Directed evolution is an iterative, selection-driven process that generates heritable molecular diversity and enriches variants according to a defined functional criterion ^[1][2]. In protein engineering, a campaign typically begins with a parent gene or a library of genes encoding protein variants, and the encoded proteins are evaluated by screening or selection ^[2]. Molecular diversity is introduced through mutagenesis and recombination, and sequences associated with the selected phenotype are recovered to seed the next round of diversification ^[1][2]. This iterative cycle requires a recoverable linkage between the measured or selected phenotype and its encoding nucleic acid sequence, so that functional information can be translated back into sequence information ^[3]. The outcome of a directed-evolution campaign is therefore determined by the starting sequence population, the accessible variation, the assay and selection conditions, and the number of iterative rounds; the final sequence distribution reflects both the variants generated and the functional constraints imposed during evaluation ^[4].