Coal Is Not Black, Snow Is Not White, Food Is Not a Reinforcer: The Roles of Affordances and Dispositions in the Analysis of Behavior.

Reinforcers comprise sequences of actions in context. Just as the white of snow and black of coal depend on the interaction of an organism's visual system and the reflectances in its surrounds, reinforcers depend on an organism's motivational state and the affordances-possibilities for perception and action-in its surrounds. Reinforcers are not intrinsic to things but are a relation between what the thing affords, its context, the organism, and his or her history as capitulated in their current state. Reinforcers and other affordances are potentialities rather than intrinsic features. Realizing those potentialities requires motivational operations and stimulus contexts that change the state of the organism-they change its disposition to make the desired response. An expansion of the three-term contingency is suggested in order to help keep us mindful of the importance of behavioral systems, states, emotions, and dispositions in our research programs.

A decade of contributions to understanding and ameliorating attention deficit-hyperactivity disorder.

BACKGROUND: It has been 10 years since Terje Sagvolden founded Behavioral and Brain Functions. BODY: After setting the context, this paper reviews some of the contributions of articles in the journal to the literature on ADHD over that decade. Those articles provide a cross section of some of the most important ongoing themes in ADHD research. CONCLUSION: Terje's faith in the new journal was well founded. It has survived the first threat of new journals, crib death, because of the continuing quality and relevance of the articles it carries. It has a diversified portfolio of similar research in many other fields of related interest.

Markov model of smoking cessation.

Survival functions from smoking cessation interventions are described by a three-state Markov model. On quitting, smokers transit through a state of withdrawal characterized by a high rate of relapse, and then into a more secure state of long-term abstinence. The Markov model embodies the dynamic nature of the cessation/relapse process; it permits stronger inference to long-term abstinence rates, provides measures of treatment efficacy, describes the outcomes of new quit attempts, and suggests mechanisms for the survival process.

From data through discount rates to the area under the curve.

The rate of discounting future goods is a crucial factor in intertemporal trade-offs, upon which depends not only individual well-being but also that of our planet: How much privation now for a temperate future for our grandchildren? What is the best way to measure how the value of future goods decreases with its delay? The most accurate discount functions involve several covarying parameters, making interpretation equivocal. A universal and robust measure is the area under the discount curve, the AuC. The AuC of a hyperbolic discount function is a logarithmic function of the discount rate, k. The same integral also approximates the area under a hyperboloid function. A simple technique converts each datum into estimates of the discount rate, eliminating rogue data points in the process. These trimmed estimates are converted into areas and tested against data, where they succeed at predicting the AuC and its relation to log(k).

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.

Adjunctive behaviors are operants.

Adjunctive behaviors such as schedule-induced polydipsia are said to be induced by periodic delivery of incentives, but not reinforced by them. That standard treatment assumes that contingency is necessary for conditioning and that delay of reinforcement gradients are very steep. The arguments and evidence for this position are reviewed and rejected. In their place, data are presented that imply different gradients for different classes of responses. Proximity between response and reinforcer, rather than contingency or contiguity, is offered as a key principle of association. These conceptions organize a wide variety of observations and provide the rudiments for a more general theory of conditioning.

The Structure of Scientific Evolution.

Science is the construction and testing of systems that bind symbols to sensations according to rules. Material implication is the primary rule, providing the structure of definition, elaboration, delimitation, prediction, explanation, and control. The goal of science is not to secure truth, which is a binary function of accuracy, but rather to increase the information about data communicated by theory. This process is symmetric and thus entails an increase in the information about theory communicated by data. Important components in this communication are the elevation of data to the status of facts, the descent of models under the guidance of theory, and their close alignment through the evolving retroductive process. The information mutual to theory and data may be measured as the reduction in the entropy, or complexity, of the field of data given the model. It may also be measured as the reduction in the entropy of the field of models given the data. This symmetry explains the important status of parsimony (how thoroughly the data exploit what the model can say) alongside accuracy (how thoroughly the model represents what can be said about the data). Mutual information is increased by increasing model accuracy and parsimony, and by enlarging and refining the data field under purview.

Variations on a theme by Rachlin: Probability discounting.

