Hyperbolae

Hyperbolic relations between independent and dependent variables are ubiquitous in the experimental analysis of behavior, mentioned in over 150 articles in the Journal of the Experimental Analysis of Behavior. There are two principal forms of hyperbolae: The first describes the relation between response rate and reinforcement rate on variable-interval schedules of reinforcement; it rises asymptotically toward a maximum. The second describes the relation between the current equivalent value of an incentive and its delay or (im)probability; it falls from a maximum toward an asymptote of 0. Where do these come from? What do their parameters mean? How are they related? This article answers the first two questions and addresses the last.

A molar view of goal direction and habit

When we treat behavior within an evolutionary framework and as temporally extended flow, two fundamental questions arise: (a) What is an organism? and (b) What is behavior? An organism is a process that stays intact by constantly exchanging energy with the environment. It takes in resources and puts out waste. The behavior of an organism consists of those process parts of the organism process that make up the exchange. These activities serve the function of reproducing, which generally depends on surviving. Surviving and reproducing depend on responding to phylogenetically important events (PIEs). A PIE induces activities that enhance or mitigate the PIE. Organisms respond not only to a PIE but also to events that covary with the PIE. Both activities and environmental features may covary with a PIE. When either type of covariance is introduced to an organism, behavior adapts over time. The early stages of adaptation constitute what researchers call "goal direction," and the later stages constitute what researchers call "habit." Behavior and environment constitute a dynamic system, and manipulations of the covariances and environmental features of the system allow many experimental interventions. This molar approach allows experiments on goal direction and habit to be understood without appeal to everyday mentalistic terms.

Choice and rate-amount independence in a titration procedure

The generalized matching law or Law of Allocation proposed by Baum (2018a, 2018b) potentially provides a broad conceptual framework within which to understand the allocation of time among activities. In its simplest form, the law incorporates power-function induction of activities by variables such as rate and amount of delivered inducers. Whether these variables affect allocation independently of one another is a central issue, because independence of the variables would allow simple multiplication of power functions and would make quantitative prediction simple too. The present experiment used a titration procedure to test the independence of rate and amount of food in determining pigeons' allocation of pecking between two keys. Amount ratio was varied within sessions to engender different peck ratios. Rate ratio was varied across two series of conditions. The results conformed to the predictions of the simple version of the Law of Allocation by strongly supporting independence of rate and amount. The Law of Allocation may have broad application for understanding activities in natural settings and everyday life.

Bridging the gap between laboratory and applied research on response-independent schedules

In 1948, Skinner described the behavior of pigeons under response-independent schedules as "superstitious," and proposed that the responses were reinforced by contiguous, adventitious food deliveries. Subsequently, response-independent schedules have been of interest to both basic and applied researchers, first to understand the mechanisms involved, and later, as "noncontingent reinforcement" (NCR) to reduce undesirable behavior. However, the potential superstitious effects produced by these schedules have been challenged, with some researchers arguing that antecedent variables play a significant role. This paper examines the evidence for adventitious reinforcement from both laboratory and applied research, the results of which suggest that antecedent, nonoperant functions may be important in fully understanding the effects of NCR. We propose an applied-basic research synthesis, in which attention to potential nonoperant functions could provide a more complete understanding of response-independent schedules. We conclude with a summary of the applied implications of the nonoperant functions of NCR schedules.

Matching, induction, and covariance with mixed response-contingent food and noncontingent food

The multiscale molar view of behavior is based on three basic laws of behavior: the Law of Allocation, the Law of Induction, and the Law of Covariance. Experiments that mix response-contingent food with noncontingent food shed light on these three laws. Food, like other phylogenetically important events, induces various activities that compete in allocation. Quantitative accounts represent induction with power functions. These power functions define activities' competitive weights, and relative time allocation among activities matches relative competitive weight. Behavior-food covariance determines which activities are induced. Phylogenetic (behavior-fitness) covariance determines which adjunctive activities are induced. Ontogenetic covariance may be represented in feedback functions. Feedback functions for variable-interval schedules may be observed even when overlaid by noncontingent food deliveries. Equations derived from the three laws describe responding in experiments with mixed response-contingent and noncontingent food. Equations derived here accounted for responding in three data sets: (a) from Rachlin and Baum (1972); (b) a new data set in which overall food rate was fixed while the proportion of response-contingent and noncontingent food varied; and (c) a new data set in which food occurred according to various variable-interval schedules. The same pigeons served throughout. All results were accommodated by the derived equations.

Behavior, process, and scale: Comments on Shimp (2020), "Molecular (moment-to-moment) and molar (aggregate) analyses of behavior"

If we study the behavior of organisms, we must understand the ontological status of both "organism" and "behavior." A living organism maintains itself alive by constantly interacting with the environment, taking in energy and discarding waste. Ontologically, an organism is a process. Its interactions with the environment, which constitute its behavior, are processes also, because the parts of any process are themselves processes. Processes serve functions, and the function of a process must be part of its identity. A process, by definition, extends in time. Time is the fundamental and universal measure of behavior. All processes have the property of scale. Activities of an organism have parts that are themselves activities on a smaller time scale. Scale varies continuously, and behavior may be studied on as large or as small a time scale as seems necessary. When researchers refer to the "structure" of behavior, they refer to smaller-scale activities. Attaching a switch to a lever or key is convenient, but one should never confuse operation of a switch with a unit of behavior. Shimp's (2020) "molecular" measures are small-scale measures. The molecular view based on discrete events has outlived its usefulness and should be replaced by a multiscale molar paradigm.