Oikos 119: 254263, 2010 doi: 10.1111/j.1600-0706.2009.17756.x, # 2009 The Authors. Journal compilation # 2009 Oikos Subject Editor: Jan van Gils. Accepted 1 September 2009
An experimental analysis of receiver economics: cost, reliability and uncertainty interact to determine a signal’s value Colleen M. McLinn and David W. Stephens C. M. McLinn and D. W. Stephens (
[email protected]), Ecology, Evolution and Behavior, Univ. of Minnesota, 1987 Upper Buford Circle, St. Paul, MN 55108, USA. Present address for CMM: Cornell Lab of Ornithology, 159 Sapsucker Woods Road, Ithaca, NY 14850, USA.
This paper investigates the effect of three important variables on signal use, theoretically and experimentally. We present a simple model and a corresponding experiment that investigates the combined effects of uncertainty about action, signal reliability and signal cost. Our experiment uses techniques drawn from the psychology laboratory to test the behavior of captive blue jays Cyanocitta cristata solving a simple feeding problem. In the experiment, individual jays must choose which of two keys to peck; one key leads to food, but the other does not. In addition, the jays can choose to see a signal that provides information about which key provides a food reward. We find that these three variables interact to determine signal use crudely as our model predicts. Specifically, we find maximal signal use when uncertainty is high, signals are reliable and signal cost is low, but the effects of these variables on signal use do not combine additively. A change in any single variable can abolish signal use. While our results agree qualitatively with our simple model, we also find in agreement with previous studies that subjects show a bias against signal use. Specifically, they tend to ignore signals and rely on prior information about the correct action in ‘intermediate’ conditions. These results are important for two reasons. First, they replicate earlier results from our laboratory using a different preparation. Second, they highlight the central interaction between uncertainty and reliability that determines the value of signals for receivers. This is significant because game theoretical models of signaling emphasize the problem of ‘reliability,’ but they pay little attention to the fundamental interaction between reliability and uncertainty.
According to Maynard Smith and Harper (2003), signal reliability ‘‘is the central problem for an evolutionary biologist interested in signals’’. As many readers will know, the central role of the reliability problem in the study of animal signaling flows from a simple ‘boy who cried wolf’ argument. This argument holds that economic conditions will often tempt signalers to provide deceptive and unreliable information; if this happens, however, receivers will begin to ignore signals, and this combination of effects tends to de-stabilize signaling systems. This simple argument has inspired many interesting and important studies (reviewed by Grafen 1990, Maynard Smith and Harper 2003, Searcy and Nowicki 2005). Notice, however, that it depends critically on a claim about receiver behavior: receivers will ignore unreliable signals. Will they? How reliable must a signal be? What determines how reliable a signal must be? This paper presents a theoretical and experimental analysis of these questions. Following several theoretical (Wiley 1994, Stephens 1989, Bradbury and Vehrencamp 1998, 2000, Koops 2004, Dall et al. 2005) and empirical studies (McLinn and Stephens 2006), this paper advocates a perspective based on statistical decision theory (reviewed by Dall et al. 2005), which focuses our attention on the economics of signaling. According to statistical decision theory, receivers 254
attend to signals because signals reduce uncertainty about the best action. To be concrete, consider a situation in which a female must accept or reject males as she encounters them. Some males in the population are ‘good males’, say proportion p, and other males in the population are ‘bad males’, proportion 1 p. The proportion p represents the uncertainty of the situation. If p 1, then all males are good and the female can safely accept every male she encounters (see Bradbury and Vehrencamp 1998 for a similar model). Obviously, a signal of male quality has no value in this situation, because (to speak anthropomorphically) the female is already certain about male quality. Suppose instead that p 0.5, now exactly half of the encountered males are good and half are bad. Now, there’s plenty for a signal to do. The female is uncertain about male quality and a signal that reliably indicates male quality can improve the female’s performance. With this example in mind, one can readily see that reliability cannot make a signal valuable without environmental uncertainty, and it follows that the extent to which a reliability reduction devalues a signal depends on environmental uncertainty. Maynard Smith and Harper’s claim, that ‘signal reliability’ represents the central evolutionary question about signals, hinges, therefore, on the implicit assumption that a reliable signal can help the receiver (and ultimately that this will
help the signaler, although this study focused on the receiver). Yet the extent to which a signal can improve the receiver’s lot depends critically on the receiver’s uncertainty about how it should act. Following McLinn and Stephens (2006), this paper explores the relationship between signal reliability and environmental uncertainty theoretically and experimentally. McLinn and Stephens presented captive blue jays with a simple signal use problem while factorially manipulating signal reliability and environmental uncertainty. They found that both variables influenced signal use. As predicted, jays used signals most in situations with high signal reliability and low environmental certainty. In less extreme situations, however, jays tended to exploit patterns of environmental certainty and ignore signals even when signal use would have improved performance. In that experiment, jays could freely choose to use or ignore a signal that was always present. The technique was simple, but it had two disadvantages. First, McLinn and Stephens only had an indirect measure of signal use. Since the signal was always present, they had to infer signal use by asking whether choice behavior followed the signal or not. Second, although models from statistical decision theory make explicit predictions about the value of signals, McLinn and Stephens’s approach only provided indirect information about whether subjects value signals. The experiment presented here replicates McLinn and Stephens’ study while addressing these two deficiencies. First, this experiment offers a direct measure of signal use, because our procedures offer subjects the choice of viewing a signal or acting without it. Second, this study directly measures the extent to which subjects value information because subjects must actively choose to receive signaled information at an experimentally controlled range of costs.
