Analysis of live weight in Corriedale sheep: a distributional regression approach

ABSTRACT

Understanding the growth and development of Corriedale sheep is critical to efficient production, as the breed is renowned for its high-quality wool and meat, as well as a variety of by-products. The main aim of this paper was to analyse the live weight of female Corriedale sheep according to five candidate variables: chest girth, abdominal girth, body length, wither height, and rump height. For this purpose, data from 100 animals from an experimental centre in Peru were examined. Generalized additive models for location, scale, and shape (GAMLSS), also known as distributional regression models, were used on account of their flexibility in describing the behavior of the response variable, allowing for the modeling of characteristics beyond the mean. Three different two-parameter distributions were tested to describe the response variable: gamma (GA), inverse gamma (IGAMMA), and inverse Gaussian (IG). A stepwise-based procedure was applied to select covariates for each parameter of the distributions. The GAMLSS based on the IG distribution was the most appropriate according to the Akaike Information Criterion (AIC), with the final model incorporating candidate variables in its two different regression structures (mean and dispersion). Finally, residual analysis indicated that the fitted model is suitable for describing the dataset under study.

Keywords:
body weight; ewes; model selection; statistical modeling

Introduction

Corriedale sheep, originating from New Zealand through crossbreeding to create a dual-purpose breed, are bred to produce high-quality wool and meat, as well as a variety of by-products, in addition to providing cultural and ecological benefits to society (Wang et al., 2014). Distinguished by its strong physique, vigor, and outstanding body composition, it also adapts well to varied temperatures and forage species under extensive farming conditions (Costa et al., 2020). The sheep population in Peru is estimated to be approximately 9.5 million, with 81 % being the Criollo breed, typically raised by rural communities (Canaza-Cayo et al., 2021).

Understanding animal growth and development is critical to efficient production (Khan et al., 2020). By understanding the mechanisms involved in the growth of carcass tissues, we can predict the best time for slaughtering each group of animals. Empty body weight is the metric that accurately represents the real mass of the animal and is used for calculating nutritional requirements (Pereira et al., 2017).

In this context, different statistical models, especially traditional linear and non-linear regression models, have been used to estimate performance in both sheep (Macedo-Barragán et al., 2021; Rather et al., 2021; Sharif et al., 2021) and cattle (Lee et al., 2020; Na et al., 2023; Weber et al., 2020), thereby acting as an important tool for reducing resource waste and optimising animal production (Tedeschi et al., 2010).

In these models, only the mean is modeled based on covariates, therefore, we are unable to explicitly model other measures, such as variance, skewness and/or kurtosis, when necessary (Roquim et al., 2021). In relation to this, generalized additive models for location, scale, and shape (GAMLSS; Rigby and Stasinopoulos, 2005), currently also known as distributional regression models (Heller et al., 2022), offer an interesting framework that can be used as an alternative.

Generalized additive models for location, scale, and shape are semi-parametric regression models that have been gaining significant popularity in different fields, particularly in agricultural sciences, such as agronomy (Ossifo et al., 2024; Righetto et al., 2019; Silva et al., 2023) and animal science (Almasi et al., 2022; Nakamura et al., 2022; Roquim et al., 2023). Thus, in this work, we employed the GAMLSS framework to model the live weight of female Corriedale sheep using several candidate covariates.

Materials and Methods

Information from 100 female Corriedale sheep aged 1.5 to 2 years was used from an experiment conducted at the Illpa Experimental Centre of the National University of the Altiplano of Puno, Peru (15°40’55.53" S, 70°4’31.89" W, altitude 3824 m). The climate in the study area is characterized by rainy summers and dry winters, with an average annual precipitation of 654.20 mm, an average temperature of 8 °C, and a relative humidity of 53.5 % (Canaza-Cayo et al., 2021). All animals were fed on natural pastures, where the major grass species in these areas are Festuca dolichophylla J. Presl, Muhlenbergia fastigiata (J. Presl) Henrard, Alchemilla pinnata Ruiz & Pav., Calamagrostis vicunarum (Wedd.) Pilg, and Stipa ichu (Ruiz & Pav.) Kunth. Measures were collected after an eight-hour fast to prevent possible mistakes caused by intestinal fullness. Live weight, our response variable, was recorded on a digital scale with a precision of 0.1 kg, and body measurements were taken by two technicians using a measuring tape and a Vernier calliper. Additionally, the following candidate characteristics were investigated to explain the response: chest girth (range: 72 - 99 cm), abdominal girth (range: 80 - 112 cm), body length (range: 83 - 104 cm), wither height (range: 50 - 66 cm), and rump height (52 - 68 cm). Further details regarding the experiment can be found in Canaza-Cayo et al. (2021).