Rachlin and colleagues laid the groundwork for treating the discounting of probabilistic goods as a variant of the discounting of delayed goods. This approach was seminal for a large body of subsequent research. The present paper finds the original development problematic: In converting probability to delay, the authors incorrectly dropped trial duration. The subsumption of probability by delay is also empirically questionable, as those are different functions of variables such as magnitude of outcome and commodity versus money. A variant of Rachlin's theme treats human discounting studies as psychophysical matching experiments, in which one compound stimulus is adjusted to equal another. It is assumed that a function of amount (its utility) is multiplied by a function of probability (its weight). Conjoint measurement establishes the nature of these functions, yielding a logarithmic transform on amount, and a Prelec function on probability. This model provides a good and parsimonious account of probability discounting in diverse data sets. Variant representations of the data are explored. By inserting the probabilistically discounted utility into the additive utility theory of delay discounting, a general theory of probabilistic intertemporal choice is achieved.

Theory of reinforcement schedules.

The three principles of reinforcement are (1) events such as incentives and reinforcers increase the activity of an organism; (2) that activity is bounded by competition from other responses; and (3) animals approach incentives and their signs, guided by their temporal and physical conditions, together called the "contingencies of reinforcement." Mathematical models of each of these principles comprised mathematical principles of reinforcement (MPR; Killeen, 1994). Over the ensuing decades, MPR was extended to new experimental contexts. This article reviews the basic theory and its extensions to satiation, warm-up, extinction, sign tracking, pausing, and sequential control in progressive-ratio and multiple schedules. In the latter cases, a single equation balancing target and competing responses governs behavioral contrast and behavioral momentum. Momentum is intrinsic in the fundamental equations, as behavior unspools more slowly from highly aroused responses conditioned by higher rates of incitement than it does from responses from leaner contexts. Habits are responses that have accrued substantial behavioral momentum. Operant responses, being predictors of reinforcement, are approached by making them: The sight and feel of a paw on a lever is approached by placing paw on lever, as attempted for any sign of reinforcement. Behavior in concurrent schedules is governed by approach to momentarily richer patches (melioration). Applications of MPR in behavioral pharmacology and delay discounting are noted.

Discounting and the portfolio of desires.

The additive utility theory of discounting is extended to probability and commodity discounting. Because the utility of a good and the disutility of its delay combine additively, increases in the utility of a good offset the disutility of its delay: Increasing the former slows the apparent discount even with the latter, time-disutility, remaining invariant, giving the magnitude effect. Conjoint measurement showed the subjective value of money to be a logarithmic function of its amount, and subjective probability-the probability weighting function-to be Prelec's (1998). This general theory of discounting (GTD) explains why large amounts are probability discounted more quickly, giving the negative magnitude effect. Whatever enhances the value of a delayed asset, such as its ability to satisfy diverse desires, offsets its delay and reduces discounting. Money's liquidity permits optimization of the portfolio of desired goods, providing added value that accounts for its shallow temporal discount gradient. GTD predicts diversification effects for delay but none for probability discounting. Operations such as episodic future thinking that increase the larder of potential expenditures-the portfolio of desirable goods-increase the value of the asset, flattening the discount gradient. States that decrease the larder, such as stress, depression, and overweening focus on a single substance like a drug, constrict the portfolio, decreasing its utility and thereby steepening the gradient. GTD provides a unified account of delay, probability, and cross-commodity discounting. It explains the effects of motivational states, dispositions, and cognitive manipulations on discount gradients. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

A trace theory of time perception.

Many comparisons involve sequentially presented stimuli, as perforce the case in comparisons of temporal intervals. Interactions of such stimuli are as inevitable as the spatial interactions that yield color and brightness contrast. A memory-trace theory of perception (TToP) is developed and applied to time perception. Duration is estimated based on the memorial strength of the stimuli that signal the initiation of an interval at the time of its termination. Memorial persistence depends on modality and character of the signals, which condition the response to them. When the constant difference limen on the memorial continuum is back-translated to the temporal one it yields a generalized Weber function. Memory traces interact as a function of generalization gradients: Memories of stimuli that are similar enough are aggregated-feature-bound-some veridically, others as illusory conjunctions. The resulting representations may then be judged in a discrimination paradigm, or translated back to the physical domain as reproductions of the intervals. The presentation of a standard stimulus affects the perception of the comparison stimulus, warping the ruler by which it is measured. Complementary effects are predicted for discrimination and adjustment paradigms. Thus configured, the TToP accounts for multiple special effects, variously referred to as distortions, anomalies, and illusions, that are observed with classical psychophysical methods: Scalar and nonscalar timing, modality effects, time-order errors, masking, time warping, lengthening, and Vierordt's law. Similar processes affect the perception of nontemporal stimuli whenever they are presented in sequential proximity to one another. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Applied Quantitative Analysis of Behavior: What It Is, and Why We Care-Introduction to the Special Section.

