Introduction

Deccani sheep is an indigenous breed of sheep, mainly found in semi-arid areas of Maharashtra, Andhra Pradesh, Telangana and Karnataka states of India. It ranks second total sheep population in India (65.06 million) with 6.22 million heads (Livestock Census, 2012). It is mutton purpose breed and plays a pivotal role in rural areas by providing income to livelihood. The wool form this breed is course type with very low value in market. Since indigenous breeds play significant role in Indian rural economy, the numerous research activities in India are functional towards conserving and improving the indigenous breeds of sheep in India (National Livestock Policy, 2013).

Growth curve describes the growth pattern over time by non-linear mathematical functions which convert weight-time information into certain number of growth parameters. These parameters provide biological interpretations, which can be used in deciding the nutritional practices, age for slaughtering and appropriate revisions in selection strategies (Bathaei and Leroy, 1996; Lambe et al., 2006; Kausar et al., 2016). It can be useful for identifying better animals in advance in order to keep superior animals at farm (Malhado et al., 2009; Canaza-Cayo et al., 2015). It is reported that growth curve had significant influence of animal level and environmental factors (Karakus et al., 2008; Keskin et al., 2009; Ulutas et al., 2010). There are several nonlinear functions reported and used by several researchers for growth curve modelling (Tekel et al., 2005; Gbangboche et al., 2008; Bahreini Behzadi et al., 2014; Lupi et al., 2015). The suitability of Brody model (Brody, 1945) for describing the growth curve of sheep have reported by many authors (Topal et al., 2004; Gbangboche et al., 2008; Bahreini Behzadi et al., 2014; Kopuzlu et al., 2014; Ganesan et al., 2015). Additionally, it has mathematical simplicity and meaningful interpretation. The genetic parameters between growth curve parameters could provide direction for assessing the selective breeding strategies and taking measures to enhance animal productivity. Recent studies have estimated genetic parameters for growth curve characteristics (Bathaei and Leroy 1998; Abegaz et al., 2010; Hossein-Zadeh, 2015a). However, the literature for growth parameters and their genetic parameters for this breed is scarce.

In view of this, the present study was carried out with objective to study effects of various factors on growth curve parameters estimated by Brody model and to estimate the genetic parameters of growth curve characteristics of Deccani sheep.

Materials and Methods

Data

The data records for present research work were obtained for 753 Deccani lambs born to 59 sires and 388 dams reared at ICAR-Network Project on Sheep (Deccani) Improvement, Mahatma Phule Krishi Vidyapeeth, Rahuri, Maharashtra (India) for the period from January 2011 to December 2015. The body weights up to 12 months of age along with other information such as year and season of birth, sex of lamb and dam’s weight at lambing were compiled from inventory and monthly weight registers. The farm managerial practices followed at the project were almost uniform throughout the year. The grazing along with feeding of green and dry fodders was followed routinely at farm. Concentrate was also fed to animals according to nutritional requirements of animals. The weaning period for lambs was three months of age and the selection criteria for rams was based on their progeny’s six months weights.

Statistical Analysis

Growth Curve Parameters

The Brody Model (Brody, 1945) was used for estimating the growth curve parameters of each animal in SPSS 20 software as follows-

Where,

Y_t represents body weight at t month of age;

A represents asymptotic weight, which is interpreted as average weight of the mature sheep; and

B is an integration constant related to initial animal weight or proportion of mature weight gained after birth;

k is the maturation rate which indicates how fast the animal approaches mature weight.

e and represent Napier’s base for natural logarithms and random error, respectively.

Factors Affecting Growth Curve Parameters

The general linear model including fixed effects of year and season of birth, sex of lamb and dam’s weight in SPSS 20 software was used to assess the influence on growth curve parameters of Deccani sheep as follows-

Where,

is observation for growth curve parameter,

is grand mean,

is effect of i^th year (i=1 to 5),

is effect of j^th season (j=1 to 2),

is effect of k^th sex of lamb (k= 1 to 2),

is effect of l^th group of ewe’s weight at lambing (l=1 to 3), and is random error.

The pairwise comparison was done using Tukey test. The statistical significance was tested at 5% level and only significant effects were considered for further genetic analysis.

Genetic Parameters

The estimates of variance components and genetic parameters were estimated by the Average Information Restricted Maximum Likelihood Method (AI-REML) using Wombat Software (Meyer, 2006). The convergence was assumed if difference in log likelihood function between consecutive iterations was lower than 5×10^-4.

The following univariate animal model accounting only direct effects with fixed effects was used,

Where,

y is a Nx1 vector of records for each growth curve parameter,

β denotes the fixed effects in model with association matrix X,

a is vector of direct additive genetic effects with incidence matrix Z and e is vector of residual effects.

For estimating the genetic and phenotypic correlations, bivariate animal model was used in this study.

Results and Discussion

Growth Curve Parameters

The Brody Model was fitted to monthly body weights of each lamb and it was revealed that values of R² for growth curves of 753 lambs were > 0.80, which indicated better goodness of fit due to model. These estimates were in accordance with reports of Ganesan et al. (2015) in Madras red Sheep. Further, effects of various factors were studied on growth curve parameters estimated due to Brody model. The least-square estimates for growth curve parameters of Deccani sheep due to Brody model are presented in Table 1. The overall estimates for asymptotic body weight (A), B and maturation rate (k) were 30.68 ± 0.26, 1.82 ± 0.04 and 0.66 ± 0.01, respectively.

