Reward Density And Variable-interval Schedule Performance In An Open Economy.

Four pigeons pecked a key on variable-interval schedules. Food came only when the birds had not eaten enough earlier in the day. This open-economy setup let the researchers watch how real reward density, not just the printed schedule, changed pecking.

They recorded every peck and every pellet. Then they plotted response rate against the amount of food the bird actually got per minute.

Three birds showed a clean hyperbolic curve: the less food they earned per minute, the faster they pecked. The fourth bird followed the same pattern but with a steeper bend.

The curve fit better when the x-axis was obtained reward density, not the programmed VI value.

Timberlake et al. (1987) saw a bitonic, hill-shaped curve under both open and closed economies. Schlundt et al. (1999) now show a one-way hyperbolic rise. The shapes differ because W et al. pushed density past satiation; once the birds were full, pecking dropped, creating the downhill side.

Davison et al. (1968) taught us that local reinforcement probability within each interval drives rate. The new data sharpen that idea: the exact number of pellets per minute, counted at the feeder, predicts rate even better than probability math.

Emmelkamp et al. (1986) found that time allocation, not local rate, shifts when reinforcer rate changes across multiple VI components. G et al. isolate the same reinforcer-rate variable but under a single schedule, showing the pure density effect without choice complications.

When you write a VI program, the density the learner actually receives can stray far from the plan if motivation, satiation, or outside food changes. Track what is earned, not just what is scheduled. If response rate looks flat or odd, graph pellets per minute on the x-axis; you may see the hyperbolic signal that tells you density is the lever to move.