Genetic and non-genetic parameters for growth traits and Kleiber ratios in Dorper x indigenous sheep

Genetic improvement program will only be successful when accompanied by a good understanding of the inuence of environmental factors, knowledge of the genetic parameters, and the genetic relationships between the traits of interest. Thus, this study aimed to evaluate the inuence of non-genetic factors on growth traits and Kleiber ratios and to estimate genetic parameters for early growth traits in Dorper x indigenous sheep. The effects of xed factors were analyzed by the general linear model procedure of SAS and the genetic parameters were estimated by AI-REML algorithm using a WOMBAT computer program tted animal model. The log-likelihood ratio test was used for selecting the best-tted model from four models. The overall least-squares means for birth weight (BW), weaning weight (3MW), six-months (6MW), nine-month (9MW), and yearling (12WT) were 3.03 ± 0.02, 14.5 ± 0.18, 20.4 ± 0.26, 24.8 ± 0.31, and 28.3 ± 0.40 kg, respectively. The overall least-square means for Kleiber ratio from birth to weaning (KR1), weaning to six-month (KR2), six to nine-month (KR3) and nine-month to yearling age (KR4) were 16.8 ± 0.10, 6.41 ± 0.17, 4.55 ± 0.21 and 3.38 ± 0.20 g/kg of metabolic weight, respectively. The inclusion of maternal genetic effect exerted a signicant inuence on BW and it explains 20% of the phenotypic variation. The total heritability (h 2t ) estimates for BW, 3MW, ADG1 and KR1 were 0.10, 0.14, 0.16 and 0.12, respectively. The phenotypic correlation varied from − 0.11 to 0.98 whereas the direct genetic correlation ranged from − 0.32 to 0.98. The mean inbreeding coecient was 0.105% with annual rate of 0.02%. The heritability estimates for growth traits and Kleiber ratio suggests that slow genetic progress would be expected from the selection. However it is, integration of selection with crossbreeding program with this level of variation would enhance the genetic gain. Therefore, selection should be conducted based on breeding values estimated from multiple information sources to increases the selection response.


Introduction
Sheep farming is a signi cant part of Ethiopia's livestock sector. There are around nine sheep breeds (Gizaw et al. 2008) and the total population is about 31.30 million (CSA 2018). The productivity of indigenous sheep breeds, on the other hand, is uneven in comparison to the human population. As a result, to supply the growing demand for animal protein, it has been suggested that sheep productivity be increased by employing more productive genotypes. Consequently, the Romney, Corriedale, Hampshire, Rambouillet, and Awassi sheep breeds have been imported to Ethiopia in various years since 1944 . However, the contribution of these breeds except Awassi sheep was negligible (Tesema and Shenkute 2019). Consequently, the project entitled Ethiopian Sheep and Goat Productivity Improvement Program (ESGPIP) launched crossbreeding of indigenous ewes with Dorper sire breed in different parts of the country with a goal of improvement of meat production since 2007. Tumele sheep is one of the indigenous sheep populations which crossed with Dorper sheep and the resulted in crossbred rams were disseminated to farmers since 2012 to improve the growth performance and meat production.
Live weight and growth rate are economically critical traits, requiring particular attention in any breeding program intended to improve meat production. Besides growth, the selection of sheep for feed utilization is a better strategy to increase the e ciency of meat production (Faid-Allah et al. 2016). Selection for this trait directly is impossible particularly in the tropics due to the absence of feed intake data for the individual animals. However, the possibility of improving feed e ciency using the Kleiber ratio is noted by several scholars (Arthur et al. 2001 The integration of crossbreeding program with selective breeding is imperative to enhance genetic gain and reduce the declining performance of crossbreds in subsequent generations (Gizaw et al. 2012). Many factors affect growth traits and Kleiber ratio, including additive genetic effects, maternal genetic effects, and nongenetic factors (Farokhad et al. 2010). The design of such type of combined genetic improvement program will only be successful when accompanied by a good understanding of the in uence of different environmental factors, knowledge of the genetic parameters, and the genetic relationships between the traits of interest.
Genetic parameter estimation for various pure breeds was conducted by several scholars (Farokhad et al. 2010;Mohammadi et al. 2010;Ghafouri-Kesbi et al. 2011;Prakash et al. 2012;Khorsand et al. 2014;Mandal et al. 2015;Faid-Allah et al. 2016;Areb et al. 2021). However, there is a lack of estimates for crossbred sheep. Because of the scarcity of such estimates for growth and Kleiber ratio in Dorper crossbred sheep, the objectives of this study were to evaluate the in uence of non-genetic factors on growth traits and Kleiber ratios and to estimate genetic parameters for early growth traits and Kleiber ratio in Dorper x indigenous crossbred sheep.

