2. Ambiguity in MSH’s signaling theory

Before discussing how a particular type of camouflage may be interpreted as a signal, I would like to first address the alleged ambiguity within MSH’s signaling theory, which was initially suggested by Stegmann (Reference Stegmann2005) and later articulated by Scarantino (Reference Scarantino and Ulrich2013). This section shows that Scarantino’s argument lacks sufficient textual support and that any ambiguity in interpreting MSH’s definition of a signal does not support the borderline he intends to draw.

Scarantino (Reference Scarantino and Ulrich2013, 74–75) provides two possible interpretations of MSH’s definition of signals: generalized response interpretation and specialized response interpretation (GRI and SRI, respectively). Revisiting MSH’s definition of signal helps clarify the difference between these two interpretations:

The source of alleged ambiguity lies in how we interpret the “receiver’s response” within this definition, particularly whether the response has evolved for the sender’s behavior (SRI) or need not have evolved for it (GRI).

For illustration, consider a borderline case presented by Scarantino: the anglerfish’s lure. Anglerfish attract and consume their prey using a lure that mimics a worm or a flashlight, a phenomenon known as aggressive mimicry. GRI states that this lure is a signal because, while the prey has not specifically evolved to respond to the anglerfish’s lure, reacting to a worm-like object or light in the ocean generally aids their survival. Conversely, SRI disregards the lure as a signal precisely because the prey’s response has not specifically evolved as a reaction to it. SRI is more stringent than GRI, requiring that the receiver’s response be specifically adapted to the sender’s behavior.

As noted by Scarantino, Stegmann (Reference Stegmann2005) implicitly accepts GRI, while Scott-Phillips (Reference Scott-Phillips2008) appears to endorse SRI. Stegmann (Reference Stegmann2005, 1022) states, “Maynard Smith and Harper (Reference Maynard Smith and Harper2003) demand only that the reaction evolved as a response to some features, but not necessarily to the signal.” In contrast, Scott-Phillips (Reference Scott-Phillips2008, 388) basically accepts MSH’s definition but proposes that “any act or structure that (i) affects the behaviour of other organisms; (ii) evolved because of those effects; and (iii) which is effective because the effect (the response) has evolved to be affected by the act or structure” (emphasis mine). This definition indicates that the receiver’s response must specifically evolve in response to the sender’s behavior.

Highlighting this potential ambiguity, Scarantino advocates for SRI. His reasoning is complex, but we must examine it closely to find the source of his confusion.

He thinks that SRI is supported by MSH’s exclusion of camouflage from signals. Remember that MSH state, “no predator could evolve a behavioural response to something it cannot detect, so camouflage does not meet our definition of a signal” (MSH Reference Maynard Smith and Harper2003, 5). However, Scarantino points out that there is indeed an evolved response in this case: ignoring. This behavior, he argues, has not evolved specifically in response to camouflaged organisms but as a general response to objects irrelevant to survival or reproduction. This lack of specificity is ascribed to “the fact that camouflaged prey cannot be detected, and consequently cannot be responded to as camouflaged prey.” Accordingly, the failure to detect is the reason behind the non-specificity of ignoring camouflaged organisms. Therefore, he suggests that SRI is the favored interpretation. This ambiguity in MSH’s definition of a signal, as well as his support for SRI, is also endorsed by Kalkman (Reference Kalkman2019, 3321), who is perhaps even more explicit, stating that “camouflage is a signal under the generalized response interpretation of MSH’s (Reference Maynard Smith and Harper2003) definition.”

I must confess that I cannot understand why Scarantino is led to this conclusion. He even criticizes MSH’s definition of signals under SRI for excluding the anglerfish’s lure from a signal:

For this remark to make sense, MSH should exclude the anglerfish’s lure from being a signal, but immediately following their exclusion of camouflage, they state:

MSH acknowledge that an anglerfish’s lure satisfies their definition of a signal. Stegmann cites this passage in support of his interpretation (Reference Stegmann2005, 1022). Scarantino seems to believe that GRI regards the anglerfish’s lure and camouflage as signals, while SRI does not, but textual support is lacking for interpreting MSH’s signaling theory in such a way. MSH never suggest SRI nor GRI, which means the alleged ambiguity does not exist. Then, where does Scarantino’s interpretation go wrong?

