# Sex and dominance: How to assess and interpret intersexual dominance relationships in mammalian societies

Peter M. Kappeler, Elise Huchard, Alice Baniel, Charlotte Canteloup, Marie

J.E. Charpentier, Leveda Cheng, Eve Davidian, Julie Duboscq, Claudia

Fichtel, Charlotte Korinna Hemelrijk, et al.

► To cite this version:

Peter M. Kappeler, Elise Huchard, Alice Baniel, Charlotte Canteloup, Marie J.E. Charpentier, et al. "Sex and dominance: How to assess and interpret intersexual dominance relationships in mammalian societies." Frontiers in Ecology and Evolution, 2022, 10, pp.918773. 10.3389/fevo.2022.918773. hal-03820273

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EDITED BY
Geoffrey M. While,
University of Tasmania, Australia

REVIEWED BY
Arrilton Araujo,
Federal University of Rio Grande do
Norte, Brazil
Scott Creel,
Montana State University, United States

*CORRESPONDENCE
Peter M. Kappeler
pkappel@gwdg.de
Elise Huchard
elise.huchard@umontpellier.fr

†These authors have contributed
equally to this work

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This article was submitted to
Behavioral and Evolutionary Ecology,
a section of the journal
Frontiers in Ecology and Evolution

RECEIVED 12 April 2022
ACCEPTED 06 July 2022
PUBLISHED 29 July 2022

CITATION
Kappeler PM, Huchard E, Baniel A, Canteloup C, Charpentier MJE, Cheng L, Davidian E, Duboscq J, Fichtel C, Hemelrijk CK, Höner OP, Koren L, Micheletta J, Prox L, Saccà T, Seex L, Smit N, Surbeck M, van de Waal E and Girard-Buttoz C (2022) Sex and dominance: How to assess and interpret intersexual dominance relationships in mammalian societies. *Front. Ecol. Evol.* 10:918773.
doi: 10.3389/fevo.2022.918773

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© 2022 Kappeler, Huchard, Baniel, Canteloup, Charpentier, Cheng, Davidian, Duboscq, Fichtel, Hemelrijk, Höner, Koren, Micheletta, Prox, Saccà, Seex, Smit, Surbeck, van de Waal and Girard-Buttoz. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Sex and dominance: How to assess and interpret intersexual dominance relationships in mammalian societies

Peter M. Kappeler<sup>1,2*†</sup>, Elise Huchard<sup>3*†</sup>, Alice Baniel<sup>4</sup>,
Charlotte Canteloup<sup>5,6</sup>, Marie J. E. Charpentier<sup>3</sup>,
Leveda Cheng<sup>7,8</sup>, Eve Davidian<sup>9</sup>, Julie Duboscq<sup>10,11</sup>,
Claudia Fichtel<sup>1</sup>, Charlotte K. Hemelrijk<sup>12</sup>, Oliver P. Höner<sup>9</sup>,
Lee Koren<sup>13</sup>, Jérôme Micheletta<sup>14</sup>, Lea Prox<sup>1,11</sup>,
Tommaso Saccà<sup>12</sup>, Lauren Seex<sup>12</sup>, Nikolaos Smit<sup>3</sup>,
Martin Surbeck<sup>7,8</sup>, Erica van de Waal<sup>5,6</sup> and
Cédric Girard-Buttoz<sup>15,16</sup>

<sup>1</sup>Behavioral Ecology and Sociobiology Unit, German Primate Center, Leibniz Institute for Primate Research, Göttingen, Germany, <sup>2</sup>Department of Sociobiology/Anthropology, Johann-Friedrich-Blumenbach Institute for Zoology and Anthropology, University of Göttingen, Göttingen, Germany, <sup>3</sup>Institut des Sciences de l'Évolution, Université de Montpellier, Montpellier, France, <sup>4</sup>Center for Evolution and Medicine, Arizona State University, Tempe, AZ, United States, <sup>5</sup>Department of Ecology and Evolution, University of Lausanne, Lausanne, Switzerland, <sup>6</sup>Inkawu Vervet Project, Mawana Game Reserve, Pretoria, South Africa, <sup>7</sup>Department of Human Evolutionary Biology, Harvard University, Cambridge, MA, United States, <sup>8</sup>Max Planck Institute for Evolutionary Anthropology, Leipzig, Germany, <sup>9</sup>Department of Evolutionary Ecology, Leibniz Institute for Zoo and Wildlife Research, Berlin, Germany, <sup>10</sup>UMR 7206 Eco-Anthropologie, CNRS-MNHN-Université de Paris Cité, Paris, France, <sup>11</sup>Department of Behavioral Ecology, Johann-Friedrich-Blumenbach Institute for Zoology and Anthropology, University of Göttingen, Göttingen, Germany, <sup>12</sup>Theoretical Research in Evolutionary Life Sciences (TRÈS), Groningen Institute for Evolutionary Life Sciences, University of Groningen, Groningen, Netherlands, <sup>13</sup>Faculty of Life Sciences, Bar-Ilan University, Ramat Gan, Israel, <sup>14</sup>Department of Psychology, Centre for Evolutionary and Comparative Psychology, University of Portsmouth, Portsmouth, United Kingdom, <sup>15</sup>Institut des Sciences Cognitives, Centre National de la Recherche Scientifique (CNRS), Lyon, France, <sup>16</sup>Department of Human Behavior, Ecology and Culture, Max Planck Institute for Evolutionary Anthropology, Leipzig, Germany

The causes and consequences of being in a particular dominance position have been illuminated in various animal species, and new methods to assess dominance relationships and to describe the structure of dominance hierarchies have been developed in recent years. Most research has focused on same-sex relationships, however, so that intersexual dominance relationships and hierarchies including both sexes have remained much less studied. In particular, different methods continue to be employed to rank males and females along a dominance hierarchy, and sex biases in dominance are still widely regarded as simple byproducts of sexual size dimorphism. However, males and females regularly compete over similar resources when living in the same group, and sexual conflict takes a variety of forms across
societies. These processes affect the fitness of both sexes, and are mitigated by intersexual hierarchies. In this study, we draw on data from free-ranging populations of nine species of mammals that vary in the degree to which members of one sex dominate members of the other sex to explore the consequences of using different criteria and procedures for describing intra- and intersexual dominance relationships in these societies. Our analyses confirmed a continuum in patterns of intersexual dominance, from strictly male-dominated species to strictly female-dominated species. All indices of the degree of female dominance were well correlated with each other. The rank order among same-sex individuals was highly correlated between the intra- and intersexual hierarchies, and such correlation was not affected by the degree of female dominance. The relative prevalence of aggression and submission was sensitive to variation in the degree of female dominance across species, with more submissive signals and fewer aggressive acts being used in societies where female dominance prevails. Thus, this study provides important insights and key methodological tools to study intersexual dominance relationships in mammals.

