  The idea of the inheritance of biological processes, such as the
developmental process or the life cycle of an organism, has been discussed in
the biology literature, but formal mathematical descriptions and plausible data
analysis frameworks are lacking. We introduce an extension of the nested
Dirichlet Process (nDP) to a multiscale model to aid in understanding the
mechanisms by which biological processes are inherited, remain stable, and are
modified across generations. To address these issues, we introduce Nested
Inheritance Dynamics Algorithm (NIDA). At its primary level, NIDA encompasses
all processes unfolding within an individual organism's lifespan. The secondary
level delineates the dynamics through which these processes evolve or remain
stable over time. This framework allows for the specification of a physical
system model at either scale, thus promoting seamless integration with
established models of development and heredity.
