A Model of Growth Trajectory Bifurcation in Animals Ontogeny

Abstract

The aim of this study was to formulate and analyse a model of ontogenetic growth cessation in pigs. The cessation of growth when an animal reaches its species-specific size in ontogeny is still a problem. Systemic factors that contribute to this process are unknown. The focus of the research is an analysis of the growth dynamic that explains some aspects of the problem. The method applied to meet the purpose of the study was mathematical modelling. To enhance the understanding of the growth trajectories in ontogeny an analytical model of growth in pigs was built. The model was formulated as a hybrid dynamic system with discrete-time and continuum equations. The novelty of the study is a concept of ontogenetic growth in the pig. Both a new modelling technique, and new variables are introduced. A central theme of the study is an analysis of the growth trajectory bifurcation, and a description of the two emerged growth trajectories. A reading of a normal form of bifurcation applied to the growth trajectory bifurcation has been offered. The results suggest that ontogenetic growth in pigs is not continuous. The growth trajectory has bifurcation at the point the animals attain their individual maximum weight. At this point, two new growth trajectories emerge. On one trajectory, animals continue to grow till a species maximum weight is reached. On other trajectory, animals continue to live till obtainable life span is attained. The emerged trajectories are genetic channels that open the way to grow for the certain phenotypes. Ontogenetic growth stops when the feed conversion coefficient grows into infinity.