KEYWORDS

dominance, sex, hierarchy, mammals, methodology

Introduction

When the Norwegian zoologist Schjelderup-Ebbe (1922)
published his dissertation on the social psychology of chickens a
century ago, he was the first to report that the directionality and
consistency with which hen peck at each other during feeding
and resting yields a stable arrangement among individuals that
he called a pecking order. As in other species, dominance
relationships among chicken are established and maintained
through agonistic interactions whereby one individual may
exhibit aggressive behavior, whereas the partner either displays
submissive behavior or avoids confrontation with the aggressor
altogether (Rowell, 1974). Other, structurally more complex
types of hierarchies have since been described for various
animal societies in which individuals recognize individual
conspecifics and remember the outcome of previous agonistic
interactions with co-residents (Reddon et al., 2021). Whereas
solitary or unfamiliar animals can also establish a dominance
relationship without prior interaction, for example, based on
mutual assessment of body size, ornaments or other intrinsic
cues of fighting ability, we are here primarily interested
in this aspect of the social structure of species that live
permanently in groups that contain both sexes because
social dominance represents a prominent feature of many
animal societies.

Dominance relationships have various determinants that
are not mutually exclusive and can feed back upon each
other in determining the outcome of an agonistic interaction

(Dehnen et al., 2022). First, in some species, a given dyadic
dominance relationship reflects differential social support
received by each member of the dyad (Clutton-Brock and
Huchard, 2013a,b), either in the form of parental (Holekamp
and Smale, 1991) or non-parental support (Schülke et al.,
2010). Second, memories of previous interactions with known
individuals can promote a learning effect that leads individuals
to exhibit submissive behavior toward certain other conspecifics
(Guhl, 1968). The effect of this dyadic interaction-outcome
history is further reinforced by the winner-loser effect (Chase
et al., 1994), according to which winning increases the
probability to be victorious again and losing makes it more
likely that the victim loses again in the next fight against any
other opponent (Rutte et al., 2006; Franz et al., 2015). Finally,
dominance relationships are often based upon an asymmetry
in agonistic power grounded on intrinsic attributes, such as
physical superiority, fighting ability, motivation, or leverage that
are often age-based (Hand, 1986; Lewis, 2002; Jonart et al.,
2007; Dunham, 2008; Clutton-Brock and Huchard, 2013a,b;
Dehnen et al., 2022; Tibbetts et al., 2022). In species with
pronounced sexual size dimorphism and/or elaborate weapons,
these intrinsic attributes are linked to sex, with members of the
larger and/or better armed sex often using their attributes to
establish and stabilize dominance relationships with members
of the opposite sex (Kappeler, 1993; Lewis, 2018), just as size and
strength are important determinants of within-sex dominance.
However, recent evidence highlighted that sex differences in
physical attributes may often fail to predict who is dominant
in an intersexual relationship, as in bonobos (*Pan paniscus*) and spotted hyenas (*Crocuta crocuta*) (Surbeck and Hohmann, 2013; Vullioud et al., 2019).

In species in which groups consist of permanently associated males and females, past research has often focused on intrasexual dominance relations because they are thought to mediate access to fitness-limiting factors, such as mates and resources. As a result, most previous studies of dominance hierarchies have been framed in separate theoretical frameworks. Studies of female dominance relations focused on the ecological drivers of interspecific variation (Sterck et al., 1997; Clutton-Brock and Janson, 2012). Studies of male dominance relationships, in contrast, focused on their functional outcomes for mating access and reproductive skew (Cowlishaw and Dunbar, 1991; Alberts, 2012). However, such a binary approach overlooks the potential importance of intersexual agonism for the fitness of both sexes. First, when males and females live in the same group, competition can occur both within and between the sexes for access to various resources, including – but not necessarily limited to – the feeding context (Valé et al., 2020; Koenig et al., 2022). Second, sexual conflict is nearly ubiquitous, and takes various forms that all generate intersexual strife (Chapman et al., 2003; Davidian et al., 2022), which affects the fitness of both sexes and may be mitigated by intersexual hierarchies. Thus, while it may make sense to use separate intrasexual hierarchies for species with pronounced sexual size dimorphism, with sex differences in the steepness, linearity and stability of the within-sex hierarchies, and in which the mechanisms of rank acquisition differ between the sexes, this approach may not be appropriate for other species.

A few studies indicate that sex is one key variable for scrutinizing dominance hierarchies in more detail. First, in some species individuals are distributed within a group's hierarchy as a function of their sex, with either all or most males outranking all females or – more rarely – *vice versa* (Kappeler, 1993; Smuts and Smuts, 1993; Stevens et al., 2007; Surbeck and Hohmann, 2013; Izar et al., 2021). Such sex clusters likely reflect sex differences in morphology, physiology or life-history that underlie agonistic power and therefore offer an opportunity to identify sex-specific determinants of dominance. Second, males and females compete for different resources, and may therefore employ different strategies to establish and maintain their dominance rank among their same-sex peers, with unknown consequences for the establishment of intersexual hierarchies. Notably, the steepness, linearity and stability of the male and female hierarchies often differ. In chimpanzees and gorillas, for example, males have conspicuous and relatively despotic dominance hierarchies, whereas dominance relations among females are more elusive and are based on age-based queuing conventions (Stevens et al., 2007; Foerster et al., 2016). In Barbary macaques, the opposite pattern has been found, with males being more egalitarian and females more despotic in dominance style (Preuschoft et al., 1998; Hemelrijk and

Gygax, 2004). Contrasting hierarchies across dyads of same- and opposite-sex members can therefore reveal informative subtleties on sex differences in social competition beyond species differences. Finally, the mechanisms of rank acquisition may differ between the sexes, with males typically relying on intrinsic attributes to compete for high rank, whereas female ranks tend to depend more often on social support (Holekamp and Smale, 1991; Clutton-Brock and Huchard, 2013b).

Nonetheless, dominance relationships between the sexes have not received the same theoretical and empirical attention as same-sex dominance relationships. Because male-biased sexual dimorphism is widespread among mammals (Lindenfors et al., 2007) and represents a default expectation based on conventional sex roles, the ability of males of these species to dominate females was typically considered an unavoidable side-effect of physical superiority and greater aggressiveness, rather than as an adaptive trait *per se* (Kappeler, 1993; Smuts and Smuts, 1993; Lewis, 2018). In contrast, the rare cases of female dominance often required special explanation and generated several hypotheses that typically invoke taxon-specific factors to explain the evolution of this sex role "reversal" (Jolly, 1984; Richard and Dewar, 1991; van Schaik and Kappeler, 1996; Wright, 1999; Dunham, 2008; Kappeler and Fichtel, 2015). These few taxa or studies were not deemed of enough general interest, however, to prompt a general synthesis of intersexual relationships.

