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. 2025 Nov 29;12(1):e70707. doi: 10.1002/vms3.70707

Non‐Linear Mixed Models for the Characterization of Growth Trajectory Measured by Ultrasound of ‘San Pedreño’ Creole Pig Breed From Colombia

Arcesio Salamanca‐Carreño 1,✉, Pere M Parés‐Casanova 2, David E Rangel‐Pachón 1, Anthony Valverde 3, Paula A Toalombo‐Vargas 4, Mauricio Vélez‐Terranova 5
PMCID: PMC12664652  PMID: 41317343

ABSTRACT

The aim was to identify non‐linear regression models, under the context of mixed models, to describe the growth trajectory of ‘San Pedreño’ Creole pigs based on two muscular measurements obtained using ultrasonography. The growth rates of 30 animals (9 barrows and 21 gilts) from 3.5 to 24 months of age, raised on traditional farms in different municipalities of Meta (Colombia), were evaluated over three replicates. In vivo ultrasonographic images for back fat thickness (BFT) and longissimus dorsi muscle width (LMA) were obtained for each animal. Ultrasound measurements of LMA and BFT were performed at a single anatomical point of the live pigs, in the dorsal midline region (left/right). Comparison between sexes was done with a one‐way PERMANOVA. Correlations were done with the Spearman's r s coefficient. The traits body weight (BW), BFT and LMA were calculated as a function of each animal age (days) using each of the following non‐linear models: quadratic, exponential, von Bertalanffy, Michaelis–Menten, Logistic, Gompertz, Gaussian and Hill's equation. Traits were not significantly different between males and females (F = 0.437; p = 0.578). The variability of BFT and LMA tended to decrease with age (r s = 0.265 and 0.317 for BFT and LMA, respectively, p < 0.001). Correlation between both carcass traits was high (r s = 0.702, p < 0.001). The BFT growth in ‘San Pedreño’ Creole pigs can be described by applying the Hill equation and LMA growth by the quadratic model, applied to field data in live pigs.

Keywords: back fat, carcass, Creole pig, growth curve, ultrasound

Using real‐time ultrasound images taken in vivo, the thickness of back fat and the longissimus dorsi muscle width can be estimated in ‘San Pedreño’ Creole pigs.

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1. Introduction

Growth functions provide a mathematical summary of time course data on the growth of an organism or part of an organism (France et al. 1996). Growth is defined as an increase in live weight or dimension against age, and this change can be explained by growth curves (Gould 1966). The shape of growth curves varies depending on the animal species, environment and trait. Analysis of animal growth performance through the life span is helpful to establish appropriate feeding strategies and the best age for slaughtering (Keskin et al. 2009; Hossein‐Zadeh 2015). Growth curve studies have increased in recent years due to the development of new computational methods that facilitate accurate and rapid analysis, as well as the availability of new models (Souza et al. 2013; Hossein‐Zadeh and Golshani 2016; Makovický et al. 2017). Slow growth rates resulting in low market weight have been identified to be one of the factors limiting profitability in production systems (Abegaz et al. 2010). Growth rate is related to rate of maturing and mature weight, and these latter traits have been suggested to be related with other lifetime productivity parameters in swine (Souza et al. 2013; Gbangboche et al. 2008).

Carcass is the main component of live weight and has the highest market value in animals used for meat production (Castro de Sousa et al. 2022). Therefore, muscles positively correlated with the animal finishing (e.g., longissimus dorsi) can be good predictors of carcass composition. Ultrasonography has been used for decades as a technique to estimate carcass condition (Hernández Zapata et al. 2019). Ultrasonography measurements offer good prediction of carcass quality and are a non‐invasive and low‐cost tool (Orozco Murillo et al. 2010; Lagonikou et al. 2024). In this sense, the technique of real‐time ultrasonography has been widely used for the evaluation of carcass and body composition in beef cattle (Mukhoty and Berg 1971; Anzai et al. 2017), small ruminants (Hossein‐Zadeh and Golshani 2016; Garcia‐Gonzalez 1986), pigs (Schinckel et al. 2009; Luo et al. 2015; Rodríguez et al. 2023), broilers (Darmani Kuhi et al. 2002) and rabbits (Castro de Sousa et al. 2022). But although much current statistical program specifically assists the convenient fitting of such equations to observations (Birch 1999), these techniques have been much less used for the description of growth patterns in Creole breeds and, thus, there is still much to be done.