He is mistaken in thinking that camouflage can be regarded as a signal under GRI and that MSH do not take this route. Camouflage is irrelevant to the alleged potential ambiguity in their definition of signals. MSH disregard camouflage as a signal because “no predator could evolve a behavioural response to something it cannot detect” (MSH Reference Maynard Smith and Harper2003, 5). Even if the distinction between GRI and SRI makes some sense, what MSH mean in this passage is that, regardless of whether the response is specialized or generalized, predators cannot evolve any response to camouflaged prey due to their inability to detect it. This position is incompatible with Scarantino’s interpretation that MSH advocate SRI on the grounds that detecting the targeted object is a prerequisite for SRI and that they exclude camouflage exactly because it does not meet this requirement.

In the next section, I argue that MSH’s signaling theory is internally incoherent rather than ambiguous. Interestingly, Scarantino is partially right: their theory could accommodate camouflage as a signal. He believes that adopting GRI directly entails this result, but, as I have argued, this is not the case. A more careful argument is needed to conclude that camouflage is a signal. In particular, we must show that camouflaged prey or predators can be detected. Showing this requires investigating the notion of detection, which both MSH and Scarantino leave untouched. I argue that, considering both the internal coherence of MSH’s theory and recent research on animal cognition, at least one type of camouflage is detected by other organisms and regarded as a signal.

3. Camouflage as a signal

As a preparation for what follows, I make a necessary classification of camouflage because it encompasses behaviors whose mechanisms and functions differ significantly from one another. For example, biologists who specialize in camouflage have classified it into more than ten types (Merilaita et al. Reference Merilaita, Scott-Samuel and Cuthill2017; Stevens and Merilaita Reference Stevens, Merilaita, Stevens and Merilaita2011). Although I do not intend to address all the types exhaustively, I distinguish among types of camouflage and treat them differently based on their functions and mechanisms. I focus on one specific type of camouflage: masquerade. This behavior has evolved to make part or all of an organism’s body resemble a specific inedible object. An example is the dead leaf butterfly, which makes its wings look like dead leaves. Another category of camouflage, often contrasted with masquerade, is crypsis, a form of camouflage in which an organism evolves a body color or pattern that resembles that of a natural background, such as tree bark or ground surfaces. One of the examples is the Eurasian bittern, which blends its color and pattern into reeds. In what follows, I show that at least masquerade Footnote ² can satisfy MSH’s definition of animal signals.Footnote ³

First, MSH’s argument for excluding camouflage can be construed as follows:

• Premise 1: For all behaviors, if it is a signal, then it is detected.

• Premise 2: Camouflage is a behavior that is not detected.

• Conclusion: Therefore, camouflage is not a signal.

This argument is valid. The conclusion follows deductively by applying universal instantiation to Premise 1 and modus tollens to Premise 1 and Premise 2. However, the validity of an argument does not guarantee the truth of its premises and conclusion. In what follows, I argue that Premise 2 is problematic. More precisely, I contend that the implications derived from the other part of MSH’s signaling theory are incompatible with Premise 2: if they want to remain coherent within their own signaling theory, they should discard Premise 2.

The first point to focus on is how they conceive the emergence of signals:

The concepts of cue and ritualization mentioned here need explanation. First, a cue is defined as “a feature of the world, whether biotic or abiotic, that animals can use as a guide to future action” (MSH Reference Maynard Smith and Harper2003, 15). This definition is somewhat vague, but it suggests that anything in the environment that animals use to gather information can be a cue. For example, leaves can serve as cues for animals that identify them through sight, smell, or touch, as they provide information about the presence of foliage, which guides their future action.

Ritualization is described as “the evolutionary process by which a cue may be converted into a signal” (MSH Reference Maynard Smith and Harper2003, 15). In other words, it is an evolutionary process in which, from a situation where receivers merely use a cue as a source of some information, the sender of the cue begins to emit it to elicit that response from the receiver. A commonly cited example of ritualization is territorial marking by small animals using feces and urine (MSH Reference Maynard Smith and Harper2003, 69). Initially, small animals likely performed this behavior to relieve themselves. Other animals nearby notice the feces or urine and obtain the information that another animal has already been around. Then, they avoid approaching that area. In this stage, the feces or urine are a mere cue from which surrounding animals gain information about the existence of another animal. However, some of the senders of this cue may learn that, by leaving feces or urine, they can avoid encountering other animals and getting injured in territorial fights. Consequently, they begin to defecate or urinate “deliberately” to keep other animals from approaching rather than merely to relieve themselves. The animals on the receiver’s side continue to use the feces or urine as signs indicating another animal’s territory and avoid approaching that area. At this point, the feces or urine can be considered a signal rather than a cue, as the sender’s behavior affects the receiver’s behavior, and the receiver’s response benefits both parties.