The dichotomous classification of species as either male- or female-dominated has been challenged by more recent studies indicating that these patterns only represent the endpoints of a continuum (Hemelrijk et al., 2008, 2020; Davidian et al., 2022; Kappeler et al., 2022). It is now more widely appreciated that there are taxa where members of one sex only win a proportion of all agonistic interactions with the members of the other sex or where they dominate only some, but not all, opposite-sex individuals (Surbeck and Hohmann, 2013; Young et al., 2017, Vullioud et al., 2019; Hemelrijk et al., 2020). In addition, different methods continue to be employed to rank males and females along a dominance hierarchy (Pereira and Kappeler, 1997; Hemelrijk et al., 2008), potentially obscuring interesting biological patterns. In order to analyze this variation in a comparative fashion, comparable data on intersexual dominance relationships are required. However, existing studies have used various methods for recording details of agonistic interactions, for inferring dominance relationships, and for determining dominance hierarchies, and different species use different types and variable proportions of acts and signals to establish dominance relationships, thereby hampering comparative studies on this topic. We are therefore only beginning to explore whether different methods to analyze agonistic interactions are equivalent or whether some methods should be preferred or discouraged (Sánchez-Tójar et al., 2018; Vilette et al., 2020).

The general aim of this study is, therefore, to systematically determine the consequences of using different behavioral data,
criteria and methods for inferring patterns of intersexual
dominance relationships. Specifically, we aim to make
recommendations about standardized methods of data
collection and analyses for future studies of intersexual
dominance relationships that go beyond taxon-specific
idiosyncrasies. We are also interested in possible similarities
across species in the nature and pattern of intersexual
dominance relationships. For instance, it remains unknown
whether an individual's position in the intrasexual hierarchy
relates to its position in the intersexual hierarchy and, hence,
whether intersexual dominance patterns are an emergent
property of intrasexual ones.

To this end, we have collated datasets from nine mammalian
species which were chosen because they differ in the degree
to which members of one sex dominate the members of
the other sex, ranging from complete male dominance to
complete female dominance. Our aim was to explore the
consequences of using different criteria and procedures
for describing intra- and intersexual dominance relations
in this sample of animal societies and not a comparative
study across a wide range of taxa and social systems. Most
of these datasets are based on observations spanning at
least a full year for at least two different groups, thereby
accounting for seasonal variation and group idiosyncrasies.
With this dataset, we (1) calculated and compared different
indices of the degree of intersexual dominance in a group,
(2) examined whether an individual's rank in the same-sex
hierarchy predicts its position in the intersexual hierarchy,
i.e., whether high-ranking females in the female hierarchy
are more likely to dominate males, for example, and if the
degree of correlation between intra- and intersexual hierarchy
changes along the intersexual dominance spectrum, and
(3) explored whether within- and between-sex conflicts
differ in nature and intensity in terms of their reliance on
aggressive and submissive behavior along the intersexual
dominance spectrum. Taken together, our study provides
a first set of recommendations and predictions for future
studies aimed at explaining interspecific variation in
intersexual dominance.

Materials and methods

Study species and data collection

Data on agonistic interactions were collected from nine
different mammalian species: spotted hyenas (Crocuta crocuta),
rock hyraxes (Procavia capensis) and seven primates including
two lemurs: Verreaux's sifakas (Propithecus verreauxi) and
redfronted lemurs (Eulemur rufifrons), four Old World
monkeys: chacma baboons (Papio ursinus), crested macaques
(Macaca nigra), mandrills (Mandrillus sphinx), and vervet
monkeys (Chlorocebus pygerythrus) and one ape: bonobos (Pan

paniscus), as part of nine long-term individual-based field
studies, including the Ngorongoro Hyena Project, Ein Gedi
Rock Hyrax Sociality Project, Kirindy Forest Lemur Project,
Tsaobis Baboon Project, Macaca Nigra Project, Mandrillus
Project, Inkawu Vervet Project and the Kokolopori Bonobo
Research Project. All studies were approved and authorized by
the respective national authorities. The localization and ecology
of each field site, as well as the demographic, life-history and
behavioral monitoring of each study population are described
in the **Supplementary Materials**, alongside the species-specific
agonistic behavioral repertoire.

Data on agonistic interactions were recorded as detailed
in the **Supplementary Materials** and grouped by year for
each species and study group, yielding 24 group-years of data
(range 1–4 per species). An agonistic interaction was defined
by the expression of at least one species-specific agonistic
behavior (see Hausfater, 1975). Following Deag (1977), agonistic
behavioral elements were functionally characterized as either
aggressive or submissive (see also Walters, 1980). Structurally,
we distinguished between acts, which involve physical contact
or locomotion, such as lunging or fleeing, and visual or vocal
signals, such as non-physical threats or grimacing (see Pereira
and Kappeler, 1997). We considered only dyadic interactions
between adult individuals.

Group size ranged between 4 and 72 adult individuals,
including 1–62 females and 2–26 males (Table 1). For each
dataset, the corresponding co-author(s) entered the data into
a standardized template. In this template, we entered only
dyadic interactions and each agonistic interaction constituted
a row. For each agonistic interaction, we entered the following
information: (1) the identity of the two participants, (2) the sex
of each participant, (3) whether the conflict was decided (i.e.,
only one opponent exhibited submissive behavior) or not, (4)
the identity of the winner of a decided conflict, and (5) whether
one or the other or both individuals displayed an aggressive act,
an aggressive signal, a submissive act and/or a submissive signal
(see Supplementary Figure 1).

The final dataset comprised a total of 11,499 agonistic
interactions, including 5,453 interactions between females, 2,373
interactions between males, and 3,673 interactions between
males and females. The majority of all agonistic interactions
(10,005 or 87%) were decided. The total number of interactions
per group ranged from 8 to 3,650 (mean ± SD = 479.1 ± 764.9,
Table 1).