For a description of the development and growth of carcass and its components, non‐linear regression models can be used to evaluate strategies that allow the improvement of animal performance, especially regarding the weight gain and feed efficiency. Parameters of non‐linear models estimated for the growth of pigs can provide information for selection for carcass traits associated with the best slaughter age and prediction of productive efficiency indexes (Das et al. 2017), specifically non‐linear growth models. Non‐linear models are used to describe the change in animal weight with age because they generate a series of parameters that can be biologically interpreted (Rodríguez et al. 2023). Non‐linear growth models such as the Logistic, Gompertz, von Bertalanffy and Michaelis–Menten models are used in the study of animal growth, for example, in pigs (Archana et al. 2017), since they adapt to the sigmoid shape of animal growth (Rodríguez et al. 2023). The lack of scientific studies regarding the use of mixed models and non‐linear regression applied to the description of ponderal (Castro de Sousa et al. 2022) and carcass growth trajectories in many local pig breeds makes it impossible to obtain more reliable definitions of the right age for the slaughter of these animals. The mathematical description of growth can be used to explain the patterns observed in the field, and to predict the productive performance of pigs (Casas et al. 2010).

In Latin America, studies on growth curves of Creole pig under extensive environments or those carried out ‘in vivo’ to measure the development of meat characteristics are scarce (Ricalde et al. 2011). With ultrasonographic measurements, it is possible to establish differences in carcass between racial groups with little margin of error, and this information can be used to qualify and/or classify pig carcass (Hernández Zapata et al. 2019).

In Colombia, pigs served as initiators of the animal industry in the different colonies that were formed in America, and as meat and fat source (Pinzón 1993; Espinosa and Ly 2015). Creole pigs are part of the tradition and culture of rural family units and represent an important source of food and income. Their management is traditional since in most cases there are no special facilities (Benítez and Sánchez 2002; Linares et al. 2011). In many areas of Colombia, traditional pig production is used as a source of protein in the human diet.

The ‘San Pedreño’ Creole pig is distributed in several regions of Colombia. It is medium‐sized, with a small head, straight ears, and is black in colour, with fur abundant (Espinosa and Ly 2015). It represents an alternative to traditional pig production by using a native or locally adapted breed with characteristics of rusticity and adaptation to the environmental conditions of some regions in Colombia, being able to be fed with alternative sources to the use of commercial concentrates, reducing production costs and guaranteeing the food security of rural communities. Currently, the Creole pig ‘San Pedreño’ is at risk (FAO 2024).

Ultrasound measurements such as longissimus dorsi muscle width (LMA) and back fat thickness (BFT) at the early growth stage of ‘San Pedreño’ individuals would provide optimal timing to sell in the market or to keep for further feeding hogs. Currently, there are no in vivo studies on carcass growth indicators using ultrasound techniques in the ‘San Pedreño’ Creole pig, which generates great interest in promoting research with the technique.

The use of growth functions is largely empirical. The form of the function will sometimes be chosen by simply looking at the data and making an informed guess. However, it is preferable to select or construct a function that has some biological plausibility, and whose parameters may be meaningful, that is, they may characterize some underlying physiological or biochemical mechanism or constraint (France et al. 1996). Therefore, this study aimed to identify non‐linear regression models, under the context of mixed models, to describe the growth trajectory of ‘San Pedreño’ Creole pigs based on two muscular measurements obtained using ultrasonography.

