Determination of a behavioral transfer function: White-noise analysis of session-to-session response-ratio dynamics on concurrent VI VI schedules.
After you change reinforcer ratios on concurrent schedules, expect the response allocation to stabilize only after about five sessions.
01Research in Context
What this study did
Researchers worked with pigeons pecking two keys. Each key paid off on its own variable-interval schedule. The team changed the reinforcer ratio between sessions in a random pattern.
They recorded how the birds split their responses from session to session. Then they built a math model to predict those shifts.
What they found
A simple second-order equation fit the data. After a ratio change, response allocation settled in about five sessions. The model still worked when the same birds were tested again ten months later.
How this fits with other research
McLean et al. (2018) later used rats and flipped the ratios every day. The rats tracked the change inside each session, but their across-session fit got worse over time. The 1985 model still holds for slower, session-to-session shifts.
White (1979) had already shown that making birds wait longer to switch keys cuts switching and can create side preferences. I et al. folded that slower switching into their transfer-function gain.
Jones et al. (1998) found that birds lose track of which schedule is which the longer they stay on one key. The five-session time constant in I et al. lines up with that fading memory.
Why it matters
If you adjust token rates, praise rates, or task ratios in a classroom, do not expect instant re-allocation. Give the learner about five sessions before you judge the effect. If you change ratios faster than that, look at McLean et al. (2018) for cues on why data might wobble.
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Keep the new token ratio in place for at least five sessions before you graph trend change.
02At a glance
03Original abstract
Six pigeons were exposed to concurrent variable-interval schedules in which the programmed reinforcer ratios changed from session to session according to a pseudorandom binary sequence. This procedure corresponded to the stochastic identification paradigm ("white-noise experiment") of systems theory and enabled the relation between log response ratios in the current session and log reinforcer ratios in all previous sessions to be determined. Such dynamic relations are called linear transfer functions. Both nonparametric and parametric representations of these, in the form of "impulse-response functions," were determined for each bird. The session-to-session response ratios resulting from the session-to-session pseudorandom binary variations in reinforcer ratios were well predicted by the impulse-response functions identified for each pigeon. The impulse-response functions were well fitted by a second-order dynamic model involving only two parameters: a time constant and a gain. The mean time constant was 0.67 sessions, implying that the effects of abrupt changes in log reinforcer ratios should be 96% complete within about five sessions. The mean gain was 0.53, which was surprisingly low inasmuch as it should equal the sensitivity to reinforcement ratio observed under steady-state conditions. The same six pigeons were subjected to a similar experiment 10 months following the first. Despite individual differences in impulse-response functions between birds within each experiment, the impulse-response functions determined from the two experiments were essentially the same.
Journal of the experimental analysis of behavior, 1985 · doi:10.1901/jeab.1985.43-43