Ewe body weight has a direct relationship to feed requirements and productivity. Maintenance requirements are a function of metabolic body weight and in sheep, they represent up to 80% of the total feed requirements (Bedier et al., 1992). Results from earlier studies showed that the relative economic value of ewe body weight in all sheep production systems is low and in some cases negative (Gallivan, 1996; Vatankhah, 2005). Genetic correlations between ewe weight and lamb weight presented in the literature are positive ranging from moderate to high (Fogarty, 1995; Safari et al., 2005). Therefore, selection for higher lamb weights would be expected to increase the ewe adult weight. On the other hand, this is a drawback, because not only are the heavier ewes more expensive to maintain, due to their greater requirements for space and food, but also because of their lower productivity compared with medium-sizes ewes (Vatankhah and Salehi, 2010). They are also harder to handle at shearing, at lambing, and on many other occasions (Näsholm and Danell, 1996). Selection to reduce or to restrict mature ewe body weight requires good estimates of genetic parameters of ewe body weights at different ages. The literature shows that the growth of an animal to a mature age is a longitudinal process whereby an animal increases in size or weight continuously over time until reaching a plateau at maturity. Such a process can be represented by a set of size-age points describing a typical trajectory process and resulting in a set of many highly correlated measures (Meyer, 1998). From an animal breeding point of view, interest lies in those genetic parameters that describe the changes in these traits in time. Kirkpatrick et al. (1990) showed that phenotypic changes with age can be represented as a function of time. Traditionally, traits that are measured in time are analyzed with a multi-trait model, defining the phenotypic values at distinct ages as different traits. One advantage of random regression models over multivariate models is that by using random regression models it is possible to calculate (co)variances between or at every age or time point. Compared with a multivariate model, a random regression model estimates (co)variances more smoothly and with less bias (Kirkpatrick et al., 1990). Heritability of ewe body weight estimated from single or multivariate models were medium to high for different breeds of sheep (Fogarty, 1995; Safari et al., 2005). The Lori-Bakhtiari sheep breed is one of the most prominent native sheep breeds in southwestern Iran (the Zagros Mountains), with a population of more than 1.7 million heads. However, there is not much information the genetic parameters of ewe body weight for Iranian native sheep breeds, particularly the Lori-Bakhtiari. The main aim of the present research was to estimate (co)variance components and genetic parameter estimates for mature ewe body weight in Lori-Bakhtiari sheep using the random regression model.
Data and flock management
The data set used in this study consisted of 22153 records of individual ewe body weight, measured up to four times per year on 1994 ewes between 371 and 3416 days of age. The progeny of 205 rams and 1010 ewes were raised in the flock stud (Lori-Bakhtiari Sheep Breeding Station in Shahrekord, Iran) during 1989 to 2008, with a total of 2225 animals in the pedigree. The flock is managed under semi-migratory or village system (Vatankhah and Talebi, 2009). The flock was kept at the station, from December to May, during which time the animals were fed with alfalfa hay, barley and wheat stubble indoors. The sheep grazed on the nearby ranges and on pastures the rest of the year. The breeding period extended from late August to late October (20-25 ewes were assigned randomly to the one ram), with the lambing starting in late January. Lambs were allowed to suckle their dams, and from 15 days of age, they had access to a creep feed ad-libitum. The lambs were weaned at an average age of 90 ± 5 days. The flock was subjected to different selection criteria generally related to increasing weaning weight (growth traits, total weaning weight per ewe expose, or Kleiber ratio) in this period.
The trait considered in this investigation was ewe body weight in kilograms. Ewe weights were recorded at mating, after parturition, after weaning and at shearing. A univariate procedure (SAS ,2000) was used to edit the data and check for normality. The GLM procedure (SAS, 2000) was used to identify important fixed effects influencing the ewe body weight. The statistical model included fixed effects of year of production (1989-2007), litter size (0, 1, and 2) and stage of production cycle (mating, parturition, shearing and weaning). All the effects were significant (P<0.05) and hence they were included in the final model. The (co)variance components and genetic parameters of ewe body weight were estimated using the restricted maximum likelihood method by WOMBAT software (Meyer, 2006). Ewe body weight at different stages of production (at mating, after parturition, after weaning and at shearing) and during various years was considered a longitudinal trait and the data set analyzed with a random regression model as follows:
In which, y, b, a, p and e are the vectors of observations, fixed effects (year of production, litter size and stage of production cycle), direct additive genetic effects with order of fit k, permanent environmental effects due to repeated records with order of fit k and residual random effects, respectively. Incidence matrices X, Z1 and Z2 connected the observations of trait to the respective fixed effects, additive genetic effects and permanent environmental effects, respectively.