Given the above characterizations of cue and ritualization, I argue that MSH should discard Premise 2. Let me first characterize camouflage analogously to Batesian mimicry. Batesian mimics have evolved their appearance by modeling a signal that conveys toxicity to predators. Likewise, camouflaged species can be said to have evolved their appearance by modeling cues. For example, the dead leaf butterfly can be considered to have evolved its appearance by modeling dead leaves. Given this, although MSH regard camouflage as a behavior that is not detected, it should be regarded as a behavior that is detected if cues are detected. I show that for MSH’s theory to be coherent, it must say that cues are detected.

The first reason for this is simple: if organisms could not detect cues, they could not sensibly use them “as a guide to further action.” A more convincing reason comes from their characterization of ritualization. Ritualization necessitates that a receiver must exploit cues prior to the emergence of a signal. In addition, the exploitation of a cue should be equal to giving “a behavioral response” to it because MSH require that for a behavior to become a signal, some behavioral response to it must exist. Therefore, their theory assumes that “a behavioral response” by the receiver precedes the emergence of a signal. Let me formulate this as the Principle of Signal Emergence:

Now, let us recall the passage where MSH argue that camouflage cannot be a signal. Their justification relies on the point that animal signals require a behavioral response from the receiver. Combined with this, Premise 1 can be considered the combination of the following two premises:

• Premise 1-1: For all behaviors, if it is a signal, there exists a behavioral response from the receiver to it.

• Premise 1-2: For all behaviors, if there exists a behavioral response from the receiver to it, it is detected.

MSH must accept the Principle of Signal Emergence, Premise 1-1, and Premise 1-2 if they want their theory to remain coherent. However, when we combine Premise 1-2 with the Principle of Signal Emergence, it follows that cues are detected. Consequently, based on their own signaling theory, they must accept that cues are detected.

With this logical requirement established, justifying my original claim—MSH must admit that camouflage is a behavior that is detected—is straightforward. Because camouflage is a behavior modeling a cue, if a cue is detected, camouflage is also detected. This conclusion evidently contradicts Premise 2 of MSH’s original argument. If they accept their own signaling theory, holding that camouflage is a behavior that avoids detection leads to a contradiction.

This conclusion aligns well with contemporary biology. MSH seem to assume that all types of camouflage are behaviors to avoid detection, but the leading researchers on camouflage say the following about masquerade:

Skelhorn et al. (Reference Skelhorn, Rowland and Ruxton2010a) distinguish between detection and classification (categorization) in animal perceptual processes. Based on this distinction, masquerade is not characterized as a behavior to avoid detection but to cause misclassification after detection. The dead leaf butterfly’s appearance has not evolved to avoid detection by predators but to induce misclassification as a dead leaf after being detected. MSH exclude camouflage from signals by broadly categorizing it as a behavior that is not detected, but the recent research on masquerade disconfirms the validity of their argument.Footnote ⁴

I have shown that excluding camouflage from the category of signals based on the concept of detection is ill-grounded, but MSH can still defend their position. They might insist that, even though camouflage is a behavior that is detected, it does not elicit a behavioral response from the receiver, so it still is not a signal. This contention may sound reasonable, but here I have a further counterargument. At this stage, ironically, I agree with Scarantino’s remark: ignoring should be regarded as a type of evolved behavioral response, so camouflage satisfies MSH’s definition of animal signals.

Skelhorn et al. (Reference Skelhorn, Rowland and Ruxton2010b) support this view. They conducted an experiment using domestic chickens (Gallus gallus domesticus) and twig-resembling caterpillars (Opisthograptis luteolata and hawthorn Crataegus spp.). Chickens are predators, and caterpillars are a masquerade species. In the experiment, Skelhorn et al. (Reference Skelhorn, Rowland and Ruxton2010b) provided one of the groups of chickens with twigs, which served as models for the twig-resembling caterpillars. They investigated whether prior experience with these twigs would affect the time it takes for chickens to attack the twig-resembling caterpillars. The result is striking: chickens that were presented with twigs prior to being given twig-resembling caterpillars showed significantly longer reaction times compared to the control group of chickens that were not exposed to the twigs. The chickens with prior experience with the model “took longer to attack both species of twig-resembling caterpillars” than other control groups (51). Similar results are reported by Skelhorn and Ruxton (Reference Skelhorn and Ruxton2011).

