Quantitative Behavior Analysis.pdf
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Quantitative Behavior Analysis At its core, the study of behavior is an effort to understand how organisms interact with the environments in which they live. Across the behavioral sciences, researchers have developed theories that range from descriptive accounts to highly precise, mathematically specified models. Quantitative analyses of behavior occupy a special place within this continuum: they allow scientists to formalize behavioral processes, generate clear and falsifiable predictions, and test the scope and limits of theories in both controlled experiments and naturalistic settings. Although quantitative approaches have been prominent since at least the 1960s, the field lacks a single volume that brings together its major theories, methods, and applications. As a result, students, instructors, and practitioners often struggle to access, learn, and apply these models, often relying on scattered, outdated articles or narrowly focused texts. This resource aims to fill that longstanding gap. By gathering leading experts to contribute chapters on the foundational quantitative theories of behavior, this volume provides a comprehensive and accessible guide for understanding mathematical approaches across the behavioral sciences. The chapters span a wide range of topics from reinforcement, extinction, relapse, and matching to behavioral economics, discounting, foraging, signal detection, and application. Together, these frameworks illustrate not only the breadth of quantitative behavioral science, but also its power: each model offers its own way of describing how behavior persists, changes, adapts, and optimizes in response to environmental contingencies. The need for such a collection has become increasingly clear. Graduate programs in areas such as psychology, neuroscience, behavioral medicine, animal behavior, and applied behavior analysis continue to teach quantitative concepts, yet instructors often rely on piecemeal sources to assemble course material. Similarly, researchers working across disciplines, including criminology, pharmacology, and ethology, frequently encounter quantitative theories without the benefit of an integrated, comparative overview. By bringing these perspectives together, this resource is designed to support students encountering quantitative analysis for the first time, instructors seeking a unified teaching resource, and researchers aiming to refine or expand the quantitative tools they use to study behavior. The chapters included here are written by experts with deep, often decades-long engagement in the models they present. Their contributions provide historical context, conceptual clarity, mathematical detail, and practical examples of how quantitative analyses can be used to understand and predict the behavior of humans and nonhuman animals. My hope is that the resource will not only serve as a timely reference but also inspire new lines of inquiry, encouraging readers to consider how quantitative models can improve research design, inform theory development, and shape applications in real-world settings. I am grateful to the scholars who have contributed their expertise, to the instructors and students who continue to advance the teaching of quantitative behavioral science, and to the broader community of researchers whose work demonstrates the value of precise and testable models of behavior. It is my hope that this volume provides the clarity, coherence, and accessibility needed to support the next generation of quantitative behavioral scientists and to encourage interdisciplinary collaboration across the many fields in which behavior is studied.
1 What Are Mathematical Models? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
M. Christopher Newland
2 Searching for a “Behavioral Neptune”: Predictions of the
Evolutionary Theory of Behavior Dynamics . . . . . . . . . . . . . . . . . . . . 17
Ryan Higginbotham and J. J. McDowell
3 Quantitative Approaches to Pavlovian Conditioning. . . . . . . . . . . . . . 47
Jorge I. Mallea, Carter W. Daniels, and Peter D. Balsam
4 The Mathematical Principles of Reinforcement. . . . . . . . . . . . . . . . . . 77
Peter R. Killeen
5 Response Disequilibrium Theory of Behavior Regulation . . . . . . . . . 95
Kenneth W. Jacobs, James E. King, and Zachary H. Morford
6 Behavioral Momentum Theory: Evidence and Limitations . . . . . . . . 117
Joel E. Ringdahl and Matthew J. O’Brien
7 Applications of Demand Theory in Behavior Analysis . . . . . . . . . . . . 135
Lesley A. Shawler, Ji Young Kim, and Shawn P. Gilroy
8 Behavioral Economics: Delay Discounting . . . . . . . . . . . . . . . . . . . . . . 161
Mariah E. Willis-Moore, Kiernan T. Callister, and Amy L. Odum
9 Time Allocation, Induction, and Matching Theory . . . . . . . . . . . . . . . 181
William M. Baum
10 Ideal Free Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
Allyson R. Salzer, Carla H. Lagorio, and Jennifer M. Gleason
11 Resurgence as Choice: Explaining Relapse and Persistence
of Operant Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
Andrew R. Craig, Sean W. Smith, and Beatriz E. Arroyo Antúnez
12 Quantitative Approaches to Timing Research . . . . . . . . . . . . . . . . . . . 241
13 Signal Detection Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
Michael J. Hautus
14 Applied Quantitative Analysis of Behavior . . . . . . . . . . . . . . . . . . . . . . 285
Wayne W. Fisher, Brian D. Greer, and Casey Irwin Helvey
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307


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