Nancy Rebout

Arianna De Marco

Andrea Sanna

Jerome Micheletta

Jean-Christophe Lone

Reinier F Van Den Berg

Elisabeth H M Sterck

Jan A M Langermans

Bernard Thierry
email: bernard.thierry@cnrs.fr

Alban Lemasson

Jérôme Micheletta

Nancy Orcid

Rebout

Jérôme Micheletta

Tolerant and intolerant macaques differ in the

Keywords: Social complexity, Uncertainty, Flexibility, Communication, Acoustics, Primates

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Living in a complex social system means interacting with different social partners in varied situations. This social complexity requires sophisticated communicative skills so that individuals can express a wide range of intentions and emotional states. This is what the 'social complexity hypothesis for communicative complexity' posits, which has become a topical issue in recent years [START_REF] Freeberg | Social complexity as a proximate and ultimate factor in communicative complexity[END_REF][START_REF] Peckre | Clarifying and expanding the social complexity hypothesis for communicative complexity[END_REF][START_REF] Pollard | Evolving communicative complexity: insights from rodents and beyond[END_REF]Robert and Roberts 2020). However, as discussed elsewhere, a recurring problem is how to define and measure complexity [START_REF] Rebout | Measuring complexity in organisms and organizations[END_REF]. The preferred measures of social complexity are the number of individuals in a social group [START_REF] Freeberg | Social complexity can drive vocal complexity: group size influences vocal information in Carolina chickadees[END_REF][START_REF] Lehmann | Network cohesion, group size and neocortex size in female-bonded Old World primates[END_REF][START_REF] Dunbar | Bridging the bonding gap: the transition from primates to humans[END_REF][START_REF] Bergman | Measuring social complexity[END_REF] and also the different types of group members [START_REF] Blumstein | Does sociality drive the evolution of communicative complexity? A comparative test with ground-dwelling sciurid alarm calls[END_REF][START_REF] Pollard | Evolving communicative complexity: insights from rodents and beyond[END_REF]). However, these measures are rather crude proxies that do not consider how individuals interact [START_REF] Shultz | Chimpanzee and felid diet composition is influenced by prey brain size[END_REF]). It has therefore been proposed to use the number of social interactions [START_REF] Freeberg | Social complexity as a proximate and ultimate factor in communicative complexity[END_REF] or the number of social relationships instead [START_REF] Bergman | Measuring social complexity[END_REF]Fischer et al. 2017;[START_REF] Morrison | Comparing measures of social complexity: larger mountain gorilla groups do not have a greater diversity of relationships[END_REF]. Such indices are valuable because they reflect social diversity, but diversity alone cannot yet sum up the entire complexity of social systems [START_REF] Rebout | Measuring complexity in organisms and organizations[END_REF].

With regard to vocal complexity, the variable most often considered is the number of units in a communicative system, and in particular the number of vocalizations in a species repertoire [START_REF] Freeberg | Social complexity as a proximate and ultimate factor in communicative complexity[END_REF][START_REF] Peckre | Clarifying and expanding the social complexity hypothesis for communicative complexity[END_REF][START_REF] Pollard | Evolving communicative complexity: insights from rodents and beyond[END_REF][START_REF] Schamberg | Call type signals caller goal: a new take on ultimate and proximate influences in vocal production[END_REF]). Another measure is the amount of information in a vocal repertoire, calculated as the number of bits of information using Shannon's uncertainty formula [START_REF] Shannon | A mathematical theory of communication[END_REF][START_REF] Freeberg | Social complexity can drive vocal complexity: group size influences vocal information in Carolina chickadees[END_REF][START_REF] Bouchet | Social complexity parallels vocal complexity: a comparison of three non-human primate species[END_REF]). These two variables only concern vocal diversity. In addition, they are difficult to implement in animals with a graded repertoire, that is, a continuum of acoustic structures without clear boundaries between different types of calls [START_REF] Hammerschmidt | The vocal repertoire of Barbary macaques: a quantitative analysis of a graded signal system[END_REF][START_REF] Wadewitz | Characterizing vocal repertoires -Hard vs. soft classification approaches[END_REF]. For this reason, it has been recommended to assess vocal complexity by quantifying the degree of gradation of the vocal repertoire [START_REF] Wadewitz | Characterizing vocal repertoires -Hard vs. soft classification approaches[END_REF]Fischer et al. 2017), and thus the flexibility of acoustic structures in a species [START_REF] Rebout | Tolerant and intolerant macaques show different levels of structural complexity in their vocal communication[END_REF]. Flexibility can also manifest itself in the extent of context specificity of vocal signals, i.e. the degree of freedom between their acoustic structure and the context in which they are emitted [START_REF] Wheeler | Functionally referential signals: a promising paradigm whose time has passed[END_REF]. Note that in statistics the degree of freedom corresponds to the number of variables that cannot be fixed by an equation; here the equation is the context, and the variables are the types of calls that can be emitted. This means that the more calls are 'fixed' by the context, the less uncertainty there is in the system. On the contrary, when the calls are little 'fixed' by the context, the system has a higher level of uncertainty.

In animal communication, the question of the relationship between structure and function is not a simple one. Many vocal signals are not context-specific, and acoustically similar calls can occur in different social situations, while acoustically dissimilar calls can be emitted in the same social situations; this has led to the idea that the structure of signals has no special relationship with their social function (see [START_REF] Owren | Sound on the rebound: bringing form and function back to the forefront in understanding nonhuman primate vocal signaling[END_REF]. On the other hand, the motivationstructural rules proposed by [START_REF] Morton | On the occurrence and significance of motivation-structural rules in some bird and mammal sounds[END_REF] assume that there is a relationship between the physical structure of sounds and the motivations behind them. Some sounds may be more likely than others to induce attention, arousal or emotional responses in conspecifics, and call structure may then be partially predicted from the context. In mammals, for instance, calls produced in affiliative contexts tend to be associated with lower amplitude and variability, higher frequency modulation and less noisy signals than agonistic and alarm-related contexts [START_REF] Morton | On the occurrence and significance of motivation-structural rules in some bird and mammal sounds[END_REF][START_REF] Lemasson | Acoustic variability and social significance of calls in female Campbell's monkeys (Cercopithecus campbelli campbelli)[END_REF][START_REF] Owren | Sound on the rebound: bringing form and function back to the forefront in understanding nonhuman primate vocal signaling[END_REF][START_REF] Briefer | Vocal expression of emotions in mammals: mechanisms of production and evidence[END_REF][START_REF] Bouchet | Social complexity parallels vocal complexity: a comparison of three non-human primate species[END_REF][START_REF] Gustison | A survey of the context and structure of high-and low-amplitude calls in mammals[END_REF][START_REF] Mercier | Correlates of social role and conflict severity in wild vervet monkey agonistic screams[END_REF]. Flexibility in the degree of correspondence between vocal signals and their context of occurrence contributes to the complexity of communication systems [START_REF] Manser | Vocal complexity in meerkats and other mongoose species[END_REF][START_REF] Pika | Unpeeling the layers of communicative complexity[END_REF][START_REF] Peckre | Clarifying and expanding the social complexity hypothesis for communicative complexity[END_REF].

Although there is no consensus on a general definition of complexity, there is agreement that the behaviour of complex systems is difficult to predict [START_REF] Mcdaniel | Do ecological factors explain variation in social organization ?[END_REF][START_REF] Schuster | How complexity originate: examples from history reveal additional roots to complexity[END_REF]). We have therefore proposed that it is possible to assess the complexity of systems based on their ability to produce uncertainty [START_REF] Rebout | Measuring complexity in organisms and organizations[END_REF]. When studying communicative complexity, we can rely on the degrees of freedom in the association between signals and their context of emission to quantify uncertainty. For instance, a strong connection between a vocal signal and a given context implies a low degree of uncertainty in the system: when hearing a highly context-specific call, the listener does not need information about the context to identify the information encoded by the acoustic structure of the call; by contrast, when a call has low contextspecificity, uncertainty about the message is greater and the listener needs additional contextual cues to respond appropriately [START_REF] Seyfarth | Meaning and emotion in animal vocalizations[END_REF][START_REF] Wheeler | Functionally referential signals: a promising paradigm whose time has passed[END_REF][START_REF] Manser | Vocal complexity in meerkats and other mongoose species[END_REF].

While the strength of the association between the structure of a vocal signal and the context in which the caller is involved is variable, there is an additional level of complexity when calls are triggered by a social context in which callers are not themselves involved. Such a situation has been reported in Barbary macaques (Macaca sylvanus) where a bystander may vocalize while attending an interaction between group mates [START_REF] Brumm | Do Barbary macaques "comment" on what they see? A first report on vocalizations accompanying interactions of third parties[END_REF]). The bystander is not involved in the social interaction and shows no other response than to vocalize, which is why Brumm and collaborators (2005) described these calls as 'comments'. They suggest that the comments draw the attention of others to the event, but that they could also include an evaluation of the event [START_REF] Brumm | Do Barbary macaques "comment" on what they see? A first report on vocalizations accompanying interactions of third parties[END_REF]. It is not known whether commenting calls have a specific acoustic structure. If they were to differ from calls emitted by individuals in the absence of any interaction -i.e. neutral calls -such flexibility would make the communication system more complex by providing individuals with a greater number of expressive options.

