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A Sheep in Wolf’s Clothing: Levels of Deceit and Detection in the Evolution of Communication

Shahab Zareyan

B.Sc., Honours in Biology and Minor in Mathematics, 2017

a thesis submitted in partial fulfillment of the requirements for the degree of

Master of Science

the faculty of graduate and postdoctoral studies (Zoology)

The University of British Columbia (Vancouver)

December 2018

c Shahab Zareyan, 2018 The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled:

A Sheep in Wolf’s Clothing: Levels of Deceit and Detection in the Evolution of Communication submitted by Shahab Zareyan in partial fulﬁllment of the requirements for the degree of Master of Science in Zoology.

Examining Committee: Christoph Hauert, Mathematics Co-Supervisor Sarah Otto, Zoology Co-Supervisor Darren Irwin, Zoology Additional Examiner

Additional Supervisory Committee Members: Michael Doebeli, Zoology and Mathematics Supervisory Committee Member

ii Abstract

Trivers has hypothesized that self-deception in our species has evolved for the better deception of others: in an arms race between deception and deception- detection, the dishonest individuals evolve ever-more complex trickery and the deceived an ever-more refined ability to distinguish honesty from deception. Detection at some point becomes so precise that a degree of self- deception can evolve to avoid emitting secondary cues that otherwise give away the deceit. In an attempt to formalize this, we focus on aspects of self-deception that can be generalized to non-humans, as human self-deception by itself relies on concepts that are difficult to define or to apply to other organisms. We formally explore one central aspect of Trivers’ hypothesis: the evolution of costly and well-integrated or deep deceptive morphs that span multiple signals and cues. We demonstrate that the depth of deception in a commu- nicative interaction is correlated with the number of signals detected, the cost of errors in judgment for signal detectors, and the benefits of successful deception. We also show that the frequency of well-integrated deceptive strategies is highest when the cost of errors in judgment is high and the cost of detection of other less well-integrated forms of deception is low. These results may partially explain variation in deception in nature and provide researchers with predictions that can be tested empirically, with obvious implications for self-deception. Moreover, we argue that self-deception under Trivers’ hypothesis is the product of a hierarchical system, in this case, the cognitive system, with some parts (ex. the subconscious) controlling and ultimately manipulating

iii the information that is received by other parts (ex. the conscious). Al- though we do not model this, we emphasize that hierarchies are integral parts of many systems such as gene regulatory networks. Thus, in response to an arms race with an adversary, these hierarchies can potentially evolve “internal deception”, with some parts transmitting manipulated information to other parts to prevent information leakage. We argue that modeling how properties of hierarchies aﬀect the evolution of deception can allow for testable predictions and a better understanding of deception and self- deception in general.

iv Lay Summary

It has been hypothesized that self-deception has evolved for the better deception of others: those that believe in their lies are better at convincing others. The focus of this thesis is using mathematical models to investigate whether aspects of the hypothesis can be generalized to non-humans and thus can be empirically tested and placed on a more ﬁrm evolutionary foun- dation. Many deceptive strategies in nature, like self-deception, are costly and exaggerated; they involve dishonest signaling as well as attempts to hide cues of dishonesty. We show that these well-integrated forms of deception evolve when many signals are detected, when there is a large beneﬁt to the deception, and when the cost of errors in judgment for those that are deceived is high. We further comment on other aspects of self-deception that can be tested in non-humans.

v Preface

Chapter 2 has been submitted for publication. The candidate’s contributions are outlined below:

• Zareyan, S. Otto, S. P. and Hauert, C. (2019) A Sheep in Wolf’s Clothing: Levels of Deceit and Detection in the Evolution of Commu- nication. submitted. Conceived and designed the experiments: SZ CH SPO. Performed the experiments: SZ. Analyzed the data: SZ SPO CH. Wrote the paper: SZ CH SPO.

vi Table of Contents

Abstract ...... iii

Lay Summary ...... v

Preface ...... vi

Table of Contents ...... vii

List of Figures ...... ix

List of Supplementary Material ...... xi

Acknowledgments ...... xii

1 Introduction ...... 1 1.0.1 Thesis Overview ...... 1 1.0.2 Trivers’ Hypothesis ...... 1 1.0.3 Evidence for Trivers’ Hypothesis ...... 4 1.0.4 Diﬃculties Modelling Self-Deception ...... 5 1.0.5 Deceptive Arms Races ...... 7

2 Evolution of Well-Integrated Deception in A Simple Sig- naling Game ...... 9 2.1 Introduction ...... 9 2.2 Evolution of Deception ...... 11 2.3 Evolution of Deception-Detection ...... 16

vii 2.4 Discussion ...... 22 2.5 Appendix ...... 25

3 Conclusion ...... 27 3.0.1 Hierarchical Information Processing Systems . . . . . 27 3.0.2 Concluding Remarks ...... 33

Bibliography ...... 34

viii List of Figures

Figure 2.1 Surface dynamics around the (H, D; T, I) equilibrium under the (a) standard and the (b) adjusted replicator dynamics. For both panels, β = 2, γ = 1, c = 2, and s = 1. Equilibria are indicated by block dots. . . . . 16 Figure 2.2 Cycles of invasions and re-invasions upon the introduction of well-integrated deceivers...... 21 Figure 2.3 Dynamics of prey (blue) and predators (black) around the (H, D, W; T, D, I) equilibrium point under the (a) standard and (b) adjusted replicator dynamics. The time period over which the replicator equations were numerically solved is indicated at the bottom of each sub-ﬁgure. For both panels, t indicates time, β = 3, c = 3, s = 1, γ = 2, δ = 1, and g = 2...... 21

ix Figure 2.4 Response to perturbations away from the tri-morphic equilibrium in prey (blue) and predator (black) populations. For all panels, we perturb the system in directions indicated at the top of the ﬁgure. We then determine the response to each perturbation using the standard replicator dynamics (second row), and visualize the response by drawing vector ﬁelds that depict selection gradients following each perturbation. Note that perturbing the system in one of the populations induces selection only in the other population - not in the original population. Parameters: β = 3, γ = 2, δ = 1, c = 3, s = 1, and g =2...... 23

Figure 3.1 Schematic representation of the hierarchical information processing system underlying Trivers’ hypothesis on the evolution of self-deception. S: subconscious module; C: conscious module; 2o: secondary module. . . . 28

x List of Supplementary Material

A Mathematica ﬁle is attached to this thesis. It contains all the calculations for deriving the results in Chapter 2, as well as the code for recreating all the ﬁgures.

