Animals must overcome a range of environmental and ecological challenges to survive and reproduce, with group-living species having to overcome additional social challenges to maximize fitness. Communicative signals can be used to navigate a number of different social situations and may need to become more elaborate as social complexity increases. The social complexity hypothesis for communicative complexity encapsulates this idea, proposing that animal societies with more complex social systems require more complex communication systems (Freeberg et al., 2012).

The social complexity hypothesis has become a topical issue in recent years, with questions regarding the definitions, measurement, and selective pressures driving both social and communicative complexity (Peckre et al., 2019; Raviv et al., 2022). Social complexity as experienced by group members can be affected by the level of differentiation of social relationships, where complexity increases as social relationships become more differentiated (Bergman and Beehner, 2015; Aureli et al., 2022). In a socially complex society, individuals interact frequently with each other in diverse ways and in many different contexts (Freeberg et al., 2012). If the types of interactions that individuals have is constrained, for example, by dominance or kinship, then social complexity decreases (Freeberg et al., 2012). Social complexity is also affected by the predictability or consistency of social interactions (Aureli et al., 2022; Aureli and Schino, 2019). When the behavior of social partners is unpredictable, such as when the dominance hierarchy is unstable, individuals likely perceive the social environment as more complex (Aureli and Schino, 2019). These operational definitions of social complexity are valuable to advance the study of social complexity but are not easy to quantify with a single measure (Kappeler, 2019).

Similarly, communicative complexity is also difficult to quantify. Many studies have used the number of signaling units as a measure of communicative complexity (Peckre et al., 2019). While a useful measure, it is not always apparent what a signaling unit is. For example, calls are sometimes graded on a continuous scale without a clear separation between different call types (Keenan et al., 2013). Fewer studies have investigated the complexity of non-vocal communication (Freeberg et al., 2012; Peckre et al., 2019), but similar issues exist. One previous study quantified the repertoire of facial behavior in macaques by the number of discrete facial expressions that a species displays and found that it was positively correlated with conciliatory tendency and counter-aggression across species (Dobson, 2012). However, classifying facial expressions into discrete categories (e.g., bared-teeth display) does not capture the full range of expressiveness and meanings that the face can convey. For example, subtle morphological variations in bared-teeth displays are associated with different outcomes of social interactions (e.g., affiliation versus submission) in crested macaques (Macaca nigra) (Clark et al., 2020). A better approach is to quantify facial behavior at the level of individual facial muscle movements (Waller et al., 2020), which can be done using the Facial Action Coding System (FACS) (Ekman et al., 2002). In FACS, visible muscle contractions in the face are called Action Units and allow for a detailed and objective description of facial behavior (Waller et al., 2020; Ekman et al., 2002). Indeed, facial mobility, as defined by the number of Action Units that a species has, is positively correlated with group size across non-human primates (Dobson, 2009a). However, isolated muscle movements still do not account for the full diversity of facial behavior because facial muscles often contract simultaneously to produce a large variety of distinct facial expressions.

One promising avenue to approximate complexity in living organisms is to quantify the uncertainty or predictability of a system (Rebout et al., 2021; Sambrook and Whiten, 1997), which are general properties of complex systems (McDaniel and Driebe, 2005; Schuster, 2016). Shannon’s information entropy (Shannon, 1948) is a measure of uncertainty that can be applied to animal communication. Conceptually, entropy measures the potential amount of information that a communication system holds, rather than what is actually communicated (Shannon, 1948; Adami, 2002). Entropy increases along two dimensions: (1) with increasing diversity of signals and (2) as the relative frequency of signal use becomes more balanced. For example, a system with three calls can hold more information than a system with one call and thus would have higher entropy. Likewise, a system with three calls used with equal frequency will have a higher entropy than another system that expresses one call more frequently than the two others. Uncertainty increases with entropy because each communicative event has the potential to derive from a greater number of units. The relative entropy, or uncertainty, of different systems can be compared by calculating the ratio between the observed and maximum entropy of each system.

The predictability and uncertainty of a communication system is also affected by how flexibly signals are used across different social contexts (Aureli et al., 2022). For instance, if signal A is always used in an aggressive context and signal B is always used in an affiliative context, then it is easy to predict the context from the signal. Conversely, if signals A and B are used in both contexts, then predictability is lower, and complexity is higher. Extremely rare signals do not substantially affect the predictability of a system regardless of whether they have high or low specificity since they are seldom observed in the majority of social interactions. Therefore, predictability is highest when signals are both highly context-specific and occur in that context often. Additionally, predictability can be measured directly by training a machine learning classifier to predict the social context that a given signal was used in. Differences in prediction error would approximate the relative uncertainty and complexity, with accuracy being lower in more complex systems. However, as complexity lies somewhere between order and randomness (Sambrook and Whiten, 1997; Adami, 2002), we should still be able to predict the social contexts better than chance, even in a complex system.

