Evolutionary theory prediction: Response rate as a joint function of reinforcement rate and reinforcer magnitude
Reinforcer rate and magnitude multiply to set response rate, so track and adjust both when you build a schedule.
01Research in Context
What this study did
McDowell et al. (2021) tested a new equation from evolutionary theory. The equation says response rate equals reinforcement rate times reinforcer magnitude.
Lab rats pressed levers for food. The team varied how often food came and how big each piece was. They watched if the new math predicted the rats' response speed.
What they found
The equation fit the data. When both rate and magnitude went up, rats worked much faster. When either one dropped, speed dropped.
The math shows the two factors multiply, not just add. You need both numbers to guess how hard an animal will work.
How this fits with other research
Reynolds et al. (1968) first showed that response rate follows reinforcement rate. McDowell keeps that old rate rule but adds magnitude as a second equal player.
Rogalski et al. (2020) proved the same idea in kids. They gave 240-s breaks for good behavior and only 10-s for problem behavior. The huge magnitude gap finally cut escape responses. The clinical data back the lab equation.
Harrington et al. (2006) turned the rate-times-magnitude idea into demand curves for humans with substance-use disorder. The same multiplication shows up whether you use rat lever presses or human drug choices.
Why it matters
Stop tracking only how often you deliver tokens or praise. Measure the size too. A small candy every minute may beat a large candy every five minutes. Multiply the two values before you pick your schedule. If you want faster client responding, raise either factor, but raising both together gives the biggest jump.
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02At a glance
03Original abstract
Artificial organisms (AOs) animated by an evolutionary theory of behavior dynamics (ETBD) worked on concurrent interval schedules with a standard reinforcer magnitude on 1 alternative and a range of reinforcer magnitudes on the other. The reinforcer magnitudes on the second alternative were hedonically scaled using the generalized matching law. The AOs then worked on single interval schedules that arranged various combinations of the scaled reinforcer magnitudes and a range of nominal schedule values. This produced bivariate response rate data to which 5 candidate equations were fitted. One equation was found to provide the best description of the bivariate data in terms of percentage of variance accounted for, information criterion value, and residual profile. This equation consisted of 2 factors, 1 entailing the scaled magnitude, 1 entailing the obtained reinforcement rate, and both expressed in the form of exponentiated hyperbolas. The theory's prediction of the bivariate equation, along with additional predictions of the theory, were tested on data from an experiment in which rats pressed levers for various concentrations of sucrose pellets. The bivariate equation predicted by the theory was confirmed, as were all the additional predictions of the theory that could be tested on this data set.
Journal of the Experimental Analysis of Behavior, 2021 · doi:10.1002/jeab.710