Indices of intersexual dominance

We computed hierarchies based on David's scores and
I&SI, using the function "DS" and "ISI" of the R package
"EloRating" (Neumann et al., 2011). David's score is calculated
based on power relationships between individuals, and the score
of each individual is calculated based on the proportion of
<table><caption>TABLE 1 Summary of the data collated for this study.</caption><thead><tr><th>Species</th><th>Group</th><th>Group size</th><th>N. females</th><th>N. males</th><th>Total N. interactions</th><th>N. interactions FF</th><th>N. interactions FM</th><th>N. interactions MM</th></tr></thead><tbody><tr><td rowspan="2">Bonobo</td><td>Ekalakala</td><td>8</td><td>5</td><td>3</td><td>387</td><td>29</td><td>120</td><td>238</td></tr><tr><td>Kokoalongo</td><td>21</td><td>13</td><td>8</td><td>580</td><td>53</td><td>254</td><td>273</td></tr><tr><td rowspan="4">Chacma baboon</td><td>J_2013</td><td>27</td><td>17</td><td>10</td><td>429</td><td>255</td><td>120</td><td>54</td></tr><tr><td>J_2014</td><td>27</td><td>18</td><td>9</td><td>1076</td><td>490</td><td>489</td><td>97</td></tr><tr><td>L_2013</td><td>30</td><td>19</td><td>11</td><td>368</td><td>131</td><td>171</td><td>66</td></tr><tr><td>L_2014</td><td>30</td><td>20</td><td>10</td><td>1467</td><td>636</td><td>674</td><td>157</td></tr><tr><td rowspan="2">Crested macaque</td><td>PB</td><td>27</td><td>18</td><td>9</td><td>459</td><td>319</td><td>79</td><td>61</td></tr><tr><td>R1</td><td>51</td><td>25</td><td>26</td><td>3650</td><td>2129</td><td>837</td><td>684</td></tr><tr><td>Mandrill</td><td>Group 1</td><td>72</td><td>62</td><td>10</td><td>555</td><td>331</td><td>193</td><td>31</td></tr><tr><td rowspan="3">Redfronted lemur</td><td>B</td><td>12</td><td>3</td><td>9</td><td>87</td><td>5</td><td>48</td><td>34</td></tr><tr><td>J</td><td>10</td><td>2</td><td>8</td><td>46</td><td>1</td><td>16</td><td>29</td></tr><tr><td>X</td><td>8</td><td>4</td><td>4</td><td>82</td><td>7</td><td>60</td><td>15</td></tr><tr><td rowspan="3">Rock hyrax</td><td>Gal</td><td>6</td><td>3</td><td>3</td><td>8</td><td>0</td><td>7</td><td>1</td></tr><tr><td>Isiim</td><td>21</td><td>10</td><td>11</td><td>37</td><td>14</td><td>9</td><td>14</td></tr><tr><td>Suckot</td><td>18</td><td>10</td><td>8</td><td>39</td><td>15</td><td>10</td><td>14</td></tr><tr><td rowspan="2">Spotted hyena</td><td>Lemala</td><td>26</td><td>14</td><td>12</td><td>574</td><td>390</td><td>154</td><td>30</td></tr><tr><td>Munge</td><td>29</td><td>13</td><td>16</td><td>195</td><td>75</td><td>63</td><td>57</td></tr><tr><td rowspan="3">Verreaux's sifaka</td><td>E</td><td>4</td><td>1</td><td>3</td><td>48</td><td>NA</td><td>20</td><td>28</td></tr><tr><td>F</td><td>4</td><td>1</td><td>3</td><td>63</td><td>NA</td><td>50</td><td>13</td></tr><tr><td>G</td><td>5</td><td>1</td><td>4</td><td>59</td><td>NA</td><td>50</td><td>9</td></tr><tr><td rowspan="4">Vervet monkey</td><td>BD_2016</td><td>17</td><td>11</td><td>6</td><td>203</td><td>79</td><td>66</td><td>58</td></tr><tr><td>BD_2018</td><td>29</td><td>16</td><td>13</td><td>703</td><td>262</td><td>117</td><td>324</td></tr><tr><td>NH_2013</td><td>16</td><td>11</td><td>5</td><td>238</td><td>131</td><td>30</td><td>77</td></tr><tr><td>NH_2017</td><td>11</td><td>9</td><td>2</td><td>146</td><td>101</td><td>36</td><td>9</td></tr></tbody></table>

conflicts won and lost with other individuals in the group. For this metric, the number of conflicts is of importance because David's score does not simply provide an ordinal rank but yields power differences between individuals. However, for the purpose of our study, we only used David's score to establish individual rank order (with the highest score receiving rank 1, the second highest rank 2, etc.). One drawback of David's score is that it is relatively sensitive to the percentage of missing dyads in the matrix and to differences in observation time between individuals (Neumann et al., 2011). I&SI, on the other hand, is based on multiple iterations of randomization of the interaction matrix, until reaching the most parsimonious rank order. The advantage of this method is that it is designed to provide ordinal rank order and is less sensitive to missing data. One drawback, however, is that it may provide several equally likely rank order solutions with large datasets and in particular when interactions are lacking for a large proportion of dyads, potentially complicating the interpretation and limiting replicability. In fact, re-running the algorithm several times on the same matrices does not provide exactly the same result.

For each hierarchy, we then calculated the percentage of males dominated by each

female ("the degree of female dominance") and averaged this percentage across all females to obtain two indices.

Index 1: average percentage of males in a group dominated by each female (Hemelrijk et al., 2008, 2020) using hierarchies based on male-female interactions only. This index was calculated twice, once using David's score (de Vries, 1998) to calculate the hierarchy (Index 1a) and once using hierarchies based on I&SI (de Vries, 1998, Index 1b).

Index 2: the female dominance index, FDI (Hemelrijk et al., 2020), calculated as the average percentage of males in a group dominated by each female using hierarchies based on all agonistic interactions (i.e., inter- and intrasexual conflicts). We also computed this index twice, using hierarchies based on either David's score (Index 2a) or I&SI (Index 2b).

To evaluate whether alternative estimates of the degree of female dominance or methodological differences in calculation may alter assessment of intersexual dominance relationships, we calculated three additional indices as follows:

Index 3: percentage of intersexual conflicts won by females, calculated for each female and averaged across all females.
Index 4: percentage of intersexual conflicts won by females in each intersexual dyad averaged across all intersex or something of that nature dyads.

Index 5: total percentage of intersexual conflicts won by females overall.

We then compared the correspondence among these indices by calculating pair-wise Spearman correlation coefficients for each species.

