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This article presents a new application of the Stochastic Theory of Volterra-Hamilton Systems of Finsler class to growth and ontogeny and particularly to the study of noise effects on the deterministic model equations for interaction of muscle and adipose tissue in mammals introduced in our previous study. Both normal development and its phenotypic deformation, due to non-optimal nutrition or disease, are considered. Efficient energy (ATP) usage by the system as a whole is centrally important. Feynman-Kac solutions to the noisy perturbation equations and sojourn time probabilities for the Sasaki lift Riemannian diffusion are obtained, based on the Riemannian Embedding Theorem for Finslerian Diffusion. Stochastic canalization of development, after C. H. Waddington, is proved for this mathematical model. AMS Subject Classification: 92C30, 53A20, 47D07, 35K40

STOCHASTIC CANALIZATION OF PHENOTYPIC DEFORMATIONS DURING ONTOGENESIS