xi Acknowledgments

I would like to thank my supervisors, Christoph and Sally, for their uncondi- tional support; for accepting me as a student even though my undergraduate background was different than their research focus; and for letting me pursue the ambitious questions I was interested in. I am deeply grateful for this - I do not think this would have been possible at any other institution or research group. I would like to thank the members of the Otto, Hauert, and Doebeli labs, and Michael Doebeli in particular, my committee adviser, for valuable feed- back on my projects, and for their support throughout my degree. I am also grateful to Darren Irwin, who, as the departmental examiner, thoroughly assessed the scholarship of this thesis and provided very helpful suggestions. I would like to thank Ali for constant, forceful, and in depth critique of the work and ideas related to the work, the likes of which - with regards to the depth of the critique - I have rarely seen. I also like to thank him for much-needed guidance on how to rigorously apply the scientific method to questions of interest, how to ask questions, and what type of questions to ask, an influence which permeates every single sentence in this thesis. I would like to thank my family who, despite unfamiliarity with my research, gave me all the tools I needed to survive. I like to particularly thank Yas for giving me much-needed hope. Finally, I am grateful to NSERC CGS-M and the Zoology Department for financial support.

xii Chapter 1

Introduction

1.0.1 Thesis Overview The core of this thesis, presented in Chapter 2, focuses on modeling the co-evolutionary arms race between deception and deception-detection. The type of deception modeled is generic, and thus, qualitatively, the results of the model apply to many diﬀerent systems of communication in nature. What is not addressed in the thesis core, however, is the original motivation behind the project, the original question, and speciﬁcally how the modeling framework in Chapter 2 relates to that question. We address these here by placing this work in the broader, but more vague, context of self-deception. We then connect this material to the formal model in Chapter 2. In Chapter 3, we expand on the relevance of the results of Chapter 2 for the original question.

1.0.2 Trivers’ Hypothesis The original intention of the thesis was to expand a hypothesis put forward by Robert Trivers on the arms race between deception and detection and the eﬀects of that on cognitive evolution in humans [38, 40]. In the 1970s, Trivers had applied the logic of natural selection to a variety of social behaviors and had provided predictions that are to this day being tested in a variety of organisms [39]. Yet he encountered an interesting puzzle around the same

1 time [39]: “On the one hand, our sense organs have evolved to give us a mar- velously detailed and accurate view of the outside world (...) But once this information arrives in our brains, it is often distorted and biased to our conscious minds. We deny the truth to ourselves. We project onto others traits that are in fact true of ourselves and then attack them! We repress painful memories, create completely false ones, rationalize immoral behavior, act repeatedly to boost positive self-opinion, and show a suite of ego-defense mechanisms. Why?” (p. 2). Trivers used the phrase self-deception, or the construction and the subsequent belief in a false sense of the world and the self [10], to encapsulate all these phenomena. His interest in the question was warranted particularly given the implications of self-deception for our intentions: if one can fabricate a false sense of the world, one can also fabricate one’s intentions. This is a source of moral dilemmas as intention plays a central part in our conception of morality [23]: we praise ourselves or our compatriots for “trying” to do the right thing or simply “having” benevolent thoughts; our criminal code is heavily based on wrongdoers’ intentions (intentional battery, intentional homicide, intentional infliction of emotional distress, etc.); and we justify wars that kill hundreds of thousands of innocent civilians by the “good” intentions of our nation states. Given the dilemmas to which self-deception gives rise, it is of no surprise that great works of philosophy, religion, and literature, since the dawn of history, have grappled with our tendency towards exercising self-deception and its colossal consequences [10]. Nevertheless, at the time when Trivers was puzzled by the concept, there existed very few testable hypotheses and little empirical work on self-deception. Indeed, the scientific study of self-deception has historically lagged behind the many debates it has elicited, perhaps because the phe- nomenon has been questioned on all possible grounds, best illustrated by the many attempts to try to define exactly what constitutes self-deception [10]. How can an organism be the deceiver and the deceived at the same time? Self-deception perhaps necessitates the conception of a non-unitary mind - itself a contested view [4] - with some parts deceiving other parts.

2 To demonstrate that an individual is self-deceiving, one would need to determine what these units are, assess the information stored in each one of them, and assess how they share information with each other, a task that is complicated by the organism hiding the information from itself and others. These roadblocks are further exacerbated when one attempts to apply the concept to non-humans. More phenomenological studies are, however, available on certain human biases that are arguably consistent with self-deception. Examples include: 1) the better-than-average effect, or the belief of the majority that they are better than average in their attributes [12], as when 94% of academics believe that their teaching abilities are better than the average at their institution [5]; 2) self-handicapping, or engaging in a costly behavior that ensures failure on tasks that one is likely to fail anyways; the benefit being that the self- handicapper can then blame the costly behavior, as opposed to ineptitude, for his/her failures, and by doing so, maintaining self-confidence in a self- deceiving manner [41]; and 3) not gathering critical information about one’s health status, or doing so in a biased way, out of fear of obtaining diagnostic results that one might not want to hear [8, 11]. In light of observations similar to above, the dominant school of thought at the time of Trivers considered self-deceptive biases as necessary illusions required for us to feel better about ourselves and to maintain our mental health [42]. Trivers, being partly a naturalist, observing psychological war- fare in primates such as baboons, began first by asking questions about self-deception’s survival value [40]. In that context, there was a problem with the aforementioned explanation [40]: “Even if being happier is associated with higher survival and reproduc- tion, as expected, why should we use such a dubious - and potentially costly - mechanism as self-deception to regulate our happiness?” (p. 4). Various hypotheses can provide an answer to the above. Trivers proposed an alternative: self-deception is an offensive strategy in the service of deceit - those that believe in their own lies are also better at convincing others of their lies [38]. This, Trivers postulated, can originate from an evolutionary arms race, where evolution of deception-detection selects for

3 better deception, which then selects for better detection. At some point, deception-detection becomes so accurate that an organism might beneﬁt from self-deceiving in order to not give away secondary cues of its deception. The advantage of Trivers’ hypothesis in comparison with previous attempts is that it, simultaneously, addresses three of Tinbergen’s four categories of explanation of animal behavior [37]: 1) phylogeny: what can lead to the evolution of self-deception; 2) survival value: what are the beneﬁts of self-deception to an organism that exercises it; and 3) mechanism, which is implicit in the hypothesis, and which we discuss in more detail in the conclusion of this thesis. As a consequence, it suggests avenues of research that previously could not be conceived.

1.0.3 Evidence for Trivers’ Hypothesis The hypothesis has led to the discovery of some interesting patterns. A series of recent papers show that people, when incentivized to argue for some position, are likely to bias their initial perception of that position [1, 28] or are likely to bias their information gathering so that they are more likely to encounter information that supports their position [34]. As a consequence, these people become more convincing in the position for which they are asked to argue, in line with Trivers’ hypothesis. Most importantly, the biases are maintained even when they are incentivized to objectively assess and correct their position, indicating that they perhaps truly believe in them, that they are self-deceived, and that their self-deception comes at the cost of inﬂexibility [34]. Although the cost in such experimental settings is negligible, one can imagine that informational distortion of this type, when practiced regularly, can have substantial consequences for those that distort. On the theoretical side, three important papers have attempted to model aspects of Trivers’ hypothesis [2, 18, 26]. All papers use some version of the hawk-dove game [33]: players are paired with one another and are given the option of engaging in a ﬁght with their opponent over a resource. If no one

4 fights, no one gets anything. If one fights but the other does not, the one that chose to fight will get all the resource at no cost. If both fight, the out- come of the fight is determined by some attribute of each player. Players’ decision to fight or not is determined by their perception of their attribute. Furthermore, players can signal their perception to their opponents, which can affect the opponent’s decision to engage in the fight. Self-deception is defined as using an exaggerated version of the attribute to decide whether to fight or not, and it can be in the service of deceit if the exaggerated perception reduces the opponents’ chance of engaging in the fight. Only one of the studies defines a non-self-deceptive deceptive strategy, involving a player that does not believe in an exaggerated attribute but nevertheless signals an exaggerated trait value, and competes this strategy against the self-deceptive one [26]. These studies, in general, report that under appropriate costs for self-deception as compared to the other strategies, and/or under assumptions about the gullibility of the opponent, self-deception is favored.