Studying closely related species offers a robust means of testing the social complexity hypothesis due to their homologous communication systems. For this reason, macaques (genus Macaca) are excellent taxa to test the social complexity hypothesis. All species have a similar social organization consisting of multi-male, multi-female groups, but vary in social style in ways that are highly relevant to predictions of the social complexity hypothesis. The social styles of macaques consist of several covarying traits that can be ordered along a social tolerance scale ranging from the least (grade 1) to most tolerant (grade 4) (Thierry, 2007; Thierry, 2022). Social interactions for the least tolerant species, such as rhesus (Macaca mulatta) and Japanese (Macaca fuscata) macaques, are generally more constrained by a steep linear dominance hierarchy (Balasubramaniam et al., 2012) and nepotism (Sueur et al., 2011; Thierry and Berman, 2010; Duboscq et al., 2013). Additionally, severe agonistic interactions are more frequent (Duboscq et al., 2013), instances of counter-aggression and reconciliation after conflicts are rare (Balasubramaniam et al., 2012; Duboscq et al., 2013), and formal signals of submission are commonly used (de Waal and Luttrell, 1985; Preuschoft and Schaik, 2000). Combined, these behavioral traits indicate that agonistic interactions of the least tolerant species are more stereotyped and formalized. Thus, the outcome of such interactions is more certain, whereas the opposite is true for the most tolerant species, such as crested and Tonkean (Macaca tonkeana) macaques. The unpredictability in the outcome of agonistic interactions of tolerant macaques potentially results in a social environment that is perceived as more complex by individuals (Aureli and Schino, 2019), where more subtle means of negotiation during conflicts may be necessary.

In this study we compared the facial behavior of three macaque species that vary in their degree of social tolerance and, therefore, social complexity: rhesus (least tolerant), Barbary (Macaca sylvanus, mid-tolerant), and crested macaques (most tolerant). For macaques (and primates in general), the face is central to communication and is a key tool in allowing individuals to achieve their social goals by communicating motivations, emotions, and/or intentions (Waller et al., 2017; Fridlund, 1994). We coded facial behavior at the level of individual visible muscle movements using FACS and recorded all observed unique combinations, rather than classifying facial expressions into discrete categories. Based on the social complexity hypothesis (Freeberg et al., 2012), we expected that tolerant species would have higher communicative complexity, given that their social relationships are less constrained by dominance and have higher overall uncertainty in the outcome of agonistic interactions. Specifically, we predicted the following: (1) relative entropy of facial behavior will be lowest in the rhesus and highest in crested macaques, (2) context specificity of facial behavior will be highest in rhesus and lowest in crested macaques, and (3) social context can be predicted from facial behavior most accurately in rhesus and least accurately in crested macaques. For all three metrics, we expected Barbary macaques to lie somewhere in-between the rhesus and crested macaques.

We investigated the hypothesis that complex societies require more complex communication systems (Freeberg et al., 2012) by comparing the complexity of facial behavior of three species of macaques that vary in their degree of social tolerance and complexity. We defined facial behavior by the unique combinations of muscle movements visible in the face. Doing so allows for a much more precise description of facial behavior and captures subtle differences that are lost if facial expressions are classified as discrete categories. We quantified communicative complexity using three measures of uncertainty and predictability: entropy, context specificity, and prediction error. Collectively, our results suggest that the complexity of facial behavior is higher in species with a more tolerant—and therefore more complex—social style; complexity was highest for crested, followed by Barbary, and lowest in rhesus macaques. In light of what we know about the differences between macaque social systems, our results support the predictions of the social complexity hypothesis for communicative complexity.

The entropy ratio of facial behavior was highest in crested compared to Barbary and rhesus macaques, both overall and within each social context (affiliative, aggressive, submissive). This result suggests that crested macaques use a higher diversity of facial signals within each social context more frequently, resulting in the higher relative uncertainty in their use of facial behavior. Information theory defines information as the reduction in uncertainty once an outcome is learned (Shannon, 1948). By this definition, our data suggest that the facial behavior of crested macaques has the potential to communicate more information, compared to Barbary and rhesus macaques, although this would need to be explicitly tested in future studies. Our findings are in line with predictions of the social complexity hypothesis (Freeberg et al., 2012) given the differences in social styles between tolerant and intolerant macaques. In tolerant macaque societies, social interactions are less constrained by dominance (Balasubramaniam et al., 2012) such that rates of counter-aggression and reconciliation post-conflict are higher (Duboscq et al., 2013; Thierry et al., 2008). Thus, there is a greater variability in the kind of interactions that individuals have, potentially requiring the use of more diverse facial behavior to achieve social goals, particularly during conflicts. Similarly, strongly bonded chimpanzee (Pan troglodytes) dyads exhibit a larger repertoire of gestural communication than non-bonded dyads, presumably due to the former having more varied types of social interactions (Amici and Liebal, 2022).