In an earlier study, we have found interspecific contrasts in the diversity and flexibility of the structure of vocal signals in four species of macaque. While phylogenetic relationships between species failed to account for these results, the social complexity hypothesis for communicative complexity successfully explained them [START_REF] Rebout | Tolerant and intolerant macaques show different levels of structural complexity in their vocal communication[END_REF]. In this study we compared the four species by analysing separately three social contexts (agonistic, affiliative, neutral) in which vocalizations were emitted. This revealed species differences in the number of call categories and the degree of gradation between these categories. However, a comparison of vocalizations occurring in different social contexts remains to be made to determine whether the degree of specificity of call structure to social context can be related to the degree of uncertainty in speciestypical social style.

Here, we extend the comparative study of flexibility by comparing the structure of calls occurring in different contexts to investigate the strength of the association between vocal structure and social context. Macaque species are well suited for this purpose. Macaques are semi-terrestrial primates. They live in groups that include both adult males and adult females. Males disperse and females remain in their natal group where they constitute matrilines, i.e. subgroups of individuals related by maternal descent [START_REF] Thierry | Unity in diversity: lessons from macaque societies[END_REF]. Although they share the same patterns of organization, macaques show a wide range of variation regarding their degree of social tolerance, which is associated with varying levels of uncertainty about the outcome of agonistic interactions [START_REF] Dobson | Coevolution of facial expression and social tolerance in macaques[END_REF][START_REF] Zannella | Yawning and social styles: different functions in tolerant and despotic macaques (Macaca tonkeana and Macaca fuscata)[END_REF]). In the more intolerant species social conflicts have unequivocal effects: in Japanese macaques (Macaca fuscata) and rhesus macaques (M. mulatta), for example, the receiver of the aggression submits or flees in nine out of ten cases in unrelated females [START_REF] Thierry | A comparative study of conflict resolution in macaques: insights into the nature of trait covariation[END_REF]. By contrast, in the more tolerant species the receiver of the aggression often protests or counter-attacks: in Tonkean macaques (M. tonkeana) and crested macaques (M. nigra), 68.0% and 45.4% of conflicts in unrelated females, respectively, remain undecided, without clear winner or loser [START_REF] Thierry | A comparative study of conflict resolution in macaques: insights into the nature of trait covariation[END_REF]. The interspecific variations found in the agonistic patterns of macaques correlate with the other components of their social styles. Tolerant macaques reconcile more frequently and have a greater number of facial displays than their more intolerant counterparts, they perform better in experimental tasks requiring individuals to display inhibitory control or pointing gestures, and their social behaviours are less constrained by kinship and dominance relationships than those of intolerant macaques; as a corollary the outcomes of their ACCEPTED MANUSCRIPT / CLEAN COPY social interactions are less predictable than those of intolerant macaques [START_REF] Thierry | Unity in diversity: lessons from macaque societies[END_REF][START_REF] Dobson | Coevolution of facial expression and social tolerance in macaques[END_REF][START_REF] Joly | Comparing physical and social cognitive skills in macaque species with different degrees of social tolerance[END_REF][START_REF] Balasubramaniam | The influence of phylogeny, social style, and sociodemographic factors on macaque social network structure[END_REF].

We compared two tolerant species (Tonkean and crested macaques) with two intolerant species (Japanese and rhesus macaques). They are mainly frugivorous, their primary habitat is forest, but rhesus macaques can live in various habitats, from forests to dry lands and regions of human settlement (Ménard 2004). Their repertoire of vocalizations is graded (Rowell and Hinde 1962;Green 1975;Masataka and Thierry 1993;[START_REF] Gouzoules | Agonistic screams differ among four species of macaques: the significance of motivation-structural rules[END_REF]Panggur 2013). Based on the social complexity hypothesis for communicative complexity, it can be assumed that the degree of flexibility of a communicative system is related to the degree of uncertainty of social interactions and relationships. Using this reasoning, we expect that ambiguous social situations create a need for greater call flexibility, allowing more information to be conveyed. This can apply both to individuals involved in social interactions and to third parties who comment on these interactions. We examined the structure of the vocal signals produced in three social contexts (agonistic, affiliative and neutral) to test the two following predictions: (1) Context specificity of calls: analysis of the structure of calls according to their contexts of emission should reveal that a given acoustic structure may occur in more contexts in tolerant macaques than in intolerant macaques, pointing to a weaker relationship between call structure and social context in the former; (2) Form of commenting calls: by conveying information about ongoing social events, comments have the potential to decrease any uncertainty individuals may have about their social environment; analysis of the structure of comments made by bystanders should reveal that their degree of differentiation from contact calls emitted in the absence of any interaction is more pronounced in tolerant than in intolerant macaques, pointing to a weaker relationship between call structure and bystander context in the former. It should be added that measuring the strength of the association between social context and vocal structure is a methodological challenge in species with a graded repertoire of vocalizations. We had to develop specific methods using clustering algorithms and Shannon's information theory to test these predictions.

Methods

Subjects and conditions

We made acoustic recordings and behavioural observations of adult females: 13 females in four groups of Tonkean macaques, 51 females in two groups of crested macaques, 29 females in two groups of Japanese macaques, 16 females in two groups of rhesus macaques. We focused on adult females as their age and sex category is the most represented in macaque groups, and also because they contribute the most to vocal activity [START_REF] Lemasson | Age-and sex-dependent contact call usage in Japanese macaques[END_REF]. Japanese, rhesus and Tonkean macaque females were born in captivity and were at least five years old. We studied crested macaques in the wild, assessing their age from their reproductive history since 2006 (Macaca Nigra Project), body size, nipple shape, and the presence of scars. The composition of groups is presented in Table 1.

Groups of Japanese macaques (Ft, Fw) were kept in two enclosures of 960 and 4,600 m² at the Primate Research Institute in Inuyama, Japan [START_REF] Arlet | Grooming-at-a-distance by exchanging calls in nonhuman primates[END_REF]. Groups of rhesus macaques (Ma, Mb) were kept in two 210-m² enclosures at the Biomedical Primate Research Center in Rijswijk, Netherlands [START_REF] Marco | Differential patterns of vocal similarity in tolerant and intolerant macaques[END_REF]. One group of Tonkean macaques (Tb) was kept in a 120-m² enclosure at the Orangerie Zoo in Strasbourg, France, and the other three groups (Tc, Td, Te) were kept in 500-m² enclosures at the rescue centre Parco Faunistico di Piano dell'Abatino in Rieti, Italy [START_REF] Marco | Differential patterns of vocal similarity in tolerant and intolerant macaques[END_REF]. Enclosures were wooded or furnished with ropes, poles and shelters. Animals were fed with commercial pellets, complemented with vegetables and fresh fruits. Water was available ad libitum. Groups of crested macaques (Npb, Nr1) lived in the Tangkoko Nature Reserve, Sulawesi, Indonesia [START_REF] Micheletta | Multicomponent and multimodal lipsmacking in crested macaques (Macaca nigra)[END_REF]. They inhabit lowland tropical rainforest and were not provisioned [START_REF] Collins | The conservation atlas of tropical forests: Asia and the Pacific[END_REF][START_REF] Rosenbaum | Population densities of Sulawesi crested black macaques (Macaca nigra) on Bacan and Sulawesi, Indonesia: effects of habitat disturbance and hunting[END_REF].

Data collection

We made outdoor observations to achieve quality recordings. Observers were within 5 m of the emitters. Data were taken by A.L. in Japanese macaques [START_REF] Arlet | Grooming-at-a-distance by exchanging calls in nonhuman primates[END_REF], N.R. in rhesus macaques, N.R, A.D.M. and A.S. for Tonkean macaques [START_REF] Marco | Differential patterns of vocal similarity in tolerant and intolerant macaques[END_REF]), and J.M. in crested macaques [START_REF] Micheletta | Multicomponent and multimodal lipsmacking in crested macaques (Macaca nigra)[END_REF]) (Table 1). The subjects were observed in a predefined random order with focal sampling. The sample duration was 10 mn for Japanese macaques and Tonkean macaques in groups Tc, Td and Te, 15 mn for rhesus macaques and Tonkean macaques in group Tb, and 30 mn for crested macaques. This gave 6.1 ± 0.16 h of focal sampling per female for Japanese macaques, 12.7 ± 0.7 h for rhesus macaques, 13.6 ± 3.2 h for Tonkean macaques, and 7.8 ± 0.4 for crested macaques.

For the Japanese macaques we made vocal recordings using a TCD-D100 Sony (Tokyo, Japan) DAT recorder (WAV format, 44,100-Hz sampling frequency, 16-bit resolution) and an ECM-672 Sony directional microphone. For rhesus and Tonkean macaques we used a Marantz (Eindhoven, Netherlands) PMD661 recorder (WAV format, 44,100-Hz sampling frequency, 16-bit resolution), and a Sennheiser (Wedermark, Germany) K6/ME66 directional microphone. For the crested macaques, we used partly a high-resolution camera Panasonic (Osaka, Japan) HDC-SD700 connected to a Sennheiser (Wedermark, Germany) K6/ME66 directional microphone. We extracted the audio tracks from the video recordings with the software FFmpeg (v 3.4.1) leading to WAV format (sampling frequency: 32 000 Hz, resolution: 16 bits). We collected observational data on the contexts of call emission using a lavalier microphone connected to the recorder in Japanese, rhesus and Tonkean macaques (at805f, audio-technica, Leeds, United Kingdom or TCM 160, Meditec, Singapore). For crested macaques, the observer filmed the focal individual while a field assistant recorded contextual data using a handheld computer.