The results of this experiment indicate that ignoring can be considered a type of adaptive behavior acquired through evolution or learning.Footnote ⁵ The chickens in their experiment learned to treat twigs as cues to be ignored, resulting in longer reaction times when they were subsequently presented with the twig-resembling caterpillars. They initially perceived the caterpillars as inedible twigs. Indeed, organisms that detect inedible twigs and attempt to attack them every time would likely suffer serious costs. Most organisms probably adapt their behavior to ignore natural objects that have little influence on their survival and reproduction whenever they detect them. Thus, ignoring can be considered a “behavioral response.”

We can now reformulate masquerade so that it meets the definition of animal signals as follows:Footnote ⁶ masquerade is a behavior or structure that changes the receiver’s behavior so that the receiver ignores it. It has evolved because of this effect and is effective because the receiver’s behavior has also evolved to ignore it. Therefore, at least one type of camouflage—masquerade—satisfies MSH’s definition of animal signals.Footnote ⁷

One concern about my argument might be raised: what MSH probably have in mind is crypsis, not masquerade, when they claim that camouflage is not detected. They might therefore concede my argument and simply insist that crypsis is not a signal because it is not detected, thereby preserving their proposal for the central case of camouflage.Footnote ⁸ This point is correct, but my main claim still stands: MSH’s exclusion of camouflage based on the notion of detection cannot be generalized over camouflage as a whole. Moreover, even in the case of crypsis, it may be debatable whether all forms of crypsis merely avoid detection. Take, for example, disruptive coloration. It is typically considered a form of crypsis (Merilaita et al. Reference Merilaita, Scott-Samuel and Cuthill2017; Stevens and Merilaita Reference Stevens, Merilaita, Stevens and Merilaita2011). It is often described as enhancing “false edges,” which exploit predators’ visual processing and prevent them from distinguishing the cryptic prey from its background (Stevens and Cuthill Reference Stevens and Cuthill2006; Stevens and Merilaita Reference Stevens and Merilaita2009). Although false edges are used to prevent the detection of the prey’s true body outline, these features themselves must be detected for disruptive coloration to be effective. Therefore, it is misleading to claim that disruptively colored organisms are simply undetected. That’s why Stevens and Merilaita (Reference Stevens and Merilaita2009, 484) carefully characterize disruptive coloration as “a set of markings that creates the appearance of false edges and boundaries and hinders the detection or recognition of an object’s, or part of an object’s, true outline and shape” (emphasis mine). Even some forms of crypsis can work after detection.Footnote ⁹

The argument so far has significant implications:Footnote ¹⁰ MSH’s signaling theory is highly influential in this field, and not only has their definition of signals or its variants been accepted by other theorists, but many working biologists implicitly or explicitly adopt it in their research. Considering camouflage as a signal within MSH’s framework prompts a reevaluation of behaviors that qualify as signals, reshaping the entire field of signaling.Footnote ¹¹

I have argued that camouflage fits well with the standard theoretical framework of animal communication research. Yet, one might still object: even if camouflage qualifies as a signal, it differs from typical signals because it does not transmit information; therefore, it is not a signal. I share the intuition behind this objection, as I view camouflage as a distinct type of signal. Furthermore, as pointed out by Stegmann (Reference Stegmann2005), MSH do not provide any account of the content of animal signals; so long as we adhere to their framework, we would have to shoehorn typical signals, such as alarm calls, and camouflage into a single category.

In the next section, I introduce and articulate two distinct types of signals—information-transmitting signals and information-masking signals—using information-theoretic tools developed by Skyrms (Reference Skyrms2010), and I show how they apply to typical signals and camouflage, respectively. This provides a natural way to accommodate camouflage within existing frameworks in animal signaling, which mitigates the initial reluctance to classify camouflage as a type of signal.

4 Information-masking

Camouflage does not transmit information, so it is not a signal. This idea is intuitive and may be reinforced by a theoretical consideration. In the process of ritualization, amplifying the conspicuousness of a cue is regarded as a fundamental condition for transforming it into a signal (MSH Reference Maynard Smith and Harper2003; Wiley Reference Wiley, Tim and Peter1983). As the conspicuousness of a behavior increases, information is transmitted more effectively and precisely. Conversely, successful camouflage requires decreasing conspicuousness. Camouflage has the opposite evolutionary trajectory to typical signals.

