1.1 Animal Communication and Science Education

Introduction

The authors have been teaching a course in animal communication since 1970, either at Cornell University or the University of California, San Diego (UCSD). One comment frequently made in student evaluations is “I understood and learned more physics in this one term biology course than I learned in a year of regular college physics.” In the 1980s and 1990s, UCSD had over 4000 biology majors and only a tenth as many physics majors. Despite the fact that most of these biology majors had to take college physics, the standard courses largely focused on classical topics of greatest interest to physics majors (and physics faculty). Given the recurrent comments made by the 200–300 students taking animal communication each year, we asked several physics faculty whether they were interested in integrating more animal communication topics into their courses. For various reasons, they were not.

The last decade has seen an enormous effort worldwide to improve STEM (science, technology, engineering, and mathematics) education. One common theme is better integration of the different STEM disciplines in K–12 education. In the USA, central online clearinghouses have been created to promote and distribute innovative and proven STEM curricula and teaching plans. Examples include the websites of the National Science Digital Library (NSDL, http://nsdl.org/) and the National Science Teachers Association (NSTA, http://www.nsta.org/). The Biosciences Education Network (BEN, http://www.biosciednet.org/portal/) focuses on biology topics, but makes a major effort to integrate other science and math disciplines into its curricula. Despite this broader approach, few programs have sought to exploit animal behavior generally or animal communication specifically as entry points to other science disciplines. A notable exception is the website of the American Biology Teacher, of the National Association of Biology Teachers (NABT, http://www.nabt.org/websites/institution/index.php?p=30), which has published theme issues on animal behavior, including bioacoustics lessons suitable for high school and college courses. Some other sites that are likely to develop biology/physics interface modules include Merlot (http://biology.merlot.org/), Bioquest (http://bioquest.org/), Ecological Society of America (http://tiee.esa.org/vol/toc_all.html), and ABLE (http://www.ableweb.org/proceedings/index.php).

Animal behavior as an educational springboard

A major difference between plants and animals is that animals overtly behave. This behavior typically takes the form of movements or the emission of signals, or both. Few anatomical or biochemical adaptations in animals are effective without some coupled behavior that invokes their use. As a result, behavior is now recognized as a major factor in the biology of any animal, and, although the study of animal behavior is occasionally claimed as a subfield of ecology, psychology, neurobiology, or physiology, the study of animal behavior is now a separate discipline. It has its own highly subscribed journals, academic departments, and international societies, including the Animal Behavior Society (http://animalbehaviorsociety.org/), the Association for the Study of Animal Behavior (http://asab.nottingham.ac.uk/), and the International Society for Behavioral Ecology (http://www.behavecol.com).

Animal behavior is intrinsically an interdisciplinary science. Many of the components studied singly by other disciplines come together in the study of behavior. For example, why different species adopt different behaviors is closely tied to their differing ecologies (Wilson 1975). The kinematics of movement (Alexander 2002), the design and mechanisms for producing and detecting signals (this book), and the energetics of behavior (McNab 2002) are just some of the many facets of animal behavior that are closely tied to basic principles of physics. The physiologies of muscles, brains, digestion, reproduction, immune systems, hormonal controls, and even aging are tightly linked to the behaviors animals perform (Alcock 2009). Animal behavior studies have proved to be superlative testing grounds for modern theories of economics and decision-making (Houston and McNamara 1999; Maynard Smith 1982), and animal models are widely used to help understand the origins of learning and culture in our own species (DeWaal and Tyack 2003; Dugatkin 2009; McGrew 2004). Finally, behavior is now seen as a critical component of any conservation or wildlife management program (Caro 1998; Clemmons and Buchholz 1997; Festa-Bianchet 2003).

The interdisciplinary nature of animal behavior makes the field superbly adapted for both novel science and for stimulating science education. The enormous diversity of behaviors performed by different species when faced with similar challenges allows scientists to examine the relative roles of ecological function, physical or chemical constraints, physiological mechanisms, economic optimality, and cultural adaptation. Scientists can also examine the conservation repercussions of behaviors by undertaking experimental manipulations or by comparing the different solutions achieved by different species, identifying correlates of either convergence or divergence, and then testing emergent hypotheses by examining additional species.

Educational opportunities arise because humans, especially children, are naturally drawn to the behavior of animals. Television programs on nature are extremely popular with both children and adults. Ecotourism is similarly popular, and often focuses on the behavior of charismatic fauna. The universal intrigue of behaving animals creates a potentially powerful entry point for teaching physics, chemistry, physiology, economics, culture, and conservation. However, several problems have hindered this approach. First, many current teachers were never exposed to courses in ecology or animal behavior in their own education. Many do not even know that animal behavior is a legitimate field of science. Thus, they do not have the background to bridge animal behavior to physics, chemistry, or even other areas of biology. Second, those that do have the background and inclination to use this approach are overwhelmed by the amount and diversity of rich media resources on the Internet. Where computer tools might help bridge the disciplines, which ones should they use? Finally, the current emphasis on standardized testing in the United States severely constrains which principles of physics, chemistry, or physiology are to be taught at each grade level. Many behaviors are interesting to students, but to bridge the disciplines effectively, a teacher must find an example that is both interesting to students but also one that leads to the teaching of a current standard. Given that few teachers have time to develop any new curricula on their own, these challenges can be insurmountable.

