Mapping Gene Drive Dynamics onto Mendelian Models

Abstract

CRISPR-based gene drives bias their own transmission and can spread even when deleterious, giving rise to evolutionary dynamics that can be substantially more complex than those governed by standard Mendelian inheritance. Identifying conditions under which gene-drive dynamics can be faithfully approximated by Mendelian models would therefore enable the extensive theoretical toolkit of classical population genetics to be applied to gene-drive systems. Here, we develop a general mapping framework that translates gene-drive models into dynamically equivalent Mendelian models, allowing their behavior to be analyzed using classical theory. By deriving both haploid and diploid effective-parameter mappings, we identify Mendelian models that closely reproduce allele-frequency trajectories of gene drives across a wide range of conversion rates, fitness costs, and dominance effects. We delineate the regions of the parameter space where a one-parameter haploid approximation provides an accurate first-order representation, and where incorporating dominance in a diploid mapping substantially improves fidelity and recovers internal equilibria and threshold behavior. Analytic approximations yield efficient mappings across most of the drive parameter space, while a trajectory-based grid search further improves accuracy near nonlinear regime boundaries. To demonstrate the utility of this framework, we apply it to predicting gene swamping in a two-deme migration-selection model and show that the mapped Mendelian system accurately forecasts transitions between fixation and loss under three relevant release scenarios: environmental variation in fitness, engineered fitness asymmetries, and environment-dependent conversion. Together, these results establish a theoretical bridge between non-Mendelian gene drives and classical population genetic models, providing an interpretable and computationally efficient foundation for predicting gene-drive outcomes and guiding the design of gene drive systems and deployment strategies.