The GAMLSS framework was used for statistical modeling. Mathematically, we define Y as the response variable, which follows any probability distribution D(θ_k) with a parameter vector θ_k = (θ₁, …, θ_p)^T, and

$$g_k\left({\text{θ}}_k\right)={\eta }_k=X_k{\beta }_k+{\displaystyle \sum _{j=1}^{J_k}{s}_{kj}\left(x_{kj}\right)}$$

where g(.) denotes an appropriate link function for the kth parameter, X_k, a design matrix, b_k, a parameter vector, and s_kj(.) are smoothing functions used to explain the relationship between parameter θ_k and the covariate x_kj. As smoothing functions, in this study, we have considered the so-called P-splines (Eilers and Marx, 1996). When they are included in the final fitted model, we typically interpret their behavior rather than performing statistical tests (Ramires et al., 2019).

The choice of distribution D is usually determined through the marginal response analysis (Nakamura et al., 2017). Thus, this study evaluated three potential two-parameter distributions that may handle the slightly asymmetric nature of the response: gamma (GA), inverse gamma (IGAMMA), and inverse Gaussian (IG). An important characteristic of these distributions is that their parameters have direct interpretations, making the models easier to interpret (Ramires et al., 2021a).

To facilitate the interpretation of GAMLSS, the parameterization of the distributions utilised frequently differs from those generally reported in the literature (Rigby et al., 2019). In the GAMLSS framework, the probability density function (pdf) of the GA distribution is given by

$$f\left({\text{θ}}_{1,}{\text{θ}}_{2,}\right)=\frac{y^{1/{\text{θ}}_2^2-1}}{{\left({\text{θ}}_2^2{\text{θ}}_1\right)}^{1/{\text{θ}}_2^2}\Gamma \left(\frac{1}{{\text{θ}}_2^2}\right)}\exp \left[-\frac{y}{{\text{θ}}_2^2{\text{θ}}_1}\right]$$

where θ₁ > 0 is the mean of the distribution, and θ₂ > 0, a coefficient of variation. Furthermore, the pdf of an IGAMMA distribution can be expressed as

$$f\left(y|{\text{θ}}_1,{\text{θ}}_2\right)=\frac{{\text{θ}}_1{}^{\text{α}}{\left(\text{α}+1\right)}^{\text{α}}{y}^{-\left(\text{α}+1\right)}}{\Gamma \left(\text{α}\right)}\exp \left[-\frac{{\text{θ}}_1\left(\text{α}+1\right)}{y}\right]$$

for y > 0, where θ₁ > 0 is a mode of the distribution and θ₂ > 0 a dispersion parameter and where $\text{α}=1/{\text{θ}}_2^2$. Finally, the pdf of an IG distribution is given by

$$f\left({\text{θ}}_1,{\text{θ}}_2\right)=\frac{1}{\sqrt{2{\text{πθ}}_2^2{y}^3}}\exp \left[-\frac{1}{2{\text{θ}}_1^2{\text{θ}}_2^{2}y}{\left(y-{\text{θ}}_1\right)}^2\right]$$

where θ₁ > 0 is the mean of the distribution, and θ₂ > 0, a dispersion parameter.

The subset of covariates in each regression structure is chosen using a stepwise-based procedure known as Strategy A (Ramires et al., 2021b). The best model based on each of the three considered distributions is selected using the Akaike information criterion (AIC; Akaike, 1974), which is then evaluated through worm plots (van Buuren and Fredriks, 2001) obtained from the normalized quantile residuals (Dunn and Smyth, 1996).