A major motivation for the establishment of NSDL, NSTA, NABT, and similar programs was to resolve the problems noted above. This meant bringing scientists and educators together to design new curricula that integrated disciplines, selected suitable rich media and experiential (e.g., lab and field) exercises, and aligned content to state standards. The resulting curricula are increasingly used nationwide and even worldwide. Many “hooks” for interesting younger students in physics, chemistry, and mathematics have been devised in these curricula. However, only a few have focused on animal behavior and animal communication. We describe two of these below. There thus remains much unexploited potential for this type of educational bridging.

Innovative curricula starting with animal communication

Several recent efforts have focused specifically on linking animal communication behavior with other disciplines, such as physics. We hope that these examples will inspire future curriculum efforts at all levels.

The Macaulay Library Project

The Macaulay Library (http://www.birds.cornell.edu/page.aspx?pid=1676) at the Cornell Lab of Ornithology is the world’s largest archive of animal sounds, with a growing parallel library of videos. With funding from NSDL and the National Science Foundation (USA), the Macaulay Library undertook an ambitious project to integrate its rich media collection with students’ natural interests in animal behavior and communication and with the teaching of basic physics. Scientists trained in animal communication and K–12 science teachers worked together to identify topics required by state standards, identify the best animal examples in the vast library, and develop lessons and hands-on exercises that demonstrated the focal physics principles. The project was performed in collaboration with the Center for Nanoscale Systems Institute for Physics Teachers (https://www.sce.cornell.edu/ss/programs.php?v=CNS&s=Overview) and the New York Wayne-Finger Lakes Board of Cooperative Educational Services (http://wflboces.org/). The former collaboration focused on modules for high school physics classes, whereas the latter examined opportunities at all ages in K–12 education. The resulting animal communication modules focus on the physics of sound (using animal acoustic signals) and the physics of light (using the generation of colors in bird plumages). Additional modules discuss aerodynamics (by examining bird flight) and the physics of forces (by examining bird beaks). These lessons and associated media are available at the Library’s “Physics of Animal Behavior” website (http://www.birds.cornell.edu/physics). Further bioacoustics lessons for college and AP high school biology can be obtained from the Online Research in Biology project website (http://birds.cornell.edu/orb), an NSF-funded educational effort from the education program at the Cornell Lab of Ornithology and the Macaulay Library.

The Sea of Sound Project

A project from the Cornell Lab of Ornithology, funded by the National Science Foundation and the National Oceanographic Partnership Program (http://www.nopp.org/), uses sound in the oceans as the “hook” topic to teach students a variety of state-standard principles in physics and biology. It is aimed at grades 6–12. The sound signals used by whales and dolphins figure prominently, but the curriculum also includes sound production by marine invertebrates and discussion of anthropogenic noise and its effects on communication of marine animals. These curriculum resources feature high-definition video footage of marine organisms and other multimedia segments that explore underwater communication and how it is impacted by sound from human-created activities, such as shipping and oil exploration. They also highlight the right whale monitoring efforts led by scientists from the Bioacoustics Research Program at the Cornell Lab of Ornithology (http://listenforwhales.org). Activities include everything from role-playing debates on the use of sonar to examining whale sounds recorded by multiple underwater buoys to calculate the speed of sound in salt water. Tables in the educator materials provide an at-a-glance overview of alignment between specific elements of the curriculum and the National Science Education Standards for middle school and high school. These classroom activities can be found at the Sea of Sound website (http://www.birds.cornell.edu/Page.aspx?pid=2207).

Literature Cited

Alcock, J. 2009. Animal Behavior: An Evolutionary Approach, 8th Edition. Sunderland, MA: Sinauer Associates.

Alexander, R. M. 2002. Principles of Animal Locomotion. Princeton: Princeton University Press.

Caro, T. 1998. Behavioral Ecology and Conservation Biology. Oxford: Oxford University Press.

Clemmons, J. R. and R. Buchholz. 1997. Behavioral Approaches to Conservation in the Wild. Cambridge: Cambridge University Press.

DeWaal, F. B. M. and P. L. Tyack. 2003. Animal Social Complexity: Intelligence, Culture, and Individualized Societies. Cambridge, MA: Harvard University Press.

Dugatkin, L. A. 2009. Principles of Animal Behavior. 2nd Edition. New York: W. W. Norton.

Festa-Bianchet, M. 2003. Animal Behavior and Wildlife Conservation. Chicago: Island Press.

