The axiomatic principle that all behavior is choice was incorporated into a revised implementation of an evolutionary theory’s account of behavior on single schedules. According to this implementation, target responding occurs in the context of background responding and reinforcement. In Phase 1 of the research, the target responding of artificial organisms (AOs) animated by the revised theory was found to be well described by an exponentiated hyperbola, the parameters of which varied as a function of the background reinforcement rate. In Phase 2, the effect of reinforcer magnitude on the target behavior of the AOs was studied. As in Phase 1, the AOs’ behavior was well described by an exponentiated hyperbola, the parameters of which varied with both the target reinforcer magnitude and the background reinforcement rate. Evidence from experiments with live organisms was found to be consistent with the Phase‐1 predictions of the revised theory. The Phase‐2 predictions have not been tested. The revised implementation of the theory can be used to study the effects of superimposing punishment on single‐schedule responding, and it may lead to the discovery of a function that relates response rate to both the rate and magnitude of reinforcement on single schedules.