Mathematical Framework for RNA - Protein Coevolution

Across scales---from ribonucleoprotein complexes, to organisms and their symbionts, to ecosystems and planetary biospheres---the same mathematical structures recur:

Trade-offs balancing robustness and adaptability.

Red Queen dynamics driving continual co-adaptation.

Bifurcations punctuating gradual trajectories with sudden shifts.

Attractors stabilizing complex configurations across levels of organization.

By formalizing these phenomena, the CAS approach provides a unifying language that bridges molecular evolution, ecological theory, and systems biology. It offers a way to reconcile divergence and convergence, continuity and punctuation, contingency and inevitability within a single mathematical framework. Reframing evolution as CAS thus not only resolves long-standing debates---such as the RNA-first versus protein-first paradox---but also lays the foundation for a general theory of adaptive complexity. This perspective transforms evolution from a collection of descriptive narratives into a predictive science of emergent dynamics, applicable across the hierarchy of life.

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