The overall entropy ratio of rhesus and Barbary macaques was similar, suggesting that they have similar communicative capacity using facial behavior. However, the entropy ratio differed when compared within social contexts; while relative entropy was higher for Barbary macaques in affiliative and submissive contexts, it was higher for rhesus macaques in aggressive contexts. One possible explanation may be due to the use of stereotyped signals of submission and dominance in each species. For example, subordinate rhesus macaques regularly exhibit stereotyped signals of submission (silent-bared-teeth), whereas dominant Barbary macaques regularly exhibit stereotyped threats (round-open-mouth) (de Waal and Luttrell, 1985; Preuschoft and Schaik, 2000). Frequent use of a stereotyped signal within a context reduces the overall diversity of signals, resulting in a lower entropy ratio for submission and aggression in rhesus and Barbary macaques, respectively. It has been suggested that in societies with high power asymmetries between individuals, such as in rhesus macaques, spontaneous signals of submission serve to prevent conflicts from escalating as well as increasing the tolerance of dominant individuals toward subordinates (Preuschoft and Schaik, 2000). In societies with more moderate power asymmetries, such as in Barbary macaques, subordinates may be less motivated to spontaneously submit and thus dominants may need to assert their dominance with formalized threats more frequently (Preuschoft and Schaik, 2000).

While the entropy ratio captures the uncertainty of facial behavior used within a social context, context specificity captures the uncertainty generated when the same facial behavior is used flexibly across different social contexts. Overall, the context specificity of facial behavior was higher for the intolerant rhesus macaques as compared to the more tolerant Barbary and crested macaques across all three social contexts. This pattern occurred for both the mean specificity values and the proportion of Action Unit combinations used that had high (>0.8) specificity. Similarly, a previous study demonstrated that vocal calls of tolerant macaques are less context specific than in intolerant macaques (Rebout et al., 2022). There was not a clear difference in specificity between Barbary and crested macaques; specificity was higher for Barbary macaques in affiliative contexts, similar for both species in aggressive contexts, and higher for crested macaques in submissive contexts. These differences in context specificity of communicative signals across macaque species may be related to differences in power asymmetry in their respective societies, particularly as it relates to the risk of injury. For macaques, bites are far more likely to injure opponents than other types of contact aggression (e.g., grab, slap) and thus provide the best proxy for risk of injury (Thierry, 2022). The percentage of conflicts involving bites is much higher in the less tolerant rhesus macaque, compared to the more tolerant Barbary and crested macaques who have similar low rates of aggression involving bites (Duboscq et al., 2013; Tyrrell et al., 2020). Risky situations may promote the evolution of more conspicuous, stereotypical signals to reduce ambiguity (Clark et al., 2022). Indeed, intolerant macaques such as the rhesus more commonly use formal signals of submission (de Waal and Luttrell, 1985; Preuschoft and Schaik, 2000). In our study, rhesus macaques used facial behavior with high specificity across all contexts but particularly in submissive contexts. If the same facial behavior (or signal in general) is used in multiple social contexts, its meaning may be uncertain and must be deduced from additional contextual cues (Seyfarth and Cheney, 2017). When facial behavior is highly context specific, there is less uncertainty about the meaning of the signal and/or intention of the signaler. In a society where the risk of injury from aggression is high, it may be adaptive for individuals to use signals that are highly context specific or ritualized to reduce uncertainty about its meaning. By contrast, the lower risk of injury in Barbary and crested macaques may allow room for a greater variety of more nuanced behaviors during conflicts as well as higher rates of reconciliation post-conflict (Duboscq et al., 2013; Thierry et al., 2008).

In all three species of macaques, at least some facial muscle movements had low specificity and were therefore used across multiple social contexts that likely differed in valence. This finding is in line with the idea that communicative signals in primates are better interpreted as the signaler announcing its intentions and likely future behavior (Cheney and Seyfarth, 2018; Fischer and Price, 2017), and not necessarily as an expression of emotional state (Waller et al., 2017; Fridlund, 1994; Cheney and Seyfarth, 2018; Barrett et al., 2019).