Houston, A. I. and J. M. McNamara. 1999. Models of Adaptive Behaviour: An Approach Based on State. Cambridge: Cambridge University Press.

Maynard Smith, J. 1982. Evolution and the Theory of Games. Cambridge: Cambridge University Press.

McGrew, W. 2004. The Cultured Chimpanzee: Reflections on Cultural Primatology. Cambridge: Cambridge University Press.

McNab, B. K. 2002. The Physiological Ecology of Vertebrates: A View from Energetics. Ithaca, NY: Cornell University press.

Wilson, E. O. 1975. Sociobiology. Cambridge, MA: Belknap/Harvard University Press.

1.2 Information and Communication

Introduction

Throughout this book, the term information is used repeatedly. In recent years, a number of authors have questioned the utility and even the propriety of invoking information concepts in studies of animal communication. Here we summarize some of these concerns, explain why we feel they are unnecessary or unsupported by recent studies, and indicate the specific steps during communication where we feel information concepts play an essential role.

The concerns

Below we list the problems that are most often raised about the use of the term “information” in studies of animal communication, ranging from doubts that the term has been sufficiently defined and consistently applied to proposals for models of animal communication in which the provision of information is irrelevant.

The duality problem

Following a lead by Cherry (Cherry 1966), W. John Smith proposed a distinction between the message and the meaning of animal signals (Smith 1968, 1977). He defined the message as “each kind of information that a display makes available about a referent.” The provision of information was dependent on the assignment of specific signals to specific referents using a code that was shared by the sender and the receiver. He then proposed two aspects of meaning. One arose from the consequences to receivers of adjusting subsequent actions on the basis of received signals, and another focused on the consequences to senders of these changes in receiver actions. In this view, without a message, there could be no meaningful change in consequences for either party, and without meaning, there was no point for either party to communicate.

While this is intuitively appealing, given the parallels with human speech, the application of these two terms (message and meaning) has proved challenging. The codes mapping animal signals on referents are invariably imperfect (e.g., different referents may elicit the same signal, and different signals may be given for the same referent), which makes identification of the message by both receivers and researchers a quantitative rather than a qualitative task. Assuming receivers accurately identify an incoming signal, subsequent authors have claimed the meaning to be the inferred referent given the code, the appropriate receiver action when that referent is present, or the likely fitness effects of taking the appropriate action. There is thus considerable confusion in the literature as to whether one of these stages or some combination is the appropriate sense of receiver meaning. There is the further complication that different receivers often respond differently and experience different consequences for the same signal, and different senders of the same signal might experience different consequences of whatever actions receivers perform. The seemingly indeterminate links between signals and referents, and between messages and meanings have undermined support for the utility of these terms, at least as originally defined.

Rather than discard the entire duality, some authors have championed one of the original components while minimizing emphasis on the other. The development of information theory (Shannon and Weaver 1949) provided new tools for measuring the amount of information provided by a signal relative to that needed to completely resolve some prior uncertainty. These computations explicitly incorporated the coding system of the sender. The emphasis here was thus the message; consequences were not considered. For over a decade, these tools were enthusiastically applied to a wide variety of animal signal systems (Quastler 1958; Attneave 1959; Johnson 1970; Dingle 1972; Wilson 1975; Hailman 1977; Bell and Gorton 1978; Losey 1978). However, the same concerns that had arisen over the initial duality were raised again: if different receivers had reasons to invoke different prior uncertainties, each would receive different amounts of information for the same signal. And even if most receivers obtained the same amount of information from a signal, the fitness consequences could differ markedly between them. The indeterminate relationships between a given coding system and the amount of information (due to variable priors), and the fact that fitness consequences, not information, are the ultimate focus of evolution, led other authors to adopt the opposite extreme and argue that information provision should not be a part of any definition of communication (Rendall et al. 2009; Owren et al. 2010). The philosopher Scott-Phillips (2008, 2010) even argued that the provision of information was at best “incidental” to the basic communication process.

Other philosophers and economists have taken a totally opposite view. D. K. Lewis (1969) used classical game theory to examine signaling games in which coding was totally conventional and both signaling and receiving were costless (often called “cheap talk” in the philosophical and economic literature). He found that perfect codes shared by senders and receivers were most likely to lead to a stable outcome. Concerns about how a population might arrive at such an equilibrium were resolved by invoking evolutionary game theory and adaptive dynamics models (Skyrms 1996, 2002; Huttegger 2007a). These analyses again found that perfect or, at worst, moderately imperfect signaling was the only likely ESS. The Lewis model has been extended to a wide variety of contexts, including coding with more than binary alternatives, finite populations, senders in one species signaling to receivers in another, presence or absence of mutation, and biologically relevant signaling (e.g., the Sir Phillip Sydney game) (Huttegger 2007a, b; Pawlowitsch 2007; Hofbauer and Huttegger 2008; Skyrms 2009; Huttegger et al. 2010; Huttegger and Zollman 2010; Skyrms 2010a, b). The outcome of these models is nearly always the same: reliable coding is not only essential to communication, it is the only stable outcome.