Although GAMLSS is theoretically a complex model, its practical application is relatively straightforward, as all the necessary functions for estimation are implemented and available in the GAMLSS package (Stasinopoulos and Rigby, 2007) and its extensions in R (R version 4.4.2). For further information, see Stasinopoulos et al. (2017).

Results

The minimum and maximum weights are 22.00 and 46.00 kg, respectively, with an average of 34.39 kg, a median of 34.00 kg, and a standard deviation of 4.68 kg. Furthermore, the skewness and kurtosis coefficients are 0.32 and 0.31, respectively, indicating a slightly positively skewed distribution with a near mesokurtic shape. These characteristics support the suitability of the three distributions described in the Materials and Methods Section: GA, IGAMMA, and IG.

The pairwise relationships between the live weight of the animal and each candidate explanatory variable wherea positive relationship with high variability is observed, can be seen in all plots. Note that by using GAMLSS, we can model both characteristics explicitly (Figure 1).

Figure 1

Relationship between live weight of female Corriedale sheep and each of the candidate covariates: A) chest girth; B) abdominal girth; C) body length; D) wither height; and E) rump height.

Following the descriptive analysis, Strategy A was implemented to identify the covariates to be included in the GAMLSS regression structures for each of the three distributions under consideration. The best-fitted model was based on the IG distribution, with the lowest AIC value of 478.52, followed by those based on the GA and IGAMMA distributions, which returned AIC values of 478.55 and 480.93, respectively. Hence, the remainder of the analysis was carried out using the fitted GAMLSS based on the IG distribution, which is given by θ₁=exp[0.746 + 0.016 abdominal girth + s(body length) + s(wither height) + 0.014 rump height] and θ₂=exp[–1.904 + s(chest girth)].

Four of the potential covariates were selected to explain the average live weight $\widehat{\text{θ}}$ of female Corriedale sheep: two linearly, both significantly at the 5 % level, and the other two through smoothing functions. For every additional 1 cm of abdominal girth, there is a multiplicative factor increase with a mean response of exp(0.016) = 1.016, i.e., for each centimeter, there is an expected increase of 1.61 % in the live weight of the ewe. Furthermore, for every 1 cm increase in rump height, there is an expected multiplicative factor increase of exp(0.014) = 1.014, implying that the sheep's live weight is expected to increase by 1.41 % for every centimeter.

The two smoothing functions considered to explain the average live weight of female Corriedale sheep are shown in Figure 2. The average live weight decreases until body length reaches around 85 cm (Figure 2A). It then remains stable until 86 cm before rapidly increasing up to 91 cm. The weight remains roughly constant up to 96 cm and then increases.

Figure 2

Smoothing functions fitted to explain the relationship between: A) average live weight and body length; B) average live weight and wither height; and C) live weight variability and chest girth.

The average live weight decreases until it reaches approximately 57 cm of wither height, remains nearly constant up to 61 cm, and then decreases thereafter (Figure 2B).

In the final fitted model, the remaining explanatory variable, chest girth, only affects the variability of live weight, which follows an almost sinusoidal pattern along the covariate values (Figure 2C).

Finally, the worm plot obtained from the normalized quantile residuals of the fitted GAMLSS was based on the IG distribution (Figure 3). Since all residuals lie within the 95 % confidence bands, we may conclude that the fitted model is appropriate for describing the live weight of Corriedale sheep.

Figure 3

Worm plot of the fitted generalized additive models for location, scale, and shape based on the inverse Gaussian distribution.

Discussion

Similar results for the relationship between the response and each of the covariates (Figure 1A: chest girth; Figure 1B: abdominal girth; Figure 1C: body length; Figure 1D: wither height; and Figure 1E: rump height) can be found in several works, such as Banerjee (2017) while examining the body indices for Garole sheep reared in West Bengal, India; Delialioglu et al. (2023) in a Polatli sheep dataset; Sam et al. (2023) in their study of West African Dwarf sheep, and Simone and Yeheyis (2024) in their study of Yearling male local sheep, among others.

As we can see, for both variables linearly included in this regression structure, the results corroborate the findings discussed in Figure 1B and E and are consistent with the literature (Djaout et al., 2022; Salazar-Cuytun et al., 2022; Vázquez-Martínez et al., 2023).

