Dynamics of waiting in pigeons.

Rapport et al. (1996) worked with six pigeons in a small chamber. A hopper gave grain every so often, but the wait changed like a smooth wave across the session.

The wave was a sine curve: short waits grew to long waits, then shrank again. The team logged how long each bird waited before pecking again.

The birds did not copy the last wait time. Their pauses tracked a blend of the last three or four waits, with the shortest wait holding the biggest vote.

When the schedule sped up again, the birds sped up too, but only after a slight lag. Memory, not the last hopper, drove the clock in their heads.

Hassin-Herman et al. (1992) saw the same short-wait power when daily sessions flipped between 5 s and 60 s. The 1996 paper widens that idea into a smooth, rolling pattern.

Fantino (1969) first showed pigeons stretch or shrink pauses across many fixed intervals. The new data say those pauses are a running average, not just a local reflex.

Arnett (1972) added extra lights that told time. Those cues lengthened pauses. Here, no added cues were needed; the birds built their own clock from recent history.

Your client’s history is alive in every response. If you thin a schedule too fast, the old short waits still tug behavior forward. Ease changes in steps and give the learner time to rewrite the average.