Abstract
This study introduces a model of the growth phenotype dynamic in pigs by applying analytical methods. The model describes a transformation of the growth phenotype from 30kg live weight up to the species maximum weight.
 
 This paper focuses on a description of the determinants, which channel growth dynamic through animals' ontogeny. Theoretical notions about the growth are explicitly included in the concept. In the model, functional relations between relevant traits obtained in the experiments and field observations are analysed. Two focal variables, a feed conversion coefficient, and an invariant of growth are explicitly integrated in the model.
 
 The novelty of the research is a proposition that deterministic, analytical model is a conceivable approach to studying a phenotype of a quantitative trait. According to this proposition, processes that contribute to the growth and development continue in later life till a species maximum weight is attained. The concept is formulated as a deterministic, hybrid model. In the model, both standard continuum methods and discrete-time difference equations have been used.
 
 Applied to experimental data, the model has produced a new insight into the problem. In domestic pigs, the following three sets of ontogenetic growth phenotypes have been identified: one set with three species maximum weight phenotypes, one set with three rapid growth phenotypes, and one set with individual maximum weight phenotypes. In the study, not only the sets of growth phenotype are identified but also a possible interpretation of a conversion mode of the sets in ontogeny as well as a reading of growth trajectory dynamic are discussed.
Highlights
The purpose of this study was to introduce a concept of the growth phenotype dynamic in pigs' ontogeny
Conclusions o In the model, the growth phenotypes emerge as a result of an interaction between the feed conversion dynamic and constraints imposed by the weight invariant
O The sets of growth phenotype are considered as a dynamic system that develops in the course of ontogenetic growth: B→U◦G→A
Summary
The purpose of this study was to introduce a concept of the growth phenotype dynamic in pigs' ontogeny. As soon as the growth rate phenotypes are identified, methods of the qualitative traits genetics become applicable to the growth analyses. The method applied in the study is mathematical modelling. To meet the study purpose, two new relevant variables are introduced. Parameter 'K', an invariant of growth, and a feed conversion coefficient, 'Z' are focal variables in the model. Along with the new variables, a deterministic hybrid model of growth was built. A biological interpretation of the results in terms of quantitative traits genetics brings a theoretical aspect in the study
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