Nested Inheritance Dynamics

TL;DR

The paper addresses the challenge of modeling the inheritance and evolution of biological processes across generations in high-dimensional time-series data. It proposes NIDA, a Bayesian nonparametric framework that combines Nested Dirichlet Process priors with a multiscale hidden Markov structure to jointly model fine-scale developmental states and coarse-scale heredity. Key contributions include a probabilistic interpretation of inheritance under $\mathrm{nDP}$, a scalable hierarchical framework for disentangling genetic and environmental influences, and empirical validation on real (GTEx) and UK Biobank–like synthetic data, demonstrating superior predictive performance and model fit. The approach offers a flexible, data-driven tool for analyzing polygenic traits and developmental trajectories across generations, bridging development, heredity, and evolution in a unified generationally aware model.

Abstract

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.