Model We framed our experiment in terms of a simple model of information as we outline below. Our model begins with five basic assumptions. 1. Alternative actions. Imagine that a receiver must periodically choose between two alternatives. In nature, these alternatives may be to accept or reject an encountered resource (a food item, a mate, etc.), or to make a binary choice between two resources (e.g. a long-tailed male vs a short-tailed male). For concreteness, we call the alternative actions action A and action B. 2. Uncertainty about actions. Uncertainty exists because choosing A yields the highest payoff sometimes, while choosing B is better at other times. We assume that A yields the best payoff on proportion p of the choice opportunities, and that the decision-maker ‘knows about’ the value of p via experience or evolution. It follows that B yields the best payoff 1 p of the time. If p 1/2, we have a situation with high uncertainty, because the animal has minimal a priori information about the best action. In contrast, when p 1 (or 0), we have a situation of low uncertainty, because the animal can choose the best action with certainty. Since
the definition of ‘state’ is arbitrary in our model, we restrict our attention to the interval between p 0.5 and p 1.0. (This means, in effect, that we assign the name ‘A best’ to the most common state.) 3. Economic consequences of action/state combinations. We can combine our two possible actions (A and B) with our two possible states (A best and B best) in four ways, and we naturally use a table to represent this. By convention, we call these tables ‘truth tables’ and they are widely used in the study of information problems such as signal detection theory and communication, (Egan 1975, Bradbury and Vehrencamp 1998, Stephens 2007). Our model assumes the simplified truth table shown below: Environmental state
Action
Choose A Choose B
A best
B best
1 0
0 1
In words, we assume that an animal receives the same payoff (1 unit of benefit) for correctly matching action and environment, and the same reduced payoff for a mismatch (0 units of benefit). Some readers may feel that an incorrect action should lead to a loss (say to 1 instead of 0). However, this change would not affect our results, because one can re-scale any two payoffs to the zero-to-one interval. 4. Signal states and signal reliability. We assume that some signal exists. This signal can exist in two observable states, such as red or green, long tail or short. We call these states Sa and Sb. If the animal observes signal state Sa, the underlying state is ‘A best’ with probability q; similarly, if the animal observes Sb, the underlying state is ‘B best’ with probability q; in symbols P(A bestjSa) P(B bestjSb) q. We restrict our attention to the interval between q 0.5 and q 1.0 (specifically, 0.55q51.0), without loss of generality. 5. Costs of signal use. We assume that the animal must pay a cost each time it observes the state of the signal. Mathematically, this cost could work in two different ways. We could imagine a simple additive cost, such that the animal loses amount c every time it observes the signal; or we could imagine that observing the signal reduces the receiver’s benefits by proportion a. For example, observing the signal could, in theory, reduce the receiver’s benefits by one-half. This distinction matters algebraically because the one type (c) enters our calculations additively, while the other (a) causes a multiplicative reduction in benefits. We imagine a two-stage process. First the decision-maker chooses whether to observe the state of a signal (i.e. whether the signal is in state Sa or Sb). The decision-maker pays a cost if it chooses to observe the signal. Second, the decisionmakers choose how to act (i.e. between action A and action B). If the decision-maker chooses to observe the signal in stage 1, then its decision in stage 2 can depend on what it observed in stage 1; otherwise it must act without signaled information. It follows that to find out how much a 255