Science evolves from prior approximations of its current form. Interest in changes in species over time was not a new concept when Darwin made his famous voyage to the Galapagos Islands; concern with speciation stretches back throughout the history of modern thought. Behavioral science also does and must evolve. Such change can be difficult, but it can also yield great dividends. The focus of the current special section is on a common mutation that appears to have emerged across these areas and the critical features that define an emerging research area-applied quantitative analysis of behavior (AQAB). In this introduction to the "Special Issue on Applications of Quantitative Methods," we will outline some of the common characteristics of research in this area, an exercise that will surely be outdated as the research area continues to progress. In doing so, we also describe how AQAB is relevant to theory, behavioral pharmacology, applied behavior analysis, and health behaviors. Finally, we provide a summary for the articles that appear in this special issue. The authors of these papers are all thinking outside the Skinner box, creating new tools and approaches, and testing them against relevant data. If we can keep up this evolution of methods and ideas, behavior analysis will regain its place at the head of the table!

Addendum to Killeen's (2019) Bidding for Delayed Rewards.

Killeen (2019) portrayed an intimate relation between diverse economic indices, in particular compensation functions, discount functions, and demand functions. The article bemused some experts, however, by its counterintuitive prediction of an increase in the amount bid as the delay increased. Furthermore, the article failed to provide an explicit treatment of the small-soon versus large-late choice paradigm, to cite several papers that provided precedent for the current work, and to demonstrate the adequacy of his expenditure functions for data on purchasing decisions. These shortcomings are remedied in the current note, and some additional extensions offered.

An additive-utility model of delay discounting.

Goods remote in temporal, spatial, or social distance, or in likelihood, exert less control over our behavior than those more proximate. The decay of influence with distance, of perennial interest to behavioral economists, has had a renaissance in the study of delay discounting. By developing discount functions from marginal utilities, this article provides a framework that resolves several anomalies of intertemporal choice. Utilities are inferred to be power functions of monetary value, delay, and probability. Utility, not value, is discounted, with decisions made by adding the utility of a good to the disutility of a delay or contingency. The theory reduces to standard treatments, such as exponential, hyperbolic and hyperboloid, and exponential-power; naturally predicts magnitude effects and other asymmetries; is consistent with subadditivity, immediacy, and certainty effects; returns conjointly measured determinations of monetary utility and temporal distance functions; and is extensible to other dimensions of distance.

Origins of altered reinforcement effects in ADHD.

Attention-deficit/hyperactivity disorder (ADHD), characterized by hyperactivity, impulsiveness and deficient sustained attention, is one of the most common and persistent behavioral disorders of childhood. ADHD is associated with catecholamine dysfunction. The catecholamines are important for response selection and memory formation, and dopamine in particular is important for reinforcement of successful behavior. The convergence of dopaminergic mesolimbic and glutamatergic corticostriatal synapses upon individual neostriatal neurons provides a favorable substrate for a three-factor synaptic modification rule underlying acquisition of associations between stimuli in a particular context, responses, and reinforcers. The change in associative strength as a function of delay between key stimuli or responses, and reinforcement, is known as the delay of reinforcement gradient. The gradient is altered by vicissitudes of attention, intrusions of irrelevant events, lapses of memory, and fluctuations in dopamine function. Theoretical and experimental analyses of these moderating factors will help to determine just how reinforcement processes are altered in ADHD. Such analyses can only help to improve treatment strategies for ADHD.

Progressive ratio schedules of reinforcement.

Pigeons' pecks produced grain under progressive ratio (PR) schedules, whose response requirements increased systematically within sessions. Experiment 1 compared arithmetic (AP) and geometric (GP) progressions. Response rates increased as a function of the component ratio requirement, then decreased linearly (AP) or asymptotically (GP). Experiment 2 found the linear decrease in AP rates to be relatively independent of step size. Experiment 3 showed pausing to be controlled by the prior component length, which predicted the differences between PR and regressive ratio schedules found in Experiment 4. When the longest component ratios were signaled by different key colors, rates at moderate ratios increased, demonstrating control by forthcoming context. Models for response rate and pause duration based on Bizo and Killeen (1997) described performance on AP schedules; GP schedules required an additional parameter representing the contextual reinforcement.