1.0.4 Difficulties Modelling Self-Deception Although the above studies address the evolution of interesting strategies, none directly tackle why the self-deceptive strategies they considered are indeed self-deceptive as opposed to simple cognitive algorithms; that is, none fully addressed what aspects of their strategies are self-deceptive, and what aspects of self-deception are not included in their modelling framework. Most importantly, although the studies demonstrate how certain cognitive algorithms outperform other algorithms, none attempted to test Trivers’ hypothesis in its entirety, that is, none considered both the survival value and the phylogeny aspects of Tinbergen’s criteria [37]. The original aim of the thesis was to begin with deception in a population and attempt to demonstrate how such forms, when placed in an arms race with deception- detection, evolve to become self-deceptive. Nevertheless, addressing the first of these problems, that is, attempting to formulate a comprehensive mathematical definition of self-deception,

5 turned out to be unfruitful. Such definitions necessitate the formulation of many different complicated assumptions that inevitably limit the generality of the model and hence constrain the applicability of its predictions. For example, what constitutes “self”? Does it refer to the conscious part of the brain? How are we to define consciousness mathematically? Unfortu- nately, these questions cannot be answered given our current understanding of humans and non-humans; attempting to provide an answer can lead to unproductive speculative work [9]. Indeed, Trivers himself had, seemingly, recognized this problem and attempted to address it. In one of his books [39], Trivers emphasized that although hypotheses on social behavior can be motivated by observations in our own species, for them to ultimately attain the vigor of a hard science as opposed to a just-so-story the researcher should focus on generalizing the behavior to non-humans. In his most comprehensive work on self-deception [40], he states that: “it stands to reason that if our theory of self-deception rests on a theory of deception, advances in the latter will be especially valuable”. Thus, by attempting to study analogous behaviors in non-humans, one is more likely to find more generalizable results with greater predictive power that can then guide future research on the question of interest. Instead of focusing exclusively on self-deception, the main aim of the thesis thus shifted towards developing a better understanding of the evolution of deception in arms races in general. Do deceivers evolve to conceal secondary cues of deception even when this would be of a very high cost? What would be the response of the deceived to sophisticated deception? Does the arms race continue forever, or does it settle on some stable equilibrium population state permanently? Yes, it is true that these questions do not address self-deception directly, but attempting to answer them can result in robust, testable predictions that ultimately allow for a better understanding of self-deception.

6 1.0.5 Deceptive Arms Races Arguably, many antagonistic interactions in nature are consequences of an arms race between deception and detection. In host-parasite interactions, the parasite attempts to mimic the host through novel strategies, and the host is constantly engaged in differentiating between new forms of deceit and non-deceit. In the context of sexual selection, individuals attempt to determine the quality of potential mates, and potential mates attempt to mislead through ever-exaggerated signals. In predator-prey interactions, predators benefit from knowing whether a potential prey is worth pursuing/eating, while prey evolve to appear toxic or able to defend themselves [24]. The importance of arms races in signaling interactions was popularized by Dawkins and Krebs in two papers in the 1980s [7, 21]. They argued that a player in a signaling interaction assumes either of two roles: a “manipulator” that sends deceptive signals as its interests do not overlap with a “mind- reader”, who nevertheless attempts to read through the deception. In an arms race between the two, signals and sensory systems evolve to become ever-more complex. At the time, however, some argued that the “cynical” view of communication proposed by Dawkins and Krebs [32] is not logical [29] because it failed to explain why the deceived do not simply evolve to ignore signals instead of evolving to detect deception. The latter would make signaling futile, causing the collapse of communication altogether [29]. This so-called “logical flaw” of Dawkins’ and Krebs’ argument lead to its dismissal by some. Alternatively, Zahavi’s handicap principle [44] proposed that full honesty might be achieved in signaling systems if receivers evolve to only pay atten- tion to signals that are very costly to fake. Theoretical work on the subject subsequently focused on the analysis of Zahavi’s alternative [29]. Indeed, to our knowledge, only one model has focused on the possibility of an arms race between deception and deception-detection [20]. Instead of looking for stable population equilibria in a game theoretical model, which has been the standard theoretical approach to the handicap principle [29, 32], the authors use simulations to show that populations of signaler and

7 receiver neural networks can be locked into never-ending arms races. They demonstrate that in such contexts, deception jumps from one type of display to another. Whether and when deception evolves to become exaggerated, however, is not explicitly addressed in their model. A main goal of Chapter 2 is to present an analytical model that simultaneously encapsulates Dawkins’ and Krebs’ arms race perspective and Zahavi’s handicap principle. Building on recent work [16, 45], we address the “logical flaw” of the arms race perspective and demonstrate that it is not really a flaw, even when the standard game theoretical approach is utilized. We demonstrate that signaling systems can easily evolve stable forms of deception and detection, even when the deceived are given the opportunity to simply ignore signals. This then provides exactly the forces required for the subsequent evolution of complex forms of detection, or “mind-reading”. Importantly, our model further finds that exaggerated displays, as argued in Dawkins and Krebs, can evolve and be stably maintained in communication systems, resulting in rich evolutionary dynamics.

8 Chapter 2

Evolution of Well-Integrated Deception in A Simple Signaling Game

2.1 Introduction Natural selection has led to the evolution of complex systems of signalling and communication across the tree of life [29, 35]. Whenever the interests of interacting partners diﬀer, however, communication systems are prone to cheating. Zahavi’s handicap principle suggests that communication remains immune to deception as long as the production cost of unreliable signaling is high [44]. When this does not hold, however, cheating invades and potentially sets oﬀ antagonistic co-evolution between deception and detection of that deception: selection could, for example, favor prey that communicate strength and high escape capability to predators even if they are truly undefended. In response, predators that are better able to discern weak prey are favoured, which in turn selects for prey that better hide their susceptibility, resulting in an arms race [7, 21]. Implicit in the notion that better discrimination evolves is the assumption that false signals are poorly coordinated with other cues that indicate