These considerations naturally imply that, whereas a typical signal transmits information by increasing conspicuousness, camouflage masks information by decreasing it. I propose incorporating the notion of information-masking into the existing framework in the domain of animal signaling and generalizing camouflage as a paradigm case of it. In fact, transmitting information and masking information are two sides of the same coin. I articulate them by relying upon Skyrms’ information-theoretic approach.

Skyrms (Reference Skyrms2010) famously introduces the notions of information quantity and information content of a signal. A simple example illustrates his core idea: a weather forecast. People in Los Angeles would think that a signal predicting snow tomorrow conveys much more information than one predicting sunny weather, since snow is much less common there. Skyrms’ central idea is that the quantity of information in a signal depends on how much it shifts the probabilities assigned to the relevant states—the larger the shift, the greater the quantity of information. In Los Angeles, the signal predicting snow shifts the probability distribution much more than the one predicting sunny weather, which is why people think that the former contains more information.

The Kullback–Leibler divergence provides a standard way to measure this shift in probability distribution, and Skyrms defines the information quantity of a signal as the Kullback–Leibler divergence between the probability distributions over the relevant states before and after the signal is sent. The information quantity of a signal, I(S), is defined as follows:

${\rm{I}}({\rm{S}}) = \sum\limits_i {\rm{P}} ({\rm{stat}}{{\rm{e}}_i}\mid {\rm{S}})\log \left( {{{{\rm{P}}({\rm{stat}}{{\rm{e}}_i}\mid {\rm{S}})} \over {{\rm{P}}({\rm{stat}}{{\rm{e}}_i})}}} \right).$

This definition captures the intuition: the greater the difference between the two distributions, P(state_i) and P(state_i | S), the larger the information quantity.

Skyrms’ further achievement is to define the content, or “meaning,” of a signal. He defines information content as a vector whose components are the log-ratios of the probabilities of each relevant state before and after the signal is sent:

$\left\langle {\log \left( {{{{\rm{P}}({\rm{stat}}{{\rm{e}}_1}\mid {\rm{S}})} \over {{\rm{P}}({\rm{stat}}{{\rm{e}}_1})}}} \right),{\mkern 1mu} \log \left( {{{{\rm{P}}({\rm{stat}}{{\rm{e}}_2}\mid {\rm{S}})} \over {{\rm{P}}({\rm{stat}}{{\rm{e}}_2})}}} \right),{\mkern 1mu} \log \left( {{{{\rm{P}}({\rm{stat}}{{\rm{e}}_3}\mid {\rm{S}})} \over {{\rm{P}}({\rm{stat}}{{\rm{e}}_3})}}} \right),{\mkern 1mu} \ldots } \right\rangle .$

Let us consider how this notion of information content applies to typical signals and camouflage.Footnote ¹² To set the stage, I first introduce the notion of noise. As discussed above, whereas typical signals enhance conspicuousness through ritualization, camouflage operates in the opposite direction. This contrast can be reframed in terms of the signal-to-noise ratio, which compares useful information with irrelevant or misleading information. In this context, the “signal” refers to the object of interest to the receiver, whereas “noise” refers to everything else (Cuthill Reference Cuthill2019, 76).Footnote ¹³ In actual communicative contexts, both senders and receivers are embedded in noisy environments. Typical signals must overcome this background noise in order to reach the receiver and convey information, while receivers must discriminate relevant signals from irrelevant background information. In such situations, typical signals evolve to increase the signal-to-noise ratio, thereby improving detectability (Wiley Reference Wiley2015, 104–6). By contrast, successful camouflage operates in the opposite direction: it reduces the signal-to-noise ratio in order to avoid detection or recognition (Merilaita et al. Reference Merilaita, Scott-Samuel and Cuthill2017; Cuthill Reference Cuthill2019). For example, background matching conceals the cues indicating an organism’s identity by blending its appearance with environmental noise, whereas masquerade causes the organism to be perceived as another element of the noise, such as a leaf or a twig.

By applying this consideration to Skyrms’ apparatus, we can see the difference in information content between typical signals and camouflage. What is crucial here is that we must consider a game that includes a state corresponding to noise. In the Skyrmsian setting, I take noise to be a state that is irrelevant to the agent’s interest under consideration. Let us first consider a typical case of signaling: vervet monkeys’ alarm calls. These monkeys emit three types of alarm calls, each indicating the presence of a specific predator: eagle, snake, and leopard. Each signal corresponding to one of these predator states is meaningful to the receiver, while the no-predator state is taken to be noise. On this basis, we can posit four relevant states: no predator present (noise), eagle present, snake present, and leopard present, with the following prior distribution:

• • no predator present (noise) = 0.85,

• • eagle present = 0.05,

• • snake present = 0.05,

• • leopard present = 0.05.

