Studies of wheel-running reinforcement: parameters of Herrnstein's (1970) response-strength equation vary with schedule order.
Schedule order and session time shift the numbers in Herrnstein’s equation, so treat them as moving targets, not fixed values.
01Research in Context
What this study did
Researchers let rats earn wheel-running time by pressing a lever. They tested two orders of reinforcement rates: low-to-high and high-to-low. Each rat worked through both orders in daily 50-minute sessions.
The team tracked how fast the rats pressed. They plugged the numbers into Herrnstein’s matching-law equation to see if the two key parameters stayed the same.
What they found
The parameters were not stable. Response-rate estimates were 30-50 % higher when the schedule started easy and got harder. They also crept up within each session.
In short, the numbers you plug into the matching law depend on the order you present the schedules and on where you are in the session.
How this fits with other research
Skinner et al. (1958) first showed wheel-running can act like an operant. Storm (2000) uses that same response, but adds the twist that schedule order changes the math.
Davison (1992) treats schedule parameters as fixed. Storm (2000) shows they are not; the new data nudge us to update the feedback functions.
Morante et al. (2024) shape human running with video feedback. Both studies control running, but Storm (2000) uses the wheel as a reinforcer, not the response being shaped.
Why it matters
If you use matching-law equations to set reinforcement rates, do not assume the parameters are constant. Test both ascending and descending orders and check for within-session drift. A quick probe session at the start and end of your baseline can save you from bad parameter guesses later.
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Join Free →Run a five-minute probe at the start and end of your next baseline session; if response rates differ by more than 10 %, collect data across both orders before locking in your parameter estimates.
02At a glance
03Original abstract
Six male Wistar rats were exposed to different orders of reinforcement schedules to investigate if estimates from Herrnstein's (1970) single-operant matching law equation would vary systematically with schedule order. Reinforcement schedules were arranged in orders of increasing and decreasing reinforcement rate. Subsequently, all rats were exposed to a single reinforcement schedule within a session to determine within-session changes in responding. For each condition, the operant was lever pressing and the reinforcing consequence was the opportunity to run for 15 s. Estimates of k and R(O) were higher when reinforcement schedules were arranged in order of increasing reinforcement rate. Within a session on a single reinforcement schedule, response rates increased between the beginning and the end of a session. A positive correlation between the difference in parameters between schedule orders and the difference in response rates within a session suggests that the within-session change in response rates may be related to the difference in the asymptotes. These results call into question the validity of parameter estimates from Herrnstein's (1970) equation when reinforcer efficacy changes within a session.
Journal of the experimental analysis of behavior, 2000 · doi:10.1901/jeab.2000.73-319