2. Materials and Methods

2.1. Study Site

This study was carried out in the Meta department, Colombian Orinoquia (latitude: 01°36′29″ and 04°54′24″ N; longitude: 71°04′42″ and 74°54′09″ W). The department is in the tropical zone, with flat and undulating topography, an altitude range of 200–450 m. Annual precipitation varies between 2700 and 3500 mm. The average relative humidity is 71%, and the average ambient temperature is 26°C (Rincón Castillo et al. 2010).

2.2. Animals and Measurements

A sample of ‘San Pedreño’ Creole pig (n = 30; 9 barrows and 21 gilts) animals, from 3.5 to 24 months of age, raised on traditional farms in different municipalities of Meta (Colombia), was studied.

The Creole pig ‘San Pedreño’ is medium‐sized, with a small head, straight ears, and black in colour, with abundant (Espinosa and Ly 2015). The animals were weighed on a digital hanging scale (IF1976, CO). The study was conducted from August 2023 to September 2024. The average weaning age was 2 months. This study was carried out with information recorded in five different farms. Among the farms, there is great diversity in terms of infrastructure: some have only rustic corrals for the confinement of the herd, built with wooden posts and barbed‐wire threads on top, while others have masonry pens equipped to house a greater number of animals (Figure 1). The diet of animals consists of grazing native and introduced grasslands. They are also fed with waste from the production of artisan cheese (whey) and organic waste from the home (vegetable and fruit scraps). Balanced feed is sometimes provided. Mounting is natural for boars.

FIGURE 1.

FIGURE 1

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A gilt belonging to San Pedreño breed. Photograph taken at the Vegón farm. Source: authors.

Ultrasonographic images for BFT and LMA were obtained for each animal. These anatomical regions are widely used for the evaluation of finishing and muscling traits in different species (Hernández Zapata et al. 2019; Lagonikou et al. 2024; García Castillo et al. 2010; Dube et al. 2013). A set of six ultrasonographic images (three right side and three left side) were obtained from each animal. For a short period of time, each pig was confined in an individual containment cage (0.6 m × 1.50 m) during the measurement (Acosta 2018). At the time of taking the measurements, the pigs were calmed with the supply of balanced feed, to avoid possible errors in the measurement due to sudden movements of the animals.

For measurements, a Chison Eco1 Vet (Chison Medical Technologies Co., Ltd.; Wuxi Jiangsu Province, CN) ultrasound device was used with a multifrequency rectal linear transducer. The equipment was calibrated with 6.5 and 7.5 MHz frequencies for adequate resolution and depth. The ultrasound transducer was impregnated with the conductive gel to facilitate the transmission of the waves. Ultrasound measurements of LMA and BFT were performed at a single anatomical point of the live pigs, in the dorsal midline region (left/right), positioning the transducer dorsoventrally, between the twelfth rib and the vertebral column, in a transverse position. Once the ultrasound image was frozen (in the cross‐section), three measurements were taken for BFT and LMA, respectively: one in the central part, and one in the lateral and medial parts (Figure 2). All images obtained were captured by the same person, and were stored in the ultrasound equipment's memory. The area of the longissimus dorsi muscle was not measured because the equipment used did not allow the measurement of the muscle length. The equipment for this area is very expensive; therefore, a multifrequency rectal linear transducer was used. Muscle width and BFT values were recorded in Excel format for analysis.

FIGURE 2 (a).

FIGURE 2 (a)

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Frozen ultrasound image in cross‐section: 1 and 4, 2 and 5 central measurement, 3 and 6 medial measurement for BFT and LMA, respectively. (b) Dorsoventral position of the ultrasound transducer in the dorsal midline region.

2.3. Statistical Analysis

Comparison between sexes was done with a one‐way PERMANOVA. Correlations were done with the Spearman's r s coefficient. The traits body weight (BW), BFT and LMA were calculated as a function of each animal age (days) using each of the following non‐linear models: quadratic, power (allometric equation), exponential, von Bertalanffy, Michaelis–Menten, Logistic (sigmoidal), Gompertz (Rodríguez et al. 2023; Archana et al. 2017; Casas et al. 2010), Gaussian and Hill's equation (Benítez et al. 2020; Nduka and Oyinebifun 2020). Functions were fit to the data to model the relationship between weight and age. Each model was fitted separately to BW records of all pigs.