We identified three different social contexts: agonistic, affiliative, neutral. We distinguished these contexts on the basis of the behaviours that could occur in the 3 s before or after the emission of a call or a sequence of calls. We defined a sequence as a series of calls separated by a maximum of 3 s. The behavioural units were based on published repertoires in macaques [START_REF] Altmann | A field study of the sociobiology of rhesus monkeys (Macaca mulatta)[END_REF][START_REF] Fedigan | A study of roles in the Arashiyama West troop of Japanese monkeys (Macaca fuscata)[END_REF][START_REF] Thierry | The social repertoire of Sulawesi macaques[END_REF]. The agonistic context was defined by the occurrence of aggression (facial threat display, supplantation, lunge, chase, slap, grab, bite) and response to aggression (aggression, submissive facial display, crouch, avoidance, flight). The affiliative context was defined by the occurrence of affiliative behaviour (affiliative facial display, approach, grasp, embrace, mount, social play, social grooming, sitting in contact). In the neutral context, the emitter was not involved in a social interaction.

To investigate the degree of differentiation of commenting calls, we distinguished three categories of calls according to the degree of involvement of emitters in social interactions: Interaction call: the emitter is engaged in an agonistic or affiliative interaction in the 3 s before or after the utterance of a call or a sequence of calls. Commenting call: an agonistic or affiliative interaction occurs in the 3 s before the utterance of the call or the sequence of calls but the emitter is not involved in the interaction. Uncontextualized call: no social interactions occur in the 3 s before or after the emission of a call or a sequence of calls; we have removed from the analysis the calls and sequences of calls where a non-social event (e.g. any event related to human activity) occurred in the 3 s preceding it. From the point of view of the emitter's calls, both commenting and uncontextualized calls occurred in the neutral context. We could not distinguish these two types of calls in Japanese macaques because the observer did not record social interactions other than those in which the emitter was directly involved. The assessment of the valence of commenting calls (agonistic or affiliative) was based on the types of calls recognized in macaques (Rowell and Hinde 1962;Lindburg 1971;Green 1975;Peters 1983;Lewis 1985;Masataka and Thierry 1993;Panggur 2013). All uncontextualized calls were identified by the human ear as coos or growls.

Recording conditions were not the same in the different species, especially in the wild population of crested macaques relative to the captive groups studied in the other three species. Rather than directly comparing the acoustic structure of the calls in the different species, we studied the strength of the relationship between the structure of the calls and their emission context in each species, then testing whether social contexts produce similar or different effects on the structure of the calls in the four species.

Acoustic analysis

We sampled 1368 calls in Japanese macaques, 1026 in rhesus macaques, 1210 in Tonkean macaques, and 1234 in crested macaques. We visualized spectrograms in the software Raven Pro 1.4 (Center for Conservation Bioacoustics 2011) with a 256 fast Fourier transform length and a Hanning window. We measured eight variables using the same software: Duration: duration in seconds from the beginning to the end of a call; Q2 time: Duration in seconds dividing a call into two intervals of equal energy; Q2 ratio: ratio in percent between Q2 time and duration; Q1 frequency: value in hertz of the frequency dividing a call into two intervals containing 25% and 75% of the energy; Q2 frequency: value in hertz of the frequency dividing a call into two intervals of equal energy; Q3 frequency: value in hertz of the frequency dividing a call into two intervals containing 75% and 25% of the energy; Wiener's aggregate entropy: degree of disorder (i.e. noisiness) of the call utilizing the total energy in a frequency bin over the entire call; Wiener's average entropy: mean of the mean entropies of the different time slices of a call.

We first sorted records according to their quality for these variables. We then randomly selected a maximum of three calls per sequence. Females whose sample size was less than five calls were removed from the analysis. We also excluded some specific types of calls that were not present in the samples of all species (alarm calls) or that had no equivalent in all species (oestrus calls, twits, cackles). Our sample yielded 2469 calls (Table 2). We provide spectrograms of the main types of vocalizations in the four species of macaques in the supplementary material ESM1.

Statistical analyses

We performed statistical analyses in R (R Core Team 2018). A first analysis focused on the context specificity of calls in order to assess the degree of association between acoustic structures and social contexts. Our goal was to examine the extent to which the classification of calls based on their acoustic structure would correspond to the classification of calls according to social context in each species, and thus address the strength of the association between the calls structure and their emission context. We developed our own methods to solve the issue. We used a cluster algorithm to group calls in an objective way, i.e. based solely on acoustic structure. Then, we evaluated in these groups of structures the proportion of the different contexts by reasoning that the higher the degree of association between the acoustic structure of the calls and their emission context, the more the groups are each mainly composed of a single emission context. On the contrary, the lower the degree of association between structure and context, the more groups are composed of calls from different contexts.

We designed a 4-step procedure. We first described the calls with seven acoustic variables. To reduce the dimensionality of the dataset and obtain a summary data space with less noise, we applied a Principal Component Analysis (PCA), which allowed us to limit correlations between factors that could influence clustering. Before the PCA, we scaled the acoustic variables to yield a standard deviation of one and a mean of zero with the R base function scale in each species. The analysis was carried out with the function PCA of the package FactoMineR [START_REF] Lê | FactoMineR: an R Package for multivariate analysis[END_REF]. To balance the contribution of each individual to the creation of the space and give equal weight to each female, we balanced females depending on the number of their calls by using the argument row.w of the function PCA.

In a second step, we performed a hierarchical cluster analysis using the function hcpc of the package FactoMineR [START_REF] Lê | FactoMineR: an R Package for multivariate analysis[END_REF]. We set the number of clusters for each species at 9, based on the mean number of broad categories of calls per context in macaques [START_REF] Rebout | Tolerant and intolerant macaques show different levels of structural complexity in their vocal communication[END_REF]. For this hierarchical cluster analysis, since our dataset contained different numbers of calls for each social context, we randomly sampled 50 calls per context, so each context had the same probability of occurring in any cluster if they were distributed entirely at random. For example, if the sample was biased towards a particular social context, it was more likely that the clusters were composed of this social context.

In a third step, we measured the extent to which the same acoustically-based cluster of calls could be emitted in different social contexts. To compare proportion of contexts in relation to uncertainty, we applied information theory to calculate an uncertainty value for each of the 9 clusters, based on the formula of [START_REF] Shannon | A mathematical theory of communication[END_REF]:

𝐻 = -$ 𝑝 ! " !#$ log 𝑝 !
h is the Shannon's uncertainty, S the number of social contexts, and pi the proportion of calls in the cluster for the context i. H varies from near zero (one social context is highly predominant in the cluster) to a maximum value of log S (the cluster is composed of the three social contexts in the same proportions).

For comparative purposes, we used the relative index [START_REF] Peet | The measurement of species diversity[END_REF][START_REF] Pielou | An introduction to mathematical ecology[END_REF]):

ℎ = 𝐻 𝐻 &'(
Hmax is the maximal value of H, i.e. log S This value quantitatively expresses the uncertainty in identifying the context associated with a particular signal structure. If there is a strict relationship between the structure of calls and their social context, then each cluster should contain mainly calls belonging to a single context (i.e. low uncertainty). On the contrary, if the relationship between acoustic structure and social context is looser, the proportions of calls belonging to different contexts within each cluster should be more even (i.e. high uncertainty). We then transformed the uncertainty values of each cluster into relative uncertainty values: the uncertainty was divided by the logarithm of the number of categories, i.e. the number of social contexts. The relative uncertainty value closes in on 0 as the cluster approaches a state where it only contains calls from the same social context. The relative uncertainty value closes in on a maximum -the log of 3 -when the cluster approaches a state where it contains as many calls from each social context. We finally calculated the mean from the relative index of the nine clusters. See the supplementary material ESM1 for more information.

Lastly, we statistically compared the mean relative uncertainty values of the four species of macaque. We repeated the sampling procedure, clustering procedure, and uncertainty analysis using bootstraps, with a number of 30 repetitions per species. We set the number of repetitions at 30 based on the central limit theorem. This allowed us to have enough data to be able to make meaningful statistics, but not so much as to push the power of the test, which could lead to significant but subtle differences. This resulted in four mean relative uncertainty values, one for each species, based on 30 random samples. We compared the relative uncertainty values between species using a linear model (LM). We compared the complete model (i.e. the one with the species) to the null model (i.e. the one without the species) with likelihood ratio tests (LRT) using the function lrtest of the package lmtest [START_REF] Zeileis | Diagnostic checking in regression relationships[END_REF]. This made it possible to test whether the species factor had an effect. Finally, we used post-hoc tests to make paired comparisons of species using the function emmeans of the package emmeans [START_REF] Lenth | emmeans: estimated marginal means, aka least-squares means (R Package version 1[END_REF].