Location
The study was conducted at the goat farm of Sirinka Agricultural Research Center which is located 508 km away from Addis Ababa at an altitude of 1850 m.a.s.l and at 11°45' 00" N and 39°36' 36" E. The mean annual rainfall amount of the area is on average about 950 mm. The area is a moderately warm temperature zone with a mean daily temperature ranges from 13.7-26.4°C.

Flock management
Flocks were reared under semi-intensive management i.e. graze for 6:00 hrs and supplemented with 0.1 to 0.4 kg based on their age and physiology when returned from grazing. Sheep were vaccinated against Anthrax, Sheep and Goat pox, and Pestis Des Petites Ruminants diseases. They were treated regularly for internal and external parasites . A natural controlled mating method was used and one ram was assigned to 20-30 ewes. The assigned rams were kept with ewes for 45 days during the daytime. During mating, herdsmen were assigned to each mating group to collect the mating data and pedigree information. The pure indigenous ewes were crossed with pure Dorper rams to produce the F1 crossbreds with 50% blood level. To evaluate the performance of crossbreds with different exotic gene levels, female crossbreds with 50% blood level were crossed with pure Dorper rams to produce crossbreds with 75 % Dorper blood level.

Data analysis
Data on growth performance and Kleiber ratio were analyzed using the general linear model procedure of SAS (2002). The model considered xed effects of type of birth in two classes (single and twin), sex of lamb in two classes (male and female), the blood level of lambs in two classes (50% and 75%), year of lambing in ten classes (2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018) and season of birth in three classes (dry, short rain and main rain). Tukey-Kramer test was employed for making all possible comparisons of means.
Genetic parameters for BW, 3MW, ADG1, and KR1 were estimated by the Average Information Restricted Maximum Likelihood (AI-REML) method tting an animal model using a WOMBAT computer program (Meyer et al. 2012). The genetic parameters for post-weaning growth traits were not estimated due to a lack of enough sample size. A detailed description of the data is presented in Table 1. Four univariate animal models were used for genetic analysis as shown below: y = X β + Z 1 a + ε (1) y = X β + Z 1 a + Z 2 m + ε with Cov (a, m) = 0 (2) y = X β + Z 1 a + Z 2 c + ε (3) y = X β + Z 1 a + Z 2 m + Z 3 c + ε with Cov (a, m) = 0 (4) Where, y is the vector of records; β, a, m, c and ε are vectors of xed ( xed effects which had a signi cant effect), additive direct genetic, maternal additive genetic, permanent environmental effects of the dam and residual effects, respectively; X, Z 1 , Z 2 and Z 3 are incidence matrices that relate these effects to the records. The (co)variance structure for the model was: Var ( a ) = Aσ 2 a , Var (m) = Aσ 2 m , Var(c) = I D c 2 , Var (ε) = I K e 2 and Cov (a, m) = Aσ am , Where, A is the numerator relationship matrix between animals; I D and I K are identity matrices with orders equal to the number of dams and the number of kids, respectively.
Likelihood ratio test (LRT) was used to determine the most appropriate model for each trait. The signi cance of model comparison was done from univariate analysis of animal models with and without including the effects as a random effect and compared log-likelihoods (Maximum log L) by chi-square (X 2 ) distribution for a = 0.05 with one degree of freedom (Chen et al. 2006;Wilson et al. 2010).
Where; ML(x) f = maximum likelihood for full model, ML(x) r = maximum likelihood for reduced model.
Genetic and phenotypic correlations were estimated using bivariate analysis. The genetic trend was obtained by regression of the average breeding values on birth year ). The inbreeding coe cient for individual animals was estimated and extracted from the additive relationship matrix. The total heritability (h 2 t ) was estimated according to Willham (1972). h 2 t = σ 2 a + 0.5 σ 2 m + 1.5 σ am σ 2 p Where; σ 2 a = additive genetic variance, σ 2 m = maternal genetic variance, σ 2 p = phenotypic variance, σ am = the covariance between additive direct and maternal genetic effects.

