High-throughput directed evolution, implemented in well-controlled in vitro conditions, provides a powerful route for enzyme engineering. Most existing technologies are based on activity screening and require the sequential observation and sorting of each individual variant. By contrast, approaches based on autonomous feedback loops, linking phenotype to genotype replication, enable autonomous selection without screening. However, these approaches are only possible in vivo, or applicable to very specific activities, such as polymerases or ligases. Here, we leverage synthetic molecular networks to create a programmable in vitro feedback loop linking a target enzymatic activity to gene amplification. After encapsulation and lysis of up to 10^7 transformed variants, the genes present in each droplet are amplified according to the activity of the encoded enzyme, resulting in the autonomous enrichment of interesting sequences. Applied to a nicking enzyme with thermal or kinetic selection pressures, this method reveals detailed mutational landscapes and provides improved variants.