A tuned-trace theory of interval-timing dynamics.
A fading one-back memory trace explains most interval-timing quirks, but it still skips the sharp scallops and sudden jumps.
01Research in Context
What this study did
Staddon et al. (2002) built a math model of timing. They call it tuned-trace theory.
The model uses one memory trace that fades fast. A single threshold decides when to respond.
They test the model against many interval-schedule data sets. No new animals were run.
What they found
The one-back trace catches most timing curves. It misses the deep scallop and sudden square-wave jumps.
In plain words: the model is good, not perfect. It covers the big picture, not every bump.
How this fits with other research
Webb et al. (1999) and McMillan et al. (1999) started the same trace family. Staddon et al. (2002) tightens the math and adds the one-back rule.
Bell (1999) warned that scalar timing still rules the lab. The new paper keeps the trace idea but admits it cannot beat scalar on every test.
Malone (1999) slammed the whole trace approach as fuzzy. Staddon et al. (2002) answer by showing exact equations, not just words.
Why it matters
If you use interval schedules in therapy, remember animals do not act like perfect clocks. A fading memory trace, not an inner stopwatch, may drive their pauses and bursts. Try adding brief signals or changes in context; these can reshape the trace and smooth out response patterns you see on your graph.
Want CEUs on This Topic?
The ABA Clubhouse has 60+ free CEUs — live every Wednesday. Ethics, supervision & clinical topics.
Join Free →Add a brief 2-s signal right before the usual payoff time and watch if the post-reinforcement pause shortens—trace models predict it will.
02At a glance
03Original abstract
Animals on interval schedules of reinforcement can rapidly adjust a temporal dependent variable, such as wait time, to changes in the prevailing interreinforcement interval. We describe data on the effects of impulse, step, sine-cyclic, and variable-interval schedules and show that they can be explained by a tuned-trace timing model with a one-back threshold-setting rule. The model can also explain steady-state timing properties such as proportional and Weber law timing and the effects of reinforcement magnitude. The model assumes that food reinforcers and other time markers have a decaying effect (trace) with properties that can be derived from the rate-sensitive property of habituation (the multiple-time-scale model). In timing experiments, response threshold is determined by the trace value at the time of the most recent reinforcement. The model provides a partial account for the learning of multiple intervals, but does not account for scalloping and other postpause features of responding on interval schedules and has some problems with square-wave schedules.
Journal of the experimental analysis of behavior, 2002 · doi:10.1901/jeab.2002.77-105