We found that a random forest classifier was least accurate at predicting social context from facial behavior for crested, followed by Barbary, and then rhesus macaques. The behavior of complex systems is generally harder to predict than simpler ones (McDaniel and Driebe, 2005; Schuster, 2016). Thus, the relatively poorer performance of the classifier in crested macaques suggests that they have the most complex facial behavior. Nevertheless, the classifier was able to predict social context from facial behavior with better accuracy than expected by chance alone for all three species of macaque, including the crested. This result confirms the assumption that facial behavior in macaques is not used randomly and most likely has some communicative or predictive value (Waller et al., 2016). It is worthwhile to reiterate here that completely random (and thus unpredictable) systems are not considered complex (Adami, 2002). Therefore, the species with the highest entropy values, or unpredictability, could be interpreted as having a simpler communication system than a species with a moderately high entropy value or unpredictability. But the communications systems of living organisms are unlikely to be observed as random, otherwise they would not have evolved as signals. Therefore, working under the assumption that animal communication systems cannot possibly be random, we can conclude that the species whose communication system has the highest relative entropy and unpredictability is in fact the most complex (Rebout et al., 2021).

In addition to social complexity, it is possible that other factors are related to the complexity of facial behavior. For example, primates with a larger body size have greater facial mobility (Dobson, 2009a; Santana et al., 2014), which could allow for greater complexity of facial behavior. However, differences in mean body mass across the three macaques species of this study are small (rhesus: 6.5 kg; Barbary: 11.5 kg; crested: 7.4 kg) (Jones et al., 2009) with substantial overlap in body weight across adult individuals of the different species (Smith and Jungers, 1997), and so it is unlikely to explain the differences in the complexity of facial behavior that we report in this study. The degree of terrestriality could also influence the evolution of facial signals due to more limited visibility in the canopy. However, differences in facial mobility across terrestrial and non-terrestrial primates are not significant once body size is controlled for (Dobson, 2009a). Furthermore, all three species included in this study have comparable levels of terrestriality, spending the majority (52–72%) of the time on the ground (Khatiwada et al., 2020; O’Brien and Kinnaird, 1997; El Alami and Chait, 2014). Spatial spread is another factor that could influence the use of facial signals. For example, when group spread is higher, reliance on facial signals could be lower since it is harder to perceive facial signals from a large distance. There are currently no reliable data on spatial spread of the three species of this study in their natural habitat but it could be a good avenue for future studies. It is also important to note that our study is correlational in nature and we cannot determine the direction of the link between social and communicative complexity. It is possible that an increase in communicative complexity evolved first, which then allowed for the evolution of more complex social systems. Finally, effectively, our comparison is limited to three species which is a small sample. However, the methodology we used is applicable to any species for which FACS is available (including other non-human primates, dogs, and horses; Waller et al., 2020), and therefore, we hope that other datasets will complement ours in the future.

Our results on the complexity of facial behavior in macaques is mirrored by previous studies showing that the complexity of vocal calls is similarly higher in tolerant compared to intolerant macaques (Rebout et al., 2022; Rebout et al., 2020). Although not all macaque facial expressions have a vocal component, vocalizations are fundamentally multisensory with both auditory and visual components, where different facial muscle contractions are partly responsible for different-sounding vocalizations (Ghazanfar and Takahashi, 2014). Indeed, some areas of the brain in primates integrate visual and auditory information resulting in behavioral benefits (Ghazanfar and Eliades, 2014). For example, macaques detect vocalizations in a noisy environment faster when mouth movements are also visible, where faster reaction times are associated with a reduced latency in auditory cortical spiking activity (Chandrasekaran et al., 2013). Combined, these findings suggest that the evolution in the complexity of vocal and facial signals in macaques may be linked and the same may be true of primates in general. For instance, humans not only have the most complex calls (language) and gestures, but most likely use the most complex facial behavior as well, given that their general facial mobility is highest among primates (most Action Units) (Ekman et al., 2002; Dobson, 2009b). In lemurs (Lemuriformes), the repertoire size of vocal, visual, and olfactory signals positively correlate with group size and each other, suggesting that complexity in all three communicative modalities coevolved with social complexity (Fichtel and Kappeler, 2022). While the complexity of different communication modalities is likely interlinked and correlated with each other, future studies would ideally integrate signals from all modalities into a single communicative repertoire for each species. While collecting and analyzing data on multiple modalities of communication has historically been a challenge, such endeavors would be an important next step in the study of animal communication (Liebal et al., 2022). By breaking down signaling units to their smallest components, as we have done for facial behavior in this study, we may be able to define a ‘signal’ by temporal co-activation of visual, auditory, and perhaps even olfactory cues, which would provide the most comprehensive picture of animal communication.

The data generated and analyzed in this study, along with the R code used for all statistical analysis is available on GitHub, https://github.com/avrincon/macaque-facial-complexity (copy archived at Rincon, 2022).

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The following is the authors’ response to the original reviews.