## Correspondence between intra- and intersexual hierarchies

Next, we examined whether the assignment of individual rank is sensitive to the type of data used to calculate dominance hierarchies. We constructed three separate hierarchies: a female-only hierarchy based on female-female interactions only, a male-only hierarchy based on male-male interactions only, and an intersexual hierarchy based on all decided agonistic interactions. We constructed these hierarchies using David's scores since they allow for reproducibility of the analyses (i.e., the same hierarchy is obtained from the same interaction matrix each time, which is not the case with I&SI method since it is based on matrix randomization). We then extracted the ordinal dominance rank of each female (i.e., between 1 and N, N being the number of females in the group) among all other females in the intersexual hierarchy. We then calculated the Spearman rank correlation coefficient between female ordinal ranks from the intrasexual versus intersexual hierarchies. We repeated this process for males, yielding two correlation coefficients per group-year: one for female-only hierarchies and one for male-only hierarchies.

For all three (female-only, male-only, and intersexual) hierarchies of each group, we compiled an index of triangular transitivity, using the function “transitivity” in the R package “EloRating” (Neumann et al., 2011), which provides an index of hierarchical linearity based on the proportion of triads in the hierarchy that have transitive dominance relationships (Shizuka and McDonald, 2012). Indices below 0.75 indicate that hierarchies are less transitive than random, and an index of 1 reflects a completely transitive hierarchy. We resorted to using triangular transitivity since it is less sensitive to missing data than alternative measures of linearity (h and h'; Shizuka and McDonald, 2012; Neumann et al., 2018).

We used two separate generalized linear mixed models (GLMMs) to assess whether the degree of female dominance in a group is sensitive to differences in individual rank as a result of using either intra- or intersexual hierarchies for both, females (Model 1a) and males (Model 1b). In Model 1a, each correlation coefficient of the females' ranks between the intra and the inter-sexual hierarchy for each group-year constituted a data point; the same applies to correlation coefficients for males in Model 1b. We used separate GLMMs with beta error structure because the response in each model was bound

between 0 and 1. We transformed the response using the following formula, recommended for models using a beta error distribution because it transforms zeros (which cannot be handled by beta models) into very small non-zero values (Smithson and Verkuilen, 2006):

$$x' = (x*(N - 1) + 0.5)/N$$

where $x'$ is the transformed value of x (here the correlation coefficient) and N the sample size.

In each model we used the degree of female dominance in the group (as expressed by Index 1a) as test predictor. Note that all five indices of intersexual dominance were found to be highly correlated (see section “Results”). We added as control predictor the percentage of male-female dyads that did not interact since this can influence David's scores (see above) and, therefore, the difference in ranks in the intra- versus intersexual dominance hierarchy. We could not include other control predictors, such as group size or adult sex ratio (e.g., Hemelrijk et al., 2008; Kappeler, 2017), because of our small sample size (only 21 data points in Models 1a and 24 data points in Model 1b) to avoid overparameterization. In addition to the fixed effects we added species as a random effect to account for the non-independent repeated measures on several groups of the same species.

## The form of agonistic interactions in male- versus female-dominated societies

Finally, we assessed whether the degree of female dominance in a group covaries with variation in the form of agonistic interactions within and between the sexes. More specifically, we used four GLMMs to test whether the degree of female dominance influenced the likelihood of at least one of the two opponents exhibiting an aggressive act (Model 2a), an aggressive signal (Model 2b), a submissive act (Model 2c), or a submissive signal (Model 2d) in an agonistic interaction. For each model, we counted both decided and undecided agonistic interactions in which it was clear whether one or both individuals exhibited an agonistic act or signal (N = 11492 interactions). We used GLMMs with binomial error structure to model whether an act or signal was produced (Y/N) during each agonistic interaction. As test predictors, we included the degree of female dominance as quantified by index 1a, the dyad type (FF, MM, FM) and their interaction. We fitted this interaction term to test whether the effect of the degree of female dominance on the likelihood to engage in certain acts or signals differed across the three dyad types. Group size and adult sex ratio were included as control predictors in each model because they can influence social dynamics (Hemelrijk et al., 2008; Kappeler, 2017). To account for the non-independence of repeated observations involving the same individuals, dyads and species, we added the four following random effects in each model: species, identity of the
actor in the interaction, identity of the recipient and identity of the dyad. For Model 2d, the incorporation of group size as a control variable created some instability in the model preventing us from obtaining meaningful estimates for the effect of the test predictors. We therefore reran the model without group size as a variable and present the results of this second model.

While the behaviors coded as submissive acts and signals and aggressive signals were broadly similar across all the study species (see *Supplementary Materials*), the behaviors coded as aggressive acts differed for some datasets. In particular, displacement was considered an aggressive act in all datasets except two, the crested macaque and spotted hyena datasets. In the latter, displacement was only considered an aggressive act if the approaching individual expressed an aggressive signal. This divergence may reflect meaningful differences in the context and function of displacement behavior and variation in aggressiveness. To account for this different coding and to assess whether it had any impact on the conclusions drawn, we re-ran Model 2a (Model 2a bis) using a reduced dataset excluding crested macaque and spotted hyena datasets.

## Statistical software and model assumption checking

We ran all statistical models in R 4.1.2 (R Core Team, 2021), using the function “glmmTMB” from the package glmmTMB (Brooks et al., 2017) for Models 1a and 1b, and the function “glmer” from the package lme4 (Bates et al., 2011) for Models 2a-2d and 2a bis. For mixed-effects models, we included the maximum random slope structure between each fixed predictor (test and control) and each random effect (Baayen et al., 2008; Barr et al., 2013). In each model, we tested for the overall significance of the test predictors by comparing the full model to a reduced model comprising all control predictors, all the random effects and random slopes, but without any test predictor, using a likelihood ratio test (LRT, Dobson, 2002). We then assessed the significance of each predictor using a LRT between the full model and a reduced model comprising all predictors except the one to evaluate. We repeated this process across all variables using the drop1 function. For each model, we tested for collinearity issues between our predictor variables using the function vif from the package “car” (Fox and Weisberg, 2011). Collinearity was not an issue (all vifs < 3). We also assessed model stability removing one level of each random effect at a time and recalculating the estimates of the different predictors that revealed no stability issue (except for model 2d, see above). Finally, we tested for overdispersion in Models 1a and 1b, which was not an issue (all dispersion parameters < 1.08). For Models 2a-d and Model 2a bis, we calculated the marginal R² (i.e., the variance explained by the fixed effects) and the conditional R² (i.e., the variance explained

by the entire model including both fixed and random effects) using the function r.squaredGLMM of the package “MuMin” (Barton, 2020). For Models 1a and 1b we could not compile the R² due to negative model’s distribution-specific variance.