The average information (AI) REML algorithm was used to maximize the likelihood (convergence criterion was 10-8), and additional restarts were performed until no further improvement in log likelihood occurred. A total of 10 models with order of 2 to 6, including one and nine measurements error classes, were compared. The best model was selected using the likelihood ratio test, contrasting the differences between 2 models with a X2 distribution at α = 0.05 and the degree of freedom equal to difference between number of parameters in two models. When differences between log likelihoods were not significant, the model with the fewest order of fit was chosen as the best model.
The description of the ewe body weight at different ages are set out in Table 1. It is clear that the average live weight of ewes increased from 53.51 kg in 1.5 years of old, to 65.19 kg in 5.5 years of old and then decreased due to oldness. The standard deviation of ewe body weight increased with age up to 3.5 years, decrease up to 5.5 years of old due to culling some animals and then increased with animals aged slightly.
The results of log likelihood showed a significant improvement in the level of fit when the heterogeneous residual variance was included in the model in comparison to homogeneous residual variance (Table 2). Since changes in likelihood value among models from simple linear (k=2) to quintic model (k=6) were significant (P<0.05).
The estimates of variance components of ewe body weight are shown in Fig. 1. Phenotypic variance component of ewe body weight increased with age of ewe (Fig. 1). The Fig 1 showed that additive genetic variance component increased with age to 2.5 years of old, remains constant approximately to 5.5 years of old and then increased with age of ewe, while permanent environment variance component increased with age up to 4.5 years of old and then remains constant approximately. The additive genetic and permanent environment variance components are equal from 4.5 to 5.5 years of age and then additive genetic variance increased with ewes aged while permanent environment remains constant.
Estimates of heritability (h2) and proportion of permanent environmental variance to phenotypic variance (c2) are shown in Fig. 2. The h2 increased with age of ewe up to 2.5 years of old, decreased steadily up to 5.5 years of old and then increased with animals aged. The estimates of c2 increased with age of ewe from 1.5 to 4.5 years of old, constant to 5.5 years of old, declined to 6.5 years of old and then constant with animals aged. In general, the estimates of h2 were greater than c2, but the value of c2 from 4.5 to 5.5 years of old was equal or slightly higher than h2. Mature ewe body weight in Lori-Bakhtiari sheep is a highly repeatable trait as indicated by the magnitude of total animal variance as a proportion of the total phenotypic variance. The estimate of repeatability (h2 + c2) of ewe body weight shows that the correlation between consecutive records of ewe body weight is high. Estimates of genetic and phenotypic correlations between ewe body weights at different ages are set out in Table 3. The estimate of genetic and phenotypic correlations are positive for any pair of ages considered and ranged from 0.45 to 0.99 and 0.37 to 0.73, respectively. The pattern changes of genetic and phenotypic correlations is similar in that the correlations decrease as the age distance between weights increase. In particular, the genetic correlation between subsequent age's approaches unity, however, the genetic correlation between early (year 1.5) and late (year 8) weights is moderate (0.45) suggesting that early weights are not under exactly the same genetic control as weights recorded at an older age.
One of the main objective in this study was the determination of change patterns in the mean and variance components of ewe body weight at different ages. Based on the results obtained in the study, in contrast of the mean of ewe body weight which followed from the quadratic curve during ages (Table 1), orthogonal polynomial regression of order 6 has been chosen as a sufficient model to fit additive genetic and environmental with heterogeneous residual variance (Table 2). Fischer et al. (2004) modeled the weight of Poll Dorset sheep from 50 to 500 days of age and concluded that the model with order 3, 2, 3 and 3 for direct additive genetic, maternal additive genetic, permanent environment and residual effects respectively, was the best model. While, in agreement with the results of this study weight record of Brazilian Nelore cattle, from birth to 630 d of age, and from birth to 730 d of age, showed that the log likelihood function increased with order (k) of the polynomial (from 3 to 9), and order of 6 were adequate to model the variation in the data (Albuquerque and Meyer, 2001).