Reviewer #1 (Public Review):

This study investigates the context-specificity of facial expressions in three species of macaques to test predictions for the 'social complexity hypothesis for communicative complexity'. This hypothesis has garnered much attention in recent years. A proper test of this hypothesis requires clear definitions of 'communicative complexity' and 'social complexity'. Importantly, these two facets of a society must not be derived from the same data because otherwise, any link between the two would be trivial. For instance, if social complexity is derived from the types of interactions individuals have, and different types of signals accompany these interactions, we would not learn anything from a correlation between social and communicative complexity, as both stem from the same data.

The authors of the present paper make a big step forward in operationalising communicative complexity. They used the Facial Action Coding System to code a large number of facial expressions in macaques. This system allows decomposing facial expressions into different action units, such as 'upper lid raiser', 'upper lip raiser' etc.; these units are closely linked to activating specific muscles or muscle groups. Based on these data, the authors calculated three measures derived from information theory: entropy, specificity and prediction error. These parts of the analysis will be useful for future studies.

The three species of macaque varied in these three dimensions. In terms of entropy, there were differences with regard to context (and if there are these context-specific differences, then why pool the data?). Barbary and Tonkean macaques showed lower specificity than rhesus macaques. Regarding predicting context from the facial signals, a random forest classifier yielded the highest prediction values for rhesus monkeys. These results align with an earlier study by Preuschoft and van Schaik (2000), who found that less despotic species have greater variability in facial expressions and usage.

Crucially, the three species under study are also known to vary in terms of their social tolerance. According to the highly influential framework proposed by Bernard Thierry, the members of the genus Macaca fall along a graded continuum from despotic (grade 1) to highly tolerant (grade 4). The three species chosen for the present study represent grade 1 (rhesus monkeys), grade 3 (Barbary macaques), and grade 4 (Tonkean macaques).

The authors of the present paper define social complexity as equivalent to social tolerance - but how is social tolerance defined? Thierry used aggression and conflict resolution patterns to classify the different macaque species, with the steepness of the rank hierarchy and the degree of nepotism (kin bias) being essential. However, aggression and conflict resolution are accompanied by facial gestures. Thus, the authors are looking at two sides of the same coin when investigating the link between social complexity (as defined by the authors) and communicative complexity. Therefore, I am not convinced that this study makes a significant advance in testing the social complexity for communicative complexity hypothesis. A further weakness is that - despite the careful analysis - only three species were considered; thus, the effective sample size is very small.

Social tolerance in macaques is defined by various covarying traits, among which rates of counter-aggression and conflict resolution are only two of many included (see Thierry 2021 for a recent discussion and review). We do not deviate from Thierry’s definition of social tolerance. We simply highlight that the constellation of behavioral traits in the most tolerant macaque species results in a social environment where the outcome of social interactions is more uncertain (see introduction lines 102-114). As we argue throughout the paper, higher uncertainty can be used as a proxy for higher complexity and thus we conclude that the most tolerant macaque species have the highest social complexity. While most social behavior in macaques is accompanied by some facial behavior, we were careful to define social contexts only from the body language/behavior (e.g., lunge for aggression, grooming for affiliation) of the individuals involved and ignored the facial behavior used (see method lines 371-381). Therefore, the facial behavior of macaques (communication signals) was not used in defining either social tolerance (and by extension complexity) or the social context in which it was used. We feel like this appropriately minimizes any elements of circularity in the analysis of social and communicative complexity.

Regarding the effective sample size of three species, we agree that it is small, and it is a limitation of this study. However, the methodology we used is applicable to any species for which FACS is available (including other non-human primates, dogs, and horses), and therefore, we hope that other datasets will complement ours in the future. Nevertheless, we now acknowledge this limitation in the discussion (lines 314317).

Reviewer #2 (Public Review):

This is a well-written manuscript about a strong comparative study of diversity of facial movements in three macaque species to test arguments about social complexity influencing communicative complexity. My major criticism has to do with the lack of any reporting of inter-observer reliability statistics - see comment below. Reporting high levels of inter-observer reliability is crucial for making clear the authors have minimized chances of possible observer biases in a study like this, where it is not possible to code the data blind with regard to comparison group. My other comments and questions follow by line number:

We agree that inter-observer coding reliability is an important piece of information. We now report in more detail the inter-observer reliability tests that we conducted on lines 384-392.

38-40. Whereas I am an advocate of this hypothesis and have tested it myself, the authors should probably comment here, or later in the discussion, about the reverse argument - greater communicative complexity (driven by other selection pressures) could make more complicated social structures possible. This latter view was the one advocated by McComb & Semple in their foundational 2005 Biology Letters comparative study of relationships between vocal repertoire size and typical group size in non-human primate species.

It is true that an increase in communicative complexity could allow/drive an increase in social complexity. Unfortunately our data is correlational in nature and we cannot determine the direction of causality. We added such a statement to the discussion (lines 311-314).