Bidding for delayed rewards: Accumulation as delay discounting, delay discounting as regulation, demand functions as corollary.

In the accumulation paradigm animals press one manipulandum to accumulate pellets or seconds of access to food, and then press another manipulandum, or run some distance, to collect it. The accumulation may be interpreted as delay discounting, with the animals adjusting the distal amount to compensate for its distance or delay. The amount accumulated before being collected is a linear function of the distance or time that the experimental paradigm stipulates for collecting it. That linear function follows from the Unit-Price/Unit-Amount axiom. The inverse of the linear compensation functions gives a delay-discount hyperbola. The advantages of the accumulation paradigm and analytic framework for delay discounting studies are noted. Compensation functions are then derived from a behavioral regulation model, which generalizes them to contexts where the individual's budget for response cost becomes over-taxed. In turn, such compensation/regulation models lead directly to representative demand functions. In sum, regulation models provide a theoretical grounding for demand functions, compensation functions, and delay discounting hyperbolas. The parameter that links them is the unit amount k, the slope of the compensation function and of the discount function, the setpoint for consumption in a regulation model, and the ideal quantity consumed at minimal price in a demand analysis.

The non-Darwinian evolution of behavers and behaviors.

Many readers of this journal have been schooled in both Darwinian evolution and Skinnerian psychology, which have in common the vision of powerful control of their subjects by their sequalae. Individuals of species that generate more successful offspring come to dominate their habitat; responses of those individuals that generate more reinforcers come to dominate the repertoire of the individual in that context. This is unarguable. What is questionable is how large a role these forces of selection play in the larger landscape of existing organisms and the repertoires of their individuals. Here it is argued that non-Darwinian and non-Skinnerian selection play much larger roles in both than the reader may appreciate. The argument is based on the history of, and recent advances in, microbiology. Lessons from that history re-illuminate the three putative domains of selection by consequences: The evolution of species, response repertoires, and cultures. It is argued that before, beneath, and after the cosmically brief but crucial epoch of Darwinian evolution that shaped creatures such as ourselves, non-Darwinian forces pervade all three domains.

Timberlake's theories dissolve anomalies.

Two of Timberlake's major contributions, amongst numerous other good notes, are Behavior Regulation Theory (BRT), and Behavior Systems Theory (BST). BRT was a refinement of the Premack Principle. What both got right was that reinforcers are responses, not stimuli. For BRT, they were responses that were occurring below the rate at which they otherwise would given free access to them. BST was a larger ethological framework for our science of behavior. We have always needed it, as it opens an important window on our field. With that window closed, it is easy to stumble over a half-dozen anomalies in the dark, ones that we say humph to, scratch our heads, and then move on. When illuminated by BST, however, such anomalies become keys to a deeper understanding of our subject. This paper reviews numerous anomalies that make sense within the joint framework of BST and BRT, and Dickinson's Dual-Process theory of learned behavior. No longer anomalous in that context, all that is now left to do is test the validity and productivity of this general framework for those many strange cases.

Predict, Control, and Replicate to Understand: How Statistics Can Foster the Fundamental Goals of Science.

Scientists abstract hypotheses from observations of the world, which they then deploy to test their reliability. The best way to test reliability is to predict an effect before it occurs. If we can manipulate the independent variables (the efficient causes) that make it occur, then ability to predict makes it possible to control. Such control helps to isolate the relevant variables. Control also refers to a comparison condition, conducted to see what would have happened if we had not deployed the key ingredient of the hypothesis: scientific knowledge only accrues when we compare what happens in one condition against what happens in another. When the results of such comparisons are not definitive, metrics of the degree of efficacy of the manipulation are required. Many of those derive from statistical inference, and many of those poorly serve the purpose of the cumulation of knowledge. Without ability to replicate an effect, the utility of the principle used to predict or control is dubious. Traditional models of statistical inference are weak guides to replicability and utility of results. Several alternatives to null hypothesis testing are sketched: Bayesian, model comparison, and predictive inference (p rep). Predictive inference shows, for example, that the failure to replicate most results in the Open Science Project was predictable. Replicability is but one aspect of scientific understanding: it establishes the reliability of our data and the predictive ability of our formal models. It is a necessary aspect of scientific progress, even if not by itself sufficient for understanding.