First, all the models mentioned above were tested considering the parameters as fixed. In this step, we used the following goodness of fit indicators for the tested models: coefficient of determination (R 2), calculated as the square of the correlation between the predicted and observed values; and Akaike Information Criterion (AIC), which is given by AIC = −log(L) + 2p, where log(L) is the logarithm of the likelihood function of the probability density function (Castro de Sousa et al. 2022; Nduka and Oyinebifun 2020). The R 2 value is an indicator measuring the proportion of total variation about the mean of the trait explained by the growth curve model. The coefficient of determination lies always between 0 and 1, and the fit of a model is satisfactory if R is close to unity (Hossein‐Zadeh and Golshani 2016). The AIC is a good statistic to compare models of different complexity because it adjusts the residual sum of squares for the number of parameters in the model. A smaller numerical value of AIC indicates a better fit when comparing models (Hossein‐Zadeh and Golshani 2016). Data were performed with PAST v. 4.17c (Hammer et al. 2001).

3. Results

Traits were not significantly different between males and females (F = 0.437; p = 0.578), so sexes were polled for ulterior analysis. The variability of BFT and LMA tended to increase with age (r s = 0.265 and 0.317 for BFT and LMA, respectively, p < 0.001) (Table 1, Figures 3 and 4), so older pigs have higher meat and fat incorporation. For both traits, the CV tended to decrease as age increased (Table 1). Correlation between both carcass traits was high (r s = 0.702, p < 0.001), indicating that animals with favourable values for one trait also have favourable values for the other traits.

TABLE 1.

Descriptive statistics of growth and carcass traits (back fat thickness [BFT]; longissimus dorsi muscle width [LMA]) of San Pedreño pigs at different ages (n = 30), from 3.5 to 24 months of age.

Age (months) Body weight (kg) Trait Mean (cm) SD CV (%) Minimum Maximum
3.5 18.2 BFT 1.84 0.369 19.9 1.15 2.76
LMA 0.91 0.242 26.5 0.60 1.52
4 21.8 BFT 1.12 0.336 30.0 0.60 1.99
LMA 0.39 0.072 18.5 0.29 0.57
5 19.0 BFT 0.92 0.339 36.7 0.54 1.42
LMA 0.50 0.026 5.2 0.47 0.53
6 26.0 BFT 1.27 0.369 29.1 0.71 2.04
LMA 0.41 0.054 13.3 0.27 0.53
7 27.0 BFT 1.26 0.381 30.1 0.76 1.97
LMA 0.50 0.049 9.8 0.43 0.59
8 52.3 BFT 1.95 0.416 21.2 1.34 2.76
LMA 0.91 0.288 31.6 0.64 1.39
17.5 76.5 BFT 2.46 0.316 12.8 1.66 2.93
LMA 1.36 0.289 21.2 1.01 1.87
24 105.0 BFT 2.41 0.674 27.9 1.11 3.74
LMA 1.58 0.201 12.7 1.29 1.95
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Abbreviations: SD, standard deviation; CV, coefficient of variation.

FIGURE 3.

FIGURE 3

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Bivariate regression (ordinary least squares) of longissimus dorsi muscle width (LMA) versus age in San Pedreño Creole pigs (n = 30, 3.5–24 months of age). The best‐fitting function is indicated by the solid line (r s = 0.317).

FIGURE 4.

FIGURE 4

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Bivariate regression (ordinary least squares) of back fat thickness (BFT) versus age in San Pedreño Creole pigs (n = 30, 3.5–24 months of age). The best‐fitting function is indicated by the solid line (r s = 0.265).

