducks: a sinusoidal model as an alternative to classical nonlinear models

The present study aimed to apply a sinusoidal model to duck body weight records in order to introduce it to the field of poultry science. Using 8 traditional growth functions as a guide (Bridges, Janoschek, logistic, Gompertz, Von Bertalanffy, Richards, Schumacher, and Morgan), this study looked at how well the sinusoidal equation described the growth patterns of ducks. By evaluating statistical performance and examining model behavior during nonlinear regression curve fitting, models were compared. The data used in this study came from 3 published articles reporting 1) body weight records of Kuzi ducks aged 1 to 70 d, 2) body weight records for Polish Peking ducks aged 1 to 70 d, and 3) average body weight of Peking ducks aged 1 to 42 d belonging to 5 different breeds. The general goodness-of-fit of each model to the various data profiles was assessed using the adjusted coefficient of determination, root mean square error, Akaike's information criterion (AIC), and Bayesian information criterion. All of the models had adjusted coefficient of determination values that were generally high, indicating that the models generally fit the data well. Duck growth dynamics are accurately described by the chosen sinusoidal equation. The sinusoidal equation was found to be one of the best functions for describing the age-related changes in body weight in ducks when the growth functions were compared using the goodness-of-fit criteria. To date, no research has been conducted on the use of sinusoidal equations to describe duck growth development. To describe the growth curves for a variety of duck strains/lines, the sinusoidal function employed in this study serves as a suitable substitute for conventional growth functions.

Application of growth models to South African Boer goat castrates and does under feedlot conditions

Mathematical models may aid researchers in describing biological processes, like growth, in animals. This study aimed to collect the body weight data of 18 Boer goat castrates and 20 Boer goat does, from birth until maturity, to model growth and determine growth trends. This is a novel investigation as sufficient information on an age-weight database for these two Boer goat sexes from birth to maturity, is lacking. Using age-weight data, four nonlinear models, namely the Brody, Gompertz, Logistic and Von Bertalanffy growth models, were plotted and evaluated. The model parameters of each growth model were compared for differences between the two sexes. The statistical effectiveness of fit was determined for each model using AIC and RMSE, with R2 also being considered. All models except the Brody model, predicted significantly heavier mature weights for castrates. The Brody model was deemed unfit to describe Boer goat growth as the function severely over-predict weights from birth until maturity for both sexes. The Von Bertalanffy (R2 = 91.3) and Gompertz functions (R2 = 91.3) showed the best fit for Boer goat castrates, while the Gompertz model (R2 = 95.1) showed the best fit for Boer goat does. The Gompertz function is the preferred model to depict Boer goat growth overall, as it accurately characterized growth of both sexes. According to the Gompertz model the age at which the inflection point of the growth curve was reached, did not differ significantly between castrates and does (141.80 days versus 136.31 days). There was also no significant difference in maturation rate between the two sexes.

Fitting of Growth Curves and Estimation of Genetic Relationship between Growth Parameters of Qianhua Mutton Merino

Qianhua Mutton Merino is a dual-purpose (meat and wool) breed of sheep that has been newly developed in China. In this study, we assessed the growth and development of the Qianhua Mutton Merino sheep breed under house feeding conditions by measuring the body weight and chest circumference of 2300 rams and ewes of this breed aged 0-24 months. Based on the fitting results of three nonlinear growth models, namely Logistic, Gompertz, and von Bertalanffy, in Qianhua Mutton Merino, we selected the von Bertalanffy model because of its highest fitting degree among all models (R2 > 0.977). The significant analysis of the combined fixation of each sheep body's weight and bust took place (A: mature body weight, B: adjustment parameter, K: instant relative growth rate). The results revealed that parameters A, B, and K of body weight and chest circumference have high heritability and thus could be used as target traits for genetic improvement. Moreover, the correlation strength among A, B, and K suggested that these parameters can be used as a reference to adjust the genetic parameters in the growth model to genetically improve the body size of Qianhua Mutton Merino during breeding.