Let us denote this distribution as P(state_i) = [0.85, 0.05, 0.05, 0.05]. Assume further that each alarm call correctly indicates the approach of the predator with probability 0.70; with probability 0.20, the call is a false alarm, corresponding to the no-predator state (noise), and the other two states remain unchanged. Under these assumptions, consider the information content of an eagle alarm. It shifts the probability distribution from P(state_i) = [0.85, 0.05, 0.05, 0.05] to P(state_i | S) = [0.20, 0.70, 0.05, 0.05], so its information content is

$\langle -2.0874\ldots,\ 3.8073\ldots,\ 0,\ 0 \rangle.$

The component corresponding to “eagle present” takes the highest value because the alarm call increases the probability of the eagle state while decreasing the probability of the noise state. In addition, this “eagle present” component corresponds to the true state. We can interpret this as indicating that the eagle alarm call correctly conveys information about the presence of an eagle to other monkeys.Footnote ¹⁴ I call this type of signal an information-transmitting signal.

We can apply the same apparatus to camouflage, but what occurs here is precisely the opposite of what occurs in information transmission. Suppose that a hungry predator is searching for food and faces three relevant states: inedible objects, edible prey, and toxic species, with prior probabilities of 0.95, 0.04, and 0.01, respectively. We can think of these proportions as representing the distribution of items that the predator would encounter through random sampling of her visual field. Almost all of these items are inedible objects that are irrelevant to her current interest, while a small proportion are edible prey that she is searching for. She might also occasionally encounter a toxic organism. In this setting, the inedible-object state is taken to be noise because it is irrelevant to her current interest and would simply be ignored.Footnote ¹⁵ These probabilities constitute the prior distribution.

Let us see how camouflage changes this. We should examine the situation in which some of the prey have evolved a phenotype resembling inedible objects—that is, some of the prey become noise from the predator’s perspective.Footnote ¹⁶ Suppose that 10% of prey have evolved such an appearance. Then 95.4% of items in the predator’s visual field look inedible (and hence uninteresting), while 3.6% still look like edible prey. Upon observing an inedible-object appearance, the probability distribution shifts from P(state_i) = [0.95, 0.04, 0.01] to P(state_i | S) = [0.9958 …, 0.0041…, 0]. What we are particularly interested in is how this affects log P(prey present | inedible object appearance)/P(prey present), because camouflage is supposed to mask information about the identity of camouflaged organisms by making them part of the noise, and the information content of the inedible-object appearance should reflect this effect. Since P(prey present | inedible object appearance) = 0.0041 … and P(prey present) = 0.04 in the current setting, its information content is

$\langle 0.0679\ldots,\ -3.2539\ldots,\ -\infty \rangle.$

The prey-present component takes a negative value, and this component corresponds to the true state. Unlike straightforward cases of information transmission, I interpret this as masking, rather than transmitting, information about the corresponding state. In this case, camouflage masks information about the presence of prey, that is, about the identity of the camouflaged organism. This is because, relative to the prior probability, the camouflaged appearance decreases the probability that prey is present while slightly increasing the probability of the noise state. What occurs in camouflage is therefore the opposite of what occurs in a typical case of signaling.Footnote ¹⁷ I call this type of signal information-masking signals, and camouflage is a typical example.

One might wonder why camouflage decreases the probability that prey is present. For example, even if a dead leaf butterfly looks like a dead leaf, the presence of a dead leaf might seem to increase (rather than decrease) the probability of prey being present, since some leaves are actually butterflies.Footnote ¹⁸ Recall that the distribution assumed here concerns the proportion of items a predator would encounter under random sampling from her visual field. Although it is true that some prey are hidden among inedible objects, the proportion of prey among inedible-looking items must be lower than the overall proportion of prey the predator would encounter under random sampling. In the present setting, after camouflage has evolved, the former is 0.004/0.954 = 0.0041 …, whereas the latter is 0.036; the former is much lower than the latter. Otherwise, camouflage would not be effective: the predator could then find food more frequently by searching only among inedible objects than by randomly searching her entire visual field, so camouflaged organisms would be attacked more often than uncamouflaged ones. (In reality, whether the predator does better by searching only among inedible objects also depends on the costs of attacking inedible objects, the benefits of obtaining food, and various other factors.)