9 the status of an organism (e.g., defended or undefended). Hence, a more integrated level of deception is possible if these other cues evolve and become consistent with the false signals. This, however, is not always possible: physico-chemical and developmental factors, for example, constrain trait co- variance, making certain alterations, such as the ones required for attaining signal consistency, very costly or impossible. This is particularly true in the context of an arms race: although there are no reasons to assume that constraints are at play initially, as the arms race proceeds, the number of signals and cues detected increases, and with it the likelihood that some co-vary in a limited number of ways. In such cases, successful deception may still be possible through highly pleiotropic and thus costly changes to the nature of development in the organism, as this can supply the variation needed for signal consistency. In light of these factors, our focus here is to determine how these well-integrated or deep forms of deception - defined more formally as deception involving manipulation of multiple signals and secondary cues that otherwise give away the deceit - evolve and are maintained in natural populations. In nature, cases of multi-signal deception, spanning multiple domains (ex. morphology, behavior) and manifested through large-scale broad-acting developmental changes, provide the most convincing evidence for stable maintenance of deep deceivers, as such deception is expected to be of particularly high cost given the nature of the underlying changes. The clearest examples of this are: 1) female mimicry in a variety of animal species, including insects, fish, birds, and mammals, initiated, in some cases, early on during development [27]; 2) Batesian mimicry in certain butterfly species, regulated by major developmental transcription factors [22, 25, 36]; 3) Mor- phological and behavioral mimicry of ants by spiders to evade predators [30], which, importantly, is also associated with substantial cost such as reduction in the number of eggs laid per eggsac due to the narrowing of the bodies in the mimics [6]; and 4) mimicry of sticks by stick insects (Phasmatodea), which necessitates very thin bodies and has resulted in loss of some of the internal organs that normally come in pairs [40]. A more relevant example for humans is self-deception, defined as decep-

10 tion of the conscious part of the mind by the subconscious, either through biasing the gathering of information or biasing the gathered information. Trivers [38] hypothesized that self-deception evolved for better deception of others: by virtue of believing in their own lies, self-deceivers do not give secondary cues that otherwise give away the deceit. Besides involving multiple signals and cues, and thus fulﬁlling the criteria of a well-integrated deception, its underlying mechanism of early information manipulation in the subconscious is interestingly analogous to the early developmental changes that underlie deception in the above examples. Self-deception is expected to come at a cost, however, in this case due to a biased perception of reality and suboptimal decision-making, which has been outlined in many diﬀerent contexts in humans [40]. The aim of this work is to formulate that which is common to all of the above cases in mathematical terms. We extend recent work on the evolution of partially honest communication [16, 17, 45] by deriving analytical conditions for the evolution of stable systems with multi-signal detection and well-integrated but costly forms of deception. We extend a signaling game that has traditionally been used to provide support for costly signaling theory to demonstrate shifts in the levels of deception. For clarity, we discuss a prey-predator signaling interaction, though various aspects can easily be applied to other situations.

2.2 Evolution of Deception The story behind the model is simple: A predator’s hunting success is af- fected by the type of prey it pursues. A prey that is strong, fast, and well-armed is unlikely to be caught; the predator wastes energy attempting to pursue such a prey, and it can also sustain injuries if the pursuit results in confrontation. However, pursuit of undefended prey, which are by definition slow and physically incapable of fighting back, is more likely to result in capture. As a result, it is beneficial for predators to distinguish between the different prey types and pursue only the undefended. Thus, prey fall into two categories of defended and undefended, a trait

11 which we assume is exclusively a function of environmental factors such as prenatal or early-life conditions. The defended corresponds to those that received adequate care and nutrition and the undefended to the ones that did not. We further assume that at any point in time a constant proportion of prey are defended, and all other are undefended. Prior to the evolution of any signaling, the predator population is expected to be composed of those that always pursue prey. We refer to these as indiscriminate (I). Their payoﬀ, ΠI, is the weighted beneﬁt of pursuing the undefended, β, added to the weighted costs of pursuing the defended, γ:

ΠI = β − γ (2.1)

Hence, if there exists phenotypic diﬀerences between the two prey types, predators could evolve to detect these and pursue only prey with the undefended phenotypes. Such a predator, which we refer to as trusting (T), as it trusts the signal conveyed by the phenotype of the prey, has a payoﬀ:

ΠT = β (2.2) which is always higher than ΠI (equation 2.1). On the other hand, we assume prey pay a weighted cost c when they are pursued by predators when they are undefended1. Thus a prey that faces a mixed population of indiscriminate and trusting predators with frequencies xi and xt, respectively, will always pay the cost of pursuit:

PH = −xic − xtc = −c (2.3)

We refer to this prey as the honest (H) prey as it honestly communicates its phenotype. With payoﬀs deﬁned for the three strategies, we can determine whether trusting predators invade a population of indiscriminate predators. The

1We could also consider the cost associated with being pursued when defended. How- ever, as we will see, the diﬀerence between the payoﬀ of the various prey strategies that we consider is manifested only when undefended. Including this additional cost does not change the qualitative results.

12 evolutionary dynamics is governed by the replicator equations:

x˙ k = xk Πk(y) − Π¯ (2.4a) y˙k = yk Pk(x) − P¯ (2.4b)

where xk yk is the frequency of predator (prey) strategy K, the dot denotes the time derivative, and x (y) is a vector that contains frequencies of all the predator (prey) strategies. The payoﬀ of predator (prey) strategy K, Πk(y)

(Pk(x)), is a function of the composition of the prey (predator) population, y (x). Π¯ P¯ corresponds to the average payoff of strategies in the predator (prey) population. Plugging in payoffs in equations 2.1-2.3 into the replicator dynamics 2.4, we realize that there exists only one locally stable equilibrium, consisting of honest prey and trusting predators (H; T) (for details, see supplement). Thus, an initial population of indiscriminate predators is always invaded and replaced by trusting ones. Note that we use the short-hand notation prey strategies; predator strategies to represent the equilibria. Evolutionary biologists have been concerned with the stability of the aforementioned equilibrium: it corresponds to a system where a reliable cue is being expressed, which allows predators to determine the defendedness of the prey. Given that the interests of prey and predator do not fully overlap, a natural question is, how does the detected trait remain reliable given that the undefended can evolve to mimic the defended? Recent advances have shed some light on this problem [16, 45]. We review the main results below. First, we refer to the prey strategy that, when undefended, mimics the defended in the trait that is used by trusting predators to differentiate between the two types, as the deceptive (D) prey, and we assume that its deception comes at a cost s. Thus, the payoff of this strategy against a population of indiscriminate and trusting predators is:

PD = −xi(c + s) − xts = −xic − s (2.5)

Conversely, the payoﬀ of the two predator strategies against a mixed popu-

13 lation of honesty and deception is:

ΠI = β − γ (2.6a)

ΠT = yhβ (2.6b)