Results And Discussion
Live weight and the effect of non-genetic factors The live weights at various ages of Dorper crossbred lambs are presented in Table 2. The birth weight (BW), weaning weight (3MW), six-month weight (6MW) of crossbred lambs in this study are higher than the report of Abebe et al. (2016) for Dorper-Afar (2.57 kg BWT, 9.45 kg 3MW and 13.2 kg 6MW) and Dorper-Menz crossbred sheep (2.77 kg BW, 12.3 kg 3MW and 17.2 kg 6MW). Likewise, a relatively lowest yearling weight (22.5 kg) than the current result was reported for Washera x Farta sheep (Mekuriaw et al. 2013). However, the yearling weight of crossbred lambs in this study is lower than the result (31.3 kg for Dorper x Menz sheep) reported by Abebe et al. (2016). Generally, the live weight of crossbred sheep observed in the present study is superior to most of the nonimproved indigenous breeds (Washera, Farta, Horo, Adilo, Menz, Wollo sheep) reported by several scholars (Tibbo 2006;Gizaw and Getachew 2009;Mekuriaw et al. 2013;Gemiyo et al. 2014). The export market needs lambs weighing 25-30 kg at yearling age. In this study, the crossbred lambs could attain the minimum requirement of the export market standard starting from 9 months of age.
Birth type exerted a signi cant (P < 0.05) in uence on the weight of crossbred lambs at various ages. Single-born lambs had a higher live weight in all growth phases than twin-born lambs. This result is in agreement with several studies (Mohammadi et al. 2010;Mekuriaw et al. 2013;Lakew et al. 2014;Mandal et al. 2015). The superiority of singletons could be attributed to the pre-and post-natal availability of nutrients i.e. enough capacity of the maternal uterus space to gestate offspring and less competition for milk among the singletons than twin born. This carry-over effect is there up to yearling age (Abegaz et al. 2002) and males will be superior to female counterparts up to yearling age.
The sex of lambs is the other important source of variation and males appear to grow faster than respective female lambs. The superiority of males has been reported by several authors (Tibbo 2006;Lakew et al. 2014;Teklebrhan et al. 2014;Mandal et al. 2015). This difference could be due to more in uence of sex hormones (androgen) on muscle development of males than females. However, oestrogen limits skeleton growth in females (Ghafouri-Kesbi and Gholizadeh, 2017). Besides, ewes that carry male lambs had higher cotyledon numbers and heavier placental weight than ewes that carry females (Jawasreh et al. 2009), this may be the other possible reason for the superiority of males.
The growth performance of crossbreds was not increased with exotic gene level, i.e. crossbred lambs with 50% exotic gene level and 75% exotic gene-level had similar (P > 0.05) live weight in all growth phases. Hence, the higher exotic inheritance must be accompanied by improved management to enable them to express their full genetic potential. Otherwise, using 50% crossbreds would be compatible with the existing management.  Weight gain and the in uence of environmental factors The least-squares mean and standard errors for the weight gain of lambs at different growth phases are presented in Table 3. Generally, the growth rate showed a decreasing trend when the age of lambs increases. In particular, higher weight gain of crossbred lambs was observed during the pre-weaning period. This result is consistent with several studies (Ghafouri-Kesbi et al. 2011;Jalil-Sarghale et al. 2014;Ghafouri-Kesbi and Gholizadeh 2017). This reduction could be explained by the reduction of maternal effect when the age of lambs is increased.
Single-born lambs had a higher pre-weaning growth rate than twin-born. This result is in line with Teklebrhan et al. (2014) and Abebe et al. (2016). However, the post-weaning growth rate of twins and singletons was found to be similar (P > 0.05). A similar observation has been made by several authors (Taye et al. 2009;Mohammadi et al. 2010;Mekuriaw et al. 2013;Lakew et al. 2014). The maternal-effect during the pre-weaning period is higher than the effect during the post-weaning period i.e. singletons are favored during pre-weaning periods than twin in terms of nutrients. Except for ADG2, the weight gain of male lambs was superior to female lambs. The superiority of males was noted elsewhere (Mohammadi et al. 2010;Ghafouri-Kesbi and Gholizadeh 2017). This could be ascribed to the secretion and function of hormones. According to Ghafouri-Kesbi and Gholizadeh (2017), oestrogen limits the growth of the long bones in females whereas testosterone has a positive effect on growth in males.

