Second-order schedules with fixed-ratio components: variation of component size.

The team built a second-order schedule. Pigeons had to finish a small fixed-ratio (FR) chunk many times before food arrived.

They tested chunk sizes from tiny (FR 16) to huge (FR 256). The question: which size keeps the birds pecking fastest?

Response rate made an inverted-U. It rose as chunks grew to FR 64–128, then fell again at FR 256.

Moderate chunks gave the best speed without long pauses. Very small or very large chunks slowed the birds down.

Crossman et al. (1985) seems to disagree. With tiny FR 1–7, pause length shrank as ratio size grew. The clash disappears when you see the ranges: small ratios act differently from the moderate 64–128 range tested here.

Cullinan et al. (2001) extended the same second-order idea to token boards. They swapped food tokens for eventual food and still saw rate drop when exchange requirements got too big.

Rider (1980) ran concurrent FR-FI schedules and found the same pause-growth pattern: bigger FR parts, longer pauses. The 1971 data now show that sweet-spot chunking can delay that slowdown.

When you chain many responses before a break, slice the work into medium-size blocks. Ask a learner to do 60–120 responses, then give a brief praise or token, not 10 and not 500. Watch pause length; if it stretches, shrink the chunk. This keeps momentum without wearing the client out.