decision-maker should be willing to pay to observe the signal in stage 1, we must first understand the consequences of using the signal in stage 2. Consider, therefore, the economic consequences of two possible stage 2 strategies that we call signal following and averaging. A signal follower chooses option A if it observes signal state Sa; and it chooses option B if it observes signal state Sb. An averager ignores the observation it made in stage 1 (i.e. it ignores the signal) and always chooses the option that is best on average. In our situation, this is the option that is correct most often. So, an averager chooses action A if p0.5 and action B if p B0.5. An averager (who always chooses the most frequently correct action, A) expects to obtain p units of benefit from every choice opportunity, because A is correct p of the time. In symbols, we write that the expected value of the averaging strategy (VA) equals p (VA p). A signal follower, who slavishly follows the signal, expects to obtain q because the signal indicates the correct action a proportion q of the time. It follows, however, that you can only follow the signal if you choose to observe its state in stage 1, and conversely that it doesn’t pay to observe the signal if you are an averager who ignores signals. The signal follower, therefore, pays costs as we described in item 5 above, so the expected value of the signal following strategy (VS) equals (1 a)q minus c [VS (1 a)q c]. Observing and following the signal is therefore superior whenever VS VA, or equivalently when (1 a)q c p. Using this simple inequality, figure 1 shows the combina-
tions of signal reliability (q), environmental uncertainty (p), and signal cost where we predict signal use. In particular, in the absence of cost (c 0) this result divides the reliabilityuncertainty space in half diagonally, and we predict that animals should use the signal for q/p combinations below the q p diagonal and ignore the signal for q/p combinations above the q p diagonal. For non-zero signal costs the result is qualitatively similar (observe and follow the signal below, ignore the signal above) except that additive costs shift the line down (reducing the intercept) while multiplicative costs reduce the slope. (The slope declines because the receiver loses a fixed proportion of its gains with multiplicative costs; so they pay higher costs when the signal is reliable). Both types of cost reduce the size of the region in which signal following pays. Procedural overview This paper describes an experiment designed to test this model experimentally. Our experiment implements the model by testing the behavior of captive blue jays Cyanocitta cristata working for food in Skinner boxes. In broad outline, our experiment offers subjects a sequence of two choices: first, the subject must choose to view or ignore a signal, and second to act (with or without signaled information) in a task that will produce food if the subject makes the ‘correct’ choice. If the subject chooses to observe the signal, it must pay a cost (implemented as a delay so we measure cost, c, in seconds of delay). However, the observed state of the signal
Figure 1. The figure shows combinations of signal reliability (q on the x-axis) and certainty about action (p on the y-axis) where we predict animals to follow signals. We predict signal use below the diagonal boundary. The position of the boundary depends on the cost of using a signal. For a free (or no cost) signal, the boundary divides the qp rectangle in half, but as cost increases the height of the boundary decreases, reducing the region in which we predict signal use. The nine filled circles and accompanying grey lines show the combinations of reliability and certainty used in the experiment.
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provides information (with reliability q) about the correct choice in the second decision. In the second decision, the subject chooses between a red stimulus and a green stimulus. The red stimulus, for example, yields food on proportion p of the trials. So we can control uncertainty by manipulating the relative frequency p. Our experiment, then, follows a factorial design with three levels of signal reliability (crudely corresponding to unreliable q 0.5, partially reliable q 0.75, and completely reliable q 1.0), three levels of uncertainty (complete uncertainty p 0.5, partial uncertainty p 0.75, and complete certainty p 1.0), and three levels of signal cost (c 0 s, 30 s or 60 s).
Methods
The rear panel consisted of a single stimulus light and a perch. We mounted this rear perch on a hinge so that the hinge depressed a microswitch when the bird occupied the rear perch. The front panel consisted of three pecking keys, two LEDs and a stationary wooden perch (Fig. 2). The two side keys served as the response keys. We positioned LEDs on either side of the response keys, and one would illuminate on each trial to provide signaled information. A pellet dispenser delivered 20 mg pellets into a food cup located on the front panel. We connected the entire apparatus to a computer running Med-PC version IV. A program written in MedState Notation language controlled all of the experimental contingencies, and recorded all of the subjects’ responses.