We conducted a second analysis to examine the form of the commenting calls. Here, the goal was no longer to study whether a given acoustic structure belongs preferentially to one context, so we needed a specific statistical approach to test whether an individual involved in one context can vocally refer to another context. We tested the existence of acoustic differences between interaction, commenting and uncontextualized calls in rhesus, Tonkean and crested macaques. To quantify the possible differences between species in terms of acoustic variables, hereafter referred to as acoustic distance, we used Permutational multivariate analysis of variance (PERMANOVA) to test whether the centroids (mean) of the three categories of calls were statistically equivalent in the multidimensional space. We used the function adonis from the package vegan [START_REF] Oksanen | vegan: community ecology Package (R Package version 2.5-5[END_REF]. Since PERMANOVA assumes no distribution, its usage fits our dataset, and its ACCEPTED MANUSCRIPT / CLEAN COPY insensitivity to multiple correlations allowed us to keep all acoustic parameters. We ran adonis using Euclidean distances -as the logical choice to represent acoustic distances -and ran 1000 permutations, as advised by Oksanen and collaborators (2019). In order to take into account the pseudoreplication of each macaque individual, we limited the permutations using the argument strata based on individual identity in the adonis function. For paired comparisons between contexts, we applied the function pairwise.adonis of the package pairwiseAdonis (Arbizu 2017), using the same strata specification to constrain permutations. The data were represented using PCA of the packages FactoMineR and factoextra, with 95% confidence ellipses.

Results

Context specificity of calls

The degree of context specificity of calls, as measured by relative uncertainty values, differed between species (LRT χ² = 71.4, p < 0.001) (Fig. 1). Post-hoc tests revealed that the relative uncertainty values of Tonkean macaques and crested macaques did not differ significantly (estimate ± SE = -0.030 ± 0.018, t = 1.67, p = 0.344). Japanese macaques had a significantly lower value compared to rhesus (estimate = -0.079 ± 0.018, t = -4.44, p < 0.001), Tonkean (estimate = -0.161 ± 0.018, t = -9.05, p < 0.001) and crested macaques (estimate = -0.131 ± 0.018, t = -7.38, p < 0.001). Rhesus macaques had a significantly lower value than Tonkean (estimate = -0.082 ± 0.018, t = -4.61, p < 0.001) and crested macaques (estimate = -0.052 ± 0.018, t = -2.94, p = 0.020).

Form of commenting calls

The degree of differentiation of commenting calls differed according to species. In rhesus macaques, the multivariate acoustic distance was not significantly different from zero between commenting and uncontextualized calls, which means that they did not differ significantly according to their acoustic variables (pseudo-F = 3.46, p = 0.110). However, the distance was significantly different from zero between interaction and commenting calls (pseudo-F = 3.70, p < 0.001) and between interaction and uncontextualized calls (pseudo-F = 41.3, p < 0.001), which means that interaction calls differed significantly from commenting and uncontextualized calls according to their acoustic variables (Fig. 2). In Tonkean macaques, the three acoustic distances were significantly different from zero (interaction vs. commenting calls: pseudo-F = 10.8, p < 0.001; commenting vs. uncontextualized calls: pseudo-F = 57.5, p < 0.001; interaction vs. uncontextualized calls: pseudo-F = 6.08, p < 0.001) (Fig. 2). In crested macaques, the acoustic distance was noticeable but not significantly different from zero between interaction and commenting calls, which means that they did not significantly differ (pseudo-F = 1.82, p = 0.493). However, the acoustic distance was significantly different from zero between commenting and uncontextualized calls (pseudo-F = 13.4, p < 0.001), and between interaction and uncontextualized calls (pseudo-F = 27.5, p < 0.001), which means that uncontextualized calls differed significantly from commenting calls and interaction calls (Fig. 2). Lastly, the context of a proportion of commenting calls (N = 52 over 116 in the three species) could be unambiguously classified by the ear as agonistic (27.6%) or affiliative (17.2%). The context of these commenting calls was in most cases (92.3%) congruent with the agonistic or affiliative content of the social interaction attended by the calling bystander.

Discussion

The comparison of several species of macaque revealed significant interspecific differences in the context specificity of their calls. We found that tolerant macaques had a higher degree of freedom than intolerant macaques in the association between vocal structure and social context. It also appears that the form of commenting calls was more differentiated in Tonkean and crested macaques than in rhesus macaques. These results on contextual flexibility in vocal signal production were made possible by using quantitative methods based on Shannon's information theory. They significantly extend the conclusions of a previous study on structural diversity and flexibility in vocal signal production [START_REF] Rebout | Tolerant and intolerant macaques show different levels of structural complexity in their vocal communication[END_REF]).

ACCEPTED MANUSCRIPT / CLEAN COPY

Analysis of the context specificity of calls showed greater relative uncertainty values in Tonkean and crested macaques than in Japanese and rhesus macaques. This finding implies either that the calls emitted in different contexts had closer acoustic structures in tolerant than in intolerant macaques, or that calls typically associated with a given context -agonistic, affiliative or neutral -were less strongly associated with that context in the former species than in the latter species. In both cases, this means that there was more uncertainty in vocal signalling in tolerant macaques than in their intolerant counterparts. The strength of the regularities between the signal and its context of emission influences the extent to which the listener can obtain accurate information from the signal; the less context-specific a signal is, the more additional information is needed by the listener about the context to give it meaning [START_REF] Smith | The behavior of communicating: an ethological approach[END_REF][START_REF] Seyfarth | Meaning and emotion in animal vocalizations[END_REF][START_REF] Wheeler | Functionally referential signals: a promising paradigm whose time has passed[END_REF]. From the degree of freedom between vocal structure and occurrence context, we can deduce the potential range of meanings in the communicative repertoire of a species. The looser association found between structure and context in tolerant macaques indicates that their vocal communication system may involve a greater variety of meanings compared to intolerant macaques.

In intolerant species such as Japanese and rhesus macaques, it can be said that individuals experience clear-cut social situations. As previously mentioned, dominance and kinship rule their social life, interindividual conflicts most often end in clear winners and losers, and subordinates commonly direct formal signs of submission at higher-ranking individuals [START_REF] Preuschoft | Dominance and communication: conflict management in various social settings[END_REF][START_REF] Thierry | Covariation of conflict management patterns across macaque species[END_REF][START_REF] Thierry | Unity in diversity: lessons from macaque societies[END_REF][START_REF] Rebout | Resource partitioning in tolerant and intolerant macaques[END_REF]. This is consistent with the use of contextspecific signals, capable of providing listeners with precise information with only a minimum of contextual cues, as documented by Gouzoules andcollaborators (1984, 1998) for rhesus macaque scream vocalizations (see also [START_REF] Mercier | Correlates of social role and conflict severity in wild vervet monkey agonistic screams[END_REF] for vervets, Chlorocebus pygerythrus). In comparison, the outcome of the social interactions of tolerant species such as Tonkean and crested macaques cannot be easily predicted from their dominance and kinship relationships, they have better skills than intolerant macaques in the social domain, and they often switch quickly from aggression to flight, protest, or reconciliation [START_REF] Thierry | Tonkean macaque behaviour from the perspective of the evolution of Sulawesi macaques[END_REF][START_REF] Thierry | Covariation of conflict management patterns across macaque species[END_REF][START_REF] Thierry | Unity in diversity: lessons from macaque societies[END_REF][START_REF] Duboscq | The function of post-conflict interactions: new prospects from the study of a tolerant species of primate[END_REF][START_REF] Joly | Comparing physical and social cognitive skills in macaque species with different degrees of social tolerance[END_REF]). In such circumstances, the use of signals that are weakly dependent on context leaves a great deal of uncertainty in the information content. Flexible calls add richness to communication, offering a wide range of expression that can allow receivers to better manage ambiguous social situations. It should be noted, however, that rhesus macaques differed significantly from Japanese macaques. It could be proposed that this difference is explained by different levels of social tolerance in these two species, but this hypothesis appears unlikely given the proximity of both species in terms of social relationships [START_REF] Thierry | Unity in diversity: lessons from macaque societies[END_REF]. We cannot exclude that the contrast found between both species is due to the intervention of another unknown factor, such as the proportion of kin-related individuals in each group for example.

The study of commenting calls lends an additional dimension to these results by examining the ability of individuals to distantiate from their immediate context and communicate as third parties about the interactions of their group mates [START_REF] Brumm | Do Barbary macaques "comment" on what they see? A first report on vocalizations accompanying interactions of third parties[END_REF]; see [START_REF] Schamberg | Call type signals caller goal: a new take on ultimate and proximate influences in vocal production[END_REF]. In rhesus macaques, the vocal performances of interacting individuals were distinct from those not directly involved in social interactions. In contrast, no differences were observed in the structure of their uncontextualized and commenting calls, indicating that the latter do not convey additional information. In more tolerant species such as Tonkean and crested macaques, interaction calls diverged from commenting calls -albeit non-significantly in crested macaques -, and we found marked discrepancies between uncontextualized and commenting calls. The latter therefore appear to be well differentiated comments from bystanders on outgoing events. Their meaning was generally in agreement with the context of the observed interaction. Not only can the callers alert other group members, but by expressing their emotional response and/or likely future behaviour remotely while witnessing a social interaction [START_REF] Waller | Macaques can predict social outcomes from facial expressions[END_REF][START_REF] Waller | Rethinking primate facial expression: a predictive framework[END_REF], they can also transmit filtered information about its content. There are indications that Tonkean and crested macaques have a particularly strong commitment to the behaviour of others, associated with frequent polyadic interactions (Petit andThierry 1994, 2000;[START_REF] Petit | Social play in crested and Japanese macaques: testing the covariation hypothesis[END_REF][START_REF] Palagi | Exploring the evolutionary foundations of empathy: consolation in monkeys[END_REF]; Puga-ACCEPTED MANUSCRIPT / CLEAN COPY [START_REF] Puga-Gonzalez | Empathy versus parsimony in understanding post-conflict affiliation in monkeys: model and empirical data[END_REF]. The information conveyed by commenting calls may contribute to this pattern and enhance social cohesion by adding communicative feedback at the collective level.