Modelling the growth curve and estimation of associated genetic parameters in Munjal sheep

The study of growth curves in sheep is an effective approach to monitor the animal development for predicting the growth rate and improving overall flock performance. The purpose of the present work was to study the growth curve traits of Munjal sheep using different non-linear models and to estimate the genetic parameters of those traits for the possibility of inclusion of them under selection strategy. Total 2285 weight records at birth, 3, 6 and 12 months of age of 706 lambs born to 48 sires and 149 dams were collected from the registers maintained from 2004 to 2019. Various non-linear growth models viz., Brody, Gompertz, logistic, Bertalanffy and negative exponential were fitted to targeted growth curve traits and then evaluated using goodness of fit criteria such as adjusted R², root means square error (RMSE), Akaike's information criterion (AIC) and Bayesian information criterion (BIC). The genetic parameters of growth curve traits were estimated using animal model. The results suggested that Brody model was best fitted to the data than other models. The growth curve estimates for mature weight (A), inflexion point (B) and rate of maturation (k) under Brody model were 25.82 ± 1.72, 0.84 ± 0.04, and 0.21 ± 0.04, respectively for female lambs, and 29.55 ± 2.04, 0.86 ± 0.03 and 0.19 ± 0.04, respectively for male lambs. The males showed superiority for mature weights whereas female lambs had higher maturation rates. The estimates of direct heritability for A, B and k were 0.33, 0.41 and 0.10, respectively. The moderate estimate of direct heritability of A and its negative genetic correlation with k indicated the scope of genetic improvement through selection based on mature weights. Therefore, it was concluded from the present findings that Brody model was the one that best describes the growth curve in the Munjal sheep and the selection based on mature weights can be employed for genetic improvement of Munjal flock.

Modelling growth in Suffolk and Charollais sheep populations using random regression models and validation of constrained polynomial correlation values

Random regression modelling has been used across multiple animal species to model longitudinal data. The random regression model for growth accounts for the genetic correlation between measures of the same trait over time and the wide environmental variability in growth, but this requires adequate weight records across the age range. However, contemporary management practices in sheep in the United Kingdom generally focus on growing lambs and neglect mature weight recordings. This study examined modelling strategies for growth data in Suffolk and Charollais sheep, provided by the Agriculture and Horticulture Development Board, with polynomial random regression modelling with many early life weight recordings but limited weight recordings in mature animals. Two methods were employed to model the data. In Method A, missing mature weight records were predicted for those animals that did not have a recorded mature weight. The animals were sorted into groups based on the identity of their sires and the year in which the animal was born. Mature weight values were predicted within each group with a multiple regression model. The dataset, including predicted values, was analysed with random regression models using polynomials and simple linear regression for animal and permanent environmental (PE) effects. In Method B, the dataset with missing mature weight records was analysed using a random linear regression animal model with random animal and PE effects. Due to problems of convergence because the parameters were close to the boundary space, fixing the correlation between the intercept and slope of the Legendre polynomial at different levels was investigated. The heritability values resulting from the model with a fixed correlation between intercept and slope parameters at 0.5 for the Suffolk dataset resulted in heritability values ranging from 0.2 to 0.5 from 1 to 619 days of age. Corresponding estimates for the Charollais dataset ranged from 0.18 to 0.49 from 1 to 640 days of age. For the Suffolk data, the genetic correlations ranged from 1.00 to 0.08 between weight at day 1 to weight at day 619, while for the Charollais, the correlations ranged from 1.00 to 0.05 from 1 to 640 days of age. Validation procedures were undertaken using a multitrait approach to examine the estimated breeding values when the correlation between the intercept and slope are fixed at different levels. The results indicated that fixing the correlation at 0.5 gave the most appropriate estimates for the Suffolk and Charollais datasets.

