Application of a Model of Animals’ Growth to Study Slowly Growing Pigs

The aim of this study was to investigate a problem in pig farming by applying results of pigs’ growth modelling. The problem this study deals with is a large amount of variation in weight between animals within groups with growing-finishing pigs with strongly negative effect of slowly growing pigs on farm efficiency. The target is to find out a breeding scheme, which can eliminate the slowly growing phenotype from commercial farms. This study was carried out by applying a mathematical model. The model is species-specific; it was built to analyse growth of pigs. In the study, the model has not been developed, it was published elsewhere. The model’s results are used to clarify some aspects of pigs’ growth under industrial conditions. The model implies that in the pig, there are three growth phenotypes that have distinct growth performances. In the study, a main theme is variation in weight between growth phenotypes in pigs. The results of the study suggest that the slowly growing pigs have a certain growth phenotype. A method to identify the phenotype, and a breading scheme to eliminate the slowly growing phenotype from commercial farms are suggested.


Introduction
In industry, the growth performance of growing-finishing pigs strongly influences efficiency and productivity of commercial farms. The performance of pigs in batches depends on many factors (Calderón Díaz et al., 2017) including variation in weight between pen mates (He et al., 2016). On farm, the smaller the variation in weight the larger is the profit (López-Vergé et al., 2018a). It is essential to develop strategies to improve the performance of lightweight animals since they significantly contribute to batch inefficiency (Huting et al., 2017). In this study variation in weight and the growth rate of pigs were analysed by applying a mathematical model.

Variation in the Growth Rate
Variation in the growth rate of pigs starts from conception, with pigs of the same litter often varying considerably in birth weight. This variation in pig growth performance both within and between litters continues through their lifetime (Magowan et al., 2007). Many factors such as housing, environmental conditions, and feeding systems influence variation in weight in groups with pigs. Applying feeding strategies based on the average pig to a group of pigs implies that requirement will be met for not more than 50% of the pigs in the group. Accounting for differences among pigs within a group is essential in precision farming, which can improve economic performance (Vautier et al., 2013). Feeding strategies need to be adjusted to cover the requirements of the most efficient animals (Saintilan et al., 2015).
Most of the economic consequences of a higher variability among batches have to do with the quality classification mainly due to the lightest pigs within the same batch. There are many factors that affect pig performance, and pigs with a delayed growth are the consequence of several factors, such as environment, nutrition, and genetic potential, among others. The target is to reduce production costs by improving batch homogeneity (López-Vergé et al., 2018b). Before weaning, weight and growth rate of animals are influenced by a number of factors (Pardo et al., 2013;López-Vergé et al., 2018b). Many authors found that low birth weight, or low weaning weight had no evident negative impact on growth potential, quality of pigs or growth performance (Pardo et al., 2013;Huting et al., 2018). Other studies did not find positive effects of increasing the weaning weight in the growth to slaughter (López-Vergé et al., 2018b). It is understandable; animals can resist the harmful effects, overcome a number of negative factors (Huting et al., 2018;López-Vergé et al., 2018a) and later grow in line with their phenotypes. This statement is supported by finding that variation in the performance of pigs from different herds was also noted when they were managed in the common environment, with variation being similar to that observed on farm (Magowan et al., 2007).
Reportedly, the variation in weight between pen mates tends to decrease with age; however, decrease in weight variation with age could be a consequence of the different management practices implemented in the farms, like sorting pigs by body weight (López-Vergé et al., 2018b). Though, it is not always the case. Sorting growing-finishing pigs by weight fails to improve growth performance or weight variation (O'Quinn et al., 2001;Nyachoty et al., 2004). In conclusion, large variation in growth rate between pigs within herds or groups is a major contributor to poor performance and reduced profitability. Research should focus on strategies to manage such variation and ultimately to maximise the full genetic growth rate potential of pigs (Magowan et al., 2007).
The main part of pigs in industry are healthy and without complications at birth or weaning. In growth stage after weaning, the genetic determined differences in the growth between pigs become noticeable in weight approximately 45 kg. The pigs, which do not grow as fast as other pen mates due to the genetic determination are healthy animals and neither veterinary investigations nor laboratory analyses can reveal health problems. It is understandable; the pigs grow in line with their phenotype, though slower than pen mates with distinct phenotypes.