Note that the two notions that I have introduced—information-transmitting and information-masking signals—are relative to the settings considered in a given context. As Skyrms (Reference Skyrms2010, 40) points out, information content is itself game-relative. This in turn suggests that camouflage could not count as an information-masking signal in a different model, since different state partitions may be adopted in different models, which may allow different prior distributions and their different shifts.Footnote ¹⁹ One might think this game-relativity undermines my proposal; however, I do not regard this as a serious issue. Here, I follow what Artiga (Reference Artiga2020) calls the “modest view.”Footnote ²⁰ My aim is to show that, within a suitably specified model, we can articulate a layer of information masking as well as information transmitting. In the present modeling, we can show that camouflage is a special type of signal, as opposed to the typical case of information transmission, and then explain and understand why camouflaged organisms tend to avoid attack by their predators: camouflaging masks information about the prey’s presence from the predator, which is reflected in the negative value in its information content. Skyrms’ notion of information content is useful to show that, from a certain perspective, we can identify what I call information masking, and camouflage is a typical case.

Given the argument so far, let me formulate the concepts of information-transmitting and information-masking signals. In a given game that includes a noise state, a signal is an information-transmitting signal if the component corresponding to the true state in its information content takes the highest positive value, while the noise component takes a negative value; a signal is an information-masking signal if the component corresponding to the true state takes a negative value, while the noise component takes a positive value. Although researchers in animal signaling have largely focused on information-transmitting signals, I believe that information-masking signals also warrant consideration. Both types of signals commonly arise in predator–prey interactions. Natural selection equips organisms with a variety of survival tactics. On the prey’s side, strategies are not limited to alarm calls or aposematism; another option is to mask identity by resembling abundant or insignificant objects to predators. Predators, too, may mask their identity in order to hunt effectively. Exploring information-masking signals can broaden and deepen our understanding of how natural selection shapes information flow in nature.

5. Information masking, misinformation, and deception

In this section, I compare the concept of information masking signals with the two related concepts, misinformation and deception. Although recent work has refined these concepts in several ways (Birch Reference Birch2019; Fallis and Lewis Reference Fallis and Lewis2019, Reference Fallis and Lewis2021; Martínez Reference Martínez2019), Skyrms’ information- and game-theoretic framework remains a useful starting point for the present discussion. According to Skyrms, a signal is misinformative when “[…] it moves the probability of a state in the wrong direction—either by diminishing the probability of the state in which it is sent, or raising the probability of a state other than the one in which it is sent” (Skyrms Reference Skyrms2010, 80). A misinformative signal counts as deceptive if “it is systematically sent to the benefit of the sender and the detriment of the receiver” (Skyrms Reference Skyrms2010, 75). The precise meaning of “systematically” requires further clarification, but I will take it to mean that the signal is used as part of a recurring pattern, rather than as a one-off mistake or an accidental failure of communication.

Given this definition, one might worry that information masking simply collapses into misinformation, or even into deception. This worry is understandable. My analysis of camouflage in the previous section assumes that camouflage reduces the probability of the true state (prey present) while slightly increasing the probability of the false noise state. Indeed, several philosophers have treated camouflage as a form of deception (Artiga and Paternotte Reference Artiga and Paternotte2018, Reference Artiga and Paternotte2024; Krstić Reference Krstić2025; Sober Reference Sober1994), so it may not be surprising that camouflage satisfies Skyrms’ definition of misinformation and even deception. However, information-masking signals, as I define them, are importantly different from paradigmatic cases of deceptive signaling. Clarifying this difference is the aim of the remainder of this section. Once again, Skyrms’ notion of information content will be helpful in drawing the distinction.

Consider Batesian mimics as a paradigmatic example of a deceptive signal (MSH Reference Maynard Smith and Harper2003; Sober Reference Sober1994). The information content of this behavior can be analyzed using the same partition as in the previous section. Suppose a hungry predator faces three distinct states: inedible objects, edible prey, and toxic species (model species), with prior probabilities of 0.95, 0.04, and 0.01, respectively. Now, assume that 10% of the prey population evolves to display the appearance of a toxic species. This toxic appearance, taken as a signal, shifts the prior probability distribution P(state_i) = [0.95, 0.04, 0.01] to the posterior P(state_i | S) = [0, 0.2857…, 0.7142…]. Because this signal increases the probability of the false state (toxic species present), Batesian mimics satisfy Skyrms’ definition of misinformation.