Subjects and housing
Experimental design
Our subjects were seven blue jays Cyanocitta cristata, which we had captured as nestlings under appropriate state and federal permits, and then hand-reared. The birds were 2 to 5 years old, and had varied experimental histories. Birds 5 and 6 were nestmates (and so, presumably, siblings) but the rest of the subjects were unrelated. We maintained the subjects in accordance with Univ. of Minnesota Institutional Animal Care and Use Committee guidelines, on a 13:11 h light-dark cycle.
The experiment followed a factorial design with three levels of environmental certainty (p 0.5, p 0.75 and p 1.0), three levels of signal reliability (q 0.5, q 0.75, q 1.0) and three levels of signal cost (c 0 s delay, c 30 s delay, and c 60 s delay; Fig. 1). The experiment used a withinsubjects (or repeated measures) design in which we tested each subject in all 27 treatments. For each subject, we selected a random testing order for the nine combinations of reliability and uncertainty. In addition, we randomized the order of cost treatments within each reliability/uncertainty combination. That is, we tested all three cost treatments with a given reliability/uncertainty treatment before moving a subject to the next reliability/uncertainty combination. To ensure that subjects had some experience with the task and procedures before testing, we ran a baseline
Apparatus We conducted the experiment in operant chambers (i.e. Skinner boxes) constructed from sheet metal and wood, measuring approximately 61.6 48.3 40.6 cm (Fig. 2).
Figure 2. Diagram of apparatus (aka Skinner box) used for the experiment. (a) overhead view. (b) rear panel, showing rear stimulus light and hinged ‘start’ perch. (c) Front panel, showing two response keys with signal LEDs next to them, magazine light to signal pellet delivery into cup, and fixed front perch.
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treatment with intermediate levels of uncertainty and reliability (p q 0.75) before testing any of the experimental conditions. As in a normal experimental condition, we tested all three levels of cost within this baseline treatment. Since we also used p q 0.75 as one of our experimental treatments, we constrained the randomization of treatment order so that the experimental p q 0.75 treatment did not follow the baseline. This procedure ensures that birds experienced changed conditions in each new treatment including the first. Color assignments As explained above, each trial consisted of two parts. In part one, the bird chose to view or ignore the signal, and in part two, it faced the task of deciding which of two alternatives would provide a food reward. In part 1 (the signal observation choice), we offered the subject a choice between a blue and yellow key. However, we randomized the consequences of pecking blue or pecking yellow. For some birds, pecking yellow led to the ‘signal present’ situation, while for others pecking yellow led to the ‘no signal’ situation. Similarly, jays chose between red and green keys in the second part of the trial. Pecking one color led to food, but pecking the other color produced nothing. To apply our model we needed to define the environmental certainty parameter p (the probability that color X is true). For example, p could be the probability that red leads to food or the probability that green leads to food. We determined the meaning of p randomly for each subject. Although we randomized color assignments as explained here, we will use the example that ‘pecking blue’ leads to the signal and the parameter p P(red leads to food), for concreteness. Within-trial procedure A typical trial proceeded as follows. (1) The running program selected the rewarded color, selecting red with probability p and green with probability 1 p. (2) The rear light flashed, indicating that the bird should hop on the rear perch. (3) After the bird occupied the rear perch, the rear light then burned steadily for a 75 s intertrial interval (ITI). (4) When the intertrial interval expired, the apparatus offered the signalno signal choice (blue vs yellow) if the bird occupied the rear perch when the intertrial interval expired. If the rear perch was vacant, the apparatus flashed the rear light until the bird occupied the rear perch, and then offered the signal-no signal choice. Flashing blue and yellow keys represented the signal-no signal choice. We randomized the positions of blue and yellow each trial so that blue occurred on the right half the time, and so on. If the subject did not peck either key during a 10 min interval, the computer aborted the trial and started a new one. The trial could continue in two different ways depending on the subject’s choice (we denote these mutually exclusive alternatives as steps 5a and 5b). (5a) No information chosen. If a bird chose the ‘no signal’ option, the stimulus lights changed to solid red and green colors for 5 s. Again, we randomized the position of the two colors, so that red occurred on the left half of the time and on the right half of 258
