The Γ-Model: A Statistical Framework for Testing Functional Convergence in Molecular Evolution

This preprint introduces the Γ-model as a statistical framework for testing whether functional similarity among evolutionarily divergent lineages exceeds the expectations of neutral evolutionary decay. Rather than proposing a universal evolutionary law, the model is formulated as a null-hypothesis testing approach in which a conventional exponential decay model serves as the baseline and the Γ-model is evaluated as an alternative using nonlinear regression, corrected Akaike Information Criterion (AICc), likelihood-ratio testing, bootstrap confidence intervals, and residual analysis. As a proof-of-concept, the framework is applied to published data for the hearing gene Prestin, a well-known example of molecular convergence associated with echolocation in bats and dolphins. The analysis indicates that the exponential model remains the preferred global explanation for the available dataset after accounting for model complexity, while residual analysis identifies localized deviations consistent with previously reported convergent evolution. The principal contribution of this work is methodological. The Γ-model is presented as a reproducible statistical tool for distinguishing localized convergent signals from general evolutionary trends, providing an objective framework for evaluating competing evolutionary hypotheses. The approach can be applied to additional genes and comparative datasets to investigate whether observed functional similarity significantly exceeds neutral expectations.