Time allocation and response rate.
Reinforcement rate sets a hard ceiling on response rate; time-allocation math tells you where that ceiling sits.
01Research in Context
What this study did
Shimp (1974) ran a single-case lab study.
The team varied how often food followed a key peck.
They tracked both peck rate and how long birds stayed at the key.
What they found
More food per hour pushed peck rate up to a ceiling.
Time spent at the key predicted that ceiling.
The paper gives a short equation you can plug numbers into.
How this fits with other research
Killeen (1970) saw the same ceiling at about 20 reinforcers per hour.
Bradshaw et al. (1978) show weaker sugar water lowers the ceiling.
Farrant et al. (1998) seems to disagree: very rich food gave the lowest rate.
The clash is only in early acquisition. Once birds settle, the ceiling rule holds.
Why it matters
When you thin a schedule, check the new rate against the time-allocation ceiling. If the math says the client can’t pass that ceiling, add bigger or tastier reinforcers first.
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02At a glance
03Original abstract
Food reinforcement for key pecking by three pigeons was arranged by a variable-interval schedule and a device that assigned each reinforcement to one of 10 component response rates corresponding to 10 classes of equally reinforced interresponse times ranging from 1.0 to 6.0 sec in 0.5-sec classes. The overall number of reinforcements per hour was varied from one to more than 60. Overall response rate was a monotonically increasing, negatively accelerated function of the overall number of reinforcements per hour. This function was decomposed into two time-allocation functions: (1) the time allocated to all of the reinforced component response rates as a function of the total reinforcement rate, and, (2) the time allocated to a particular reinforced component response rate as a function of the reinforcement rate for that component. Asymptotic response rate was predicted by combining the asymptotes of the two separate time-allocation functions: virtually all of the time was spent responding, and the percentage of the time spent responding that was allocated to a particular reinforced component response rate roughly equalled the relative reinforcements per hour for that component.
Journal of the experimental analysis of behavior, 1974 · doi:10.1901/jeab.1974.21-491