An alternative approach replaced the original notion of message with signal reliability (Maynard Smith and Harper 2003; Searcy and Nowicki 2005) and the original notion of meaning with the value of information (Gould 1974; Stephens 1989; Bradbury and Vehrencamp 2000; Koops 2004; Dall et al. 2005; McLinn and Stephens 2006, 2010). The value of information integrates signal reliability with receiver decoding, decision making, and fitness consequences into one number that is subject to selection. We outline an example of its use in more detail at the end of this document. This and related arguments have led to a chorus of support for the continued inclusion of information concepts in studies of animal communication (Hasson 2000; Dall et al. 2005; Stegmann 2005, 2009; Castellano 2009; Carazo and Font 2010; Font and Carazo 2010; Seyfarth et al. 2010). In fact, information sharing is now recognized as one of the key adaptations that has led to major evolutionary changes throughout organismal history (Maynard Smith and Szathmàry 1995; Maynard Smith 1999; Lachmann et al. 2000; Maynard Smith 2000; Jablonka 2002).

The arms race problem

Early ethologists largely ignored the possibility of deceit in animal communication either because they assumed that neither party was capable of actions outside the norm (e.g., they were locked into fixed action patterns) or because they assumed communication was a cooperative venture. These views were challenged by Krebs and Dawkins who argued that senders should, and usually do, try to manipulate receivers to the sender’s advantage, and receivers should, and usually do, try to “read the minds” of senders to the receiver’s advantage (Dawkins and Krebs 1978; Krebs and Dawkins 1984). There is now little disagreement that senders and receivers can have conflicts of interest: the optimal interaction for one party may not be identical with that of the other. The question is then where the subsequent evolutionary trajectories will lead. One possibility is that the arms race between the two parties is unending over evolutionary time—each adaptation that gives one party an advantage will eventually be overcome by a counter-adaptation in the other party. This does not seem to be the case. As outlined in the text, most (but not all) communication systems in animals appear to be at some sort of equilibrium. There are three possible types of equilibria: one in which the sender is able to keep the system at its optimum at a net cost to the receiver; one in which the receiver is at its optimum at the expense of the sender; and one (or more) in which both parties have a net benefit, but neither does as well as it would at its own optimum.

Some authors have asserted that arms races are only likely to end when the sender acquires a strategy that the receiver cannot counter (Rendall et al. 2009; Owren et al. 2010). This might occur if the sender can mimic some stimulus that the receiver attends to for other reasons (sensory exploitation); any attempt by the receiver to escape the exploitation would undermine some other necessary adaptation. The equilibrium in these authors’ view is thus a sender dominant one. Since receivers cannot help but respond, the issue of information provision is irrelevant and these authors have argued that term be dropped from discussions of signal evolution.

The weight of evidence does not support these propositions. A number of the studies originally proposed in support of persistent sensory exploitation now appears better explained by recurrent loss and recovery of an early adaptation that benefitted both parties (see Ron 2008 for túngara frog; see Chapter 10 for other examples). In addition, there are numerous evolutionary models identifying realizable conditions under which receivers can eventually escape persistent exploitation. These models usually lead to an intermediate equilibrium in which both parties obtain an average net benefit that is contingent upon the provision of minimally reliable information to the receiver by the sender. The last few decades have seen a major effort to test these models in a wide variety of taxa and signaling contexts. As reviewed in the text, the conditions favoring intermediate equilibria are much more often found to be present than absent, and where fitnesses can be measured, both parties gain an average net benefit by communicating. While sender exploitation of receiver sensory biases remains one of several likely starting points for signal evolution, it appears that most systems subsequently move on to intermediate equilibria.

The coding problem

Traditional models of animal communication assume that senders and receivers have at least reasonably concordant, if not identical, coding schemes. Signals given randomly cannot provide information to receivers. Signals given selectively can provide information, but senders must show some consistency in which signal they emit for a given referent, and receivers must have some previously acquired expectations about likely sender assignments.

Several authors have questioned the use of the coding concept in animal communication. Some argue that the terms “encoding” and “code” are never explicitly defined, and are indiscriminately applied to very different signaling phenomena (Rendall et al. 2009; Owren et al. 2010). Other authors challenge the utility of the coding concept because the contexts in which a given signal is emitted may completely change the assigned referent implied: examples include human sarcasm (Scott-Phillips 2010) and context-dependent signaling in birds (Smith 1977).