A genetic Aspect of Pig Growth
To explain variations in growth rate between pigs a mathematical model of animals' growth has been used. In this section one aspect of the growth determination has been discussed, namely the growth rate phenotypes. Rapid growth in domestic pigs has been observed between 30 kg and 96 kg live weight. In this weight range, growth rate maxima have been reported in most pigs. In the pig the growth rate maximum is inherent quality, it is genetically determined and physiologically conditioned. Identification of the growth phenotypes in pigs is associated with finding the growth rate maximum in individual animals over a stage of the rapid growth. A growing pig unavoidably has individual growth rate maximum, which characterises both its ontogenetic trajectory and the growth phenotype. The model says that in the pig, there are three growth rate phenotypes (Stass, 2019). Phenotype BB has growth rate maximum in weight approximately 70 kg, phenotype Bb has growth rate maxim in weight approximately 60 kg, and phenotype bb has growth rate maximum in weight approximately 45 kg. This result is supported by Green et al. (2003) findings. Slowly growing pigs have phenotype bb; in this study, growth of animals with this phenotype has been analysed.

Materials and Methods
The growth of pigs is discussed and modelled in terms of body weight and daily gain. The performance of a phenotype, a trait, is considered as a function of the underlying causal factors. Identification of such factors or variables is a separate task to complete prior to formulate a model. The method that has been used in this study was mathematical modelling.

Data Set
The data set was obtained in experiments with growing domestic pigs, LW, fed from 30±6 kg up to 96±4 kg live weight. The pigs were housed and fed under non-industrial conditions, either in a pig testing station or in research facilities. The animals were kept loose in groups of up to four to a pen, or individually in pens. Pigs were fed a dry commercially available balanced feed with unlimited access to water contingent on the experiment design, ad libitum, or a constrained diet. The quantity of the feed was adjusted once a week in accordance with the animals' current body weight. The experiments were performed in compliance with Declaration of Helsinki, National legislation, and institutional rules.

A Model of Pig's Growth
A detailed analysis of data set was used to build a mathematical model of pig's growth. The modelling technique enabled the formulation of a model that describes the growth of individual pig. The growth of pigs is considered as a dynamic system; it is based on a functional relation between studied traits. The model was formulated as a set with nonlinear equations with discrete current time (Stass, 2019). In this section only necessary for this study equations are given.
Journal of Agricultural Science Vol. 12, No. 9;2020 where, M denotes current weight, and m denotes initial considered weight; under the model conditions m o = 30 kg. t denotes current discrete time measured in days from animal birth, t o corresponds to m o . The following two equations may be useful to see the process of growth.
where, Z denotes current feed conversion coefficient, Z corresponds to M.

Results
In this section data published by He et al. (2016), and results published by Stass (2019) were used. Together, the above-mentioned studies lead to a possible explanation of growth variation in batches with pigs. In the experiments, slow growers accounted for 10% of pigs marketed, average growers accounted for 49% of pigs marketed, and fast growers accounted for 41% of pigs marketed (He et al., 2016). Similar result has been reported by other researchers (Calderón Díaz et al., 2017). Indirectly, the finding was supported by Vautier et al. (2013) data.

Genetic Interpretation of the Data
A data set obtained in experiments and published by He et al, (2016) was used. Between analysed pigs (n = 440), 10% were slowly growing, 49% average growing, and 41% fast-growing animals. The genetic interpretation of the data set is given in Table 1. The interpretation was comparable with the results of He et al. (2016). This interpretation approves the opinion that the distribution of animals by growth rate can be well explained (Stass, 2019). The above genetic explanation of the He et al, (2016) finding confirms the genetic determination of growth rate by phenotypes of two allelic gene B. It follows that slowly growing pigs have phenotype bb, average growing pigs have phenotype Bb, and fast-growing pigs have phenotype BB. This is in full agreement with earlier research (Stass, 2019) ( Figure 1).

Growth Phenotypes
The above result, Table 1, explains qualitative aspect of growth phenotypes distribution. Namely, the growth rate of pigs is inherently determined by the growth phenotypes. However, quantitative description of the growth phenotypes is needed as well. The quantitative explanation of the growth phenotypes trajectory in pigs follows from the model (Stass, 2019). The growth trajectories of the three identified phenotypes are shown in Figure 1.  Figure 2.

Figure 2
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