Given the above, we can formally address the question of when a trait is expected to remain a reliable indicator. A system composed of honest prey and trusting predators (H; T) is immune to invasion by mutant deceptive prey when the ﬁtness of the resident honest prey is higher than that of the deceptive mutant, that is, when:

s > c (2.7) or when the cost of deception is high (for details, see supplement). This is consistent with Zahavi’s handicap principle and costly signaling theory [14, 44]. When s < c, however, deception invades and the populations move towards an equilibrium composed of deceptive prey and trusting predators (D; T). The trusting predators then respond as if all prey were defended, that is, they never pursue any prey. Consequently, their payoff at this equilibrium is zero (see 2.6 for yh = 0). What happens next? Given the natural assumption that pursuing prey is better than not pursuing any prey (β > γ), the payoff of predators at the (D; T) equilibrium is lower than indiscriminate pursuit (β − γ > 0). Although one can devise new gain-of-function strategies capable of invading this (D; T) equilibrium, predators may easily revert to being indiscriminate as this simply involves a loss-of-function change. Thus, indiscriminate predators return and the populations evolve towards a (D; I) equilibrium. This, however, makes deception futile: the payoff of honesty against an indiscriminate predator (−c) is always higher than the payoff of the deceptive against the same predators (−c − s). As a result, the honest strategy is favored and the populations return to the original (H; I) equilibrium. Hence, the cycle restarts. All in all, the general

14 conclusion is that depending on the costs and the beneﬁts of deception, the populations either remain at the fully honest equilibrium or undergo cycles of invasions and re-invasions. The above story, however, is not complete because it focuses on the spread of one strategy at a time in the prey or the predator population. Im- portantly, there exists an interior equilibrium with non-vanishing frequen- ∗ ∗ ∗ ∗ γ cies for all four strategies (H, D; T, I), with (yh, yd; xt , xi ) = (1 − β , γ s s β ; c , 1 − c ), with the asterisks representing equilibrium frequencies (see supplement). This hybrid equilibrium [16, 45] is locally stable when:

s < c (2.8) or in other words, when deception has a net benefit. The equilibrium turns out to be a center surrounded by closed orbits (Figure 2.1 (a)) [15]. For the adjusted replicator dynamics [31], all equilibria remain the same [43], but in contrast, the cycles contract and ultimately converge to the interior equilibrium (Figure 2.1 (b)). The only difference in the adjusted replicator dynamics is that fitness is always relative to mean fitness:

Π (y) − Π¯ x˙ = x K (2.9a) k k Π¯ P (x) − P¯ y˙ = y K (2.9b) k k P¯

Thus, if the mean ﬁtness of a population is low, selection is stronger and change happens more rapidly under the adjusted regime as compared to the standard dynamics. Other processes, including mutation [17], can also lead to the asymptotic stability of the hybrid equilibrium. Thus, under slight and reasonable changes to the underlying assumptions, the equilibrium with all the strategies becomes stable. The evolutionary stability of this equilibrium highlights that communication can evolve under arbitrarily small signaling costs [45], contrary to Zahavi’s conjecture (equation 2.7, [44]). The cost of signals determines presence/absence of deception in the population; but, the important point

15 (a) (b) Deceptive Honest Trusting Indiscriminate Trusting Indiscriminate

Figure 2.1: Surface dynamics around the (H, D; T, I) equilibrium under the (a) standard and the (b) adjusted replicator dynamics. For both panels, β = 2, γ = 1, c = 2, and s = 1. Equilibria are indicated by block dots. is that such deception evolves and can be maintained alongside the deceived without destabilizing signaling systems.

2.3 Evolution of Deception-Detection At the hybrid equilibrium, the response of the indiscriminate predator against the defended prey is a false positive (it pursues when it shouldn’t), and the response of the trusting predator against the undefended mimic is a false negative (it does not pursue when it should). The dearth of information behind these miscalculations creates opportunities for the rise of new strategies that ultimately change the nature of communication. First note that new strategies could take two diﬀerent paths. The indiscriminate might mutate to detect a more reliable trait and completely rely on that trait for distinguishing between the two types. If this invades, the population at least temporarily moves towards a fully-honest equilibrium. However, new deceptive forms can then evolve that deceive through the new

16 trait, and the population ultimately ends up at a hybrid equilibrium similar to above. Thus, qualitatively, not much would be different. Alternatively, the trusting predator could mutate to detect a new trait to distinguish the mimic from the model, that is, to detect deception. For example, deception through the old trait might cause physiological, anatom- ical, or behavioral changes that act as signs that give away the deceit: if, for instance, the length of legs was originally detected to differentiate between defended and undefended prey, then the undefended could evolve longer legs to deceive the predators. An unintended consequence of this, however, is that the ratio of leg length relative to other traits changes, and this asymme- try can then be detected as a secondary cue that gives away the deceit. Most importantly, evolution of such sophisticated detection can then favor the evolution of deceivers that deceive by manipulating the signals and the secondary cues, a type of deception that may necessitate broad-acting changes for attaining near-perfect mimicry - what we refer to as well-integrated or deep deception. In contrast to the trusting and the indiscriminate predator strategies, the deception-detector mutant, which we refer to as the detector (D), reduces instances of both negatives and positives. We assume, however, that superior detection comes at a cost δ. Thus, the detector’s payoff against a mixed population of honest and deceptive prey is:

ΠD = yh(β − δ) + yd(β − δ) = β − δ (2.10)

Comparing equations 2.10 and 2.6, we realize detectors have a higher payoﬀ than trusting predators if:

δ < ydβ, (2.11) that is, if the cost of improved detection is less than the weighted beneﬁts of reducing false negatives. Moreover, detectors have a higher payoﬀ than indiscriminate predators if: δ < γ, (2.12) that is, if the cost of improved detection is less than the cost of false positives

17 γ. In our case this corresponds to the cost of pursuing defended prey, but in other cases it could refer to the cost of providing food to an offspring that does not need it, or mating with a low-quality individual. Detectors invade the hybrid equilibrium (H, D; T, I) whenever condition 2.12 is met. Thus, the (H, D; T, I) hybrid equilibrium represents an evolutionary endpoint only if improved detection is too costly. In order to analyze the consequences of invasion, we first adjust the payoffs of the honest and the deceptive prey to account for the new detecting predators with frequency xd:

PH = −xic − xtc − xdc = −c (2.13a)

PD = −xi(s + c) − xts − xd(s + c) = −(xi + xd)c − s (2.13b)

If detectors invade, an equilibrium analysis shows that the only locally stable equilibrium is one composed of honest and deceptive prey, and trusting and detector predators (H, D; T, D). Given that this equilibrium exhibits asymptotic stability under the adjusted dynamics [15], it is as robust as the original hybrid equilibrium. This implies that populations where false positives are very costly can aﬀord multi-signal detection even if this reduces ﬁtness. Thus, in natural populations, there should exist a positive correlation between the cost of false positives γ and the cost (δ) and complexity of detection. ∗ ∗ ∗ ∗ δ δ At the new (H, D; T, D) equilibrium, (yh, yd; xt , xd) = (1 − β , β ; s s δ c , 1 − c ). The frequency of deceivers β is lower than their frequency at γ the previous equilibrium ( β ) because δ < γ. In other words, the original hybrid’s prey population evolves towards more honesty upon evolution of deception-detection. Most importantly, the evolution of detection allows directional selection along new trait dimensions, allowing selection to act on secondary cues. The prey can now evolve to deceive detectors by manipulating these secondary cues. This deception, nevertheless, necessitates concealment of not only the undefended state of the prey but also the deception itself. In contrast to simple deception, it requires the decoupling of not only the primary trait

18 from the state of the organism, but also cues of deception from deception itself. For this reason, more sophisticated, or well-integrated levels of deception, are more likely to require costly broad-acting changes compared to adaptations involving manipulation of a single trait.