Modeling and predicting the growth of indigenous Harnai sheep in Pakistan: non-linear functions and MARS algorithm

Five non-linear functions, i.e. Gompertz, Logistic, Negative exponential, Brody and Bertalanffy, and multivariate adaptive regression splines (MARS) data mining algorithm were implemented with the objective to describe the body weight-age relationship of Harnai sheep of Balochistan, Pakistan. The data comprised of 1317 records of body weight from birth to 1 year were provided from Multi-Purpose Sheep Research Station Loralai, Balochistan. Each non-linear function and MARS algorithm were fitted to the data of male and female, single and twin and all lambs. Comparison among different non-linear models was based using the adjusted coefficient of determination ([Formula: see text]), Durbin-Watson statistic (DW), root mean square error (RMSE), Akaike's and Bayesian information criteria (AIC and BIC) and the coefficient of correlation (r) between observed and fitted live body weight. The best fit was provided by the Brody model in terms of the highest [Formula: see text] and r values and lowest RMSE, AIC and BIC values in male and female, single and twin and all lambs followed by Bertalanffy, Gompertz, Negative exponential and Logistic model in order of their goodness. The negative correlation between asymptotic weight and maturing rate inferred that animals with smaller mature weight mature fast. Though males and singles were found heavier at mature weight than females and twins, respectively, they mature more slowly. The results of the study suggested the use of the Brody model to accurately describe the weight-age relationship of Harnai sheep. The present study also showed a very high predictive performance of the MARS data mining algorithm for describing the growth of sheep. In conclusion, MARS algorithm may be a good alternative for breeders aiming at describing the weight-age relationship of Harnai sheep.

Predicting the Digestive Tract Development and Growth Performance of Goat Kids Using Sigmoidal Models

The transition from monogastric to rumination stage is crucial in ruminants' growth to avoid stressors-weaning and neonatal mortalities. Poor growth of the digestive tract could adversely affect the performance of the animal. Modeling informative growth curves is of great importance for a better understanding of the effective development pattern, in order to optimize feeding management system, and to achieve more production efficiency. However, little is known about the digestive tract growth curves. For this reason, one big goat farm of Laiwu black breed was chosen as a basis of this study. Forty-eight kids belonging to eight-time points (1, 7, 14, 28, 42, 56, 70, and 84 d; 6 kids for each) were selected and slaughtered. The body weight, body size indices, rumen pH, and stomach parts were determined and fitted to the polynomial and sigmoidal models. In terms of goodness of fit criteria, the Gompertz model was the best model for body weight, body oblique length, tube, and rumen weight. Moreover, the Logistic model was the best model for carcass weight, body height, and chest circumference. In addition, the Quadratic model showed the best fit for dressing percentage, omasum weight, abomasum weight, and rumen volume. Moreover, the cubic model best fitted the ruminal pH and reticulum percentage. The Weibull model was the best model for the reticulum weight and omasum percentage, while the MMF model was the best model describing the growth of chest depth, rumen percentage, and abomasum percentage. The model parameters, R squared, inflection points, area under curve varied among the different dependent variables. The Pearson correlation showed that the digestive tract development was more correlated with age than body weight, but the other variables were more correlated with body weight than age. The study demonstrated the use of empirical sigmoidal and polynomial models to predict growth rates of the digestive tract at relevant age efficiently.

Estimation of heritability and genetic correlation of body weight gain and growth curve parameters in Korean native chicken

Objective

This study estimated the genetic parameters for body weight gain and growth curve parameter traits in Korean native chicken (KNC).

Methods

A total of 585 F₁ chickens were used along with 88 of their F₀ birds. Body weights were measured every 2 weeks from hatching to 20 weeks of age to measure weight gain at 2-week intervals. For each individual, a logistic growth curve model was fitted to the longitudinal growth dataset to obtain three growth curve parameters (α, asymptotic final body weight; β, inflection point; and γ, constant scale that was proportional to the overall growth rate). Genetic parameters were estimated based on the linear-mixed model using a restricted maximum likelihood method.

Results

Heritability estimates of body weight gain traits were low to high (0.057 to 0.458). Heritability estimates for α, β, and γ were 0.211±0.08, 0.249±0.09, and 0.095±0.06, respectively. Both genetic and phenotypic correlations between weight gain traits ranged from −0.527 to 0.993. Genetic and phenotypic correlation between the growth curve parameters and weight gain traits ranged from −0.968 to 0.987.

Conclusion

Based on the results of this study population, we suggest that the KNC could be used for selective breeding between 6 and 8 weeks of age to enhance the overall genetic improvement of growth traits. After validation of these results in independent studies, these findings will be useful for further optimization of breeding programs for KNC.