The R 2 values indicated that the BFT and LMA growth functions presented a low degree of accuracy (Table 2). For BFT, we observed that Hill's model (also known as ‘the four‐parameter logistic equation’ or ‘the variable slope sigmoidal equation’, these three names all refer to exactly the same model curve) (Motulsky and Christopoulos 2003) was the most appropriate (Figure 5), while the quadratic model (also known as ‘second‐order polynomial’) (Motulsky and Christopoulos 2003) was the most appropriate for LMA (Figure 6).

TABLE 2.

Criteria of adjustment of non‐linear regression models in function of back fat thickness (BFT) and longissimus dorsi muscle width (LMA) to age in San Pedreño Creole pigs (n = 30).

Trait Model R 2 AIC
BFT Quadratic 0.302 57.234
Power 0.305 57.048
Exponential 0.301 57.312
von Bertalanffy 0.300 57.411
Michaelis–Menten 0.205 62.302
Logistic 0.302 57.257
Gompertz 0.302 57.292
Gaussian 0.302 57.268
Hill 0.395 52.568
LMA Quadratic 0.572 21.767
Power 0.569 21.864
Exponential 0.560 22.190
von Bertalanffy 0.543 22.861
Michaelis–Menten 0.447 24.258
Logistic 0.558 22.247
Gompertz 0.558 22.278
Gaussian 0.558 22.261
Hill 0.596 22.976
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Abbreviation: AIC, Akaike Information Criterion; R 2, Coefficient of determination.

FIGURE 5.

FIGURE 5

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Hill's model (also known as ‘the four‐parameter logistic equation’ or ‘the variable slope sigmoidal equation’) for back fat thickness (BFT) in San Pedreño Creole pigs (n = 30, 3.5–24 months of age). The best‐fitting function is indicated by the solid line.

FIGURE 6.

FIGURE 6

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Quadratic model (also known as ‘second‐order polynomial’) for longissimus dorsi muscle width (LMA) in San Pedreño Creole pigs (n = 30, 3.5–24 months of age). The best‐fitting function is indicated by the solid line.

4. Discussion

From the analysis of the information, it was found that ‘San Pedreño’ Creole pigs show greater BFT than the LMA, which can be considered as animals tending to produce fat, a result also reported in another study (Hernández Ortiz et al. 2016). The variability for the two traits tended to decrease with age, although other studies indicate that these variations may be related to changes in feed consumption (Aymerich et al. 2019). In another study, although not in Creole pigs (Duroc × Landrace × Yorkshire), they report lower BFT in pigs that were slaughtered in the summer with an average temperature of 28.8°C (Wang et al. 2023). Our study highlights that the coefficients of variation for both traits decrease with increasing age, indicating greater uniformity in the BFT and LMA, respectively. It is also important to mention that the two traits present a high correlation, an important parameter in a genetic improvement program.

Growth models for estimating BFT and LMA showed a low degree of accuracy. The Hill model was the most appropriate for the BFT growth curve, while for LMA the quadratic model was the most appropriate. These models suggest being useful for monitoring animal growth under farm conditions (Keskin et al. 2009; Hossein‐Zadeh 2015; Hossein‐Zadeh and Golshani 2016; Gbangboche et al. 2008); and they have the potential to identify alternative strategies to improve the efficiency of pig production (Luo et al. 2015). On the other hand, the mathematical description of growth dynamics can be used to predict the productive behaviour of pigs observed in the field (Casas et al. 2010). Furthermore, the use of validated equations makes it possible to know the growth of the carcass without the need for slaughter (Carabús et al. 2017).

Polynomials are the most flexible tool to describe biological processes. They are simple and, although curvilinear, they are linear in parameters and can be fitted by using linear regression (Welham et al. 2014). In this study, the asymptotic process in LMA starts at 25 months of age. The results of this type of comparison rely on the data set used, which allows one to infer that there is not a single mode, that is, the best model in each situation, but there is indeed a model appropriate for each case (Maxwell et al. 2017). Observing the R 2, it is possible to note that this function was less accurate for BFT, as R 2 can be considered low for adjustment. However, it is important to emphasize that this value is an estimate based on the data to hand and can vary considerably from set to set if the data are not representative of the full range of conditions to which the breed may be subjected through successive seasons or years, or over the full growth cycle.