the time. After 5 s, the red and green lights started flashing, and the subject could choose between them. (5b) Information chosen. If a bird chose the signal key, the pecking keys changed to solid red and green colors, as above; with two differences. First, the red and green key lights burned steadily (indicating a delay) for 5c seconds, where c represents the cost parameter specified by the experimental treatment. Second, the apparatus switched on the ‘signal’ (an LED adjacent to one of the choice lights). The LED indicated the correct choice (that is, the key that will produce food) with probability q (signal reliability) as determined by the experimental treatment. (6) The subject’s first peck to one of the response keys indicated its choice and determined the outcome (i.e. food or no food). If the subject pecked the ‘rewarded key’ as determined in step 1, then the computer extinguished all the lights and delivered food; if it pecked the ‘unrewarded key’, then the computer extinguished all the lights, but delivered nothing. If, after 10 min, the subject had not pecked either key, then the computer aborted the trial and initiated a new one. Aborted trials occurred very rarely after initial training. Treatment duration (stability criterion) Within each of the 27 treatments, the subjects experienced several hundred trials. Each treatment lasted for a minimum of 300 free choice trials and a maximum of 1000. Within these bounds, we terminated a treatment when the subject’s behavior met a stability criterion. Our stability criterion required that proportional choice of the red or green key (in the second phase of the trial) changed less than 10% in five consecutive blocks of free choice trials (32 free choice trials per block). Our examination of the stability data showed no systematic variation due to age or experimental history in the number of trials required to reach the criterion, although we did find a simple treatment effect (birds took a shorter time to reach criterion in treatments with complete environmental certainty p 1.0). Although it happened rarely (less than 10% of the time), some birds in some treatments failed to reach stability (as defined above) within the maximum of 1000 trials. This was most common in the high uncertainty treatments and least common in the low uncertainty treatments (22% of the time when p 0.5; 2% of the time when p 0.75; and 0% of the time when p 1.0). Dependent measure We used the final 160 trials in a given treatment to calculate the dependent measure [P(view info)], regardless of whether the treatment ended after reaching the 1000 trial maximum or by attaining the stability criterion. Forced trials In addition to free choice trials, 20% of all trials were forced or no-choice trials. In these trials, the computer illuminated only one information or no-information color (either blue or yellow) and one choice color (either red or green). Thus, the subjects were sometimes forced to choose with
information, sometimes without, and sometimes forced to choose the signaled color, sometimes not. Forced trials were otherwise exactly like normal trials for the prevailing treatment (i.e. with the appropriate p, q, and c values in effect). In a block of 40 trials, the first eight were forced trials half forced information trials and half forced noinformation trials and the final 32 were free choice, datarecording trials. This procedure ensured that subjects had recent experience with all possible outcomes. Dependent measure and analyses As explained above our experiment followed a withinsubjects (or repeated measures) design (meaning that we tested each individual blue jay subject in all 27 experimental treatments). We used the repeated measures routines of the Statistica software package to analyze the resulting data. These routines follow the procedures for within-subjects ANOVA outlined by Myers and Well (1995). Readers who are unfamiliar with within-subjects designs may be surprised at the small number of subjects used here; as Myers and Well explain: ‘‘Repeated measures designs make efficient use of subjects, both in the sense of using fewer subjects than between-subjects designs, and in the sense of having less error variance’’ (Myers and Well 1995, p. 236). Since our procedures offered subjects the option to view or ignore the signal, we have a direct measure of signal use that we call P(view info). This is, of course, the relative frequency with which subjects choose the ‘information’ option. Figures and non-parametric analyses use the raw proportions, but we use arcsinesquare-root transformations in our analyses of variance (Zar 1999). Due to a calculation error, bird 78 completed one
treatment (p 0.75, q 0.75, c 30 s) with fewer than the minimum number of trials (i.e. fewer than 300); we excluded these data from our analysis, so that one ‘cell’ of our otherwise complete factorial design is missing. Deriving predictions To identify the experimental conditions in which our model predicts signal following, we followed classical foraging theory (Stephens and Krebs 1986) in assuming that our subjects would follow signals if this increased their long term rate of food intake. For our experimental conditions, the calculated intake rate for a signal follower is: q/(tc) where c is the experimental delay associated with choosing to view the signal, and t is the time between choice presentations (80 s in our experiment). The calculated intake rate for averaging is p/t.
Results Overview Figure 3 gives an overview of our results. The figure shows the relative frequency with which subjects chose to view the signal [denoted by P(view info)] in each of our 27 treatments. As the figure shows, all three variables (signal reliability, environmental certainty, and the cost of information) influence the subjects’ signal use broadly as expected. Specifically, we see: 1) that increasing signal cost decreases signal use as we expected; 2) increasing signal reliability tends to increase signal use, although our subjects seldom used costly signals even when they were reliable;
Figure 3. Interaction between environmental certainty, signal reliability, and cost. P(view info) decreases with increasing cost and environmental certainty, but increases as signal reliability increases. Lines show the mean of the seven subjects with 95% confidence intervals.