Estimation of genetic relationships between growth curve parameters in Guilan sheep

The objective of this study was to estimate variance components and genetic parameters for growth curve parameters in Guilan sheep. Studied traits were parameters of Brody growth model which included A (asymptotic mature weight), B (initial animal weight) and K (maturation rate). The data set and pedigree information used in this study were obtained from the Agricultural Organization of Guilan province (Rasht, Iran) and comprised 8647 growth curve records of lambs from birth to 240 days of age during 1994 to 2014. Marginal posterior distributions of parameters and variance components were estimated using TM program. The Gibbs sampler was run 300000 rounds and the first 60000 rounds were discarded as a burn-in period. Posterior mean estimates of direct heritabilities for A, B and K were 0.39, 0.23 and 0.039, respectively. Estimates of direct genetic correlation between growth curve parameters were 0.57, 0.03 and −0.01 between A-B, A-K and B-K, respectively. Estimates of direct genetic trends for A, B and K were positive and their corresponding values were 0.014 ± 0.003 (P < 0.001), 0.0012 ± 0.0009 (P > 0.05) and 0.000002 ± 0.0001 (P > 0.05), respectively. Residual correlations between growth curve parameters varied form −0.52 (between A-K) to 0.48 (between A-B). Also, phenotypic correlations between growth curve parameters varied form −0.49 (between A-K) to 0.47 (between A-B). The results of this study indicated that improvement of growth curve parameters of Guilan sheep seems feasible in selection programs. It is worthwhile to develop a selection strategy to obtain an appropriate shape of growth curve through changing genetically the parameters of growth model.

Analysis of growth and feed conversion in purebred and crossbred German Merinolandschaf lambs

Abstract. In this study, ewes of "Merinolandschaf", a breed widespread in southern Germany, were crossed with rams of five meat breed types (Ile de France, Charollais, German black-headed mutton sheep (Deutsches Schwarzköpfiges Fleischschaf), Suffolk, Texel) and Merinolandschaf rams. The resulting lambs (179 individuals) were fattened intensively from 55.3 days and body weight of 20.4 kg until 121.7 days and a weight of 40.9 kg. While fattening, feed intake was recorded and lambs were weighed weekly. Ile de France × Merinolandschaf and Texel × Merinolandschaf seem to be of greatest economic interest for intensive fattening because they showed the best feed conversion rate and energetic feed conversion rate. Only these crosses were significantly superior compared to purebred Merinolandschaf in feed conversion rate and also in daily body weight gain during the fattening period. Except Charollais × Merinolandschaf, all crosses showed at least a tendency of improvement in all three traits compared to Merinolandschaf, although this is not always significant. This underlines the advantage of one-way cross-breeding for efficiently producing lamb meat. The growth was modelled with a linear model and the Gompertz model. The results showed that both models fit the data well, although the average R2 was slightly higher and the average mean square error was slightly lower for the Gompertz model. In addition, the use of the Gompertz model provided some interesting biological insights concerning the growth of lambs and differences between the crosses, even though the lambs were slaughtered before reaching their mature body weight.

Effects of low protein diets on performance of pigs with a lean genotype between 40 and 115 kg liveweight

The aim of the work was to assess the effects of three dietary protein regimes on pig performance and nitrogen (N) excretion, in particular, whether performance can be maintained in lean, fast growing pigs when protein levels are reduced to limit N excretion. Entire male pigs of a lean genotype (Pietrain × Large White × Landrace), 192 in total in four batches, were grown from 40 to 115 kg in pens with four pigs per pen. The diets were: (i) a high-protein control regime; (ii) a low-protein regime in which protein was reduced by ~2 percentage units in each growth stage, but with levels of five essential amino acids the same as in the control (LP1); (iii) an even lower protein regime in which levels of essential amino acids were not maintained beyond 60 kg (LP2). The LP2 regime was designed to promote intramuscular fat deposition rather than efficient growth. Excretion of N was reduced by 17% and 19% in LP1 and LP2, respectively, compared with the control. Average daily gain was lower and feed conversion ratio higher in LP2 than the other regimes, as expected. The control and LP1, which differed in protein but not essential amino acid levels, produced broadly similar results for performance, but pigs in LP1 had poorer feed conversion than control pigs, which could be due to slightly greater fat deposition. The results show the difficulty in maintaining consistently high levels of performance in fast-growing, lean pigs when dietary protein levels are reduced.

