An Analytical Model of Animal Growth

Abstract

The purpose of this study was to explain some aspects of ontogenetic growth in pigs by analysing the relationships between variables that are significant to the development of animals. The novelty of the study is a new modelling approach to the growth problem, with the attention that has been paid to both a new set of variables, and an analytical discrete-continuous hybrid model, innovative for the field. This is a first species-specific hybrid model for animal growth formulated in discrete-time difference equation technique. The efficiency of the model is not only due to the modelling technique but also due to a set of relevant variables, especially a feed conversion coefficient, which provides a link between macro and micro physiological scales. The model is based on functional relationships between relevant variables acquired from experimental data analyses, and field observations. The concept explains some aspects of growth in pigs from 30 kg to 600 kg, which is considered the maximum individual weight for a boar, and further growth up to a species maximum weight. The model predicts that boar can reach their maximum individual weight of 600 kg when 6,40 years old and are required to consume 62,51 kg of feed to put on the last kilogram. The phenotypes that can attain their maximum individual weight go through bifurcation of the growth trajectory, a transform in the growth mode. After bifurcation, the smallest number of the phenotypes go on the growth trajectory that leads to a set of species maximum weights of over 1205 kg, and the greatest number of phenotypes continue to live until aged 24,90 years, provided their maximum weights do not change. The study includes growth rate equations, identifies species maximum weight phenotypes, and produces insight into pig longevity. The results suggest that species maximum weight growth trajectories are phenotype-dependant. A modified discrete-time difference equation technique combined with standard continuum methods is an appropriate formalism to model ontogenetic growth in animals.