Florida State University Libraries Electronic Theses, Treatises and Dissertations The Graduate School 2013 The Evolution of Deception in Signaling Systems Candace Ohm Follow this and additional works at the FSU Digital Library. For more information, please contact [email protected] FLORIDA STATE UNIVERSITY COLLEGE OF ARTS AND SCIENCES THE EVOLUTION OF DECEPTION IN SIGNALING SYSTEMS By CANDACE OHM A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy Degree Awarded: Fall Semester, 2013 Candace Ohm defended this dissertation on October 10, 2013. The members of the supervisory committee were: Mike Mesterton-Gibbons Professor Directing Dissertation Mark Isaac University Representative Alec Kercheval Committee Member Warren Nichols Committee Member The Graduate School has verified and approved the above-named committee members, and certifies that the dissertation has been approved in accordance with the university requirements. ii This is dedicated to my best friend, my limelight, and a man I lost along the way. To my dearest Grandpa, I will always love you. iii ACKNOWLEDGMENTS Thank you to my advisor, Dr. Mike Mesterton-Gibbons. Thank you for challenging me every step along the way, thank you for never accepting anything less than perfect, and most of all, thank you for teaching me the definition of independence. I couldn’t have asked for a better advisor. I’d also like to thank a few good mentors and committee members I had along the way. To my committee, Dr. Nichols, Dr. Kercheval, and Dr. Isaac, thank you for your outstanding service to the academic community. Thanks to Jonathan Rowell and Patrick Fletcher, you were good friends that offered great advice. Thanks to an undergraduate professor and best friend, Dr. Pam Warton. I owe my graduate school career to Pam’s persistence, intelligence, stubbornness, and faith in me. I’d also like to thank my friends and family. I made six irreplaceable friends along the way that made Tallahassee the place I grew up and the place I call home. Michelle, Tamzyn, Celes, Jenn, Jules, and Tara-thank you for standing by me through the process. Miss Jules—thanks for assisting with your technical editing skills. Thanks to my oldest friends, my brother Matt and cousin Ciressa, for always sharing your honest opinion and for always staying close. Thanks to my uncles, Uncle Craig and Uncle Ruggy, for always making me smile. Finally, thank you to my parents, especially my father, for teaching me the value of hard work. iv TABLE OF CONTENTS ListofTables.......................................... vii ListofFigures ......................................... viii Abstract............................................. ... ix 1 Introduction 1 1.1 DeceptiveSignaling................................. 2 1.2 Signals and Learning . 4 1.3 Agenda ........................................... 5 1.4 Definitions........................................ 7 2 Review of the Literature 9 2.1 Classical Game Theory . 9 2.1.1 The Hawk-Dove Game . 10 2.2 SignalingGames ...................................... 11 2.2.1 The Frequency Dynamics of Signaling Games . 13 2.2.2 Stability Analysis . 15 2.3 Deceptive Signaling in Animal Behavior . 17 2.3.1 One-ReceiverReducedGame . 20 2.3.2 Bluffing by Berritory Holders . 23 2.4 ExtendingtheCurrentLiterature. 26 3 The Two-State Signaling Game with One Receiver 28 3.1 TheGeneralModelwithTwoStates . 28 3.1.1 The Replicator Equations . 30 3.1.2 The Learning Dynamic Equation . 35 3.1.3 A Brief Commentary . 37 3.2 Example:ManipulativeMimics . 39 3.2.1 The Dynamical System . 40 3.2.2 Results ....................................... 45 4 The Two-State Signaling Game with Multiple Receivers 49 4.1 The Replicator Equations . 50 4.2 DeceptioninRHP ..................................... 57 4.2.1 TheModel ..................................... 58 4.2.2 Strategies Within the Signaling System . 61 v 4.2.3 Creating the Payoff Functions . 64 4.2.4 The Dynamical System . 65 4.2.5 Results ....................................... 68 A n−State Games 73 A.1 The Replicator Equations . 74 A.2 TheLearningDynamics ................................. 77 B Code 80 C Copyright Permission 81 References......................................... 82 BiographicalSketch ..................................... 86 vi LIST OF TABLES 1.1 Requirements for a general theory on signaling . 6 2.1 TheHawk-Dovegame .................................... 10 2.2 Local stability analysis . 17 2.3 Payoffs in the one-receiver game . 20 2.4 Payoffsinthebluffingbyterritoryholdersmodel . 24 2.5 Parameters of the bluffing by territory holders model . 25 3.1 Summary of state variables and payoff functions . 31 3.2 Dynamical system for the two-state two receiver model . 38 3.3 Actions of the manipulative mimics game when a mimic is present. 43 3.4 Actions of the predator against a toxic model. 44 4.1 Variables in the n-receiver signaling game . 51 4.2 Dynamical system for the two-state n receivermodel................... 55 4.3 Possible states in the deceptive strength game. 58 4.4 List of values for the deceptive strength game . 59 4.5 Possible states of the deception in RHP game . 