Psychological Review 1088,Vof.95,No.2,274-2<>S Copyright 1988 by the American Psychological Association, Inc. 0033-295X/88/I00.75 A Behavioral Theory of Timing Peter R. Killeen and J. Gregor Fetterman Arizona State University We base a theory of timing on the observation that signals of reinforcement elicit adjunctive behav- iors. The transitions between these behaviors are well described as a Poisson process, with a rate constant proportional to the rate of reinforcement in the experimental context. These behaviors may come to serve as the basis for conditional discriminations of the passage of time. Varying the rate of reinforcement will generate distributions of behavior whose mean and standard deviation vary proportionately. Holding the rate of reinforcement constant while manipulating the intervals to be judged will generate different functional relations between the mean and standard deviation, and these will lead to bisection at or slightly above the geometric mean, depending on the measure of bisection employed. The correlation between the rate of the Poisson process and the rate of reinforce- ment implies that psychometric functions should be affected by the rate of reinforcement. This prediction is confirmed. We extend the models derived from this theory to other phenomena, such as temporal generalization and discrimination, subjective shortening, and paired comparisons of intervals. Current models of choice between delayed reinforcers are consistent with our theory of timing. We propose a simple theory of timing based on the following premises: Stimuli that signal reward engender responses. These responses may be elicited or emitted, interim or terminal. We shall genetically call them adjunctive, recognizing that tradi- tional usage restricts the term adjunctive to behaviors that are not instrumental. We use the term in a broader sense in this article because the literature shows that there are elicited prop- erties to responses formerly treated as operant (e.g., Moore, 1973). Furthermore, we do not believe that the collateral behav- iors of which we speak emerge because they are instrumental in aiding timing; however, their utility in that role may affect the rate of reinforcement and thus feed back on and shape their expression, either beneficially or detrimentally. We hold that transitions between adjunctive behaviors are caused by pulses from an internal clock. Impressive evidence for the existence and properties of such a clock has been ad- duced by Church and his associates (see, e.g., Church, 1984). For convenience in describing our basic model, we speak of states corresponding to each class of adjunctive responses, with each pulse that is registered moving the system from one state to the next. Each of the states may be of variable duration, and the responses associated with it may occur at different rates, This research was supported in part by National Institute of Mental Health (NIMH) Grant MH39496 to Peter R. Killeen and in part by an NIMH NRS Award F32 MH09306 to 3. Gregor Fetterman. We thank J. R. Platt, N. Weiss, and an anonymous reviewer for their comments on an earlier draft of this article. The present form of this article owes much to the careful eye of J. Gibbon. None of these col- leagues are responsible for any remaining errors, nor do they necessarily agree with all the points we make. Correspondence concerning this article should be addressed to either Peter R. Killeen or J. Gregor Fetterman, Department of Psychology, Arizona State University, Tempe, Arizona 85287. including a rate of zero. The states are not taken as a cause of the behavior. An efficient cause of the behavior in state n + 1 is the reception of a pulse while the animal was engaged in a be- havior corresponding to state n. A material cause is the presence of an environment that will support the behaviors of a suitably motivated organism. We eschew specification of any final cause, such as the presumption that the adjunctive behaviors evolved to assist the animal in making temporal judgments. A formal cause is described by our theory. We presume that the adjunctive behaviors may come to serve as discriminative stimuli for subsequent responses. In timing experiments, if an animal is interrupted while in some state and asked to respond short or long, it will make whichever response has been most often associated with reinforcement in the con- text of the behaviors associated with that state. Choice re- sponses thus constitute the end of a simple chain of behavior. When asked to judge whether a stimulus is longer than a stan- dard, the animal will make the choice response long if, at the time of the question, it was in the state it had come to associate with the long training stimulus. Likewise, early adjunctive states may become conditioned to short responses. Intermediate states will be unreliable predictors of reinforcement, and short and long responses will be probabilistically reinforced in the context of them. Although it might be possible for animals to use the pulses alone as a cue, the pulses are presumed to be of brief duration and indiscriminable from one another. Conditioning to the ad- junctive behavior that characterizes the state aids counting, in much the same manner as does the use of fingers and feet by civilizations not blessed with numbers. This behavioral theory of timing constitutes a formalization of the view that behavior is the mediator of temporal control (see Richelle & Lejeune, 1980, for an excellent discussion of the role of collateral behavior in temporal control). Other explana- 274