The fitted smoothing function used to explain the relationship between the average live weight and body length (Figure 2A) contradicts other published papers, such as Yilmaz et al. (2013) and Slavova et al. (2021). The behavior of the variable may seem confusing; however, as there is, unfortunately only limited information for smaller body lengths, the P-spline captured the behavior based on only three observations up to 85 cm. Nevertheless, if we disregard this initial part, it becomes clear that using a model that solely considers a linear relationship may not be the most appropriate for fully describing the effect of body length on the average live weight of female Corriedale sheep.

Similarly, the fitted smoothing function used to explain the relationship between the average live weight and wither height (Figure 2B) contradicts the findings of Canaza-Cayo et al. (2021), who reported a positive correlation between both variables. However, if we disregard the observation with the smallest wither height (Figure 1D), the relationship between these two variables may not be exactly linear as initially thought. Furthermore, other studies also found a positive correlation between them, and their linear regression model revealed a negative coefficient between them, which is consistent with the results of our fitted smoothing function (Simone and Yeheyis, 2024).

Identifying that chest girth affects the variability of live weight (Figure 2C) is possible only because of the GAMLSS framework considered in this study, which can directly explain both average live weight and its dispersion.

In conclusion, the use of GAMLSS based on the IG distribution was appropriate for modeling the data related to the live weight of female Corriedale sheep. The proposed model was useful because it allowed for the explicit identification of characteristics that affect both the average weight and its variability, enabling a more robust description and interpretation of the response variable's nature, which was explained by all candidate covariates: chest girth, abdominal girth, body length, wither height, and rump height. It worth noting that the applied methodology can be expanded to include additional relevant covariates and applied to different animal studies.

• Declaration of use of AI Technologies
  AI technology was used to paraphrase some original content.

Acknowledgments

The authors are grateful to the Illpa Experimental Centre of the National University of Altiplano, Peru, for providing the dataset. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001, by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), and by Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG).

Data availability statement

A sample of the dataset used in this study is available upon request from the authors.