Table 1: Least-square estimates for growth curve parameters of Deccani sheep due to Brody model

The values bearing different superscripts (a, b, c) differ significantly (p < 0.05) in same column

The figures in parenthesis indicates number of observations

Year of birth showed significant influence on growth curve parameters (A, B and k) in Deccani sheep, which was in accordance with findings reported by Abegaz et al. (2010) in Horro sheep. However, ewe’s weight at lambing had non-significant effect on growth curve. The asymptote weight had increasing trend over years and ranged from 29.06 (2011) to 32.21 (2015). These differences might be due to changes in managerial and feeding practices over the years. Although parameter B had inconsistent trend over years, it was significantly higher in 2013 to 2015 years than 2012. The maturation rate was ranged from 0.54 to 0.75 and it was revealed that there was significant reduction in k during 2015 after achieving peak in 2014. Season of birth had significant effect on all growth curve parameters, which was also reported by Bathaei and Leroy (1998) in Mehraban Iranian fat-tailed sheep. Lambs born during main season had lower asymptote weight with higher maturation rate as compared to that in off season. The availability of green fodders according to seasons might be responsible for discrepancies in growth curve characteristics of Deccani sheep.

The asymptotic weight was significantly (p < 0.05) higher for male (33.84 ± 0.36 kg) than female lambs (27.52 ± 0.35 kg), which was also reported by Bathaei and Leroy (1998) in Mehraban Iranian fat-tailed sheep and Hossein-Zadeh (2015b) in Iranian Shall sheep. However, these estimates were lower than findings of Gbangboche et al. (2008) in West African Dwarf sheep and Bahreini Behzadi et al. (2014) in Baluchi Sheep. Despite of higher asymptote weight in male lambs, the maturation weight was significantly (p < 0.05) higher in females (0.74 ± 0.02) than male lambs (0.57 ± 0.02), which was in accordance with Lupi et al. (2015).

Genetic Parameter Estimates

The estimates of variance components of growth curve parameters are given in Table 2.

Table 2: The estimates of variance components with heritability for growth curve parameters in Deccani sheep

Variance	A	B	k
Additive genetic variance ( )	3.35	0.11	0.01
Residual variance ( )	40.73	0.87	0.11
Phenotypic variance ( )	44.08	0.98	0.11
Heritability ( )	0.08 ± 0.06	0.11 ± 0.07	0.07 ± 0.06
Environmental proportion ( )	0.92 ± 0.06	0.89 ± 0.07	0.93 ± 0.06

The heritability estimates for parameters A, B and k were low as 0.08 ± 0.06, 0.11 ± 0.07 and 0.07 ± 0.06, respectively. These estimates were lower than reports of Bathaei and Leroy (1998) in Mehraban Iranian fat-tailed sheep, Abegaz et al. (2010) in Horro sheep and Hossein-Zadeh (2015a) in Iranian Shall sheep. Lupi et al. (2015) reported higher estimates for growth curve parameters under logistic and Verhulst models in Segurena sheep. The environmental proportion in total variance was observed very high for all parameters, which was ranging from 0.89 to 0.93. This indicated high variations in grazing and managemental practices practiced at farm, and which subsequently influenced the genetic variability and estimates of heritability for growth curve parameters. Additionally, low genetic variability may be attributed due to low nutritional level and changes in flock structure over time. The low estimates of heritability in this study does not supports as appropriate criteria for selection, however, indicates that choosing appropriate nutritional practices and control measures for seasonal variations could improve the growth curve parameters of Deccani sheep.

Correlation

The estimates of genetic, residual and phenotypic correlation among growth curve parameters are shown in Table 3. The genetic correlation between A and B was positive but very low (0.07), which was lower than reports of Abegaz et al. (2010) in Horro sheep (0.39). However, phenotypic and residual correlation of A with B were highly negative (ranged from -0.43 to -0.48). All correlations between B and k were highly positive (ranged from 0.87 to 0.93) indicated strong relationship between those parameters, which was also reported by Lupi et al. (2015) in Segurena sheep. However, it was contrary to reports of Hossein-Zadeh NG (2015a) in Guilan sheep (-0.01).

Table 3: The estimates of correlations among growth curves parameters of Deccani sheep

Pair	Genetic Correlation ( )	Residual Correlation ( )	Phenotypic Correlation ( )
A:B	0.07 ± 0.04	-0.48 ± 0.05	-0.43 ± 0.03
B:k	0.87 ± 0.12	0.93 ± 0.01	0.93 ± 0.01
A:k	-0.17 ± 0.45	-0.69 ± 0.03	-0.64 ± 0.02

Among the growth curve parameters, only A and k have biological interpretation and therefore, relationship between them may provide necessary conclusions. The genetic correlation between A and k was negative (-0.17), which was similar to reports of Bathaei and Leroy (1998) in Mehraban Iranian fat-tailed sheep and Abegaz et al. (2010) in Horro sheep. Further, residual and phenotypic correlation between A and k were high and negative (ranged from –0.68 to -0.69). This supports to our earlier findings that early maturity in female lambs results in lower mature weights than in male lambs. The phenotypic and genetic antagonism between A and k indicates that rapid reduction in growth rate after inflexion point results in lower mature weights (Canaza-Cayo et al. 2015). This finding would be helpful for improving selection by identifying the animal who reaches inflexion point earlier and attend higher mature weights later.

Conclusion

It was concluded that growth curve parameters had significant influence of year and season of birth, and sex of lamb. The genetic variability and estimate of heritability was low for all parameters. The antagonistic relationship between asymptote weight and maturing rate indicated that early maturing animal would have lower mature weights. The high environmental variability needs to reduce by adopting appropriate measures for effective implementation of breeding program.

Acknowledgements

The authors are thankful to the Director, ICAR-Central Sheep and Wool Research Institute, Avikanagar (Rajasthan), India for providing funding and the necessary facility to conduct this study. The authors also express their gratitude to the learned referee and the Editor-in- Chief for their valuable comments on the original version of the paper.

Conflict of Interest Statement

The authors declare that they have no conflict of interest.

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