## Results

The interaction matrices compiled for this study were highly heterogeneous in terms of missing dyads, from being almost full, with most dyads interacting with each other, as in the Ekalakala bonobo group, to being largely empty, with interactions absent for > 85% of dyads, as in the mandrill or rock hyrax groups (Table 2 and Supplementary Tables 1–3). Most inter- and intrasexual hierarchies were highly transitive (transitivity index ≥ 0.97, Tables 2 and Supplementary Tables 1–3), but a few hierarchies had a transitivity index close to the random level of transitivity set at 0.75 as in redfronted lemurs (group X) or well below this random level as in rock hyraxes (group Isiim) (Table 2). There were no strong correlations between the degree of female dominance and the degree of transitivity (correlation coefficient = 0.07, Supplementary Figure 2).

## Indices of intersexual dominance

The species included in this comparative study represent a continuum in terms of the degree of intersexual dominance, from strictly male-dominated species as in the two chacma baboon groups (all indices ≤ 0.09% group males dominated by each female), to strictly female-dominated species as in the three Verreaux’s sifaka groups (all indices ≥ 0.94, Figures 1, 2 and Supplementary Table 4). Importantly, our dataset does not comprise only species at the extreme ends of the spectrum of intersexual dominance but also several species where dominance is not very biased toward one sex (e.g., some redfronted lemur, bonobo or vervet monkey groups, Figures 1, 2 and Supplementary Table 4).

All five female dominance indices correlated strongly with each other (Spearman R2 range: 0.92–0.98, Figures 1, 2), indicating that different indices of female dominance can be used interchangeably, as they do not influence the position of each group/species on the spectrum of the extent of female dominance. Please note however that for datasets with a large proportion of missing dyads the different indices provided more variable values (Figure 2 and Supplementary Tables 1–3).

## Correspondence between intra- and intersexual hierarchies

In models 1a and 1b, the full model was not significantly different from the null model (Model 1a: *N* = 21 group\_years,
<table><caption>TABLE 2 Characteristics of the intersexual hierarchies and conflict types used in this study.</caption><thead><tr><th>Species</th><th>Group</th><th>N dyads</th><th>Prop. Missing dyads</th><th>Transitivity (Pt)</th><th>Ratio of act vs. signal</th><th>Ratio of submissive vs. aggressive behaviors</th><th>Prop. of decided conflicts</th></tr></thead><tbody><tr><td rowspan="2">Bonobo</td><td>Ekalakala</td><td>28</td><td>0.04</td><td>1.00</td><td>387.00</td><td>0.78</td><td>0.62</td></tr><tr><td>Kokoalongo</td><td>210</td><td>0.39</td><td>0.97</td><td>64.11</td><td>0.77</td><td>0.56</td></tr><tr><td rowspan="4">Chacma baboon</td><td>J_2013</td><td>351</td><td>0.48</td><td>1.00</td><td>10.07</td><td>0.98</td><td>0.98</td></tr><tr><td>J_2014</td><td>351</td><td>0.26</td><td>0.98</td><td>7.81</td><td>0.98</td><td>0.98</td></tr><tr><td>L_2013</td><td>435</td><td>0.60</td><td>1.00</td><td>9.94</td><td>0.97</td><td>0.97</td></tr><tr><td>L_2014</td><td>435</td><td>0.23</td><td>1.00</td><td>5.31</td><td>0.96</td><td>0.97</td></tr><tr><td rowspan="2">Crested macaque</td><td>PB</td><td>351</td><td>0.50</td><td>1.00</td><td>2.27</td><td>1.23</td><td>0.82</td></tr><tr><td>R1</td><td>1275</td><td>0.45</td><td>0.98</td><td>1.43</td><td>1.84</td><td>0.85</td></tr><tr><td>Mandrill</td><td>group 1</td><td>2556</td><td>0.86</td><td>1.00</td><td>3.78</td><td>0.98</td><td>1.00</td></tr><tr><td rowspan="3">Redfronted lemur</td><td>B</td><td>66</td><td>0.62</td><td>1.00</td><td>NA</td><td>0.36</td><td>0.36</td></tr><tr><td>J</td><td>45</td><td>0.58</td><td>1.00</td><td>NA</td><td>0.52</td><td>0.52</td></tr><tr><td>X</td><td>28</td><td>0.46</td><td>0.83</td><td>NA</td><td>0.30</td><td>0.30</td></tr><tr><td rowspan="3">Rock hyrax</td><td>Gal</td><td>15</td><td>0.67</td><td>NA</td><td>1.00</td><td>1.00</td><td>1.00</td></tr><tr><td>Isiim</td><td>210</td><td>0.87</td><td>0.50</td><td>1.00</td><td>1.00</td><td>1.00</td></tr><tr><td>Suckot</td><td>153</td><td>0.84</td><td>1.00</td><td>1.00</td><td>1.00</td><td>0.92</td></tr><tr><td rowspan="2">Spotted hyena</td><td>Lemala</td><td>325</td><td>0.56</td><td>1.00</td><td>1.02</td><td>1.49</td><td>0.91</td></tr><tr><td>Munge</td><td>406</td><td>0.73</td><td>1.00</td><td>1.17</td><td>1.57</td><td>0.87</td></tr><tr><td rowspan="3">Verreaux's sifaka</td><td>E</td><td>6</td><td>0.17</td><td>1.00</td><td>0.32</td><td>3.54</td><td>0.96</td></tr><tr><td>F</td><td>6</td><td>0.17</td><td>1.00</td><td>1.00</td><td>1.13</td><td>0.87</td></tr><tr><td>G</td><td>10</td><td>0.40</td><td>1.00</td><td>0.74</td><td>1.47</td><td>0.85</td></tr><tr><td rowspan="4">Vervet monkey</td><td>BD_2016</td><td>136</td><td>0.40</td><td>0.97</td><td>1.77</td><td>0.87</td><td>0.57</td></tr><tr><td>BD_2018</td><td>406</td><td>0.43</td><td>0.99</td><td>2.23</td><td>0.95</td><td>0.71</td></tr><tr><td>NH_2013</td><td>120</td><td>0.44</td><td>1.00</td><td>1.42</td><td>0.93</td><td>0.63</td></tr><tr><td>NH_2017</td><td>55</td><td>0.16</td><td>0.97</td><td>2.46</td><td>1.34</td><td>0.88</td></tr></tbody></table>

NA: Transitivity could not be computed for the rock hyrax group Gal. For all redfronted lemurs, the ratio of act vs. signal could not be computed since no signal has been recorded in the dataset for this species.

$df = 1, \chi^2 = 0.096, P = 0.756$; Model 1b: $N = 24$ group\_years, $df = 1, \chi^2 = 1.613, P = 0.204$) indicating that variable degrees of intersexual dominance did not significantly impact the differences in dominance rank observed between the intra- and the intersexual dominance hierarchy for both males and females (Supplementary Table 5 and Figure 3). These changes were rather influenced by the structure of the datasets, at least for the female hierarchies in which correlation between the intra- and the intersexual dominance hierarchies were influenced by the percentage of missing dyads ($P = 0.051$, Supplementary Table 5). Nevertheless, overall, intra- and intersexual hierarchies were highly correlated, across variable degrees of intersexual dominance, especially for females (Figure 3).