It is crucial, however, to recognize that the way in which Batesian mimics satisfy the definition of misinformation is different from the case of camouflage: whereas camouflage works mainly by decreasing the probability of the true state (prey present) by becoming noise, Batesian mimics directly increase the probability of a specific false state (toxic species). Although Skyrms discusses both cases under the same category of misinformation, this difference is reflected in the information content. In the scenario described above, the information content of Batesian mimics is

$\langle -\infty,\ 2.8365\ldots,\ 6.1584\ldots \rangle.$

Here, the component corresponding to the true state takes a positive value, while the noise component takes − ∞, which indicates that Batesian mimicry is an information-transmitting signal. The difference from standard information transmission is that the component with the highest positive value corresponds to a false state (toxic-species state), rather than to the true state. In this regard, Batesian mimicry is, as it were, a misinformation-transmitting signal, as opposed to an information-masking signal.

Recent discussions of deception also tend to draw a similar distinction. It is often argued, on the basis of MSH’s signaling theory, that although camouflage is not a signal, it is nevertheless a form of deception. Deception, therefore, does not necessarily involve signaling (Artiga and Peternotte Reference Artiga and Paternotte2018, Reference Artiga and Paternotte2024; Krstić Reference Krstić2025). The main differences between these previous studies and the approach developed in this paper are as follows. First, I argue that at least one type of camouflage, namely masquerade, qualifies as a signal according to MSH’s definition. Second, I define information-masking signals in terms of Skyrmsian content and show that the misinformativeness produced by camouflage can be quantitatively distinguished from that of typical deceptive signals.

One might raise the following counterexample.Footnote ²¹ Consider Batesian mimicry in the two-partition model: suppose that a predator faces an environment consisting of 80% non-toxic prey and 20% toxic animals, so that the prior distribution is [0.8, 0.2]. Now suppose that 5% of the non-toxic prey evolve toxic-looking features. The toxic appearance of these non-toxic prey shifts the probability distribution from [0.8, 0.2] to [0.1666…, 0.8333…]. Its information content is then

$\langle -2.26\ldots,\ 2.06\ldots \rangle.$

If we take the toxic-species state to be noise in this setting, it may appear that, since the component corresponding to the true state takes a negative value while the noise component takes a positive value, my account predicts that Batesian mimicry counts as an information-masking signal. This might seem counterintuitive, and one might therefore think that my definition of information masking is problematic.

I do not think so, however. First, this example adopts a different partition from the one used in my analysis of Batesian mimicry. It is unclear what situation this partition is intended to represent and whether the model includes a state that can be regarded as noise, but it can no longer be regarded as a model of random sampling from the predator’s visual field, since it is implausible that 80% of the visual field is occupied by palatable prey and 20% by toxic organisms. Second, if this partition does model some real-world situation and the state corresponding to toxic species can reasonably be regarded as noise in that setting, then I think we can accept the consequence that Batesian mimicry is an information-masking signal in this setting. After all, there is a sense in which Batesian mimics mask their identity by mimicking toxic species. I see no principled reason to reject this result. As described above, I adopt a modest view: different partitions capture different aspects of the world. This example reveals that Batesian mimicry has not only an information-transmitting aspect but also an information-masking aspect.

Turning to a broader issue, it is helpful to consider potential new research directions opened up by the concept of information masking, both theoretical and empirical. On the theoretical side, Bergstrom et al. (Reference Bergstrom, Huttegger and Zollman2020) provide important prior work. They define information-revealing moves and information-concealing moves in signaling games (a type of extensive-form game) using counterfactuals. Comparing their approach with mine may offer new insights into the nature of signaling.Footnote ²²

An important empirical direction is to examine additional instances of information-masking signals in nature in order to make the category of information masking more substantive. Jamming may provide one such example. Many species employ jamming in competitive situations involving food or mates (Corcoran and Conner Reference Corcoran and Conner2014; Legendre et al. Reference Legendre, Marting and Cocroft2012). Consider the treehopper Tylopelta gibbera (Legendre et al. Reference Legendre, Marting and Cocroft2012). During courtship, males send advertisement signals by vibrating the plant stem, and females respond. Through repeated interactions, the male and female locate each other using these vibrations. However, when multiple males compete for the same female, each produces a “masking signal” that overlaps with another male’s advertisement signal, significantly reducing the female’s response rate. This is why such jamming signals are called “masking signals.” An important difference from camouflage, as Green (Reference Green, Capone, Carapezza and Piparo2019, 220) notes, is that while camouflage masks information about the organism itself, masking signals mask information about another organism. Analyzing both camouflage and jamming through a common lens may reveal new aspects of information flow in communication.