It may be noted that there is only limited interest in providing specific comments on interactions whose outcome is foreseeable, as is the case with rhesus macaques. On the contrary, when results remain uncertain -as observed in more tolerant species -the diffusion of information within the group through circumstantial comments can be beneficial in the same way that food calls disseminate information on food availability [START_REF] Clay | Food-associated calling sequences in bonobos[END_REF][START_REF] Hauser | Food-associated calls in rhesus macaques (Macaca mulatta): I. Socioecological factors[END_REF]. Moreover, our results point to a possible link between communicative flexibility and emotional expressiveness, in accordance with Morton's 'motivation-structural hypothesis' (1977), which states that a wide range of sounds corresponds to more numerous points along motivation gradients and quick changes in motivation. A low degree of association between structure and function in tolerant macaques can allow signallers to gradually move from one call to another, and express a broad spectrum of emotions and intentions in a given context [START_REF] Freeberg | Social complexity as a proximate and ultimate factor in communicative complexity[END_REF].

Using uncertainty as an indicator of complexity, our results support both predictions of the social complexity hypothesis for communicative complexity regarding the context specificity of calls and the form of commenting calls. Species with a higher degree of uncertainty in social interactions (i.e. social complexity) were also those with a lower degree of association between acoustic structure and social context, and therefore uncertainty in vocal signals (i.e. vocal complexity). This is consistent with the findings of a previous study where we examined the relationship between the diversity of macaque vocal signals (number of call categories) and the flexibility of their acoustic structure (degree of gradation between call categories), showing that the diversity and flexibility of the acoustic structure of vocal signals were greater in species that display a higher degree of social complexity [START_REF] Rebout | Tolerant and intolerant macaques show different levels of structural complexity in their vocal communication[END_REF]). In the present study, we addressed another dimension of vocal complexity, that of contextual flexibility. The relationship found between the acoustic structure of the calls and their context of emission points to a link between the contextual flexibility of vocal signals and the level of uncertainty in the social style of macaques. Taken together, these results reveal that the vocal signals of more tolerant and socially complex macaques have a greater information potential than those of less tolerant and socially complex macaques, likely due to a higher degree of gradation of signals, and a higher degree of freedom in the association between acoustic structure and social context. It should be noted that causal direction is still under discussion regarding the social complexity hypothesis [START_REF] Peckre | Clarifying and expanding the social complexity hypothesis for communicative complexity[END_REF]. Complex social situations may require complex communicative abilities. However, complex communicative abilities may also contribute to the emergence of complex social situations. These two processes are unlikely to be mutually exclusive.

The physical structure of habitats may affect variables such as the amplitude and frequency of auditory signals [START_REF] Waser | Habitat acoustics and primate communication[END_REF][START_REF] Hauser | The evolution of communication[END_REF]), but we do not know of any variations in the ecological environment of macaques that could explain the interspecific differences we have highlighted. It may be added that we have investigated the vocalizations of three species in captive conditions, and in the wild for a fourth species, but we have not found any contrasts between the species that could be attributed to the conditions of recording. Phylogenetic relatedness between species is another possible confounding factor. Japanese and rhesus macaques on the one hand, and Tonkean and crested macaques on the other belong to two different macaque lineages, respectively [START_REF] Fooden | Classification and distribution of living macaques (Macaca Lacépède)[END_REF][START_REF] Tosi | Paternal, maternal, and biparental molecular markers provide unique windows onto the evolutionary history of macaque monkeys[END_REF]. One may wonder to what extent this could account for the contrasts observed between the two pairs of species. However, the measurement of acoustic distances between call categories gave rise to cross-species contrasts that could not be explained by phylogenetic relationships between species [START_REF] Rebout | Tolerant and intolerant macaques show different levels of structural complexity in their vocal communication[END_REF]. Future research should expand the analyses to more groups and species to confirm our current conclusions. In particular, the data needed to analyse the commenting calls were only available for one intolerant macaque species; other intolerant species have to be studied to further test the association between the acoustic structure of commenting calls and levels of social tolerance. The present study focused on the communication potential of the acoustic structure of macaque vocalizations in three main contexts. It would be interesting to extend the investigation to more specific categories of social contexts ACCEPTED MANUSCRIPT / CLEAN COPY (see [START_REF] Gouzoules | Rhesus monkey (Macaca mulatta) screams: representational signaling in the recruitment of agonistic aid[END_REF][START_REF] Cheney | Flexible usage and social function in primate vocalizations[END_REF]. It is also necessary to address vocal signals such as commenting calls through playback experiments and test the ability of listeners to attribute meanings to comments that have different levels of context-specificity.

Table 1 Information about groups and subjects [START_REF] Takahashi | Characterization of obesity in Japanese monkeys (Macaca fuscata) in a pedigreed colony[END_REF]Micheletta et

FIGURE CAPTIONS Fig. 1 Fig. 2

 CAPTIONS12 FIGURE CAPTIONS

  Fig. 1

Fig. 2 ACCEPTED

 2 Fig. 2

  al 2013; Arlet et al 2015; De Marco et al 2019) Adi, Bea, Bas, Cin, Dor, Ern, Fen, Glo, Hel, Isa, Jos, Kat, Leo, Min, Nur, Oli, Pol, Qut, Ros, Sup, Tut, Eli, Vod, Wi, Big, Yan, Zoe Dea, Eva, Fio, Geu, Her, Iye, Jan, Kri, Lid, Nao, Oma, Ram, Ste, Jam, Mal, Zor, Pap, Val, Tem, Upi

	Groups	Dates of group	Composition of	Name and age in years of females 1
		foundation and study	groups
	rhesus macaque	founded in 2004,	10 adult females,	Pip (14), But (13), Isa (11), Nil (10),
	group Ma	studied in Jul-Oct	3 adult males,	Hoe (10), Wie (9), Lok (7), Aus (6), Mon
		2016	22 immatures 2	(5), Pan (5)
	rhesus macaque	founded in 2004,	6 adult females,	Tro (13), Plo (12), Hat (10), Jah (8),
	group Mb	studied in Jul-Oct	1 adult male,	Kwe (7), Ymi (6)
		2016	24 immatures
	Tonkean macaque	founded in 1978,	4 adult females,	Gil (27), Gai (9), Giu (9), Lis (5)
	group Tb	studied in Feb-May	6 adult males,
		2016	5 immatures
	Tonkean macaque	founded in 2005,	4 adult females,	Pal (13), Sop (11), Pam (8), Pap (6)
	group Tc	studied in Sept-Dec	4 adult males,
		2014	8 immatures
	Tonkean macaque	founded in 2007,	3 adult females,	Sib (12), Tet (11), Tan (11)
	group Td	studied in Mar-May	5 adult males,
		2015	7 immatures
	Tonkean macaque	founded in 2009,	2 adult females,	Nin (15), Nif (9)
	group Te	studied in Sept-Dec	3 adult males,
		2014	5 immatures
	Japanese macaque	founded in 1974,	13 adult females,
	group Fw	studied in Mar-Aug	4 adult males, 10
		2005	immatures
	Japanese macaque	founded in	16 adult females,	Ame (25), Iwa (11), Kak (8), Kin (15),
	group Ft	1970/1971,	6 adult males, 24	Kam (5), Kur (9), Mor (22), Shi (10),
		studied in Mar-Jul	immatures	Sha (8), Tan (24), Tak (17), Tsu (21),
		2005		Umi (19), Ume (8), Yam (13), Yuk (21)
	Crested macaque group Nr1 Ani, Crested macaque wild population, studied between Sept 2010 & Feb 2011 28 identifiable adult females wild population, 23 identifiable Agn, Bia, Cic,
	group Npb	studied between Sept	adult females
		2010 & Feb 2011

Has (10), Min (6), Mia (5), Nir (6), Rek (14), Rum (17), Mil (9), Bel (5), Lar (5), Som (18), Sar (8), Jes (7),

Ren (20)

Table 2

 2 Total number of calls and mean number (± SD) of calls processed in each species

	Species (number	Agonistic context	Affiliative context	Neutral context
	of subjects)
		Total	Mean number	Total	Mean number	Total	Mean number
		number	± SD	number	± SD	number	± SD
	Japanese macaque	79	3.30 ± 3.77	94	3.92 ± 4.16	255	10.6 ± 5.48
	(N = 24)
	rhesus macaque	118	7.38 ± 6.75	59	3.69 ± 3.22	461 1	28.8 ± 16.0
	(N = 16)
	Tonkean macaque	270	20.8 ± 26.3	226	17.4 ± 14.3	202 2	15.5 ± 8.42
	(N = 13)
	crested macaque	201	10.6 ± 6.61	297	15.6 ± 11.8	191 3	10.1 ± 7.40
	(N = 19)

ACCEPTED MANUSCRIPT / CLEAN COPY

Age at the beginning of data collection. The names of the sampled females are in italics

Individuals less than 5 years of age

including 31 comments and

uncontextualized calls, 2 including 36 comments and 115 uncontextualized calls, 3 including 39 comments and 122 uncontextualized calls

Acknowledgments

We thank the keepers and managers of the Parco Faunistico di Piano dell'Abatino in Rieti, the Zoo de l'Orangerie in Strasbourg, the Biomedical Primate Research Center in Rijswijk, and the Primate Research Institute in Inuyama for their valuable help. We are grateful to S. Louazon and V. Biquand for their technical assistance. The Indonesian State Ministry of Research and Technology (RISTEK), the Directorate General of Forest Protection and Nature Conservation (PHKA), the Agricultural University of Bogor, the Department for the Conservation of Natural Resources (BKSDA, North Sulawesi), and the staff of the Macaca Nigra Project supported the collection of data in crested macaques.