In response, it is instructive to note that a reliance on coding schemes is not unique to communication, but instead is a condition for most sensory processing. The primary function of sensory organs is to detect changes in ambient conditions. Animals must be able to categorize conditions or there would be no benefit to sampling the environment. This is true even for the simplest case in which an animal only monitors the presence or absence of a single stimulus; it is even more relevant to the many organisms that routinely discriminate between multiple stimuli. The sampling and sorting of ambient stimuli, particularly those emitted by other organisms, is ubiquitous in animals (Danchin et al. 2004; Wagner and Danchin 2010). Stimuli vary in how well their emission is correlated with specific and unique conditions. Few stimuli of  interest to animals will be “natural” in the sense that they are guaranteed to be available if and only if a given condition is true (Scarantino 2010). Many will be “normative,” in that the correlation between a given stimulus and a given condition is sufficiently high that it is worth attending to them (Millikan 1989, 2004; Stegmann 2009). Stimuli that are moderately reliable indicators of the presence of particular conditions are called cues. Whether acquired through genetic inheritance, learning, or some combination of the two, nearly all animals rely on interpretive codes to make sense of the many cues that they might encounter. They can then generalize these codes as necessary to deal with novel stimuli (Ghirlanda and Enquist 2003). The reception and classification of a cue stimulus, when combined with the interpretive code, provides information that can then be used to influence decisions about whether and how to change current actions and physiological states.

Seen in this light, signal codes are just a special case of a more general sensory strategy used by all animals. In fact, many receivers appear to rely on a combination of cues and signals to make decisions. The relative weighting of signals and contextual cues can be quite variable: some signals elicit the same responses regardless of contexts, whereas others elicit responses that are very sensitive to ambient conditions (Smith 1977; Marler et al. 1992). Reliable signals that are more heavily weighted than ambient cues are often singled out as “referential.” However, there appears to be a continuum rather than a dichotomy in most taxa, and it is not surprising that relative weightings should vary with the relative reliabilities of the stimuli and the fitness consequences of alternative actions.

Secondly, the claim that coding schemes are never explicitly defined in animal signal literature (Rendall et al. 2009; Owren et al. 2010) is inaccurate. Explicit and quantitative definitions of animal signal coding schemes are provided in the prior and current editions of this text and in countless other publications (including a whole book, Hailman 2008) ignored by these authors. The critics may not agree with these definitions, but claiming they don’t exist is spurious. While the same authors who claim coding schemes are never defined acknowledge that receiver actions may be sensitive to both cues and signals, they see the observed variability in relative weightings as undermining any formal definition of signal coding schemes. We would argue that once you acknowledge the overlap of cue and signal coding schemes, variable weighting is an adaptation that natural selection is sure to favor.

Finally, it seems appropriate to ask just how reliable animal signal codes really are. If the codes do not enhance decision making above random choice, any invocation of coding is moot. As discussed in the text, signal reliability depends on the consistency with which senders assign signals to referents, the level of signal distortion during propagation, and the degree to which receivers share the sender’s coding scheme and can correctly assign incoming stimuli to expected templates. Because the minimal reliability that justifies communication depends significantly on the fitness consequences of receiver actions (Bradbury and Vehrencamp 2000; Koops 2004), one might expect observed values to be highly variable among taxa, modalities, and contexts. In fact, measures of signal reliability obtained in recent decades find most animals using intermediate levels of reliability: signals provide much better information than relying on prior probabilities alone, but signal coding is almost never perfect (see Chapter 8; Maynard Smith and Harper 2003; Dall et al. 2005; Searcy and Nowicki 2005; Seyfarth et al. 2010). In exceptional cases where signal reliability is found to be surprisingly low, the contexts are such that the value of information for those signals remains positive for all parties (Gyger and Marler 1988; Møller 1988).

The black box problem

The use of metaphorical models for animal and human behaviors has been a long tradition in psychology. It was also an early tool of ethologists who tried to explain phenomena such as vacuum and displacement behaviors (see Chapter 10) by postulating hypothetical “drives” whose dynamics and interactions could be adjusted to replicate the observed patterns. Perhaps the most famous of these was the hydraulic model proposed by Lorenz and Leyhausen (1973). However, as neurobiology became more sophisticated, one after another of these hypothetical constructs was found wanting (see Web Topic 10.4; Berridge 2004). In parallel, the enthusiasm for applications of information theory to animal behavior in the 1970’ waned as it became clear that receiver actions after receipt of a signal were not a good guide to underlying decision processes: did a receiver fail to respond to a stimulus because it could not discriminate it from some alternative (an amount of information issue), or because it did not pay to change its current behavior (a fitness consequences issue)? As a result, most ethologists, and those in the descendent field of behavioral ecology, began to eschew speculations about brain mechanisms and instead focus on the economics of animal behavior: what ecological factors caused one species to be polygynous but a related species to be monogamous, what payoffs justified being territorial in a given habitat, and what were the costs to a male of directing carotenoids into coloration instead of into immune function? Reviewers often chastised authors who treated the brain as anything except a black box and suppressed any speculations about the mechanisms behind assessment and decision making.