In the present study, no differences were found between males and females for the two traits; similar information to that reported for Creole pigs from Peru where no differences were found for BFT (Paredes Arana et al. 2017). In commercial crossbreed pigs, no differences were found for BFT (Aymerich et al. 2019). Another study reports that sex is probably the most important factor affecting fat and that castration increases fat (Carabús et al. 2017). It is also reported that fast‐growing pigs have fatter carcasses than slow‐growing pigs, although this effect has not been widely studied (Aymerich et al. 2019). Studies report that the quality of pork products is due to the amount of fat, so it is important to assess the amount of fat since it can be included in improvement programs (Solís et al. 2001).

In pig production, it is relevant to know the variability of BFT and LMA based on the genotype and in different production systems, as a goal of improving production (Araújo et al. 2018); however, no information is reported on Creole pigs, even less in Colombia, therefore, the results of the present study are relevant for pig production. The LMA is considered a significant predictor of carcass characteristics and weights of meat cuts (Lagonikou et al. 2024).

Real‐time ultrasonography measurements are a non‐invasive method that allows predicting BFT and LMA growth before slaughter, to evaluate the carcass characteristics of animals and prepare them for slaughter (Dias et al. 2020). In addition, these measurements can be used in genetic selection programs, since there is evidence that they have been included for decades in selective breeding schemes (Lagonikou et al. 2024). Therefore, in Creole pigs, such as the San Pedreño, the study of carcass measurements in live animals is promising for understand growth performance. Although the sample size is small, studies on ‘San Pedreño’ Creole pig are scarce, in part due to the fact that animals are difficult to catch and sample them. The data presented here are totally novel. In any case, we consider the results relevant to continuing future research. There are no data between 9 and 16 months, which could have reinforced the selection of the regression model.

5. Conclusion

In the study, the BFT growth in ‘San Pedreño’ Creole pigs can be described by applying the Hill's equation and LMA growth by the quadratic model, applied to field data in live pigs. Real‐time ultrasonography images taken in vivo allow an estimation of BFT and LMA growth in pigs at field level.

Author Contributions

Arcesio Salamanca‐Carreño: writing – original draft preparation, methodology, writing–review and editing, formal analysis, methodology. Pere M. Parés‐Casanova: writing – original draft preparation, methodology, formal analysis, methodology, writing–review and editing. David E. Rangel‐Pachón: writing – original draft preparation, methodology. Mauricio Vélez‐Terranova: writing–review and editing; methodology. Paula A. Toalombo‐Vargas: writing–review and editing. Anthony Valverde: writing–review and editing. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Research Committee—CONADI (ID3353)—of the Universidad Cooperativa de Colombia.

Ethics Statement

Bioethical Concept No. BIO394 was issued by the Research Bioethics Subcommittee of the Bucaramanga Sectional Universidad Cooperativa de Colombia (Act No. 4, 26, October 2023).

Consent

The authors have nothing to report.

Conflicts of Interest

The authors declare no conflicts of interest.

Acknowledgements

The authors thank the owners of the Mata de Agua, Vegón and Casa Blanca farms for providing the animals for taking images; the students who helped with data collection; and the anonymous referees for their valuable comments on the manuscript.

Salamanca‐Carreño, A. , Parés‐Casanova P. M., Rangel‐Pachón D. E., Valverde A., Toalombo‐Vargas P. A., and Vélez‐Terranova M.. 2026. “Non‐Linear Mixed Models for the Characterization of Growth Trajectory Measured by Ultrasound of ‘San Pedreño’ Creole Pig Breed From Colombia.” Veterinary Medicine and Science 12, no. 1: e70707. 10.1002/vms3.70707

Data Availability Statement

The data presented in this study are available on request from the second author. This is because the data is needed to perform other analyzes.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Data Availability Statement

The data presented in this study are available on request from the second author. This is because the data is needed to perform other analyzes.

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