Data availability

The dataset generated and analysed in the study is available as supplementary material (ESM2).

Declarations

Funding

The Fondazione Ethoikos, the Fondation des Treilles, and the Département d'Écologie, Physiologie et Éthologie (CNRS IPHC) funded the work. The Japan Society for the Promotion of Science funded the collection of data in Japanese macaques. An Eole Scholarships granted by the French-Dutch Network financed the collection of data in rhesus macaques.

Conflict of interest

The authors declare that they have no conflict of interest.

Ethics approval

The study followed the ASAB/ABS guidelines for the treatment of animals in behavioural research as published in Animal Behaviour (2005, 69:i-vi). It complied with the legal requirements of the French, Italian, Dutch, Japanese, and Indonesian governments. Research was observational and did not include any experimental intervention, so no review by an ethics committee was required.

Supplementary material

Tolerant and intolerant macaques differ in the context specificity of their calls and how they 'comment' on interactions

Behavioral Ecology and Sociobiology

Spectrograms of the main types of calls in rhesus, Japanese, Tonkean and crested macaques

The calls were labelled according to the main vocal types commonly recognized in macaques (Rowell & Hinde, 1962;Lindburg, 1971;Green, 1975;Peters, 1983;Lewis, 1985;Masataka & Thierry 1993;Panggur, 2013). The spectrograms were drawn with the software Raven Pro 1.4 (Center for Conservation Bioacoustics, 2011). They show the frequency (kHz) as a function of time (sec).

Calculation of the relative uncertainty index

The calculation of the relative uncertainty index is illustrated in Table 1. The application of the formula can be seen in the row General case. If a cluster is composed of calls from a single context, the uncertainty and the relative uncertainty are equal to 0 by convention (case 2). If a cluster is composed of calls from two contexts only, the uncertainty is calculated on these two contexts, which allows to avoid applying logarithms on null values, but still allows comparisons because thereafter the uncertainty value is divided by the logarithm of three (case 1).

The diagrams in Figure 1 illustrates two extreme cases of clustering results. Each of the nine large circles represents a cluster. Each cluster consists of a group of calls (small circles) identified according to the acoustic structure of these calls. Calls are coloured according to their context of occurrence (three colours for three social contexts). In the case of a high relative uncertainty value (1), each context is distributed over a large number of clusters. In the case of a low relative uncertainty value (2), each context is limited to a small number of clusters, and each cluster consists mainly of one context. When relative uncertainty is low, knowing the cluster to which a call belongs provides reliable information about the context in which it was probably emitted. This is not true when the relative uncertainty is high.


Céline Vion
email: celine.vion@insp.jussieu.fr

Carlos Barthou

Paul Bénalloul

Catherine Schwob

Laurent Coolen

Alex Gruzintev

Gennadi Emelchenko

Wladimir Masalov

Jean-Marc Frigerio

Agnès Maître

Gennadii Emel'chenko

Vladimir Masalov

Manipulating emission of CdSe/ZnS nanocrystals embedded in 3D photonic crystals

Keywords: numbers: 42.50.Nn, 42.70.Qs, 61.72.uj, 61.46.Hk, 78.67.Bf

come

I. INTRODUCTION

Photonic crystals are characterized by a periodic dielectric constant at wavelength scale, creating photonic energy bands where light propagation is forbidden. The emission of light sources embedded inside a photonic crystal can be strongly affected by these bandgaps: according to Fermi's golden rule, the spontaneous emission rate is proportional to the photonic local density of states (LDOS), which describes the interaction between emitters and the local field in the sample. As the photonic local density of states is strongly dependant on the material structure, photonic crystals are used for tailoring the emission of embedded light sources. This active field of research leads to applications ranging from quantum information processing [1], to light emitting devices (miniature lasers) [2] or solar cells [3].

Most devices use 2-dimensions (2D) photonic crystals, consisting in a lattice of holes etched in a high index transparent material. In the weak coupling regime, emission of single quantum dots in 2D photonic crystals has been improved, as well for their photoluminescence intensity [4] as for the polarization of emission [5]. In the strong coupling regime [6], achieved with InAs quantum dots embedded in a GaAs photonic crystal membrane, vacuum Rabi splitting [7] and emission of indistinguishable single photons [1] have been demonstrated. All these devices have been realized by electron lithography, requiring heavy technological equipments. Alternatively to this top-down approach, impregnation of 2D photonic crystals with solutions of colloïdal nanocrystals is a versatile way to couple emitters to photonic structures and to allow enhancement of spontaneous emission [8,9].

3-dimensions (3D) photonic crystals take advantage of the spontaneous self organization of spherical colloidal particles. Indeed, various techniques provide a low-cost and relatively easy protocol to obtain synthetic opals. It has been shown that the quality of opaline structures strongly depends on synthesis techniques [10]. Just as in 2D photonic crystals, the spontaneous emission of optical sources embedded in direct and inverted opals is affected by the crystal structure and can be inferred by the local density of states [11].

However, the modification of spontaneous emission lifetime by 3D silica opals is reported to be weak since the refractive index contrast is low [12]. Larger effects require a higher refractive contrast and a complete photonic band gap which can be obtained in inverted opals [13][14][15]. For colloidal CdSe nanocrystals infiltrated in titania inverse opals, lifetime reductions up to 30% have been reported [16]. Nevertheless, good quality inverse opals over large scale are still difficult to synthesize and most experimental studies on coupling emitters to 3D photonic crystals have been achieved in opals exhibiting a pseudo-band gap (infiltrated with nanocrystals [17][18][19][20][21][22] or molecules [14,[23][24][25]).

Even incomplete, the photonic bandgap affects both the luminescence spectrum of the emitter and its spontaneous lifetime. Nevertheless, disorder in opal structures can hide or limit these phenomena. To get rid of the disorder, experiments have to be performed at a scale smaller than the typical size of the opal for which it can be considered as a monocrystal. The use of a microscope can reveal the quality of the opals at a micronic scale by selection of a high quality opal zone [17,25]. At this scale, stop-band effect on nanocrystals luminescence spectra [26], single nanocrystal emission modification [17] and sligth effects on luminescence lifetime [25] have been reported. Nevertheless the pseudo gap effect is averaged over the whole numerical aperture of the microscope objective, and the dip in fluorescence spectrum due to the gap disappears for a large aperture [23]. Therefore, the use of a microscope limits the possibilities to study angle-resolved luminescent properties and does not reveal the quality of the opal over a large scale (mm) which is essential for applications.

The aim of this work is to study at macroscopic scale the coupling of colloidal CdTeSe nanocrystals to artificial direct opals. In the first part, we present the preparation and optical characterization of opaline structures. The second section presents the modification of nanocrystals emission diagrams. In a third section, a lifetime modification due the photonic bandgap is evidenced and interpreted by LDOS calculations.

II. OPALS CHARACTERIZATION

Two opals, which will be called respectively A and B, were prepared by sedimentation of 400 nm and 270 nm diameter silica balls in suspension in water, with a post selection of the 0.5 mm thick upper part of the deposit. The balls got organized spontaneously as a face-centered-cubic (fcc) structure, the highest density plane (111) being along the slab plane. The samples were then dried at 150°C, and annealed at 600°C during 5 hours in free atmosphere. Robust 5x5x0.5 mm 3 samples were obtained (≈ 2000 layers) [27,28]. Figure 1 presents the opal band diagram calculated numerically by a direct computation of the eigenstates and eigenvalues of Maxwell's equations (using a planewave basis) [29],

showing a photonic pseudogap at the L point of the photonic Brillouin zone.

The two opals were optically characterized by specular reflection, from which the diameter of the balls and the effective refracting index of the medium were inferred. The samples were illuminated with a fibered and collimated halogen source covering the whole 350-820nm spectral range, and the reflected light was collected by a second optical fiber symmetric to the first one. The fibers were mounted on rotating stages allowing a precise selection of the incident and collection angles. The light spot on the opal had a size of 4 mm 2 ( at 20°i ncidence ) and the distances between the sample and the optical fibers were 10 cm.