## Differences in agonistic interactions in female vs. male-dominated societies

Individuals in most study species used acts more than signals in agonistic interactions, with some species, like redfronted lemurs and bonobos, using acts almost exclusively (Table 2).

Verreaux's sifakas diverge from this general trend: they used acts and signals equally in one group and signals more often than acts in the two other groups. Together with mandrills, Verreaux's sifakas are also the study species using the highest ratio of submissive to aggressive behaviors.

The full model was significantly different from the null model in three out of four models testing the effect of the degree of female dominance and of the dyad type (M-F, F-F, M-M) on the probability of using aggressive and submissive acts or signals ($N_{interactions} = 11.492, N_{dyads} = 2908, N_{individuals} = 508, LRT, df = 5, Model 2a: $\chi^2 = 34.97, P < 0.001$; Model 2b: $\chi^2 = 57.25, P < 0.001$; Model 2c: $\chi^2 = 8.30, P = 0.141$, and Model 2d: $\chi^2 = 37.15, P < 0.001$). In Model 2a investigating the probability of using aggressive acts, the interaction between the degree of female dominance and dyad type was marginally non-significant ($P = 0.070$, Table 3). For FM and FF dyads, the probability to use aggressive acts decreased slightly with increasing female dominance, and such decrease was steeper for MM dyads (Figure 4A and Supplementary Figure 4). We found similar results in Model 2a bis with a reduced dataset excluding crested macaques and spotted hyenas (Supplementary Figure 5) with the exception that the interaction between the degree of
<figure><img src="image_3.png" /><figcaption>FIGURE 1</figcaption></figure>

Correlations among the five female dominance indices. All pairwise comparisons among the five indices are shown, with each point representing one social group of the nine species. The 7 indices are abbreviated on the axis as follow: *P. male dominated*_FM_DS: percentage of males dominated by each female in the hierarchy compiled using David's score and based on heterosexual conflicts only (*Index 1a*); *P. male dominated*_FM_ISI: percentage of males dominated by each female in the hierarchy compiled using I&SI and based on heterosexual conflicts only (*Index 1b*); *FDI_DS*: female dominance index based on hierarchies compiled using David's score and based on all conflicts (*Index 2a*); *FDI_ISI*: female dominance index based on hierarchies compiled using I&SI and based on all conflicts (*Index 2b*); *Indiv. fem*.dom.: Individual female dominance, percentage of intersexual conflicts won by females calculated for each female and averaged across all females (*Index 3*); *Dyadic fem*.dom.: Dyadic female dominance, percentage of intersexual conflicts won by females in each male-female dyad and averaged across all heterosexual dyads (*Index 4*); *Overall fem*.dom.: Individual female dominance, percentage of intersexual conflicts won by females over males overall across all heterosexual conflicts (*Index 5*). "Cor": correlation coefficient calculated using Spearman rank correlation tests.

female dominance and dyad type was significant (*P* = 0.001, **Supplementary Table 6**) and that the probability to use aggressive acts did not decrease with increasing female dominance for FF dyads. In Model 2b, we found a significant interaction between the degree of female dominance and the probability of expressing aggressive signals (*P* = 0.033, **Table 3**). For FM and FF dyads, the probability for aggressive signals to occur in agonistic interactions decreased with increasing degree of female dominance but remained stable for MM dyads (**Figure 4B** and **Supplementary Figure 4**). In Model 2c, the degree of female dominance and dyad type did not significantly affect the probability for submissive acts to occur during agonistic interactions (**Figure 4C** and **Supplementary Figure 4**). Finally, Model 2d revealed a significant interaction between the degree of female dominance and dyad type on the probability for submissive signals to occur (*P* = 0.004, **Table 3**). While the probability for submissive signals to occur during agonistic interactions increased steadily with the degree of female dominance, this positive relationship was less pronounced for FM dyads compared to MM and FF dyads (**Figure 4D** and **Supplementary Figure 4**). The marginal R²

were 0.142, 0.202, 0.050, 0.057, and 0.190 for Models 1a,1a bis, 1b,1c, and 1d, respectively. The conditional R² were 0.819, 0.608, 0.864, 0.531, and 0.907 for Models 1a, 1a bis, 1b, 1c, and 1d, respectively.

## Discussion

Our study confirmed that intersexual dominance varies along a continuum from strict female dominance to strict male dominance independent of the measure used. All indices of the degree of female dominance were well correlated with each other, and the rank order among same-sex individuals was highly correlated between the intrasexual and intersexual hierarchies, and such correlation was not significantly affected by the degree of female dominance in the group. In most study groups, within sex ranks were highly correlated between the intra- and the intersexual hierarchies and variations in this correlation were function of the dataset property (i.e., % of missing dyads in Model 1a). Interestingly, the relative prevalence of each type of agonistic behavior was sensitive
<figure><img src="image_4.png" /></figure>

to variation in the degree of female dominance, with more
submissive signals and fewer aggressive acts being used by
both sexes and across all dyad types in societies where female
dominance prevails. Below, we discuss each of these main results
in light of the current knowledge of heterosexual relationships
across mammalian societies.

Indices of intersexual dominance

One of the novelties of the present study was the
standardized application of several methods to calculate
intersexual dominance across a range of mammalian species
with different social systems. We found the degree of female
dominance to vary continuously from strict male dominance to
strict female dominance, adding to a growing number of studies
(Hemelrijk et al., 2008, 2020; Rina Evasoa et al., 2019; Davidian
et al., 2022; Kappeler et al., 2022) breaking with traditional
binary categorizations into female-dominant vs. male-dominant
species. Clearly, binary categories are insufficient to capture the
variation in intersexual dominance relationships occurring both

across and within species. The latter insight is illustrated by
species for which we had data from more than one group, such
as bonobos, redfronted lemurs and vervet monkeys, confirming
results of several recent studies (Surbeck and Hohmann, 2013;
Vullioud et al., 2019; Hemelrijk et al., 2020; Izar et al., 2021).
These patterns open the way for future investigations of the
sources of inter- and intraspecific variation in intersexual
dominance patterns.

