Order and chaos in fixed-interval schedules of reinforcement.
Even the bumpy scallop of FI responding follows a predictable, nonlinear rule.
01Research in Context
What this study did
The author built math models from chaos theory.
He tested them against real pigeon data on fixed-interval schedules.
The goal was to see if the messy scallop shape could be predicted.
What they found
The models fit the birds' peck patterns very well.
Even the wiggles inside the scallop showed up in the equations.
This hints that FI behavior is lawful, not random.
How this fits with other research
Byrd (1972) had already shown the scallop survives when only 7% of intervals pay off.
Blough (1992) now gives those old data a clean math engine.
Kono (2017) extends the same logic to space: pigeons peck in spots that drift toward the last feeder, and longer intervals make the drift more jumpy.
Okouchi et al. (2006) adds a twist: past signaled rates can speed or slow later FI performance.
That history effect is a variable the 1992 model leaves open, not a flaw.
Why it matters
If FI patterns are deterministic, you can tweak inputs and forecast the new curve.
Try plotting your client's minute-by-minute responding during a 5-min FI.
Look for the tiny wiggles the model captures; they tell you the schedule is working.
When the curve flattens, check for hidden reinforcers or history effects before you blame motivation.
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02At a glance
03Original abstract
Fixed-interval schedule performance is characterized by high levels of variability. Responding is absent at the onset of the interval and gradually increases in frequency until reinforcer delivery. Measures of behavior also vary drastically and unpredictably between successive intervals. Recent advances in the study of nonlinear dynamics have allowed researchers to study irregular and unpredictable behavior in a number of fields. This paper reviews several concepts and techniques from nonlinear dynamics and examines their utility in predicting the behavior of pigeons responding to a fixed-interval schedule of reinforcement. The analysis provided fairly accurate a priori accounts of response rates, accounting for 92.8% of the variance when predicting response rate 1 second in the future and 64% of the variance when predicting response rates for each second over the entire next interreinforcer interval. The nonlinear dynamics account suggests that even the "noisiest" behavior might be the product of purely deterministic mechanisms.
Journal of the experimental analysis of behavior, 1992 · doi:10.1901/jeab.1992.57-339