A Hybrid Analytical Model of Growth Regulation in Animals

Abstract

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.

Scales Bridging in the Model of Growth of Animals, a Holistic Slant

“…The data set was obtained in the experiments with pigs (Stass, 2020). The model was built as an extension of an earlier created model (Stass, 2022). In the study both continuum and hybrid techniques were used.…”

“…In biology, to build a meaningful mathematical model of a process one must have a concept of the process, and theoretical framework of the concept (Hyman, 2011). Besides, one must find a mathematical technique to implement the concept in a model (Stass, 2022). This scheme is valid also for scales bridging models.…”

“…Initially stable growth trajectory m o → M in the point (M x , Z x ) loses its stability as Z grows into infinity Z → ∞. As a result, the first-order phase transition with following bifurcation develops (Stass, 2022). As a result, new growth trajectories emerge.…”