Evolution of Well-integrated Deception Given a population at the hybrid equilibrium discussed above, (H, D; T, D), we next consider the appearance of well-integrated deception in prey (W). We denote the collective cost of well-integrated deception by g, which we naturally assume is greater than simple deception (g > s). The payoﬀ of this strategy is:

PW = −xi(c + g) − xtg − xdg = −xic − g (2.14)

Comparing equations 2.13 and 2.14 shows that in a population of trusting and detective predators, well-integrated deception has a higher payoﬀ than simple deception if:

g − s < xdc (2.15) or in other words, when the residual cost of well-integrated deception (g −s) is less than the cost of being pursed when undefended, weighted by the frequency of detectors. Note that more costly forms of well-integrated deception can evolve when detectors are more common. Furthermore, well- integrated deception has a higher payoﬀ than honest prey against trusting and detector predators if: g < c (2.16) that is, if the overall cost of well-integrated deception does not exceed the costs of being pursued. Importantly, the condition for well-integrated deceivers to invade the hybrid equilibrium (H, D; T, D) is also g < c. This means that evolution of well-integrated deception does not depend on what deceptive forms already exist in the population. Well-integrated morphs evolve as long as they deceive the undeceived and as long as their cost is less than c. In this model, c is the weighted cost of being pursued when un-

19 defended. More generally, c represents the benefits of deception, or the cost not paid if the deception is successful. Thus, in parent-offspring signaling, c would correspond to the amount of food parents provide to needy offspring, or in courtship displays, c would be the benefits of securing a mate. All in all, this means that there should exist a positive relationship between the benefits (c), and the cost (g) and the depth of deception in nature. In order to analyze the invasion of well-integrated deception with frequency yw, we first modify the payoffs of the three predator strategic types:

ΠI = β − γ (2.17a)

ΠT = yhβ (2.17b)

ΠD = yh(β − δ) + yd(β − δ) − ywδ = (yh + yd)β − δ (2.17c)

Analysis of the replicator equations shows that, following the invasion, well- integrated deceivers replace honest prey, and the populations move towards a (D, W; T, D) equilibrium. Thus, the prey population is composed only of deceivers, and as a result, the trusting predators are always subjected to deception: they never pursue any prey and their payoff is zero. What will happen next? If only one strategy is introduced at a time, the system shifts from one hybrid equilibrium to another in an endless cycle (see Figure 2.2 and appendix). If, however, we allow all strategic types to occur, a central hybrid equilibrium exists, composed of honesty, normal deception, and well-integrated deception in the prey population, and trusting, detector, and indiscriminate in the predator population (H, D, W; T, D, I), ∗ ∗ ∗ ∗ ∗ ∗ γ δ γ−δ s g−s g with (yh, yd, yw; xt , xd, xi ) = (1 − β , β , β ; c , c , 1 − c ). The tri- morphic equilibrium of the replicator dynamics is again a neutrally stable center (see supplement). Numerical analysis of the dynamics under the adjusted replicator equation shows convergence towards the equilibrium point (Figure 2.3). Thus, if enough variation exists in the population, the cyclical dynamics are instead replaced by convergence towards a single equilibrium point, where costly detection and well-integrated deception co-exist indefi- nitely; even though the cost and benefits of pursuing and being pursed have

20 H, D; T, I H, D; T, D Prey H: Honest D: Deceptive W: Well-integrated Deceptive H, W; T, I D, W; T, D Predator T: Trusting D: Detective I: Indiscriminate H, W; D, I D, W; D, I

Figure 2.2: Cycles of invasions and re-invasions upon the introduction of well-integrated deceivers.

(a) (b)

500 1400 t t 0 0 honest deceiver well-integrated deception trusting detector indiscriminate

Figure 2.3: Dynamics of prey (blue) and predators (black) around the (H, D, W; T, D, I) equilibrium point under the (a) standard and (b) adjusted replicator dynamics. The time period over which the replicator equations were numerically solved is indicated at the bottom of each sub-ﬁgure. For both panels, t indicates time, β = 3, c = 3, s = 1, γ = 2, δ = 1, and g = 2. remained the same, the costs of signaling, and the costs of detecting signals, have increased. A few things about this equilibrium are noteworthy. First, to develop a better understanding of why co-existence is possible, we visualize the interactions between the various strategies by plotting the

21 vector ﬁelds that represent the selection dynamics (Figure 2.4). As can be seen, the antagonistic interactions between pairs of strategies prevents any one strategy from driving another extinct. Second, an increase in the cost of false positive responses (predators pursuing defended prey, γ), is expected to result in an increase in the frequency of undetected deceivers. This is seen both at the above equilibrium of (H, D, γ−δ W; T, D, I), where the frequency of well-integrated deceivers, β , increases as γ increases, and at the original hybrid equilibrium of (H, D; T, I), where γ undetected deception has frequency β . Third, although the total frequency of deceivers at this (H, D, W; T, D, I) equilibrium is the same as their frequency at the original (H, D; T, I) hybrid γ equilibrium ( β ), the relative proportion of the two deceptive strategies is determined by δ, the cost of detecting simple forms of deception. When this is not costly, well-integrated deception becomes more frequent than simple deception. Thus, the frequency of well-integrated and costly forms of deception is likely to be high in a population when two conditions are met: 1) false positives are costly (γ high) and 2) there is a low cost for detecting simple forms of deception in the population (δ low). Lastly, there exists a correlation between the frequency of detectors of simple deception, and the costs of various forms of deception: the higher the relative cost of well-integrated deception as compared to simple deception (g − s), the higher the frequency of detectors. Thus, when γ and g are high, but δ and s are low, we expect the populations at the central hybrid equilibrium to consist mostly of predators that have costly ﬁne-tuned detection abilities, and prey that exercise elaborate and costly deception.

