Based on allometric theory and scaling laws, numerous mathematical models have been proposed to study ontogenetic growth patterns of animals. Although deterministic models have provided valuable insight into growth dynamics, animal growth often deviates from strict deterministic patterns due to stochastic factors such as genetic variation and environmental fluctuations. In this study, we extend a general model for ontogenetic growth proposed by West et al. to stochastic models for ontogenetic growth by incorporating stochasticity using white noise. According to data variance fitting for stochasticity, we propose two stochastic models for ontogenetic growth, one is for determinate growth and one is for indeterminate growth. To develop a universal stochastic process for ontogenetic growth across diverse species, we approximate stochastic trajectories of two stochastic models and apply random time change and obtain a geometric Brownian motion with a multiplier of an exponential time factor. We conduct detailed mathematical analysis and numerical analysis for our stochastic models. Our stochastic models predict well not only average growth, but also variations of growth within species. This stochastic framework may be extended to studies of other growth phenomena.

The coevolution of species drives diversity in animals and plants and contributes to natural selection, whereas in host–parasite coevolution, a parasite may complete an incomplete evolutionary/developmental function by utilizing the host cell’s machinery. Analysis of related older data suggests that Plasmodium falciparum (P. falciparum), the pathogen of malaria tropica, cannot survive outside its human host because it is unable to perform the evolutionarily first protein glycosylation of serologically A-like, O-GalNAcα1-Ser/Thr-R, Tn antigen (“T nouvelle”) formation, owing to its inability for synthesizing the amino sugar N-acetyl-d-galactosamine (GalNAc). This parasite breaks the species barrier via hijacking the host's physiological A-like/Tn formation through abundantly expressing serine residues and creating hybrid A-like/Tn structures, which in the human blood group O(H) are attacked by the germline-encoded nonimmune polyreactive immunoglobulin M (IgM), exerting the highly anti-A/B/H-aggressive isoagglutinin activities. These activities physiologically undergo the ABO(H) blood group phenotype formation, occurring on the surfaces of red blood cells (RBC), epithelial and endothelial cells and on plasma proteins by identical glycosylation, performed by the ABO(H)-allelic glycotransferases, phenotypically downregulating the anti-A/B/H-reactive IgM (isoagglutinin) activities in the non-O blood groups. ABO(H) phenotype diversity, this way glycosidically linked and molecularly connected to humoral immunity, becomes exposed to the evolution.