Generative Network Capacity and the Island Paradox: Topological Barriers in Gene Regulatory Networks

Macro-evolutionary innovation is commonly modeled as emerging through accumulated genetic variation filtered by selection. This paper develops an information-theoretic and graphtheoretic framework for examining how network topology may constrain the accessible space of biological states. Through exhaustive evaluation of the Boolean state space for a baseline architecture, 1-edge rewiring analyses, and Monte Carlo analyses of independently generated optimized networks, the simulations indicate that highly functional network architectures can possess strongly constrained mutational neighborhoods. In the model, 1-edge rewiring of an optimized baseline frequently produces substantial losses in navigability, with some intermediate architectures falling below a defined functional threshold (N_min = 0.90). Under strict selection dynamics in the model, such intermediate states would be strongly disfavored. The central hypothesis of this work is that biological evolution operates on at least two coupled spaces: a state space generated by a given network architecture and an architecture space in which the generative properties of the network itself can change. The simulations indicate that these spaces can have substantially different accessibility structures, supporting the distinction between state-space accessibility and architecture-space accessibility.