Guide

Schedules of reinforcement on a cumulative record

A schedule of reinforcement is the rule that decides which responses produce a reinforcer. Ratio schedules count responses. Interval schedules wait for time to pass and then reinforce the next response. Each rule leaves its own signature on a cumulative record, and learning to read those signatures is most of the work.

How to read a cumulative record

Time runs left to right. The line steps up by one with every response and never comes down, so the slope is the response rate: steep means fast, flat means pausing. The short diagonal ticks mark pellet deliveries. As on a paper recorder, the pen drops back to the baseline every 200 responses. Every record below comes from the same engine that runs the Leverlore lab, using a rat that already presses the lever.

The four simple schedules compared
Schedule	Reinforcer follows	Typical pattern
FR n	Every nth response	Pause, then a fast run to the next pellet
VR n	A varying number of responses, n on average	High, steady rate with short, rare pauses
FI t	The first response after t seconds	Pause after each pellet, responding picks up as the interval ends
VI t	The first response after a varying time, t on average	Moderate, steady rate without systematic pauses

Fixed ratio (FR): pause, then run

On FR 40 the 40th press produces a pellet, then the count starts again. The record looks like a staircase: a flat step after each pellet, then a steep run. The pause gets longer as the ratio gets bigger. A long review of rat and pigeon work (Schlinger, Derenne and Baron, 2008) found that the pause is controlled mostly by the upcoming ratio, which is why many behavior analysts now call it a pre-ratio pause rather than a post-reinforcement pause. Thin a ratio too quickly and pauses stretch out until responding breaks down: ratio strain.

Figure 1. FR 40, four minutes. Flat steps after the pellet ticks, then steep runs. 517 responses, 12 pellets, about 129 responses per minute.

Run FR 40 in the lab

Variable ratio (VR): fast and steady

On VR 40 a pellet arrives after 40 presses on average, but the next requirement could be 3 or 90. Because any press might pay off, pauses are short and rare, and the record is a steep, nearly straight line. At the same rate of reinforcement, ratio schedules sustain higher response rates than interval schedules. Gambling is the everyday example usually given.

Figure 2. VR 40, four minutes. A steep, even slope with pellets at irregular points. 570 responses, 14 pellets, about 143 responses per minute.

Run VR 40 in the lab

Fixed interval (FI): the scallop, looked at closely

On FI 60 s the first press after 60 seconds produces a pellet; presses before then do nothing. Rats pause after each pellet and respond more as the interval runs out. Averaged over many intervals this gives the textbook scallop. Single intervals in rats look more like break-and-run: a pause, then a steady burst of pressing. In a detailed rat analysis, Daniels and Sanabria (2017) found the pause averaged about half the interval on most trials, and what grew across the interval was mainly the length of each burst. The lab’s FI average graph shows the averaged curve next to the raw record.

Figure 3. FI 60 s, ten minutes. A pause after each pellet, then pressing that starts partway through the minute. 424 responses, 9 pellets, about 42 responses per minute.

Run FI 60 s and open the FI average

Variable interval (VI): moderate and even

On VI 30 s a pellet becomes available after a varying time averaging 30 seconds, and the next press collects it. There is no point in the interval where pressing reliably pays, so the rate is steady without systematic pauses, and lower than on a ratio schedule. Richer VI schedules support faster responding, with diminishing returns. VI is the usual baseline for extinction, discrimination and matching-law experiments because it is so stable.

Figure 4. VI 30 s, ten minutes. A moderate, even slope. 511 responses, 14 pellets, about 51 responses per minute.

Run VI 30 s in the lab

When reinforcement stops

In extinction the slope flattens. A brief burst of faster responding right after extinction begins is possible, not guaranteed: in one rat study the share of animals showing a burst ranged from about 7% to 69% depending on how a burst was defined and measured (Nist and Shahan, 2021). After a break, some responding returns at the start of the next session. That spontaneous recovery is partial, fades within the session, and shrinks across repeated rounds of extinction (Rescorla, 2004). Guided lab 3 in Leverlore walks through all of this.

Open the lab and pick guided lab 3

Study notes

The Leverlore guided labs on this material carry content-area tags that align with the BCBA Test Content Outline (6th ed.): B.4 positive reinforcement, B.9 simple schedules, C.4 rate, IRT and latency, C.10 cumulative records, and G.16 schedule thinning. The tags are a study aid only. Not affiliated with or endorsed by the BACB. Simulated records illustrate typical patterns; they are not real animal data.

To test yourself, the mystery schedule exercise hides the schedule and asks you to name it from the record.

Sources

Daniels, C. W., & Sanabria, F. (2017). Interval timing under a behavioral microscope: Dissociating motivational and timing processes in fixed-interval performance. Learning & Behavior, 45, 29–48.
Nist, A. N., & Shahan, T. A. (2021). The extinction burst: Impact of reinforcement time and level of analysis on measured prevalence. Journal of the Experimental Analysis of Behavior, 116, 131–148.
Rescorla, R. A. (2004). Spontaneous recovery. Learning & Memory, 11, 501–509.
Schlinger, H. D., Derenne, A., & Baron, A. (2008). What 50 years of research tell us about pausing under ratio schedules of reinforcement. The Behavior Analyst, 31, 39–60.