72-84 and 95-96. In the paragraph here, the authors outline an argument about increasing uncertainty / entropy mapping on to increasing complexity in a system (social or communicative). In lines 95-96, though, they fall back on the standard argument about complex systems having intermediate levels of uncertainty (complete uncertainty roughly = random and complete certainty roughly = simple). Various authors have put forward what I think are useful ways of thinking about complexity in groups - from the perspective of an insider (i.e., a group member, where greater randomness is, in fact, greater complexity) vs from the perspective of an outside (i.e., a researcher trying to quantify the complexity of the system where is it relatively easy to explain a completely predictable or completely random system but harder to do so for an intermediately ordered or random system). This sort of argument (Andrew Whiten had an early paper that made this argument) might be worth raising here or later in the discussion? (I'm also curious where the authors sentiments lie for this question - they seem to touch on it in lines 285-287, but I think it's worth unpacking a little more here!)

In this study we used three measures of uncertainty (entropy, context specificity, and prediction error) to approximate complexity. However, maximum entropy or uncertainty would be achieved in a system that is completely random (and thus be considered simple). Therefore, the species with the highest entropy values, or unpredictability, could be interpreted as having a simpler communication system than a species with a moderately high entropy/unpredictability value. Our argument is that animal communication systems cannot possibly be random, otherwise they would not have evolved as signals. In systems where we know the highest entropy (or unpredictability) will not be due to randomness, as is the case with animal social interactions and communication, we can conclude that the system with the highest uncertainty is the most complex. We have now expanded upon this point in the discussion (lines 286-294). See also response to reviewer 1 below.

115-129. See also:

Maestripieri, D. (2005). "Gestural communication in three species of macaques (Macaca mulatta, M. nemestrina, M. arctoides): use of signals in relation to dominance and social context." Gesture 5: 57-73.

Maestripieri, D. and K. Wallen (1997). "Affiliative and submissive communication in rhesus macaques." Primates 38(2): 127-138.

On that note, it is probably worth discussing in this paragraph and probably later in the discussion exactly how this study differs from these earlier studies of Maestripieri. I think the fact that machine learning approaches had the most difficulty assigning crested data to context is an important methodological advance for addressing these sorts of questions - there are probably other important differences between the authors' study here and these older publications that are worth bringing up.

Our study differs from these two studies in that the studies above classified facial behavior into discrete categories (e.g., bared-teeth, lip-smack), whereas we adopted a bottom-up approach and made no a priori assumptions about which movements are relevant. We broke down facial behavior down to their individual muscle movements (i.e., Action Units). Measuring facial behavior at the level of individual muscle movements allows for a more detailed and objective description of the complexity of facial behavior. This is a general point in advancing the study of facial behavior that is discussed in the introduction (lines 60-71) and discussion (lines 206-208). The reason we don’t draw a direct comparison with the studies above is because they had a slightly different focus. Our study was more focused on complexity of the (facial) communication system in general rather than comparing whether the different species use the same facial behavior in the same/different social contexts.

220-222. What is known about visual perception in these species? Recent arguments suggest that more socially complex species should have more sensitive perceptual processing abilities for other individuals' signals and cues (see Freeberg et al. 2019 Animal Behaviour). Are there any published empirical data to this effect, ideally from the visual domain but perhaps from any domain?

This is an interesting point. We are not aware of any studies showing differences in visual perceptions within the macaque genus. Both crested macaques and rhesus macaques are able to discriminate between individuals and facial expressions in match-to-sample tasks with comparable performances (Micheletta et al., 2015a, 2015b; Parr et al. 2008; Parr & Heinz, 2009). Similarly, several macaque species are sensitive to gaze shifts from conspecifics (Tomasello et al. 1998; Teufel et al. 2010; Micheletta & Waller, 2012).

274-277. I am not sure I follow this - could not different social and non-social contexts produce variation in different affective states such that "emotion"-based signals could be as flexible / uncertain as seemingly volitional / information-based / referential-like signals? This issue is probably too far away from the main points of this paper, but I suspect the authors' argument in this sentence is too simplified or overstated with regard to more affect-based signals.

Emotion-based signals could, in theory, also produce flexible signals and it is possible that some facial expressions reflect an emotional state. However, some previous studies have suggested that facial expressions are only used as a display of emotion, rather than such signals having evolved for a different function such as announcing future intentions. In our study we found that macaques used, in some cases, the same facial expressions (i.e. combination of Action Units) in at least two different social contexts that, presumably, differed in their emotional valence. Thus, it is unlikely that particular facial expressions are bound to a single emotion. We think that this is an important point to make even though it is slightly beyond the scope of our paper.

288 on. Given there are only three species in this study, the chances of one of the species being the 'most complex' in any measure is 0.33. Although I do not believe this argument I am making here, can the authors rule out the possibility that their findings related to crested macaques are all related to chance, statistically speaking?