Kleiber ratio and the effect of non-genetic factors
Kleiber ratio (KR) could be used as a useful indicator of feed conversion and an important selection criterion for the e ciency of growth as suggested by different scholars (Kleiber 1947;Köster et al. 1994;Ghafouri-Kesbi et al. 2011). The least-squares means and standard errors for KR of lambs are presented in Table 4. The highest KR was observed from birth to weaning growth phase and the lowest KR was observed between nine-month and yearling age. Likewise, Ghafouri-Kesbi and Gholizadeh (2017) noted a higher growth rate and Kleiber ratio in the pre-weaning growth phase than post-weaning. The KR1 observed in this study is comparable with the value (16.8) reported by Mandal et al. (2015), higher than the value (15.6) reported by Mohammadi et al. (2010), 15.3 reported by Abegaz et al. (2005), but lower than 18.2 reported by Ghafouri-Kesbi et al. (2011). The observed variation among breeds could be due to the variability of the genetic potential of breeds, weaning age of lambs, forage abundance, and other husbandry practices.
Single-born lambs had a higher Kleiber ratio during the pre-weaning growth phase and that superiority was not continued thereafter. However, multiple born lambs had a superior Kleiber ratio during the post-weaning age.
This trend could be due to compensatory growth of lambs i.e. the period of ampli ed growth after a spell of limited development and growth. Animals that have a high KR are considered e cient users of feed (Ghafouri-Kesbi et al. 2011), i.e. single-born lambs were more e cient in feed utilization than twin contemporaries during the pre-weaning period and the reverse is true during post-weaning. Season and year of lambing also exerted a signi cant in uence on Kleiber ratios of crossbred sheep. The sizable in uence of year and season on Kleiber ratios was documented elsewhere (Mohammadi et al. 2010;Mandal et al. 2015;Faid-Allah et al. 2016). The variation across year and season could be due to the variability of climatic conditions that directly or indirectly associated with feed availability, quality of forage, and disease prevalence. Estimates of genetic parameters for birth weight (BW), weaning weight (3MW), pre-weaning weight gain (ADG1), and pre-weaning Kleiber ratio (KR1) along with their likelihood values for each analysis under the four different models are summarized in Table 5. As per the log-likelihood test, model 2, 3, 3, and 1 were the optimal models for BW, 3MW, ADG1, and KR1, respectively. Based on optimal models, the direct heritability (h 2 a ) was varied from 0.003 for BW to 0.16 for ADG1. The h 2 a for ADG1 and KR1 in the present study is higher than the value (0.11 for ADG, and 0.10 for KR1) reported by Ghafouri-Kesbi et al. (2011). However, higher estimates (0.16 for BW, 0.27 for 3MW, 0.26 for ADG and 0.15 for KR) than the present results were noted by Mohammadi et al. (2010). Likewise, higher h 2 a (0.164) and lower c 2 (0.078) than the current result were reported by Khorsand et al. (2014) for Afshari sheep. The variability of estimates could be ascribed to the type of breeding program (crossbreeding or selection), selection intensity, data structure, the model used for estimation, and overall management of the ock.
The inclusion of maternal genetic effect exerted a signi cant in uence on BW, reduces the h 2 a estimate and it explains 20% of the phenotypic variation. Likewise, higher maternal heritability (h 2 m ) estimates ranging from 0.18 to 0.24 for BW were documented in several studies (Roshanfekr et al. 2011;Rashidi 2012;Shokrollahi and Zandieh 2012;Khorsand et al. 2014;Faid-Allah et al., 2016). This depicts that birth weight is strongly in uenced by the maternal gene than by the lambs own gene and this suggests that maternal genetic effects need to be considered in selecting for early growth. However, 21% of the phenotypic variation in 3MW and 19% in ADG1 were explained by a maternal permanent environmental effect (c 2 ). The c 2 of 3WW in this study was higher than those reported for dual purpose (0.09), meat (0.19), and wool (0.10) sheep (Safari et al. 2005). This indicates that maternal genetic effect is more important in birth weight than other traits. This result is in line with Prakash et al. (2012) who noted that the maternal genetic effects directly affect the lamb's birth weight and its effect usually diminishes slowly as the age of lamb increases. The in uence of genetic and non-genetic maternaleffect on early growth traits suggests that intervention in ewes and considering in selection may have a considerable in uence on the pre-weaning growth performance of lambs.
When the maternal genetic effect is considered in the model, the total heritability (h 2 t ) estimate is ideal for the estimation of selection response. Higher total heritability estimates for BW than the current study were reported by Abegaz et al. (2005) for Horo sheep and Mandal et al. (2015) for Muzaffarnagari sheep. However, the estimates for 3MW (0.12) and ADG1 (0.13) of Horo sheep were lower than the present estimates. In general, the heritability estimates in this study was found within a lower range and this could be explained by the inconsistency of management, fodder quality, and malnourishment of ock, as these factors increase the proportion of phenotypic variance due to environmental variance (Mandal et al. 2015;Gholizadeh and Ghafouri-Kesbi 2017).