References

• Akaike H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control 19: 716-723. https://doi.org/10.1109/TAC.1974.1100705
  » https://doi.org/10.1109/TAC.1974.1100705
• Almasi F, Nguyen H, Heydarian D, Sohi R, Nikbin S, Jenvey CJ, et al. 2022. Quantification of behavioural variation among sheep grazing on pasture using accelerometer sensors. Animal Production Science 62: 1527-1538. https://doi.org/10.1071/AN21464
  » https://doi.org/10.1071/AN21464
• Banerjee S. 2017. Body indices of Garole sheep reared in west Bengal (India). Proceedings of the Zoological Society 70: 61-73. https://doi.org/10.1007/s12595-015-0162-7
  » https://doi.org/10.1007/s12595-015-0162-7
• Canaza-Cayo AW, Mota RR, Amarilho-Silveira F, Duarte DAS, Cobuci JA. 2021. Principal component analysis for body weight prediction of Corriedale ewes from Southern Peru. Journal of Animal Health and Production 9: 417-424. https://doi.org/10.17582/journal.jahp/2021/9.4.417.424
  » https://doi.org/10.17582/journal.jahp/2021/9.4.417.424
• Costa PT, Mendonça G, Brum LP, Vieira TP, Feijó FD, Vaz RZ. 2020. Body mass index, energy reserves, and tissue composition of cuts of Corriedale lambs. Pesquisa Agropecuária Brasileira 55: e01908. https://doi.org/10.1590/S1678-3921.PAB2020.V55.01908
  » https://doi.org/10.1590/S1678-3921.PAB2020.V55.01908
• Delialioglu RA, Pehlivan E, Altay Y. 2023. Morphological characterization of the Polatli sheep in terms of live weight using data mining algorithms. Tropical Animal Health and Production 55: 416. https://doi.org/10.1007/s11250-023-03811-0
  » https://doi.org/10.1007/s11250-023-03811-0
• Djaout A, El-Bouyahiaoui R, Belkheir B, Moulla F, Mansouri H, Benidir M. 2022. Prediction of the body weight of Algerian Tazegzawt sheep breed from body measurements. Iraqi Journal of Agricultural Sciences 53: 1138-1144. https://doi.org/https://doi.org/10.36103/ijas.v53i5.1627
  » https://doi.org/https://doi.org/10.36103/ijas.v53i5.1627
• Dunn PK, Smyth GK. 1996. Randomized quantile residuals. Journal of Computational and Graphical Statistics 5: 236-244. https://doi.org/10.1080/10618600.1996.10474708
  » https://doi.org/10.1080/10618600.1996.10474708
• Eilers PHC, Marx BD. 1996. Flexible smoothing with B-splines and penalties. Statistical Science 11: 89-121. https://doi.org/10.1214/ss/1038425655
  » https://doi.org/10.1214/ss/1038425655
• Heller GZ, Robledo KP, Marschner IC. 2022. Distributional regression in clinical trials: treatment effects on parameters other than the mean. BMC Medical Research Methodology 22: 56. https://doi.org/10.1186/s12874-022-01534-8
  » https://doi.org/10.1186/s12874-022-01534-8
• Khan NN, Ganai NA, Alam S, Shanaz S, Hamadani A, Rather MA, et al. 2020. Genetic evaluation of growth performance in Corriedale sheep in J&K, India. Small Ruminant Research 192: 106197. https://doi.org/10.1016/j.smallrumres.2020.106197
  » https://doi.org/10.1016/j.smallrumres.2020.106197
• Lee DH, Lee SH, Cho BK, Wakholi C, Seo YW, Cho SH, et al. 2020. Estimation of carcass weight of Hanwoo (Korean native cattle) as a function of body measurements using statistical models and a neural network. AJAS 33: 1633-1641. https://doi.org/10.5713/ajas.19.0748
  » https://doi.org/10.5713/ajas.19.0748
• Macedo-Barragán R, Arredondo-Ruiz V, Haubi-Segura C, Castillo-Zamora P. 2021. Comparison of linear and nonlinear models to estimate body weight of Pelibuey ewes from body measurements. Tropical Animal Health and Production 53: 56. https://doi.org/10.1007/s11250-020-02515-z
  » https://doi.org/10.1007/s11250-020-02515-z
• Na MH, Cho W, Kang S, Na I. 2023. Comparative analysis of statistical regression models for prediction of live weight of Korean cattle during growth. Agriculture 13: 1895. https://doi.org/10.3390/agriculture13101895
  » https://doi.org/10.3390/agriculture13101895
• Nakamura LR, Ramires TG, Righetto AJ, Pescim RR, Roquim FV, Savian TV, et al. 2022. Cattle reference growth curves based on centile estimation: A GAMLSS approach. Computers and Electronics in Agriculture 192: 106572. https://doi.org/10.1016/j.compag.2021.106572