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and 3) environmental certainty also decreases signal use. As predicted we observed the highest levels of signal use in our most uncertain condition (p 0.5). A repeated-measures ANOVA supports these interpretations. The ANOVA reveals a significant three-way interaction (F8,40 2.2, p 0.048), supporting the observation that our three experimental variables interact to determine signal use. Recall that if the three variables influenced signal use via simple additive (main) effects, then Fig. 3 would show a pattern of parallel lines. Instead, in the two higher certainty cases (panel B and C), we see curves that converge toward no signal use as cost increases. Presumably, this curvature derives from a floor effect. In our most uncertain situation (panel A, p 0.5), we find that signal use decreases with cost, but we do not see a striking convergence toward zero.
reasonable agreement between predictions and observations. Typically, we observed that signal use increases with reliability as we predict. However, we do see a fairly striking disagreement between predictions and observations in conditions of low environmental certainty and higher signal cost (the two panels at the bottom of the first column). Here, we see that subjects chose to act without the signal even in situations where they could have achieved a higher rate of gain by using the signal. This agrees (qualitatively) with our earlier results (McLinn and Stephens 2006) in suggesting a bias favoring information acquired via prior experience over signal use. Indeed, we note that overall observations are somewhat lower than predictions.
Discussion Predictions versus observations Figure 4 shows a comparison of observations and predictions for P(view info). Observations agree with predictions reasonably well. For example, in the four cases of highest cost and highest environmental certainty (the four panels in the lower right of Fig. 4), we predict that subjects will choose to not to view the signal and that is what we observe. Our ‘no cost’ treatments (c 0, the top row of Fig. 4) should promote signal use, and here again we see a
Our results show that key economic variables influence learned signal use. Specifically, we show that environmental uncertainty (our treatment parameter p) and signal reliability (our treatment variable q) influence the cost that animals will pay to view a signal. Moreover, at the extremes (that is, in the situations that most strongly promote or discourage signal use) our data agree well with our model’s predictions. In intermediate situations, however, subjects show a bias against signal use: relying on patterns of
Figure 4. Results versus predictions. Each panel shows the predicted frequency of ‘viewing the signal’ [denoted by P(view info) on the y-axis] as a function of signal reliability. The three rows show data from the treatments where we varied the cost of signal use. The top row show the no cost treatment, the middle row shows the intermediate cost treatment (30 s delay to signal) and the bottom row shows the high cost treatment (60 s delay to signal). Similarly the three columns show the different environmental certainty treatments. The first column shows the least certain situation (p 0.5), the middle column shows the intermediate treatment (p 0.75) and the third (on the far right) shows the most certain situation. The text discusses the patterns of agreement and disagreement that this figure reveals.
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environmental certainty (e.g. always choosing the green key) even when a signal could, in theory, improve their performance. Our results are significant for two reasons. First, they emphasize the role of environmental uncertainty in animal signal use. This is important because game theoretical models of signal use emphasize ‘the problem of reliability’ and virtually ignore the fundamental role of uncertainty in the economics of signal use (Maynard Smith and Harper 2003, Searcy and Nowicki 2005). Second, our study represents the first attempt to experimentally assess the value that animals place on signals. It offers direct experimental evidence of how costs affect animal signal use. While students of animal information processing acknowledge the central role of costs in information use (Dall et al. 2005), identifying and assessing these costs can be quite difficult. Our experimental approach can, of course, only address a limited set of questions about animal signal use; yet it represents a new empirical tool in the study of animal signaling.
recognize the songs of conspecifics and neighbors (Catchpole and Slater 2008). Similarly, the classical work of Cheney and Seyfarth (1988) shows that vervet monkeys can learn that some individuals signal less reliably than others. More broadly, we have a great many fascinating and even exotic examples of how experience influences the behavior of receivers. These examples range from loser effects in animal conflicts (Rutte et al. 2006) to copying behavior in female mate preferences (Dugatkin 1992). Yet we have not modeled our experiment on any particular problem in the natural history of blue jays. Instead, we have exploited the behavioral flexibility of these small corvids to test a general economic model of signal use. So, while we certainly do not think that jays choose between colored lights in nature, we do feel that our situation caricatures many information use problems in blue jay natural history. For example, a jay facing a novel model-mimic system must somehow adjust its choice behavior to the relative frequency of models (uncertainty) and the reliability with which prey colors indicate quality (signal reliability).
