The Gamma-Model: A Unified Framework for Similarity in Evolutionary Systems – Theory, Empirical Validation, and Extensions

We propose a mathematical model that decomposes total similarity between evolving entities into ancestral similarity (S_A) and functional attraction (S_Γ). Functional similarity follows S_f(T) = A * exp(-k*T) + B * (1 - exp(-m*T)), where B is the asymptotic lower bound as divergence time T → ∞. Using published Prestin gene data from bats and dolphins, we fitted the model and obtained B = 0.682 ± 0.027, with a statistically significant improvement over a simple exponential decay (p < 0.01). After 160 million years, functional similarity remains at 72% while neutral similarity drops to 2%, supporting a non-zero lower bound due to functional attraction. The model extends to cancer, AI, mathematics, and exobiology.