Despite of reducing the number of records after 5.5 years of old due to oldness and low production, and the effect of selection on additive genetic variance (Bulmer effect), but increasing trend resulted in this study for additive genetic variance in older age shows that it is possible some genes with additive effects activated in the older ages. This pattern of changes in additive genetic variance indicated that body weight of Lori-Bakhtiari ewes are different traits in early, mid and older ages. This increasing pattern of additive genetic variance as animals aged is agreement with Nephawe (2004). As the permanent environmental variance is due to non-additive genetic and non-genetic permanent environmental effects, the pattern changes in permanent environment variance component showed that there are not any genes with non-additive genetic that activated after 4.5 years of old and or there are not any non-genetic permanent effects that add to this component after this age of the ewe.
In general, the values obtained for heritability in this study were in the range reported in the literature (Fogarty, 1995 and Safari et al., 2005). But the trend of changes for heritability during different ages obtained in this study was not consistent with literature values obtained using current animal models, summarized by Fogarty (1995) and Safari et al. (2005) which reported the value of heritability increased with the age of the animal. The reducing trend of h2 from 2.5 to 5.5 years of old could be contributed to reducing the number of records in a data set due to oldness and low production. The estimate of h2 appears to increase sharply towards the end of the trajectory, accompanied by a declining trend of variance for the other effects at later ages. Similar behavior of covariance function estimates for ages where the least data is present has been shown, i.e. at the edge of the trajectory (Meyer, 2002; Fischer et al. 2004). In general, estimates of moderate heritability of ewe body weight in Lori-Bakhtiari sheep over 1.5 to 8 years of old, indicating that selection for this trait could be effective.
The values of genetic correlations among ewe body weight at different ages obtained in this study implies that if animals selected on the weights, an animal can be below average weight at younger ages, but can be above average weight at older ages, however, this has implications for potential to select on the shape of the growth curve of animal. In addition, genetic and phenotypic correlations between weights at younger ages (1.5 vs. 2.5 years) are lower (0.86 and 0.57) than correlations between weights taken at older ages (6.5 vs. 7.5 years) with the same time lag (0.97 and 0.71). This is attributable to the influence of the part-whole relationship between weights, whereby weights at later ages depend on earlier weights, thus as time progresses correlations between later weight increases as they are more dependent on the previous weight measures (Fischer et al., 2004). A similar pattern has been reported in correlations between weights measured at different ages on sheep (Lewis and Brotherstone, 2002; Fischer et al., 2004) and cattle (Meyer, 2002).
Random regression models allow differences between animals to be accounted for and hence are a useful tool in analyzing variation in growth curve patterns. This methodology offers a powerful means to evaluate repeated live weight information and determine the genetic merit (Fischer et al., 2004). The genetic parameter estimates in this study using RRM were in agreement with estimates proposed in the literature at specific ages (Vatankhah, 2005; Safari et al., 2005). However, heritability at ages with the least records was considered too high, in particular after 6.5 years of old. Similar estimates reported for ages with the least data using polynomials (Meyer, 2002), and this remains an unresolved problem for this type of modeling. The results of the present study showed that considerable genetic variation exists in the growth curves of ewe in Lori-Bakhtiari sheep. Mature weight early in life is a different trait genetically to mature weight later in life, and lower correlations have implications for potential to select on the shape of the growth curve.
The present study indicated that random regression model of order 6 to fit additive genetic and environmental with heterogeneous residual variance is the best to modeling growth curve in the mature Lori-Bakhtiari ewes. There is a good potential for the selection of reducing mature ewe body weight due to moderate heritabilities. Thus, due to moderate genetic correlations between ewe body weight at early and older ages, genetic analysis using RRM is recommended to improve Lori-Bakhtiari ewe body weight.