2.4 Discussion This study emphasizes that, even with a low signaling cost, the spread of deception does not necessarily result in the collapse of communication. We ﬁnd that deception can co-exist indeﬁnitely in a heterogeneous population alongside honesty, in line with [45]. The mechanism that allows for this heterogeneity is a simple one: once common, deception is counter-selected

22 perturbation well-integrated honest ↑ trusting ↑ deceiver ↑ detector ↑ indiscriminate ↑ deceiver ↑ response well-integrated trusting ↑ deceiver ↑ detector ↑ indiscriminate ↑ honest ↑ deceiver ↑ visualization 23 honest deceiver well-integrated deception trusting detector indiscriminate

Figure 2.4: Response to perturbations away from the tri-morphic equilibrium in prey (blue) and predator (black) populations. For all panels, we perturb the system in directions indicated at the top of the figure. We then determine the response to each perturbation using the standard replicator dynamics (second row), and visualize the response by drawing vector fields that depict selection gradients following each perturbation. Note that perturbing the system in one of the populations induces selection only in the other population - not in the original population. Parameters: β = 3, γ = 2, δ = 1, c = 3, s = 1, and g = 2. by the spread of strategies that ignore signals, which leads to the stable co-existence of multiple strategies in both populations. Given the simplicity of the mechanism, we expect it to apply to many systems of communication in nature and expect them to be heterogeneous [45]. Although previous work had predicted that heterogeneous signaling systems are likely to include types that never respond to signals [45], here we demonstrated that other alternatives are possible: indefinite existence of deception in a population can result in selection for those mutants that detect and avoid the deception. Thus, besides the presence of constitutive responders, it is also likely for signal receivers to evolve the ability to detect multiple signals or seek multiple sources of information. Deception is nevertheless maintained in the population because detection is costly and only favored when deceivers are common, and deceivers are common only when detectors are rare: neither can drive the other extinct. Importantly, we showed that, as a consequence of the evolution of multi- signal detectors, deceptive signaling can evolve to be well-integrated, pos- sibly involving broad-acting changes that allow for the decoupling of cues of deception from the deception itself, even though costly. Certainly, the many forms of deception in nature that are manifested through major developmental changes are consistent with this conclusion. Indeed, it is con- ceivable for the cost of deception due to broad-acting changes (g) to be so high that its net potential benefit (c − g) approaches zero, and yet such complex and well-integrated deception is maintained stably in the population. Thus, high signaling cost should not be taken as necessarily providing support for the costly signaling theory, as complex forms of deception can invade systems with simpler forms of deception, raising the apparent costs of signaling. Most importantly, the analysis predicts that in heterogeneous signaling populations positive correlations exist between the degree to which deceptive morphs are well-integrated and: 1) the cost of false positives (γ); 2) the value of the resources gained if the deception is successful (c) and 3) the number of signals detected, which is a measure of the amount of information the predator has about the prey, or, in other words, a measure of predator’s ability to differentiate between deceptive morphs and those that

24 are truly defended. Thus, the arms race between deception and detection does not continue forever as it is regulated by the latter two parameters (c and γ), which are extrinsic factors not manipulated by the strategies. Note that our arguments are also in line with Trivers’ hypothesis on the evolution of self-deception. Trivers notes: “It stands to reason that if our theory of self-deception rests on a theory of deception, advances in the latter will be especially valuable” [40]. Here we provide a systematic analysis of the dynamics of well-integrated deception to better understand levels of deception in nature and in humans.

2.5 Appendix Each step of the cycle in Figure 2.2 is described below. All results are obtained through invasion and stability analysis of the replicator equations:

• (D, W; T, D) → (D, W; D, I): All prey are deceiving (D or W), and hence trusting predators perform poorly such that indiscriminate predators can invade and displace them as β − γ > 0.

• (D, W; D, I) → (H, W; D, I): The evolution of indiscriminate predators then makes normal deception futile: their signals are either ignored by the indiscriminate or their deception is detected by detectors. The payoﬀ of honest prey (H) is always higher than that of deceivers (D, see Equation 2.13), and hence honest prey can invade and replace deceivers.

• (H, W; D, I) → (H, W; T, I): Against honest prey detection is futile: predators either face well-integrated deception, which they cannot detect, or honesty, against which deception-detection is unnecessary. As a consequence trusting predators outperform and replace detectors (see equation 2.17) because they avoid the costs of detection.

• (H, W; T, I) → (H, D; T, I): The absence of detecting predators renders costly, well-integrated deception (W) useless. Thus, regular deception (D) is favored (see equations 2.13 and 2.14).

25 • (H, D; T, I) → (H, D; T, D): The presence of deceiving prey (D) now gives detecting predators (D) an advantage over indiscriminate ones (I) and hence they invade and displace them.

• (H, D; T, D) → (D, W; T, D): In order to avoid detection, well- integrated deception in prey (W) is now favoured, which replaces regular deception (D). This recovers the ﬁrst hybrid equilibrium.

These invasions involve both reversions back to the ancestral strategies, as well as the evolution of detection and well-integrated deception, which after the completion of each round of cyclical invasions, should evolve anew. The latter are analogous to gain-of-function mutants, and it is thus natural to assume that their evolution happens on a slower time-scale than reversions to the ancestors. For this reason, it can be argued that detection and well-integrated deception are, in a sense, ephemeral phenomena: it takes a long time for them to evolve, and once they evolve, they are not sustained for long, quickly replaced by their ancestral forms. As discussed in the main text, however, a stable equilibrium is possible if all six strategies are simultaneously present.

26 Chapter 3

Conclusion

How are we to extend the work presented above to develop a better understanding of deception and self-deception in nature? As was mentioned in Chapter 1, the diﬃculties we encountered in addressing self-deception naturally led to the reformulation of the original hypothesis and a shift of focus towards investigating one aspect of Trivers’ formulation, namely, the evolution of well-integrated deception in an arms race. Can a similar approach be used to explore other aspects of Trivers’ hypothesis? In other words, are there other properties of self-deception that can be explored without necessarily exploring self-deception in its entirety? Below we demonstrate a second aspect of Trivers’ hypothesis that can be extended to non-humans and, if explored, can lead to valuable predictions that can be tested. The goal is not to present a comprehensive overview of this alternative interpretation of the hypothesis, but rather to summarize some interesting applications of it and ultimately ague that the approach we have pursued in this thesis, namely, addressing a complex human behavioral phenotype by analyzing its analogues in other contexts, is one of the main ways through which we can build a constructive science of self-deception.

3.0.1 Hierarchical Information Processing Systems Trivers, in his hypothesis, implicitly assumes a very particular cognitive ar- chitecture. Speciﬁcally, he assumes that a system capable of self-deception

27 top/deep bottom/signaling module modules

input S adversary

organism

Figure 3.1: Schematic representation of the hierarchical information processing system underlying Trivers’ hypothesis on the evolution of self-deception. S: subconscious module; C: conscious module; 2o: secondary module. has to be: 1) a hierarchically organized network of modules within which 2) information flows unidirectionally. Thus, under the most simple assumptions, the brain is divided into three modules, with the subconscious module sitting at the top of the hierarchy, receiving information from the environment and transmitting it to: 1) the conscious module, within which dishonest information can be constructed and communicated with the outside; and 2) another module, which we call the secondary module, that regulates the production of secondary cues (Figure 3.1). We collectively refer to these two modules as the signaling modules, as they send signals to the environment. Trivers specifically assumes that if the conscious module produces dishonest information, then the secondary module inevitably produces secondary cues that give away the deceit. Such a network structure can easily be formulated mathematically, with the strategy of a module being defined as some simple input-output function, and the strategy of the individual as the set of all the strategies of its modules. Deception can be defined as deviation from some honest strategy and implemented through changes in the functioning of the modules. The evolution of networks can be driven by a population of adversaries attempt-