As the first bandgap of the direct opal is not complete, light propagation in this frequency range is allowed for certain directions and prohibited for others. An important reflectivity is awaited for the wavelengths for which the phase difference induced by reflections on two consecutive (111) planes of the face-centered cubic lattice is a multiple of 2π. This condition is fulfilled for an incidence angle corresponding to the Bragg angle which can be expressed

1). opal A: D

A = 391nm, n ef f A =1.29, opal B: D B = 269nm n ef f B = 1.34
as [30]:

λ max = 2 (2/3)D (n 2 ef f -sin 2 (φ)) ( 1
)
where D is the diameter of the balls, φ is the incidence angle relative to the normal of the (111) plane and n ef f is the effective refractive index of the medium with n ef f = α silica + (1 -α) 0 , and α is the filling factor (α = 0.74 for close packed structures). between these two values may be attributed to a more porous silica structure in larger balls [31].

At an angle φ larger than 50°, a second peak can be distinguished on the reflection spectra on figure 2(b). This peak unlike the first one shifts toward higher wavelengths for increased incident angles, as described in PMMA-sphere opals [32]. The interpretation of this phenomenon requires exact band structure calculations. On figure 3 the photonic band structure calculated along the LU and UX lines inside the first Brillouin zone (for

n ef f B = 1.34
) is superimposed on the experimental peaks of specular reflection spectra as a function of the external incidence angle φ, which is related by Snell's law sin(φ) = n ef f B sin(θ) to the internal angle θ with the L direction normal to the (111) plane. At the U point (corresponding to an external angle φ of 50.2°), a second pseudo-gap can be attributed to the constructive interference reflections on the planes (200).

III. MODIFICATION OF NANOCRYSTALS EMISSION SPECTRA

We focus first on emission spectra modifications of nanocrystals embedded in the opal. We use a nanomolar solution of CdTeSe nanocrystals [START_REF] Pons | Synthesis of Near Infrared Emitting Water Soluble CdTeSe/CdZnS Core/Shell Quantum Dots[END_REF] diluted in decane of index n decane = 1.41, a value close to the measured silica index for large balls size(n silica B = 1.39). The luminescence spectrum of the solution is centered at 685 nm and presents a Full Width Half Maximum (FWHM) of 60 nm (see fig. 2). These nanocrystals exibit a good photostability.

Their decay time (45ns in decane) is longer than for standard CdSe nanocrystals.

Both opals are infiltrated with 1µL of this solution and become translucent, demonstrating that the solution spread all over the opal: the decane infiltrated opal is equivalent to an homogeneous medium with an effective index of 1.39. As a consequence, the nanocrystals are distributed randomly in the whole volume of the sample, with much less than one nanocrystal per void. Indeed, this low density of emitters prevents nanocrystals aggregation and interactions among them, and the optical properties of the opal are not modified : after 15 min, the decane solution is totally evaporated, and specular reflection spectra realized on the infiltrated opal are identical to the ones realized prior to infiltration.

The infiltrated nanocrystals are then excited at a wavelength of 337.1 nm by a pulsed nitrogen laser (0.6 ns pulse width). Their luminescence is collected by an optical fiber mounted on a rotary stage and located at a distance of 10 cm from the surface. In this setup, for an illumination spot of 1mm 2 size on the opal surface, the detection angle resolution is approximately 1°. The emission is analyzed with a spectrometer coupled to a nitrogencooled Si Charged-Coupled Device (CCD) detector. This setup has a wavelength resolution of 0.3 nm/point. The experimental specular spectra of opal A infiltrated with nanocrystals are plotted in figure 4(a) for different collection angles. As the FWHM of quantum dots luminescence spectrum is of the same order as the stop band FWMH, the incidence angle dependent gap does not induce a dip on luminescence spectra but induces a shift of the peak wavelength (see fig. 4(a) ). Depending of the angle of collection, the central wavelength of the emission line is shifted from 685nm to 670nm for incidence angles from 0°to 45°. In this opal, the gap at 0°incidence is at 589nm (see fig. 2(b)) so that emission at 700nm is well above the bandgap. In this part of the band structure the sample is equivalent to an homogeneous medium (see fig. 1 for a/λ = 0.54 < 0.62), so that this opal, like the decane infiltrated opal, can serve as a reference for which no bandgap effect is expected.

In figure 4(c), we plot for different wavelengths the radiation diagrams normalized with respect to the corresponding reference diagrams in the decane infiltrated opal. For each wavelength, the luminescence reduction is observed for specific angles. In figure 5, these specific wavelengths for which quantum dots luminescence is reduced, are plotted as a function of the external angle φ. The curve is fitted by Bragg's law, like the central wavelength photonic bandgap measured previously by specular reflection (fig. 2). These results are a clear demonstration of the modification of nanocrystals spontaneous emission diagrams by the photonic bandgap.

IV. MODIFICATION OF NANOCRYSTALS EMISSION LIFETIME

Let us now consider the influence of the photonic crystal on the nanocrystals emission decay rate. We experimentally compare the lifetime of nanocrystals embedded in opals A (D A = 391nm) and B (D B = 269nm). Their gaps are respectively located at 824nm and 589nm at 0°incidence. We performed the experiments at 700nm by selecting spectrally through a monochromator the emission of the nanocrystals. For this wavelength, the nanocrystal emission is located inside the gap for opal A and outside the gap for opal B. The samples are kept in vacuum to prevent nanocrystal oxydation, since we observed a lifetime decrease of a few nanoseconds over tens of minutes when the experiment was performed in air. The decay curves are measured by a photomultiplier coupled to an oscilloscope. The time constant of the setup is of one nanosecond. In the following, the fiber is normal to the surface. Each measurement was performed at six different locations on both opals.

The decay analysis has to be very careful because the expected lifetime modification is rather weak for low index contrast opals as reported in the literature [12,25]. As seen on figure 6, opals exhibit self-luminescence under 337nm excitation wavelength, but this luminescence decay is much faster than the nanocrystals one. It can be seen on the emission (3) nanocrystals in the opal A infiltrated with decane (blue line). ( 4) Red line: self-luminescence of the opal. The fits using the log-normal distribution are plotted in black. The inset presents the luminescence spectrum in opal A at 0°collection. spectrum (inset on fig. 6) that, for such pulsed excitation, the self luminescence is more than 10 times less intense than the nanocrystals emission. If, for times shorter than 10 ns, the fast self-luminescence of silica balls influences the decay curves, after 10 ns it can be considered as negligible. The nanocrystal luminescence lifetimes are therefore calculated by fitting the decay curves for times between 10ns and 320ns. We fit the non-exponential decay curves with a continuous log-normal distribution of decay rates as suggested in reference [START_REF] Van Driel | [END_REF] and used with success in references [15] and [25]:

I(t) = I(0) ∞ γ=0 Φ(γ)e -γt dγ (2)
with a log-normal distribution function of the form:

Φ(γ) = A exp(- ln 2 (γ/γ M F ) w 2 ) ( 3
)
where γ M F is the most-frequent decay rate corresponding to the maximum of Φ(γ), and w is a dimensionless width parameter. The decays are fitted on more than two decades (see fig. 6) with only two free parameters γ M F and w by a least squares fit with 1/y weighting of the data (y being the data value I(t)). The mean value of decay rates with their standard deviation are summaries in table I. TABLE I: Mean most frequent decay rate γ M F and width parameter w of the distribution for opals A and B, at 700nm detection wavelength with their standard deviations σ(w) and σ(γ). The percentage of decay rate variations of opal A with respect to opal B are given in the fourth column.

opal A opal B difference

D A = 269nm D B = 391nm γ M F 0.0222ns -1 0.0192ns -1 -12.8% σ(γ M F ) 0.0002ns -1 0.0002ns -1 1.1% w 0.65 0.48 σ(w) 0.03 0.05 γ M F /n ef f 0.0172ns -1 0.0150ns -1 -9.4 ± 1.2%
We calculate the relative difference (γ the nanocrystals in opal B, with a standard deviation of 1.1%.

M F A -γ M F B )/γ M F B by
In order to explain this lifetime modification, the variation of the local density of states at the emitter positions has been calculated. According to Fermi's golden rule, the excited state of an emitting dipole decays exponentially to the ground state with a decay constant:

γ = 2π 2 n, → k ∈BZ | → µ . → E→ k ( → r )| 2 δ(ω -ω n, → k ) (4)
where → µ is the dipole moment, and

→ E → k (r)
, a plane wave function, is the electric field of mode → k . n refers to the number of the band. The non radiative decay channels can be neglected [35]. The dipole moment → µ is assumed to be constant and randomly oriented in space. The decay rate when averaged over all orientations becomes:

γ = 2π 3 2 | → µ | 2 n, → k ∈BZ |E→ k ( → r )| 2 δ(ω -ω n, → k ) = 2π 3 2 | → µ | 2 ρ(ω, → r ) (5) ρ(ω, → r
) is the photon LDOS and is strongly dependent on the index modification at wavelength scale.

Starting from the band diagrams, the distribution of electromagnetic field is calculated in the first Brillouin zone by the standard plane-wave expansion method, and the LDOS inside the opal is inferred [12]. To improve the numerical accuracy, we used a linear interpolation technique as implemented within the abinit package [36] to obtain a stable numerical result with a small number of k points in the Brillouin zone: we used 7106 k points in the first Brillouin zone (equivalent to 79507 equally spaced k points). The primitive cell was divided into 32x32x32 segments, giving a resolution of 36nm considering 391nm balls size.