Luckily, recent advances in cognitive science and neurobiology have changed the situation completely. Clever signal detection theory paradigms now allow one to measure the amount of information and the value of information separately and non-invasively (see Web Topic 8.10). A multitude of neurobiological efforts now focus explicitly on elucidating how the brains of animals and people accomplish the tasks associated with communication. On the sender’s side, the neurobiology of Drosophila displays, frog and cricket calls, and passerine song acquisition and production are largely worked out. On the receiver’s side, significant advances have been made in our understanding of sensory processing, stimulus categorization, encoding and decoding, the storage of perceived valence, and decision making in a wide variety of taxa. In growing numbers, the relevant genes have been identified.

It is thus no longer taboo to ask whether animal receivers can use receipt of a given signal to perform a Bayesian update on stored probability estimates or instead invoke some sort of heuristic shortcut. One can now identify specific parts of a vertebrate or invertebrate brain that carry out individual stages in decision making (see Web Topic 8.7). The many efforts to understand this type of process in humans, where self-reporting can be used to confirm neurobiological models, are now being applied and tested in animals (see Chapter 8). Results so far confirm the basic model of receiver updating and decision making outlined in this book. The steps outlined in this and other models can increasingly be tested at both the proximal (mechanistic) and ultimate (fitness consequence) levels. So far, results are supportive. The initial success of the basic Bayesian design has spawned second-generation models that can explain hierarchical processing (e.g., Yang and Shadlen 2007; Tennenbaum et al. 2011). Clearly, the black box has come a long way since the early days of hydraulics.

The math problem

The most effective way to view the interaction between the amount of information in a signaling system and the fitness consequences involves algebraic formulations (see below). It is a curious fact that nearly all of the publications arguing against the incorporation of information in definitions of communication rely on entirely verbal arguments, excluding algebra. Most do not even cite the many models defining the quantitative conditions that favor stable signaling equilibria, and, even if these appear in the reference list, the models themselves receive no serious attention in the associated texts (Scott-Phillips 2008; Rendall et al. 2009; Owren et al. 2010; Scott-Phillips 2010). While some of these authors are philosophers, for whom a persuasive verbal argument is the gold standard, the avoidance of any mathematics seems odd when so much effort has gone into deriving rigorous evolutionary models for communication.

While algebraic formulation does not guarantee that all terms will be included or clearly defined, it often makes deletions conspicuous and badly defined terms clearly unmeasurable. In contrast, it is very easy, as can be seen in several of the cited papers, to construct a plausible verbal argument that hides the omission of contrary citations and data. Verbal arguments also make it easy to claim that a critical term (such as information) is “poorly defined” or to recast an opposing argument with such hyperbole that it becomes an easily disproved straw man.

Perhaps the most pernicious aspect of verbal arguments is the perceived need to partition quantitatively varying phenomena into discrete categories. Much of the dissent over definitions of communication arises from one group finding a case that cannot be assigned to available discrete categories or is inappropriately assigned by another’s definition. The problem is that many of the phenomena associated with animal communication do not fit into tidy, discrete categories. Behaviors performed during physical conflicts can both provide information to an opponent and set up a tactical advantage. The relative importance of the two can vary continuously between fights, and even shift during the same fight by the same two animals. Is such a behavior a signal or a fighting tactic? Discrete categories simply cannot handle these cases. Many biological parameters of interest vary continuously—forcing them into discrete categories, though intellectually convenient, is thus artificial. Many discrete definitions for biological phenomena end up having multiple criteria. What should one do with cases that meet all but one of these criteria? Such cases are often the most instructive, and ignoring them is foolish. Slavish obedience to discrete definitions is a recurrent problem; it is much better to accept the existence of continua and mixtures. Since this is often hard to do verbally, it is best left to algebraic expressions.

An integrated model of animal communication

Below, we briefly summarize two similar algebraic treatments of animal communication that explicitly integrate information provision with fitness consequences. Several more recent formulations are also available, but these two set the scene and will suffice to make our point. One model was published by Bradbury and Vehrencamp (1998, 2000) and the other by Koops (2004). The two models share the following assumptions and components:

