Robustness (homeorhesis) of developmental trajectories in Waddington’s landscape

Characterize and explain the mechanisms that confer robustness (homeorhesis) to developmental trajectories in Waddington’s epigenetic landscape, specifically determining how and when valley branching remains robust along the developmental path of cellular states.

Background

The paper discusses Waddington’s epigenetic landscape as a framework for understanding robust developmental processes, where valleys represent stable cell types and their successive branching encodes differentiation. Although the horizontal axis captures a high-dimensional cellular state and the vertical axis reflects slow developmental progression, the authors highlight that the timing and occurrence of valley branching are robust features, termed homeorhesis.

Amid this context, the authors explicitly note that understanding how the developmental path itself exhibits robustness—distinct from the stability of a final state—remains unresolved, framing it as a central open question within the development-evolution relationship.