Temporal context in concurrent chains: I. Terminal-link duration.
Lengthen the terminal link and choice rises in a predictable hyperbolic curve—use the 2Tt/(Tt + Ti) formula to set schedules.
01Research in Context
What this study did
The team ran a lab study with concurrent-chain schedules. Birds chose between two keys. Each key led to a terminal link that lasted a set time.
The researchers changed only the terminal-link length. They watched how choice shifted as the ratio of terminal to initial links grew.
What they found
As terminal links got longer, birds picked that side more. The rise followed a hyperbolic curve.
A simple math model, 2Tt/(Tt + Ti), tracked the data best. Time context, not just reward size, steered preference.
How this fits with other research
Diaz‐Salvat et al. (2020) also used single-case methods to probe reinforcement. They showed that more response options cut resurgence. Both papers reveal how small parametric tweaks reshape behavior.
Whitehouse et al. (2014) used an alternating-treatments design like the one here. They compared token earn versus loss in first graders. Both studies show that the way contingencies are arranged, not just the payoff, drives results.
Rasing et al. (1992) offered a linear-systems lens for any time-based data. Their framework could extend the hyperbolic model to real-world sessions with steady trends.
Why it matters
You can apply the 2Tt/(Tt + Ti) idea when building schedules for clients. Lengthen the terminal activity you want to boost, and shorten the rival links. The math gives you a quick forecast of how choice should shift before you even start.
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Join Free →Plot your current terminal-link times, apply 2Tt/(Tt + Ti), and lengthen the preferred side’s terminal link by 20 % to shift choice toward it.
02At a glance
03Original abstract
Two experiments are reported in which the ratio of the average times spent in the terminal and initial links (Tt/Ti) in concurrent chains was varied. In Experiment 1, pigeons responded in a three-component procedure in which terminal-link variable-interval schedules were in constant ratio, but their average duration increased across components by a factor of two. The log initial-link response ratio was a negatively accelerated function of Tt/Ti. Overall, the data were well described by Grace's (1994) contextual choice model (CCM) with temporal context represented as (Tt/Ti)k or 2Tt/(Tt + Ti), and by Mazur's (2001) hyperbolic value-added model (HVA), with each model accounting for approximately 93% of the variance. In Experiment 2, fixed-parameter predictions for each model were generated, based on the data from Experiment 1, for conditions in which Tt/Ti was varied over a more extreme range. Data were consistent with the predictions of CCM with temporal context represented as 2Tt/(Tt + Ti) and to a lesser extent as (Tt/Ti)k, but not with HVA. Overall, these results suggest that preference increases as a hyperbolic function of Tt/Ti when terminal-link duration is increased relative to initial-link duration, with the terminal-link schedule ratio held constant.
Journal of the experimental analysis of behavior, 2004 · doi:10.1901/jeab.2004.81-215