• Basic question: Both models address the question of if and when a receiver should incorporate signals into a decision about subsequent actions.
• Basic format: Both models invoke the value of information as the relevant criterion subject to selection. This measure compares the average fitness of a receiver when it incorporates a given set of signals in its decisions against when it does not incorporate them. Signal usage will only be favored if the value of information is positive.
• Alternative comparisons: The value of information can compare the use of a given signal set to any of a variety of alternatives. For example, one could compare the value of information if the animal were to switch from using one set of signals to using an alternative set in the same contexts. However, to answer the basic question listed above, the two cited models focus on the value of information for receivers using signals when compared to those using some non-signal default strategy.
• The default strategy: Some prior discussions of signal evolution have naïvely assumed that animals without access to signals would resort to random decisions. That is probably never the case: heritable biases and prior personal experience will allow most animals to estimate both the likelihoods of alternative conditions being true and the relative fitness consequences of alternative actions given each alternative condition. Both models thus assume that receivers without signals will combine some estimate of prior probabilities with potential payoffs to identify an optimal default action. In the absence of signals or new cues, the receiver will always perform this default action. Since this is only a best guess, sometimes the default action will be the right thing to do, but at other times it will be the wrong action. Despite some errors, the default action is the best choice on average.
• The role of reliability: Most animal signal schemes are also imperfect. Thus, a receiver relying on a given code and sender signals will sometimes make the right choice of action and sometimes the wrong one. The difference between relying on signals versus using the default strategy is a quantitative shift in the relative frequencies of correct and erroneous decisions.
• The costs of communication: Acquiring the coding scheme and investing time and sensory organs in attending to signals will impose costs on receivers that are not experienced by receivers adopting the default strategy.

The way in which these components can be combined into the value of information is most easily seen in the Bradbury and Vehrencamp model. Here is a brief outline of that approach:

• Alternative conditions: Suppose a receiver is concerned about which of two alternative conditions, C₁ or C₂, is currently true (e.g., predator present versus predator absent).
• Prior probabilities: Based on recent experience, the receiver can expect C₁ to occur a fraction p of the time, and C₂ to occur (1–p) of the time. Note that both probabilities are nonnegative by definition.
• Fitness consequences: The receiver can perform either of two actions: A₁ and A₂. Suppose A₁ is the correct choice (higher payoff) when C₁ is true, and A₂ is the correct choice when C₂ is true. Let ΔW₁ be the difference in fitness payoffs for making the correct versus the wrong choice of action when C₁ is true, and ΔW₂ be the equivalent difference between right and wrong decisions when C₂ is true. Note that both ΔW₁ and ΔW₂ are nonnegative by definition.
• Costs of communication: Let the absolute value of the costs of acquiring the coding scheme and attending to signals be K. This number is also nonnegative, but will be subtracted from the value of information because it is a cost.
• Reliabilities: Suppose that when the receiver only uses its default strategy, it correctly identifies that C₁ is true a fraction ϕ₁ of the time and makes the wrong identification (1 –  ϕ₁) of the time; similarly, it correctly identifies that C₂ is true a fraction ϕ₂ of the time and makes the wrong identification (1 –  ϕ₂) of the time. When the receiver relies on signals, it is now correct in identifying C₁ as the current condition a fraction ϕ₁´ of the time, and is incorrect (1 – ϕ₁´) of the time; when C₂ is true, it is now correct a fraction ϕ₂´ of the time, and is incorrect (1 – ϕ₂´) of the time. As with consequences, it is simpler to consider the changes when signaling is used compared to when it is not. Thus we define Δϕ₁ = ϕ₁´ – ϕ₁ and Δϕ₂ = ϕ₂´ – ϕ₂.
• Value of information: After Bradbury and Vehrencamp 1998, the value of information for this simple 2-condition/2-signal/2-action case can then be computed to be
  
  VI = p Δϕ₁ ΔW₁ + (1 – p) Δϕ₂ ΔW₂ – K.
  VI must be > 0 if signals are to be favored over the default strategy by selection. When is this the case? Note that:
  • The values of p, (1 – p), ΔW₁, and ΔW₂ are all positive and are unchanged in value whether a receiver uses signals or not.
  • The only variables that are sensitive to the use of signals are the values of Δϕ₁ and Δϕ₂ and the cost –K.
  • Because a receiver using the default strategy is always correct in its choice of action when one of the conditions is true, and always wrong when the other condition is true, the switch to using signals has to decrease reliability for one condition and increase it for the other. This means that one of Δϕ₁ or Δϕ₂ has to be negative and the other has to be positive.
  • Assuming neither ΔW_i = 0, this means that one of the p_i Δϕ_i ΔW_i terms in the value of information expression is negative, and the other one is positive. For the overall value of information to be positive, the positive term on the right side of the expression has to be large enough to more than cancel out the two other terms which are negative.
  • The magnitude of the positive term on the right hand side of the expression depends on the magnitudes of the corresponding p_i, Δϕ_i, and ΔW_i. We thus see that both the amount of information, as measured by the reliability of the signals, ϕ_i´, and the fitness consequences of making correct instead of wrong decisions, ΔW_i, are important in determining whether it is worth relying on signals or not. The amount of information, as measured by reliability, is not just an “incidental” property: it is an essential property determining the selection for or against communication.
  • Note that as the reliabilities of the signal set increase, the positive p_i Δϕ_i ΔW_i term gets larger and the negative p_iΔϕ_i ΔW_i term gets closer to zero. Both effects increase the value of information.
  • If the reliabilities are not sufficiently high, the value of information will not be positive and the use of signals will not be favored by selection. Both models show that this effect alone predicts a minimum reliability that must be present before it pays for receivers to shift from the default strategy to attending to signals.
  • Because increasing reliabilities usually increases the costs of participating in communication (–K), the optimal reliability for the receiver will depend in part on the shape of the cost function. If it accelerates with increasing reliability, or is linear but improvements in reliability are asymptotic, the optimum reliability for receivers is predicted to be intermediate between default values and that providing perfect information.
  • Note that a similar expression for the value of information can be derived for senders. The optimal value for senders will depend on their own set of fitness consequences (ΔW_i) and their own set of costs (–K_s). The optima for the two parties need not be the same.