We are not aware of a way to rule out this possibility. However, we believe that we are appropriately cautious throughout the paper and acknowledge that having only investigated three species is a limitation of this study in the discussion (lines 314-317, see also our response to reviewer 1 above).

329-330. The fact that only one male rhesus macaque was assessed here seems problematic, given the balance of sexes in the other two species. Can the authors comment more on this - are the gestures they are studying here identical across the sexes?

We agree it would have been preferable to collect data on more than one male rhesus macaque, but that was unfortunately not possible. We are not aware of any studies showing differences in the use of facial behavior between male and female rhesus macaques. If differences exist, most likely these would occur in a sexual/mating context. However, in our study we only considered affiliative (non-sexual), submissive, and aggressive contexts, where we have no a priori reason to believe that there are sex differences.

354-371. Inter-observer reliability statistics are required here - one of the authors who did not code the original data set, or a trained observer who is not an author, could easily code a subset of the video files to obtain inter-observer reliability data. This is important for ruling out potential unconscious observer biases in coding the data.

We agree this is an important piece of information. We now report in more detail the inter-observer reliability tests that we conducted on lines 384-392:

“An agreement rating of >0.7 was considered good [Ekman et al 2002] and was necessary for obtaining certification. To obtain a MaqFACS coding certification, AVR, CP, and PRC coded 23 video clips of rhesus macaques and the MaqFACScodes were compared to the data of other certified coders (https://animalfacs.com).

The mean agreement ratings obtained were 0.85, 0.73, 0.83 for AVR, CP, and PRC, respectively. In addition, AVR and CP coded 7 videos of Barbary macaques with a mean agreement rating of 0.79. AVR and PRC coded 10 videos of crested macaques with a mean agreement rating of 0.74.”

Reviewer #1 (Recommendations For The Authors):

Given the long debate on the concept of information exchange in animal communication, I would also recommend being more careful with the term 'exchanges of information' (line 271). Perhaps it's better to be agnostic in the context of this paper.

As suggested, we now changed the phrasing to focus on the behavior of the animals, rather than suggesting that information is being exchanged (lines 270-273),

Line 281: "This result confirms the assumption that facial behaviour in macaques is not used randomly": the authors are knocking down a straw man. Nobody who has ever studied animal communication would consider that signals occur randomly. Otherwise, they would not have evolved as signals.

Indeed, nobody claims that animal communication signals are used randomly. Although it may be taken for granted, we feel it is worthwhile to reiterate this point, given that we used relative entropy and prediction error as measures of complexity. For instance, maximum entropy or unpredictability would be achieved in a system that is completely random (and thus be considered simple). Therefore, the species with the highest entropy values, or lowest predictability, could be interpreted as having a simpler communication system than a species with a moderately high entropy value. But if we are working under the assumption that animal communication systems cannot possibly be random, then we can conclude that the species whose communication system has the highest entropy is in fact the most complex. We tried to make this justification clearer in the discussion (lines 285-294).

I did not follow why there is a higher reliance on facial signals when predation pressure is higher. Apart from the fact that the authors cannot address this question, they may want to reconsider this idea altogether.

We now expand on the logic of why predation pressure might affect the use of facial signals (see lines 308-309): “When predation pressure is higher, reliance on facial signals could be higher than, for example vocal signals, such as to not draw attention of predators to the signaller.”

Technical comments:

One methodological issue that requires clarification is what the units of analysis are. The authors write that each row in their analysis denoted an observation time of 500 ms. How many rows did the authors assemble? The authors mention a sample size of > 3000 social interactions in the abstract. How did they define social interactions? And how many 'time windows' of 500 ms were obtained? Did they take one window per interaction or several? If several, then how was this move accounted for in the analysis? The reporting needs to be more accurate here. Most likely, the bootstrapping took care of biases in the data, but still, this information needs to be provided.

We have now added some additional information to the method section. Social interactions for each context had the following definitions: “Social context was labeled from the point of view of the signaler based on their general behavior and body language (but not the facial behavior itself), during or immediately following the facial behavior. An aggressive context was considered when the signaler lunged or leaned forward with the body or head, charged, chased, or physically hit the interaction partner. A submissive context was considered when the signaler leaned back with the body or head, moved away, or fled from the interaction partner. An affiliative context was considered when the signaler approached another individual without aggression (as defined previously) and remained in proximity, in relaxed body contact, or groomed either during or immediately after the facial behavior. In cases where the behavior of the signaler did not match our context definitions, or displayed behaviors belonging to multiple contexts, we labeled the social context as unclear. Social context was determined from the video itself and/or from the matching focal behavioral data, if available.” (lines 371-382). The total duration of all social interactions per social context, and thus the number of 500ms windows/rows, have been added to Table 1 (lines 395-397). There were several 500ms windows per social interaction. All 500ms time blocks per interaction were used in the statistical analyses in order to retain all the variation and complexity of the facial behavior (Action Unit combinations) used by the macaques (lines 403-405). Indeed the bootstrapping procedure was used to account for any biases in the data.