60 4.6 Nash mixed strategy equilibria of the deception in RHP game . 60 4.7 Players’ actions in the deception in RHP game . 63 4.8 Payoffs in the deception in RHP game . 65 4.9 Dynamical system for the deception in RHP game . 68 A.1 Variables in the n-state signaling game . 75 vii LIST OF FIGURES 2.1 Lewis signaling games . 13 2.2 The one-receiver game with interior equilibrium . 22 3.1 Extensive form manipulation game . 29 3.2 Themimicoctopus ................................... 40 3.3 A tree of the manipulative mimics game . 42 3.4 Manipulative mimics game vector field . 48 4.1 Manipulation game with n receivers ............................ 50 4.3 Stable interior fixed points for 0.973 / γ ≤ 1 ....................... 69 4.2 DeceptioninRHPequilibria ........................... 72 A.1 The n-statemodel ...................................... 74 viii ABSTRACT In this dissertation, we create a dynamical learning model that helps to explain the evolution of deception in signaling systems. In our model, the signaler may choose to signal either of two possible states. We apply this model to Batesian mimicry and to deceptive signaling of fighting ability, or resource holding potential. We show how to expand this model to allow for multiple receivers as well as multiple possible states. External code for the Batesian mimicry and deceptive signaling of fighting ability models can be accessed via the following link: https://dl.dropboxusercontent.com/u/18728677/Dissertation%20Code.zip ix CHAPTER 1 INTRODUCTION John Maynard-Smith and David Harper define a signaling device as, “An act or structure that alters the behavior of another organism, which has evolved because of that effect, and which is effective because the receiver’s response has also evolved” [28]. Signals can be externally visible features, behavior patterns, or sounds, all of which are, “designed by natural selection” [25]. Darwinian theory suggests that signaling systems exist because communication, on average, increases the long-term fitness of both the signaler and receiver. The value of a signal to a receiver is as a source of information. The receiver uses this information to choose the behavioral, physiological, or developmental responses that will maximize its fitness [37]. A signal is honest if some characteristic of the signal (which can include its absence or presence) is consistently correlated with some attribute of the signaler or its environment and receivers benefit from having information about this attribute [37]. A signal is a handicap when its honesty is guaranteed because the signaler’s associated costs of the signal are greater than the signal’s requirements for being effective [28]. For example, the antlers of a stag are a sign of strength and dominance because antlers are a stag’s primary tool in battle. However, larger antlers are more costly because there is a direct correlation between antler size and weight, and so larger antlers incur a greater cost over a stag’s lifetime. Thus, antlers are a handicap [50]. According to Zahavi’s handicap principle, all signals must be, on average, honest [50]. The handicap principle explains how honest signaling is able to evolve when a signaler has an obvious motivation to deceive or exaggerate the signal [11, 50]. The three conditions of the handicap 1 principle state that: (1) on average signals must be honest, (2) signals are costly, and (3) the differential costs of signaling correlate to the true quality of the signaler [11, 50]. Zahavi’s handicap principle, initially rejected by many scientists [28, 36, 37, 48], became gener- ally accepted when Alan Grafen constructed various game-theoretic models. The models created by Grafen clarified the handicap principle and substantially increased its importance and scope. The handicap models created by Grafen [11] show under fairly general conditions that if the handicap principle’s conditions are met, then an evolutionarily stable signaling equilibrium exists and any signaling equilibrium must satisfy the conditions of the handicap principle. A signaling equilib- rium is a pair of signaler and receiver strategies such that neither individual gains by selecting a different strategy [11]. Grafen further explained three possible interpretations of the handicap principle. These are: (1) the possession of the handicap puts an extra predation risk upon the individual, (2) differences in quality are exhibited by revealing the handicap (for example, a stag’s quality is revealed in a battle because its antlers, which are a handicap, are being utilized. In contrast, differences in quality are not exhibited when a stag is foraging because antlers do not aid in foraging), and (3) only high quality males are capable of expressing the handicap. 1.1 Deceptive Signaling If honesty is used to define the fundamental conjunction of signal level and perfect information, where information is based on what the receiver wants to know, then virtually no signaling system will be completely honest [41]. Deceit occurs when the signaler’s fitness increases at the cost of the receiver’s fitness [30].