Relevance to earlier concerns

What is information?

Information in these models is the change in a receiver’s estimated probabilities that a given condition is currently true. It is not a substance so it cannot “flow” from sender to receiver. The Δϕ_i can be used as measures of the amount of information provided by signals. Note that the change will depend on the prior probabilities: receipt of a signal can create big change if the initial expectation was chance, but a small change if the signal only confirms the receiver’s strong prior bias. An average for a signal set can be obtained by discounting each Δϕ_i by the probability that it will be used,

Δϕ = pΔϕ₁ + (1 – p) Δϕ₂.

This can be scaled in various ways to make it more useful. The typical approach is to scale it relative to the maximum reliability. Since ratios can get very small or very large, log scales (bits) are often used.

Restoring the duality

While none of the terms in the computation of VI fit the original definitions of message and meaning, it should be clear from the algebraic model that an improvement in either signal reliability or payoffs can trigger a shift from a default strategy to reliance on signals. While it is true that it is the net fitness payoff (value of information) that is the focus of selection, this payoff is equally dependent on how much information is provided and how much getting it right versus getting it wrong affects fitness. Quantifying reliabilities and fitness payoffs are thus equally important tasks when examining signal economics.

Where is the code?

Reliability is a measure of the probability that a receiver correctly identifies the current condition given available cues and signals. To do that, it must combine receipt of a particular cue or signal, consultation of the coding scheme, and its prior probability estimates to generate an updated estimate of the probability that a condition is true. The protocols by which the receiver processes and categorizes the signal, retrieves correlations from a stored coding scheme, generates an update, and makes a decision are all parts of increasingly well-understood brain functions. It no longer pays to ignore this formerly “black box.” Sensory processing and classification have been dissected in detail in many species. Many animals appear to use Bayesian updating or nearly Bayesian heuristics to generate updates. How this is achieved neurobiologically is currently a subject of intense research but considerable progress has already been made. We do not specify how a given reliability is achieved in the model presented above, but likely scenarios are discussed in Chapter 8 and its associated Web Topics.

Receiver variability

The problem that different receivers might invoke different priors and have different values of ΔW_i can be accommodated for by computing a different VI for each type of receiver. While critics might argue that this simply puts numbers on the problem of indeterminacy noted earlier, the fact is that variation among individuals in fitness consequences for a given strategy is a normal part of evolutionary dynamics. The selective advantage of using signals must be based not on a few individual cases but on the population-wide average value of information. One expects that this average will be positive in populations where the use of signals is the norm.

Arms races

The problem that senders and receivers might have different optima is best handled with one of the many models of signal evolution using evolutionary game theory. If the optima for both parties are intermediate, (due to accelerating costs or decelerating improvements in reliability), the interesting question is whether or not the equilibria predicted by game theory are above the minimum reliabilities for both parties. Most existing models do not predict a net fitness loss (negative value of information) for either party at an equilibrium (ESS).

Verbal versus algebraic descriptions

The problem that receivers may rely on variable weightings of cues and signals for decisions remains intractable given an insistence on discrete verbal classifications, but is easily accommodated by these algebraic models.

Conclusions

The amount of information provided by a set of signals, the differences in fitness payoffs for correct versus wrong decisions, and the costs of participating in communication all play parallel roles in determining whether selection will favor signaling over alternative strategies. Because cue monitoring grades into signaling, and most receivers base decisions on both cues and signals, discrete categories separating what is a signal and what is not can be very misleading. Conflicts of interest are common in signaling dyads, and these can interact in complicated ways to determine the equilibrium levels of reliability. However, most animal signals appear to have an intermediate level of reliability. This may reflect the opposing forces exerted by the two parties on the system, or it may be more a result of the fact that increased investments (costs) in communication likely result in asymptotic benefits for both parties, and thus the optima for both have intermediate values. Any conflict is then over which optimum is closer to the equilibrium.

Not everyone accepts this viewpoint, and a recent compendium edited by Ulrich Stemann (2013) shows that the arguments, with new examples of each of the “problems” listed above, continue unabated. We have tried to make our case in this textbook and the accompanying online units, and will let history decide who, if anyone, got it right.

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