Learned versus evolved signal use? What is a signal? Our model makes an economic claim about when signal use will evolve, yet our experiments have asked the question: When will an animal learn to use signals? At one level, this is a matter of simple practicality, we can study learned signal use in the course of a few months, but an analogous experiment that strictly studied the evolution of signal use would require many generations. As described in the methods, we used a stability criterion to assess the learned response to our experimental signal. That is, we observed each subject’s behavior after we changed treatment parameters (uncertainty, reliability and signal cost), yet we only report behavior after this behavior has stopped changing. This is an accepted technique to ensure that subjects have adjusted to changed conditions, yet it leaves the question of how learned behavior relates to evolutionary models open. Traditionally, models in behavioral ecology take the view that selection favors outcomes, not mechanisms (Alcock and Sherman 1994), and so they predict the form of behavior in particular conditions (e.g. levels of uncertainty and reliability) but not the mechanisms animals use to achieve this. The behavioral ecology perspective, then, certainly allows learning as a mechanism, even though it does not require it as our experimental approach does. This means, we argue, that it can be hard to interpret negative evidence from an experiment like ours. For example, we feel that the points of agreement between our model and data provide reasonably strong support for our model as we explained above. However, points of disagreement do not clearly reject our evolutionary model. To see this limitation, consider our observation that subjects tended to be biased against signal use in intermediate situations. This may reflect an error in our model, or it could be the consequence of some property of the learning mechanism that is beneficial ‘on average’ but tends to produce sub-optimal behavior in our experimental situation. Notwithstanding these caveats, several studies show that learning plays a role in the behavior of signal receivers. For example, the literature on bird song learning shows not only that songbirds learn how to produce song, but also to
Use of the word ‘signal’ varies widely depending on the author’s field and the type of analysis involved. Within behavioral ecology, we recognize two extremes. At one extreme, any stimulus that can change a receiver’s behavior without directly providing the power of this change may be called a signal (Wiley 1994). This agrees with use of the word signal in psychophysics and engineering (e.g. in the phrases ‘signal detection theory’, or ‘signal-to-noise ratio’) and with how we use signal in everyday English (e.g. ‘traffic signal’). Clearly, the stimuli used in this study qualify as signals under this everyday definition; and obviously this is the definition we have adopted when we use the word ‘signal’ in this paper. On the other hand, some behavioral ecologists see this as too permissive and advocate a definition that would restrict the word signal to biological stimuli that are somehow ‘intended’ to change receiver behavior. Searcy and Nowicki (2005), for example, offer a definition that restricts the word signal to displays that have evolved to change receiver behavior. These authors would use the word ‘cue’ for stimuli that change receiver behavior but have not been selected to do so. So, according to this more restrictive view, the stimuli used in our study are cues and not signals. We make two points about these definitions. First, while it may be useful to recognize the special properties of evolved biotic signals, doing so by claiming that other important stimuli are not signals is probably a mistake and ultimately impractical (because it disagrees with everyday usage and the usage in other fields). It would make more sense to recognize a special class of signals (say biotic, social or strategic signals) when these issues become important. Second, from the perspective of a study on ‘receiver economics’ (like ours), the important question is, does it make a difference? Theoretically, we feel that the answer is clearly no. From a purely economic perspective, reliability is reliability whether the stimulus is biological or abiotic. Yet it is certainly possible that receivers will treat a reliable social stimulus differently from an equally reliable abiotic stimulus; ultimately this is an 261
empirical question. Indeed, we feel that the techniques developed here could be modified to ask this question. In the absence, however, of specific empirical evidence showing (for example) that ‘social reliability’ differs from the ‘abiotic reliability’ studied here, parsimony would seem to demand that we assume that the underlying processes are the same. Similar studies This study adopts the statistical decision theory approach to animal information processing advocated by Dall et al. (2005, see also Stephens 1989, 2007). Statistical decision theory differs from a purely statistical perspective, because it considers the economic consequences of information use. Our experiment replicates the earlier work of McLinn and Stephens (2006), because like that study, it shows that jays adjust their signal use in response to both uncertainty and reliability. However, it extends this result in several ways. First, it measures signal use more directly by allowing subjects to choose between viewing the signal or acting without. Second, it considers the effects of cost on signal use. Finally, this study used a different type of signal. McLinn and Stephens used a ‘color-matching’ signal that was always in the same position (so that a red center light indicated that the red key was correct). The signal in this study indicated the correct choice spatially (the key with a lit LED beside it was correct). While