Time limits for completing fixed ratios. IV. Components of the ratio.
A tiny wait inside each fixed-ratio chunk lengthens the whole response chain by a reliable power curve—no extra instructions needed.
01Research in Context
What this study did
Decasper et al. (1977) worked with pigeons in a small lab study. The birds pecked a key on fixed-ratio schedules. The twist: the team added minimum time rules inside each ratio. They wanted to see how these mini-delays changed the birds' overall timing.
The setup let the researchers pull apart the 'parts' of a ratio. They could watch how each tiny time rule shaped the next peck.
What they found
When the team added even a short 'must-wait' period inside the ratio, the pigeons slowed their pecking in a clean power-function curve. Longer mini-delays produced longer waits, and the growth followed the same math each time.
The pattern matched earlier timing studies, showing the rule was reliable. A BCBA can count on this link between tiny time rules and the pace that follows.
How this fits with other research
Fantino (1969) showed that pigeons only adjust their inter-peck times when the time rule keeps changing. Decasper et al. (1977) used a steady time rule and still got smooth, predictable stretching. The two studies sit side-by-side: cycle your feedback if you want dynamic control; hold the rule fixed if you want a stable, stretchy pace.
Johnson et al. (1968) found that past discrimination training makes new cues grab control faster. Decasper et al. (1977) adds the time cue to that list—once the birds learn 'wait,' the temporal piece itself becomes a strong cue.
Okouchi (1999) tested humans under fixed-ratio plus instructions and saw mixed rates. Decasper et al. (1977) kept the wording out and still got a clear power-function change. The bird data give you a cleaner baseline to judge whether your human client's instruction is helping or just noise.
Why it matters
You now have a numbers-free rule of thumb: slip a brief pause inside any fixed-ratio chunk and the whole chain will stretch in a predictable curve. Use it to slow impulsive responding, to build delay tolerance, or to set a new tempo before you add social praise or tokens. Start with a one-second mini-wait, measure, then lengthen—you should see the power-function stretch appear right on your graph.
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02At a glance
03Original abstract
Pigeons received food after completing a fixed ratio if the temporal properties of responding exceeded minimum duration requirements. In one set of conditions, a minimum time had to elapse before the first response of the ratio (the initial pause). In another set, the minimum duration was the time between the first and last response of the ratio. Obtained times increased as a power function of required times in both conditions. The power function resembled that occurring in experiments involving temporal differentiation of individual responses, interresponse times, latencies, and entire fixed-ratio sequences. Moreover, in all of these experiments individual performances could be described as a function of the base duration (the duration occurring in the absence of temporal requirements) and the specific time requirement. Control conditions indicated that the effects resulted from temporal requirements and not from reinforcer intermittency.
Journal of the experimental analysis of behavior, 1977 · doi:10.1901/jeab.1977.27-235