  » https://doi.org/10.1016/j.compag.2021.106572
• Nakamura LR, Rigby RA, Stasinopoulos DM, Leandro RA, Villegas C, Pescim RR. 2017. Modelling location, scale and shape parameters of the Birnbaum-Saunders generalized T distribution. Journal of Data Science 15: 221-238. https://doi.org/10.6339/JDS.201704_15(2).0003
  » https://doi.org/10.6339/JDS.201704_15(2).0003
• Ossifo ME, Nakamura LR, Pedro C, Muchico JMJ, Ferreira DF, Souza JC, et al. 2024. Maize productivity based on a distributional regression approach. Pesquisa Agropecuária Brasileira 59: e03690. https://doi.org/10.1590/s1678-3921.pab2024.v59.03690
  » https://doi.org/10.1590/s1678-3921.pab2024.v59.03690
• Pereira ES, Lima FWR, Marcondes MI, Rodrigues JPP, Campos ACN, Silva LP, et al. 2017. Energy and protein requirements of Santa Ines lambs, a breed of hair sheep. Animal 11: 2165-2174. https://doi.org/10.1017/S1751731117001185
  » https://doi.org/10.1017/S1751731117001185
• Ramires TG, Nakamura LR, Righetto AJ, Pescim RR, Mazucheli J, Cordeiro GM. 2019. A new semiparametric Weibull cure rate model: fitting different behaviors within GAMLSS. Journal of Applied Statistics 46: 2744-2760. https://doi.org/10.1080/02664763.2019.1611748
  » https://doi.org/10.1080/02664763.2019.1611748
• Ramires TG, Nakamura LR, Righetto AJ, Carvalho RJ, Vieira LA, Pereira CAB. 2021a. Comparison between highly complex location models and GAMLSS. Entropy 23: 469. https://doi.org/10.3390/e23040469
  » https://doi.org/10.3390/e23040469
• Ramires TG, Nakamura LR, Righetto AJ, Pescim RR, Mazucheli J, Rigby RA, et al. 2021b. Validation of stepwise-based procedure in GAMLSS. Journal of Data Science 19: 96-110. https://doi.org/10.6339/21-JDS1003
  » https://doi.org/10.6339/21-JDS1003
• Rather MA, Bashir I, Hamdani A, Khan NN, Ahangar SA, Nazki M. 2021.a Prediction of body weight from linear body measurements in Kashmir Merino sheep. Advances in Animal and Veterinary Sciences 9: 189-193. https://doi.org/10.17582/JOURNAL.AAVS/2021/9.2.189.193
  » https://doi.org/10.17582/JOURNAL.AAVS/2021/9.2.189.193
• Rigby RA, Stasinopoulos DM. 2005. Generalized additive models for location, scale and shape. Journal of the Royal Statistical Society Series C - Applied Statistics 54: 507-554. https://doi.org/10.1111/j.1467-9876.2005.00510.x
  » https://doi.org/10.1111/j.1467-9876.2005.00510.x
• Rigby RA, Stasinopoulos DM, Heller GZ, De Bastiani F. 2019. Distributions for Modelling Location, Scale and Shape: Using GAMLSS in R. 1ed. Chapman and Hall, London, UK. http://dx.doi.org/10.1201/9780429298547
  » http://dx.doi.org/10.1201/9780429298547
• Righetto AJ, Ramires TG, Nakamura LR, Castanho PLDB, Faes C, Savian TV. 2019. Predicting weed invasion in a sugarcane cultivar using multispectral image. Journal of Applied Statistics 46: 1-12. https://doi.org/10.1080/02664763.2018.1450362
  » https://doi.org/10.1080/02664763.2018.1450362
• Roquim FV, Ramires TG, Nakamura LR, Righetto AJ, Lima RR, Gomes RA. 2021. Building flexible regression models: including the Birnbaum-Saunders distribution in the gamlss package. Semina - Ciências Exatas e Tecnológicas 42: 163-168. https://doi.org/10.5433/1679-0375.2021v42n2p163
  » https://doi.org/10.5433/1679-0375.2021v42n2p163
• Roquim FV, Lima RR, Nakamura LR, Ramires TG, Blanco YAC. 2023. Dealing with highly kurtotic count data with excess zeroes: comparing different treatments in the control of dairy cattle gastrointestinal parasites. Brazilian Journal of Biometrics 41: 412-423. https://doi.org/10.28951/bjb.v41i4.646
  » https://doi.org/10.28951/bjb.v41i4.646
• Salazar-Cuytun R, Portillo-Salgado R, García-Herrera RA, Camacho-Pérez E, Zaragoza-Vera CV, Gurgel ALC, et al. 2022. Prediction of live weight in growing hair sheep using the body volume formula. Arquivo Brasileiro de Medicina Veterinária e Zootecnia 74: 483-489. https://doi.org/10.1590/1678-4162-12624
  » https://doi.org/10.1590/1678-4162-12624