Overall, I would recommend providing more information on the actual behaviour of the animals. The paper is strong in handling highly derived indices representing the behaviour, but the reader learns little about the animals' behaviour. Thus, it would be great if statements about the entropy ratio were translated into what these measures represent in real life. For context specificity, this is clear, but for entropy, not so much.

A high entropy ratio essentially suggests that a species uses a high variety of unique facial behavior/signals and all signals in the repertoire are used roughly equally often (rather than one facial behavior being used 90% of the time and others rarely used). We have tried our best to better explain this point in the introduction (lines 75-81) and discussion (lines 215-222). Discussing exactly what these signals are and what they mean was beyond the scope of this paper.

Line 106: nepotism, not kinship

Changed as suggested (line 106).

Line 113: I would avoid statements about how a monkey society is perceived by its members.

We think that noting how individuals may perceive their social environment is worthwhile when defining social complexity, so have retained this point but changed the phrasing to be more speculative (lines 112-113).

Line 329: I was very surprised that only one male was represented in the data for rhesus monkeys. The authors try to wriggle their way out of this issue in the supplementary material ("Therefore, we have no a priori reason to expect an overall difference in the diversity and complexity of facial behaviour between the sexes"), but I think this is a major shortcoming of the analysis. They should ascertain whether there are no sex differences in the other two species regarding their variables of interest. They could then make a very cautious case for there being no sex differences in rhesus either. But of course, they would not know for sure.

As with our response to reviewer 2 above, we agree that it would have been preferable to collect data on more than one male rhesus macaque, but that was unfortunately not possible. We are not aware of any studies showing differences in the use of facial behavior between male and female rhesus macaques. If differences exist, most likely these would occur in a sexual/mating context. However, in our study we only considered affiliative (non-sexual), submissive, and aggressive contexts, where we have no a priori reason to believe that there are sex differences. Looking at sex differences in the use of facial behavior would be a worthwhile study on its own, but it is outside the scope of this paper.

This paper would make a stronger contribution if it focussed on the comparative analysis of facial expressions and removed the attempt of testing the social complexity for communicative complexity hypothesis.

A comparative analysis of the contextual use of specific facial movements is important. But this paper is focused on making a more general comparison of the communication style and complexity across species. The social complexity hypothesis for communicative complexity is one of the key theoretical frameworks for such an investigation and allows us to frame our study in a broader context. We contribute important data on 3 species with methods that can be replicated and extended to others species. Therefore, we believe that it is a worthy contribution to investigations of the evolution of complex communication.

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Author details

1. Alan V Rincon

   Department of Psychology, Centre for Comparative and Evolutionary Psychology, University of Portsmouth, Portsmouth, United Kingdom

   Contribution

   Conceptualization, Data curation, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing - original draft, Writing - review and editing

   For correspondence

   avrincon1@gmail.com

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-6181-0152

2. Bridget M Waller

   Centre for Interdisciplinary Research on Social Interaction, Department of Psychology, Nottingham Trent University, Nottingham, United Kingdom

   Contribution

   Conceptualization, Supervision, Funding acquisition, Methodology, Project administration, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-6303-7458

3. Julie Duboscq

   CNRS-MNHN-Université Paris Cité, Paris, France

   Contribution

   Conceptualization, Supervision, Funding acquisition, Methodology, Project administration, Writing - review and editing

   Competing interests

   No competing interests declared

4. Alexander Mielke

   School of Biological and Behavioural Sciences, Queen Mary University of London, London, United Kingdom

   Contribution

   Software, Methodology, Writing - review and editing

   Competing interests

   No competing interests declared

5. Claire Pérez

   Department of Psychology, Centre for Comparative and Evolutionary Psychology, University of Portsmouth, Portsmouth, United Kingdom

   Contribution

   Data curation, Investigation, Writing - review and editing

   Competing interests

   No competing interests declared

6. Peter R Clark

   1. Department of Psychology, Centre for Comparative and Evolutionary Psychology, University of Portsmouth, Portsmouth, United Kingdom
   2. School of Psychology, University of Lincoln, Lincoln, United Kingdom

   Contribution

   Data curation, Investigation, Writing - review and editing

   Competing interests

   No competing interests declared

7. Jérôme Micheletta

   Department of Psychology, Centre for Comparative and Evolutionary Psychology, University of Portsmouth, Portsmouth, United Kingdom

   Contribution

   Conceptualization, Supervision, Funding acquisition, Methodology, Project administration, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-4480-6781

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