Four pigeons repeatedly chose between a fixed-ratio (FR) 20 and a variable-ratio (VR) 40 schedule of reinforcement, in which the minimum ratio of the VR cycled within each session. The minimum ratio ascended and descended (ASCDESC), descended and ascended (DESCASC), or remained constant (unchanging). In Phase 1, 2 birds (Group 1) were exposed to ASCDESC series and 2 birds (Group 2) were exposed to the DESCASC series. Choice proportions changed with the cycling minimum ratio for Group 2 but not for Group 1. In Phase 2, Group 1 subjects were exposed to the DESCASC series and Group 2 subjects were exposed to the unchanging condition. Although Group 1's choice proportions appeared to be undifferentiated in Phase 2, Group 2's choice proportions continued to cycle for more than 100 sessions. Group 2 subjects were then moved to the ASCDESC series in the third phase, and choice proportions cycled with the minimum ratio as in the first phase. The descending portion of the series was the more powerful determinant of cyclicity. Response rates also changed with the minimum component ratio, a finding that goes against the claim of universality of a rise-and-fall within-session pattern of responding. That preference varied despite the constancy of the average ratio requirement suggests nonlinear averaging in quantitatively representing a variable schedule's value. The strong perseverance observed also lends support to a growing body of literature on history effects.