this may seem like a small difference to human observers, it is important to show that the same economic principles control signal use regardless of signal type. As we remarked in the introduction, students of signal evolution especially those who build game theoretical models have long emphasized the problem of signal reliability (Maynard Smith and Harper 2003). The existence of this well-known problem hinges on the assumption that receivers will ultimately ignore unreliable signals. This experiment (together with the earlier paper by McLinn and Stephens 2006) directly tests this claim. In addition, the ideas and data presented extend this basic claim because they develop the idea that reliability and uncertainty interact to determine the value of a signal. We argue, specifically, that reliability per se is not enough to make a signal valuable, and moreover that underlying uncertainty determines the level of reliability required to make a signal valuable. We might infer, for example, that when environmental uncertainty is high, signaling systems can be stable even with partially reliable signals; in contrast when environmental uncertainty is low, even a small reduction in reliability could destabilize a signaling system. We used delay to create a cost of signal use. This is a powerful way to create a cost, because many studies show that animals have strong preferences for immediate food reward (reviewed by Stevens and Stephens 2009). There is, we acknowledge, a mismatch between the method we used to calculate predicted behavior and these experimental results. To make our predictions we assumed that an animal maximizes the rate of food intake, but studies of delayed reward often show that animals prefer more immediate gains even when they could achieve a higher intake rate by choosing a larger more delayed option. This 262
may explain why even our intermediate cost treatment had such a powerful effect on signal use. Limitations Although our model accurately predicted the transition between signal use and averaging in the most extreme conditions, we found that our jays favored averaging in intermediate conditions; especially conditions of intermediate reliability. If this were generally true it would have important implications of studies of animal signaling. We argue however that we need further evidence from other preparations before we can say more than that this happened in our experimental preparation. Specifically, one might hypothesize that this ‘averaging bias’ is a property of learned signal use, because if receivers must learn the consequences of both the averaging options and signal following, they will often have more experience with the simpler average options. An averaging strategy (such as: ‘when in doubt always choose red’) may represent a simple and more easily learned strategy. We varied the cost of signal use with the goal of tracing out a dose-response style relationship between cost and signal use that would show how uncertainty and reliability influence the value of a signal. In retrospect, this was only partially successful, because we observed relatively little difference between our intermediate (30 s delay to signal) and high cost (60 s delay to signal) treatments. This leads us to think manipulating costs over a narrower range may have given more clear-cut results. Future studies This study suggests many questions for further investigation. We mention only two. First, one would obviously like to extend these simple economic ideas to more naturalistic situations. In particular, studies that consider the interaction between uncertainty and signal reliability in signals of mate quality would be quite important. Second, we have assumed that receivers can detect and discriminate signals without error. While one can approximate this situation experimentally, it cannot be true in general. Moreover, issues of detectability and discriminability are surely important to our understanding of issues like signal ‘exaggeration’ and multi-component signaling. The laboratory techniques developed here lend themselves to further study of detectability and discriminability, and our laboratory is actively pursuing these questions. Summary Our experiment demonstrates that uncertainty, reliability and cost interact to determine animal signal use. This is important because although students of signaling acknowledge the importance of these three entities, they have seldom considered the interactions between them experimentally. To explore these interactions, we have adopted techniques from the psychological laboratory. Some students of signaling will undoubtedly object to these techniques as artificial, and we acknowledge that this may
limit the generality of our results. Yet, we find that our experimental subjects respond to our artificial signals in broad agreement with our economic models. In addition, we remark that it will often be quite difficult to manipulate these variables in natural signaling situations. Even in the face of its imperfections, this ‘psychological’ approach offers an important tool for future investigations of receivers and their response to signals. Acknowledgements We thank Matthew Scott, Carmen Silvers, Jean Johnson, and the numerous undergraduate students who helped to complete this research. We thank Aimee Dunlap for reviewing a draft of this manuscript. This project was approved by the Institutional Animal Care and Use Committee at the Univ. of Minnesota (Animal Subjects Code 0301A40421). Funding for CMM was provided by a Rothman Fellowship from the Bell Museum of Natural History, and by the Biological Basis of Behavior Group and the Department of Ecology, Evolution, and Behavior, Univ. of Minnesota. The National Science Foundation supported our research group during the preparation of this study via grants numbered IBN-0235261 and IOS-0727221.
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