Genetic effects and correlations between production and fertility traits and their dependency on the lactation-stage in Holstein Friesians

Background

This study focused on the dynamics of genome-wide effects on five milk production and eight fertility traits as well as genetic correlations between the traits. For 2,405 Holstein Friesian bulls, estimated breeding values (EBVs) were used. The production traits were additionally assessed in 10-day intervals over the first 60 lactation days, as this stage is physiologically the most crucial time in milk production.

Results

SNPs significantly affecting the EBVs of the production traits could be separated into three groups according to the development of the size of allele effects over time: 1) increasing effects for all traits; 2) decreasing effects for all traits; and 3) increasing effects for all traits except fat yield. Most of the significant markers were found within 22 haplotypes spanning on average 135,338 bp. The DGAT1 region showed high density of significant markers, and thus, haplotype blocks. Further functional candidate genes are proposed for haplotype blocks of significant SNPs (KLHL8, SICLEC12, AGPAT6 and NID1). Negative genetic correlations were found between yield and fertility traits, whilst content traits showed positive correlations with some fertility traits. Genetic correlations became stronger with progressing lactation. When correlations were estimated within genotype classes, correlations were on average 0.1 units weaker between production and fertility traits when the yield increasing allele was present in the genotype.

Conclusions

This study provides insight into the expression of genetic effects during early lactation and suggests possible biological explanations for the presented time-dependent effects. Even though only three markers were found with effects on fertility, the direction of genetic correlations within genotype classes between production and fertility traits suggests that alleles increasing the milk production do not affect fertility in a more negative way compared to the decreasing allele.

Meta-analysis of the effects of dietary vitamin E supplementation on α-tocopherol concentration and lipid oxidation in pork

Meta-analyses have been carried out to quantify the effect of dietary vitamin E on α-tocopherol accumulation and on lipid oxidation in porcine M. longissimus. Published results of 13 (vitamin E accumulation) and 10 (lipid oxidation) experiments respectively were used for the analyses. After a number of standardization procedures, a nonlinear relationship was found between the supplementary vitamin E and the accumulation of α-tocopherol in pork which approached a maximum value of 6.4 μg/g tissue. Pork lipid oxidation levels were described in terms of Thiobarbituric Acid Reacting Substances (TBARS) values. The statistical analysis revealed significant effect of vitamin E dose, muscle α-tocopherol concentration and supplementation time on TBARS, resulting in two prediction models for lipid oxidation. Meta-analysis has proven to be a valuable tool for combining results from previous studies to quantify the effects of dietary vitamin E. Further studies, carried out with standardized experimental protocols would be beneficial for model validation and to increase the predictive power of the derived models.

A two-step approach combining the Gompertz growth model with genomic selection for longitudinal data

Background

We used the Gompertz growth curve to model a simulated longitudinal dataset provided by the QTLMAS2009 workshop and applied genomic evaluation to the derived model parameters and to a model-predicted trait value.

Results

Prediction of phenotypic information from the Gompertz curve allowed us to obtain genomic breeding value estimates for a time point with no phenotypic records. Despite that the true model used to simulate the data was the logistic growth model, the Gompertz model provided a good fit of the data. Genomic breeding values calculated from predicted phenotypes were highly correlated with the breeding values obtained by directly using the respective observed phenotypes. The accuracies between the true and estimated breeding value at time 600 were above 0.93, even though t600 was outside the time range used when fitting the data. The analysis of the parameters of the Gompertz curve successfully discriminated regions with QTL affecting the asymptotic final value, but it was less successful in finding QTL affecting the other parameters of the logistic growth curve. In this study we estimated the proportion of SNPs affecting a given trait, in contrast with previously reported implementations of genomic selection in which this parameter was assumed to be known without error.