The present heritability estimates for pre-weaning growth traits and Kleiber ratio suggest slow genetic progress would be expected through selection. According to Cassel (2009) andFaid-Allah et al. (2016), when the heritability is below 0.15, the selection of animals based on own performance is less effective. Therefore, selection for both early growth traits and Kleiber ratio should be according to the breeding values estimated from multiple information sources such as progeny, pedigree, sibs, and other relative information besides to own performance record. Genetic and phenotypic correlation The correlation estimates for considered traits are presented in Table 6. The phenotypic correlation varied from − 0.11 to 0.98 whereas the direct genetic correlation ranges between − 0.32 and 0.98. Higher direct genetic correlations for BW-3MW (0.72) and BW-ADG1 (0.52) than the current nding were noted by Jalil-Sarghale et al.
(2014). The direct genetic correlation estimate for BW-3MW, BW-ADG1, 3MW-KR1, and 3MW-ADG1 were reported to be 0.29, 0.04, 0.74, and 0.96, respectively according to Abegaz et al. (2005) and these values were lower than the current estimates. The variation of correlation estimate among breeds or studies likely due to the variation of sample size, data structure, management, number of random and xed factors considered.
The antagonistic phenotypic and genetic relationship was observed between BW and KR1. A lower genetic correlation among these traits was reported by Mohammadi et al. (2010), Mandal et al. (2015), and Faid-Allah et al. (2016). This suggests that these two traits cannot be improved simultaneously through selection and thus selection should focus on the trait of the highest importance. On the other hand, high and positive genetic correlations were observed among 3MW and other pre-weaning growth traits (ADG1 and KR1). These results are in line with previous studies (Prakash et al., 2012;Mandal et al., 2015) and this suggests that genes that in uence these traits were in a similar direction or the presence of linkage between these genes and thus, selection could be carried out based on either one of them. Genetic trend for early growth traits The genetic trend for pre-weaning growth traits of Dorper crossbred sheep are presented in Fig. 1. The coe cient for genetic trend for BWT, WWT, ADG, and KR were 0.01 kg/year, -0.105 kg/year, -1.103 g/year, and − 0.044 g/metabolic weight/year, respectively. This implies that except BWT, all investigated traits were decreased genetically by determined coe cient per year. In the contrary, a positive genetic trend (0.028 kg/year) was noted by Areb et al. (2021) for weaning weight of Bonga sheep under selection. This genetically reduction of preweaning growth traits could be due to the absence of selection for rams and ewes based on their estimated breeding value. Hence, the ram and ewes must be evaluated properly and selected based on their estimated breeding value to enhance the genetic progress.
Inbreeding coe cient (F) The overall mean probability of the two alleles at a randomly chosen locus being identical by descent (inbreeding coe cient) was 0.105% with annual rate of 0.021% (Fig. 2). The average inbreeding level for inbred sheep was found to be 14.1%. A relatively higher inbreeding level than this result was reported by Patiabadi et al. (2016) for Iranian Shal sheep (F = 6.28%),  for Boer crossbred goats (F = 0.58%), and Areb et al. (2021) for Bonga sheep (F = 0.36%). This could be ascribed to excessive use of very few rams and a high number of progenies per ram. According to Ryan (2018), the inbreeding coe cient of up to 6.25% is acceptable.
Inbreeding depression is unlikely to occur in this study because the inbreeding level is below the threshold.

Conclusion
In conclusion, the growth performance of Dorper x indigenous sheep was higher than most of the non-improved indigenous sheep breeds/populations in Ethiopia. Birth type, sex, season, and year of lambing are the main determinants of growth traits and Kleiber ratios. Considering the maternal effect is vital for accurate genetic evaluation of early growth traits. The observed low heritability estimates for growth traits and Kleiber ratio suggests that slow genetic progress would be expected from the selection. However, the integration of selection with crossbreeding programs and improving the ock management would further enhance the genetic gain. Therefore, selection should be conducted based on breeding values estimated from multiple information sources to improve its e ciency. Figure 1 Genetic trend for pre-weaning growth traits of Dorper crossbred sheep Figure 2 Trend of average inbreeding coe cient by year of birth observed for Dorper crossbred sheep