For numerical reasons, the sharp transition between the silica and air dielectric constants lead to diverging results and had to be replaced by a smoother one, of thickness equal to 3x36=108nm (see fig. 8a).

The calculation of LDOS were performed with a silica index of 1.39 for opal A and 1.44 for opal B (values deduced from Bragg's fit in section II). As seen on figure 8b, the LDOS variation in opal A ρ(ω, → r ) over the cell is high and can become larger than 80% between voids and inner silica balls. As a consequence, in the simulations, the exact localization of the nanocrystals is critical, as their total diameter (core+ligands) is close to 10nm. We assume that nanocrystals are randomly located in the three pixels interface between air and silica, and we calculate the average LDOS (<LDOS>= < ρ(ω, → r ) >) for the opal A over this intermediate region for which the dielectric constant varies between 1.1 and 1.9 (between 1.1 and 2 for opal B).

Apart from bandgap effects, our experimental lifetime difference might be explained just by the small effective index difference between opals A (n ef f A = 1.29) and B (n ef f B = 1.34), as the decay rate in a homogeneous medium is proportional to the medium index. In order to distinguish the index-difference effect (n ef f A /n ef f B = 0.962) from the pure bandgap effect, we write:

γ A γ B = n ef f A n ef f B × g (6)
where g is the pseudogap effect which is analysed in this paper:

g = ρ A /n ef f A ρ B /n ef f B ( 7
)
On figure 9, we plot ρ(ω) /n ef f as the function of the emission wave number 1/λ, for opals A and B and for a homogeneous medium.

We can distinguished three different regimes on these curves.

For a wave number 1/λ < 1.21µm -1 we are below the gap of both opals and both LDOS can be described by the LDOS of a homogeneous medium (which scales as λ -3 ). The small difference between the calculated LDOS and the λ -3 curve is attributed to noise of numerical origin and provides an estimate of the corresponding error (2%).

For 1/λ between 1.21 and 1.70µm -1 , opal B still behaves like a homogeneous medium, but the LDOS of opal A is modified due to the presence of the photonic pseudogap. Like in the previous section, the opal B can be used as a reference in order to evidence the pseudogap effects in opal A in this spectral range.

When 1/λ is above 1.70µm -1 , photonic effect are expected on both opals.

From the value of these curves at λ = 700nm, we calculate the theoretical pseudogaprelated ratio between opal A and the homogeneous medium: g=0.93 (with the previously mentioned numerical error 0.02).

By averaging over all experimental 36 values of g, we find the experimental pseudogaprelated decay difference between opals A and B : g -1 = 9.4% (see figure 7 andtable I) with a standard deviation of 1.2%. This result is in good agreement with the g -1 = 7 ± 2% theoretical value obtained from the above LDOS calculation, and within the experimental and numerical margins of error.

One might want to performed a comparison between nanocrystals in opal A and nanocrystals in opal A filled with decane, since it was taken as the reference in the previous section.

Experimental pseudogap effect ratio g=0.98 was measured, in comparison with a theoretical value of 0.93. In this case, the difference between experimental and theoretical values is slightly outside our margin of error and suggests that other effects could be included in lifetime modification calculations. Such conclusion was given in reference [12] to explain larger variations of lifetime compared with LDOS predictions for molecules embedded in colloidal photonic crystals. For single nanocrystals on glass coverslips, large decay rate fluctuations have been reported and attributed to the opening of non-radiative decay channels due to defects at the sample surface [37]. Other effects like local field electronic environment corrections may cause lifetime modification as considered in reference [38].

V. CONCLUSIONS

Opals prepared by sedimentation techniques and infiltrated by colloidal CdTeSe semiconductor nanocrystals have demonstrated a sufficient quality at a macroscopic scale to induce a modification of both the spectrum and lifetime of the nanocrystals emission. The dependence of the intensity with the collection angle is large and its dependence on detection wavelength has been described by Bragg's law. The emission lifetime was compared in an opal presenting a pseudogap effect at the emission wavelength and a reference opal for which emission is outside the gap. An experimental variation of 12.8% was measured and attributed to effective index difference between the opals (known to be 3.8% from reflection experiments) and the pseudogap effect (for which we deduce an experimental value of 9.4%). These results are close to the theoretical value of 7% obtained from numerical LDOS calculations.

A more significant influence of the photonic bandgap on the lifetime would require a larger index contrast, or an inverse opal for which complete photonic bandgap can be achieved.

The insertion of a defect [39,40] inside opals, inducing a large modification of the LDOS, is a promising alternative to monitor the lifetime of nanocrystals embedded in 3D photonic crystals.

FIG. 1 :

 1 FIG. 1: Photonic band structure of the fcc lattice calculated with effective index n ef f =1.29 as a function of reduced frequency a/λ (where a is the primitive cell parameter a = √ 2D, with D the diameter of the balls), for wave vectors between the high symmetry points X, U, L, Γ, K and W of the Brillouin zone.

FIG. 2 :

 2 FIG. 2: Reflectivity spectrum of opals (a) A and (b) B for various incidence angles. (on figure (b) squares indicate the position of the second peaks). Red line: CdTeSe nanocrystals luminescence spectrum in decane, (c) Comparison of the experimental results with Bragg's law (Eq.1). opal A: D A = 391nm, n ef f A =1.29, opal B: D B = 269nm n ef f B = 1.34

Figures 2 (FIG. 3 := 1 .= 1 .

 2311 Figures 2 (a) and (b) present the spectra obtained by specular reflection on the two opals for non polarized light at different incidence angles. The wavelengths for which the specular reflectivity is maximum are plotted according to the angle of incidence for the two opals. An adjustment with Bragg's law (fig. 2c) yields with a precision of 5% for the two samples the balls diameters D A = 391 nm and D B = 269 nm and the effective indices n ef f A = 1.29

FIG. 4 :

 4 FIG. 4: (a) Luminescence spectra of infiltrated nanocrystals in opal A sample at different collection angles. (b) Diagrams of radiation in polar representation at 700 nm of CdTeSe nanocrystals in opal A (black line) compared to nanocrystals in opal A infiltrated with decane (purple line) and in opal B (orange). (c) Diagrams of radiation of infiltrated CdSeTe nanocrystals in opal A at different wavelengths normalized with respect to the corresponding reference diagrams in the decane infiltrated opal.

figure 4 (

 4 figure 4(b), the radiation diagrams at 700nm is plotted as a function of the angle of detection φ. A reduction of luminescence is observed at 45°. In order to confirm the influence of the crystalline structure, the infiltrated opal A is filled with a solution of decane, removing the gap. The dip in the emission diagram of nanocrystals disappears for the decane filled sample, as expected for an homogeneous medium (fig. 4(b)). On figure 4(b), we also plot the emission diagram at 700nm for opal B. No dip appears and the emission diagram is similar to the diagram of the opal A filled with decane. For

FIG. 5 :

 5 FIG. 5: Comparison of the experimental results with Bragg's law for opal A. Red line: nanocrystals in decane luminescence spectra. The red circles indicate the position of the minima on the diagrams of radiation. The black squares are the positions of the reflection maxima. The dotted line is a fit of the reflexion maxima by Bragg's law with parameters D A = 391nm and n ef f A = 1.29.

FIG. 6 :

 6 FIG. 6: Decays measured at 700nm for 381nm balls size opal. (1) Luminescence decay of nanocrystals infiltrated in the opal A (green line), (2) nanocrystals in opal B (black line),

FIG. 7 :

 7 FIG. 7: (a) Most frequent decays γ M F measured in the opals A (red line) and B (blue line) on six different positions. (b) Theoretical pseudogap-related pourcentage of difference between opals A and B (g-1) (see equation 7).

FIG. 8 :

 8 FIG. 8: (a) Assumed opal dielectric constant on a plane (111) for opal A. Calculation resolution: 36 nm for 391nm balls size opal. The transition zone between silica and air has a width of 108nm (b) Calculated percentage of variation of the local density of state around its mean value in the primitive cell in the pseudo gap for opal A at a/λ = 0.79 (for a = √ 2 × 391nm and λ = 700nm).

6 FIG. 9 :

 69 FIG.9: Averaged ρ/n ef f ratio at air/SiO 2 interface for opal A (black line) and B (dash line), homogeneous medium (gray line). For the opals, the LDOS is averaged on regions for which the dielectric constant varies between 1.1 and 1.9 for opal A and between 1.1 and 2 for opal B. Green line: luminescence spectra of nanocrystals emitting at 685nm as a function of 1/λ. The black arrows indicate the appearance of a pseudogap. The red arrow indicate the 700nm detection of our experiment.

Acknowledgments

Thomas Pons, Benoit Mahler and Benoit Dubertret are warmly acknowledged for the synthesis of the high quality CdTeSe nanocrystals which were crucial to the success of this study.

The authors also gratefully acknowledge Karel Kunc for helpfull discussions and Emmanuelle

Lacaze for AFM measurements. This study was supported by the Russian Foundation for Basic Research (projects N 07-02-90000 and N 07-02-92176) and C'Nano Ile de France.