28 ing to decrypt the input of each network to the network’s disadvantage and the adversary’s beneﬁt. If it is impossible to coordinate fully all the signaling modules at the time when executing the deception, then such a model would resemble exactly the model presented in Chapter 2, with well-integrated deception corresponding to a strategy that manipulates multiple signals and cues in a coordinated manner, through changes in the subconscious (deep) module to avoid producing secondary cues of deception. The most important consequence of the above reformulation of Trivers’ hypothesis is that it highlights that what leads to deception jumping from signaling modules to deeper levels of the hierarchy are the aforementioned two assumptions of hierarchical organization and uni-directional information ﬂow, coupled with some constraints that prevent changes at the signaling modules. This thus implies that any group of entities with these properties can evolve internal deception, that is, deception of some entities within the hierarchical system by other entities, if it is caught in an arms race with an external adversary that is capable of becoming superb at decoding the inputs of the hierarchy based on its outputs. Critically, there are many systems that share these properties: cognitive modules outside of the conscious and the subconscious, a hierarchically-organized internal biological system, genes organized in a regulatory network, or even individuals placed hierarchically in a group. This is critical as it demonstrates that analyzing evolution of hierarchical networks not only applies directly to self-deception, but also to other contexts within which the predictions of these analyses can be tested. For the purposes of illustration, we discuss two of these applications below.

Group Self-Deception Although not a biological system strictly, we ﬁrst explore groups of individuals organized in a hierarchy. Like a cognitive system involved in information interpretation and ultimately information transmission to the outside, information can ﬂow from individuals placed at the top of a hierarchy to those at the bottom. Hence, it can be manipulated along the way. The information can then be transmitted to adversaries, such as other groups, whose

29 interests do not fully align with the original group’s interests. If the hierarchy expands extensively with too many individuals at the base, leakage of important information to the adversary cannot be prevented because fully coordinating individuals at the bottom would be challenging. But leakage can be prevented by having individuals at the top of the hierarchy deceive those at the bottom, the indirect consequence of which would be the deception of the adversary. Many entities fit the description above. The groups can represent corporations attempting to deceive consumers, a government attempting to deceive its people, or a highly unequal society with concentration of power at the top attempting to prevent leakage of information to other nations. The colossal consequences of this self-deception can be further exacerbated by those at the top becoming themselves self-deceived in order deceive their in-groups better, resulting in nested self-deception. Indeed, Trivers, in his most comprehensive work on self-deception [40], dedicates five chapters to the so-called group self-deception: “When an organization practices deception towards the larger society, this may induce self-deception within the organization, just as deception between individuals induces individual self-deception.” He analyzes many different examples of this, from aviation and space disasters, to false historical narratives, to wars [40]. One interesteing case is the explosion of NASA’s Challenger disaster about a minute after its launch in 1986, resulting in the death of all the crew members. Trivers, basing his arguments on the thorough analysis of the disaster by Richard Feynman [13], provides many pieces of evidence that show deliberate attempt by NASA’s executives to suppress safety concerns that clearly demonstrated the high likelihood of disaster. This led to the spread of misinformation within the organization and ultimately the launch of this very risky flight. The reason for this internal deception? Trivers argues that NASA was originally founded to land the first person on the moon before the Russians [40]. Once that was completed, what was left was a $5 billion bureaucracy that had to justify its existence to congress and the people. Glamour and cost took precedence over safety in different ways, and independent internal investigation units were

30 suppressed in an apparent attempt to increase the appeal of NASA’s projects to others. The eﬀect was an unfortunate disaster, which, regrettably, was to be repeated in a similar manner during the Columbia disaster seventeen years later. Indeed, one can imagine that organizations and their employees that are best able to hide internal weaknesses from the public and stockholders would be more likely to persist, facilitating the evolution of organizational self- deception, until disaster strikes. This particularly applies to corporations, where internal organizational structure arguably aﬀects the success of a corporation in a free competitive market. Clearly, this would not be a case of biological evolution, but the forces that regulate markets are very similar to forces that control evolution in nature.

Gene Networks Another context within which the hierarchical interpretation of Trivers’ hypothesis would be particularly useful are gene regulatory networks. These are organized hierarchically in that the activities of a few regulatory genes aﬀect the expression of the many genes downstream that directly code for traits. Traits can then act as signals that other organisms can detect. Given that regulatory networks are integral parts of all organisms, changes to their functioning are particularly essential for organisms caught in a communication arms race attempting to escape detection by an adversary. Indeed, in the introduction to Chapter 2, we provided a few examples of well-integrated deception in nature that are manifested at the genetic level. Deception in these cases can come about through mutations in the many genes that sit at the bottom of the hierarchy or the few changes in genes that sit at the top. What tips the balance? There has been a long debate on this topic. The most clear example is the literature on the genetics of Batesian and Mullerian mimicry, where there has been debates as to whether complex mimetic traits are encoded by supergenes, that is, clusters of tightly linked genes each coding for a different aspect of the mimicry, or by few changes in regulatory genes [3]. For

31 example, in the butterfly Heliconius numata, mimicry is regulated by a clus- ter of at least eighteen linked genes [19]. On the other hand, in butterflies Papilio polytes [22, 25] and Papilio Dardanus [36], regions of chromosomes that were originally thought to be supergenes, were found to be occupied by single major regulatory genes. Many factors, such as the rate at which the adversary evolves, the rate at which new mutants are introduced into the population, and the rate of recombination, can tip the balance in favor of one mechanism or the other. Importantly, however, the structure of the genetic network itself can have major consequences on the form of adaptation that evolves. The effects of this can be determined step-by-step through simple models: tri-modular gene regulatory networks with simple input-output functions can be built, placed in an arms race, and subjected to some baseline mutation and/or recombination rate. Through simulations, one can then analyze the relationship between the strengths of the various constraints and the evolution of hierarchically-deep versus shallow but ex- tensive deception at the signaling level.

Other Systems Besides the above cases, hierarchy is arguably a property of many internal biological systems. These system can thus conceivably fall into an arms race and evolve internal deception. However, specific empirical data on these fronts is much-needed and is currently lacking. Overall, the above demonstrates that the hierarchical interpretation of Trivers’ hypothesis applies widely, that it has substantial effects on the evolution of deception, and that, consequently, exploring it can result in a better understanding of variation in dishonest signaling in nature. The many properties of networks, such as the number of modules in each level of the hierarchy, the number of levels in the hierarchy, and how the modules are connected to one another, can be modified and their impacts on the depth of deception can be analyzed using simple mathematical models. Given that much is known about genetic networks, and that models of these networks can lead to results that can potentially be tested, we believe that explor-

32 ing the hierarchical aspect of Trivers’ hypothesis in that realm would be particularly fruitful.

3.0.2 Concluding Remarks Exploring the evolution of well-integrated deception in Chapter 2 lead to concrete predictions: exaggerated deceptive displays evolve when many signals are detected, and when the beneﬁts of deception and the cost of false positives are high. More importantly, it brought to the forefront the hierarchical property embedded within Trivers’ hypothesis. Given this, we believe that simple models of the evolution of hierarchies can not only allow for new testable predictions, but also the discovery of other aspects of self-deception that, once modeled, add to our general understanding of the evolution of deception and self-deception in nature.

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