Conclusions

The two-step approach used to combine curve fitting and genomic selection on longitudinal data provided a simple way for combining these two complex tasks without any detrimental effect on breeding value estimation.

Influence of major genes for crested-head, frizzle-feather and naked-neck on body weights and growth patterns of indigenous chickens reared intensively in Kenya

The influence of major genes for crested-head (Cr), frizzle-feather (Fr) and naked-neck (Na) on body weights and growth patterns of indigenous chickens reared intensively was investigated and compared with normal-feather (na) gene. Birds were individually weighed at hatch and every two weeks up to 30 weeks of age. Growth patterns were modelled using the Gompertz-Laird function. The genes influenced body weights and growth patterns at various ages. The Cr gene had significant (P < 0.05) negative effects on body weights (between 52.2 g and 112.3 g) from 18 weeks onwards and low absolute growth rate from 10 to 22 weeks than na, but higher initial specific growth and maturation rates than the Na gene. The Fr gene had significant negative effects on body weights (between 28.2 g and 75.1 g) from 8 to 16 weeks than na, but a higher relative growth rate than Cr from 12 to 16 weeks. The Na gene had significant negative effects on body weights (between 24.7 g and 134.6 g) from 8 weeks onwards than na. It was concluded that Frfr and Nana genotypes are not ideal for cool environments in Kenya and indigenous chicken genotypes have varied growth potentials and patterns that can be improved to increase production.

Age-dependent quantitative trait loci affecting growth traits in Scottish Blackface sheep

To dissect age-dependent quantitative trait loci (QTL) associated with growth and to examine changes in QTL effects over time, the Gompertz growth model was fitted to longitudinal live weight data on 788 Scottish Blackface lambs from nine half-sib families. QTL were mapped for model parameters and weekly live weights and growth rates using microsatellite markers on chromosomes 1, 2, 3, 5, 14, 18, 20 and 21. QTL significance (using alpha = 0.05 chromosome-wide significance thresholds, unless otherwise stated) varied with age, and those for growth rate occurred earlier than equivalent QTL for live weight. A chromosome 20 QTL for growth rate was significant from 4 to 9 weeks (maximum significance at 6 weeks) and for maximum growth rate. For live weight, this QTL was significant from 8 to 16 weeks (maximum significance at 12 weeks). A nominally significant chromosome 14 QTL was detected for growth rates from birth to week 2 in the same families and location as an 8-week weight QTL. In addition, at the same position on chromosome 14, a QTL was significant for growth rate for 17-28 weeks (maximum significance at 24 weeks). A chromosome 3 QTL was significant for weights at early ages (birth to week 4) and a growth rate QTL on chromosome 18 was significant from 8 to 12 weeks. Fitting growth curves allowed the combination of information from multiple measurements into a few biologically meaningful variables, and the detection of growth QTL that were not observed from analyses of raw weight data. These QTL describe distinct parts of an animal's growth curve trajectory, possibly enabling manipulation of this trajectory.

Application of random regression model to estimate genetic parameters for average daily gains in Lori-Bakhtiari sheep breed of Iran

A random regression model was applied to estimate (co) variances, heritabilities and additive genetic correlations among average daily gains. The data was a total of 10876 records belonging to 1828 lambs (progenies of 123 sires and 743 dams) born between 1995 and 2001 in a single large size flock of Lori-Bakhtiari sheep breed in Iran. In the model, fixed environmental effects of year-season of birth, sex, birth type, age of dam and random effects of direct and maternal additive genetic and permanent environment were included. Orthogonal polynomial regression (on the Legendre scale) of third order (cubic) was utilized to model the genetic and permanent environmental (co) variance structure throughout the growth trajectory. Direct and maternal heritability estimates of average daily gains ranged from 0.011 to 0.131 and 0.008 to 0.181, respectively in which pre-weaning average daily gain (0-3 in months) had the lowest direct and highest maternal heritability estimates among the other age groups. The highest and lowest positive direct additive genetic correlations were found to be 0.993 and 0.118 between ADG (0-9) and ADG (0-12) and between ADG (0-3) and ADG (0-12), respectively. The direct additive genetic correlations between adjacent age groups were more closely than between remote age groups.