  Most protocols for the high-throughput directed evolution of enzymes rely on
random encapsulation to link phenotype and genotype. In order to optimize these
approaches, or compare one to another, one needs a measure of their performance
at extracting the best variants. We introduce here a new metric named the
Selection Quality Index (SQI), which can be computed from a simple mock
experiment with a known initial fraction of active variants. As opposed to
previous approaches, our index integrates the random co-encapsulation of
entities in compartments and comes with a straightforward experimental
interpretation. We further show how this new metric can be used to extract
general trends of protocol efficiency, or reveal hidden mechanisms such as a
counterintuitive form of beneficial poisoning in the Compartmentalized
Self-Replication protocol.
