Feedback functions for variable-interval reinforcement.

Bacon-Prue et al. (1980) wrote math that predicts how animals respond on variable-interval (VI) schedules. They assumed the animal works in bursts, then pauses. The new equation fit three old rat experiments.

The paper is pure theory. No new animals were run. The authors just rearranged algebra to make VI feedback clearer.

The math showed that response rate on VI is driven by the same burst-pause pattern seen on VR. If you know the burst length and the pause length, you can forecast the overall rate.

The curve matched the data points without extra fudge factors. One clean equation did the job.

Delamater et al. (1986) later showed adult humans on VR behaved just like humans on VI plus a simple feedback loop. Their real data backed up the 1980 algebra.

Herrnstein et al. (1979) had offered a different VI equation that added reinforcer "power." Bacon-Prue et al. (1980) kept things simpler by folding power into the burst-pause idea.

Lincoln et al. (1988) went further, using linear systems theory to cover both VI and VR in one frame. They kept the feedback heart of A et al. but widened the map.

If you write token boards or fluency programs, you now have a quick way to guess how rate will change when you stretch the VI value. Think "bursts and pauses," not just "average time." Try plotting your client’s response bursts; if the pause after each burst stays steady, the VI math in this paper can predict whether rate will rise or fall before you ever change the timer.