A Hybrid Analytical Model of Growth Regulation in Animals

The aim of this study was to build and analyse a model of ontogenetic growth of animals. The model was built based on experimental data and field observations. The growth of pigs was modelled by a non-local hybrid technique. This technique treats time as a discrete variable. In this study the growth of pigs was modelled beginning the stage of the rapid growth up to the maximum weight. The growth was modelled as a dynamic system. It was shown that the trajectory of the growth is neither smooth nor continuous. The main theme in this study is transition to a new growth phenotype. There are two results in this study. At a certain point in animal's ontogeny the trajectory of the growth undergoes a first-order phase transition. In the next stage, during bifurcation, new trajectories of growth emerge; this sequence of events has a biological meaning. The emerged trajectories differ from the initial trajectory, and from each other in essence. In the model, one trajectory of the growth emerges instantly. For other growth trajectory to emerge it takes half a year. In a population of animals, it is a general situation. Individual animals can take on only one of the emerged trajectories. In this study, a two-stage process of a transition to a new ontogenetic trajectory or a new phenotype was revealed. The transition to the new growth phenotype is to consider as the model of the pattern of the systemic regulation of growth.