• Sam IM, Usoro OO, Udo AF. 2023. Relationship of linear body measurements with live body weight in West African Dwarf sheep raised in Tropical Rainforest of Nigeria. Journal of Animal Science and Veterinary Medicine 8: 46-51. https://doi.org/10.31248/JASVM2023.365
  » https://doi.org/10.31248/JASVM2023.365
• Sharif N, Ali A, Mohsin I, Ahmad N. 2021. Evaluation of nonlinear models to define growth curve in Lohi sheep. Small Ruminant Research 205: 106564. https://doi.org/10.1016/j.smallrumres.2021.106564
  » https://doi.org/10.1016/j.smallrumres.2021.106564
• Silva PV, Schedenffeldt BF, Medeiros ES, Molina DZ, Pagliarini MK, Salmazo PAV, et al. 2023. Selectivity of herbicides used in corn on Crotalaria ochroleuca G. Don. Brazilian Journal of Biology 83: e277798. https://doi.org/10.1590/1519-6984.277798
  » https://doi.org/10.1590/1519-6984.277798
• Simone SK, Yeheyis L. 2024. Prediction of live weight and carcass characteristics from linear body measurements of yearling male local sheep. Turkish Journal of Agriculture - Food Science and Technology 12: 625-630. https://doi.org/10.24925/turjaf.v12i4.625-630.6676
  » https://doi.org/10.24925/turjaf.v12i4.625-630.6676
• Slavova P, Dimova N, Mihaylova M, Slavova S, Laleva S, Popova Y, et al. 2021. Live weight, body condition score, body dimensions, and phenotypic correlations between them in sheep of Bulgarian dairy synthetic population. Agricultural Science and Technology 13: 141-146. https://doi.org/10.15547/ast.2021.02.023
  » https://doi.org/10.15547/ast.2021.02.023
• Stasinopoulos DM, Rigby RA. 2007. Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software 23: 1-46. https://doi.org/10.18637/jss.v023.i07
  » https://doi.org/10.18637/jss.v023.i07
• Stasinopoulos DM, Rigby RA, Heller GZ, Voudouris V, De Bastiani F. 2017. Flexible Regression and Smoothing: Using GAMLSS in R. 1ed. Chapman and Hall, London, UK. https://doi.org/10.1201/b21973
  » https://doi.org/10.1201/b21973
• Tedeschi LO, Cannas A, Fox DG. 2010. A nutrition mathematical model to account for dietary supply and requirements of energy and other nutrients for domesticated small ruminants: The development and evaluation of the Small Ruminant Nutrition System. Small Ruminant Research 89: 174-184.https://doi.org/10.1016/j.smallrumres.2009.12.041
  » https://doi.org/10.1016/j.smallrumres.2009.12.041
• van Buuren S, Fredriks M. 2001. Worm plot: a simple diagnostic device for modelling growth reference curves. Statistics in Medicine 20: 1259-1277. https://doi.org/10.1002/sim.746
  » https://doi.org/10.1002/sim.746
• Vázquez-Martínez I, Tirink C, Salazar-Cuytun R, Mezo-Solis JA, Herrera RAG, Orzuna-Orzuna JF, et al. 2023. Predicting body weight through biometric measurements in growing hair sheep using data mining and machine learning algorithms. Tropical Animal Health and Production 55: 307. https://doi.org/10.1007/s11250-023-03717-x
  » https://doi.org/10.1007/s11250-023-03717-x
• Wang Z, Zhang H, Yang H, Wang S, Rong E, Pei W, et al. 2014. Genome-wide association study for wool production traits in a Chinese merino sheep population. PLoS One 9: e107101. https://doi.org/10.1371/journal.pone.0107101
  » https://doi.org/10.1371/journal.pone.0107101
• Weber VAM, Weber FL, Gomes RC, Oliveira Junior AS, Menezes GV, Abreu UGP, et al. 2020. Prediction of Girolando cattle weight by means of body measurements extracted from images. Revista Brasileira de Zootecnia 49: e20190110. https://doi.org/10.37496/RBZ4920190110
  » https://doi.org/10.37496/RBZ4920190110
• Yilmaz O, Cemal I, Karaca O. 2013. Estimation of mature live weight using some body measurements in Karya sheep. Tropical Animal Health and Production 45: 397-403. https://doi.org/10.1007/s11250-012-0229-7
  » https://doi.org/10.1007/s11250-012-0229-7

Edited by

• Edited by:
  Luiz Alexandre Peternelli

Publication Dates

• Publication in this collection
  21 Nov 2025
• Date of issue
  2025

History

• Received
  06 Sept 2024
• Accepted
  05 Apr 2025