Concurrent schedules: Interaction of reinforcer frequency and reinforcer duration.

The team ran two concurrent VI schedules on pigeons. They changed both how often and how long grain was given.

By mixing fast, short pay-offs with slow, long ones they tested the concatenated matching law. That law says animals weigh rate and duration together.

When overall reinforcer rate went up, birds treated the two keys almost the same. They stopped following the duration ratio.

The concatenated matching law predicted the opposite. More food per minute should have made duration count more, not less.

Davison et al. (1984) saw the same break-down when durations were mixed within a schedule. Both studies show the law fails once duration joins the game.

Macdonald et al. (1973) and Pierce et al. (1983) found clean matching when only rate mattered. Adding duration flips the story, so the papers do not truly clash; they map different turf.

Hall (2005) widens the hole. He showed that earning versus obtaining rates also break the law. Together these works mark a boundary: simple rate ratios are not enough.

If you run concurrent reinforcement in the classroom, do not assume kids will weigh rate and duration like the formula says. When both dimensions shift, preference can flatten and you may need extra probes or different schedules to keep responding differentiated.