Our study will facilitate future comparative studies by
demonstrating strong positive correlations among the five
indices that measure the degree of female dominance. Some
indices, namely 1 and 2, required the construction of intersexual
hierarchies while others, namely 3–5, simply quantified the
proportion of dyadic interactions won by one sex. Their high
correlation suggests that they capture the same behavioral
phenomenon, and validate the use of dominance hierarchies to
measure asymmetries between the sexes in the propensity to
win intersexual agonistic interactions. Special care should be
taken for datasets with high uncertainty induced by missing
interactions for a large number of dyads, as in redfronted lemurs
and rock hyraxes (Supplementary Figure 3) for which female
dominance indices varied greatly. However, even with such a
variation, the study groups were positioned in the same area
of the spectrum characterizing the degree of female dominance,
regardless of the index chosen (Figure 2). Overall these indices
are thus robust and consistent. This is further confirmed by
the similar values generated by David's score or I&SI methods.
These results indicate that all five indices capture meaningful
aspects of dominance relationships between males and females,
ensuring the comparability of past, present and future studies
using one or several of these indices.

By positioning each study group along the intersexual
dominance gradient using a standardized approach, we
generated a fine-grained picture of their relative order. Such
positions were largely consistent with previous descriptions
of intersexual dominance for most of these species; some
were already described as predominantly male dominant, like
mandrills (Setchell et al., 2001), chacma baboons (Kalbitzer
et al., 2015), and crested macaques (Duboscq et al., 2013; Tyrrell
et al., 2020), or predominantly female dominant, like Verreaux's
sifaka (Richard and Heimbuch, 1975), spotted hyenas (Vullioud
et al., 2019), bonobos (Parish, 1996; Parish et al., 2000), or
rock hyraxes (Koren et al., 2006; Koren and Geffen, 2009).
Similarly, redfronted lemurs exhibited no sex-biased or slightly
male-biased intersexual dominance as previously studied in
captive and wild populations (Pereira et al., 1990; Ostner and
Kappeler, 1999). The relatively balanced and flexible intersexual
dominance characterizing vervet monkeys (Young et al., 2017;
Hemelrijk et al., 2020) was also reported by recent studies
of capuchin monkeys (Izar et al., 2021). For other groups or
species, indices of female dominance contrasted with previous
empirical evidence. For example, this study revealed that female
dominance in bonobos is far from strict, since one group appears
<figure><img src="image_5.png" /><figcaption>FIGURE 3</figcaption></figure>

Degree of female dominance and correlation between intra- and intersexual hierarchies for females (left panel) and males (right panel). Each species is depicted using a different color. Apes, old world monkeys, lemurs and non-primates are depicted using squares, diamonds, circles and triangles, respectively. Each dot represents one study group in a given year. The black lines indicate the model's predictive lines for the effect of the degree of female dominance on the correlation between individual ranks from the intra- and from the intersexual hierarchies for females (Model 1a, left panel) and for males (Model 1b, left panel). The lines are only indicative since the *p*-values for these effects were non-significant in both models. Verreaux's sifakas do not appear in the left panel since there was only one female in each of the three groups and correlations between female ranks in the intra and intersexual hierarchies could thus not be calculated.

predominantly male dominant (Table 3). Generally, intersexual
dominance relationships have been particularly well studied in
the set of species selected for this study, but much remains to
be learned about the generality of the patterns reported here
from future studies of many other species and populations
where social hierarchies have so far been examined separately
for males and females.

Correspondence between same-sex
and opposite-sex hierarchies

One cannot simply assume that an individual's position in
the intrasexual hierarchy is directly predictive of its position
in the intersexual hierarchy given the functional and structural
differences between male and female intrasexual hierarchies
(Clutton-Brock and Huchard, 2013b). Males and females
often – but not always (Vullioud et al., 2019) – show distinct
mechanisms of rank acquisition (de Waal, 1984; Holekamp
and Smale, 1991; Foerster et al., 2016), as well as different
hierarchical properties, such as steepness (Stevens et al., 2007)
or stability (Holekamp and Smale, 1991). We found that in
most cases, individuals maintained their same-sex dominance
ordering in the intersexual hierarchy. For example, if four males
are ranked A-B-C-D in the intrasexual hierarchy, it is very
likely that the rank order of these males will be maintained in
the intersexual dominance hierarchy, even if some females are
ranked in between or above those males. This result clarifies
an important aspect of the structure of intersexual hierarchies.

Like intrasexual hierarchies in most species included in this
study, intersexual hierarchies are mostly highly transitive (with
the exception of one group of rock hyrax and one group of
redfronted lemurs, **Supplementary Figure 2**). Intersexual ranks
are simply obtained by merging both intrasexual hierarchies,
respecting their initial order, but at variable levels, i.e., from
a full entanglement, sometimes referred to as “codominance”
(Lewis, 2018), to strict male or female dominance, where all
members of one sex outrank all members of the other sex.
The fact that the degree of female dominance was not found
to influence these patterns suggests that this effect persists
across the whole gradient of intersexual dominance. Overall,
individuals of both sexes can thus be ordered together in a
common, meaningful intersexual hierarchy, according to their
competitive abilities, whatever they might be based on. While
models suggest that an individual's experiences with the self-
reinforcing effects of winning and losing fights may concern
interactions with both males and females (Hemelrijk et al.,
2008), this is not necessarily so, as indicated by evidence
of a sex difference in the winner-loser effect in hamsters
(Solomon et al., 2007).

A few social groups in our dataset showed a relatively
low correlation between an individual's position in the same-
sex vs. intersexual hierarchy, as in males of one chacma
baboon group, or in females of one bonobo, one crested
macaque and one rock hyrax group (Figure 3). It is possible
that the number of dyads for which no interaction was
recorded may affect the robustness of hierarchies. Yet, this
is unlikely to explain our results given that the percentage
<table><caption>TABLE 3 Effect of the degree of female dominance and dyad type (FM, FF, MM) on the probability of using aggressive acts (Model 2a), aggressive signals (Model 2b), and submissive signals (Model 2d).</caption><thead><tr><th>Model</th><th>Response</th><th>Predictor</th><th>Estimate</th><th>SE</th><th>CI<sub>low</sub></th><th>CI<sub>high</sub></th><th>χ<sup>2</sup></th><th>P</th></tr></thead><tbody><tr><td rowspan="8">2a</td><td rowspan="8">Did the conflict comprise an aggressive act (Y/N)</td><td>Intercept</td><td>2.37</td><td>1.25</td><td>-0.17</td><td>5.03</td><td></td><td></td></tr><tr><td>Dyad type (FM)</td><td>0.51</td><td>0.11</td><td>0.18</td><td>0.83</td><td></td><td></td></tr><tr><td>Dyad type (MM)</td><td>-0.12</td><td>0.17</td><td>-0.56</td><td>0.29</td><td></td><td></td></tr><tr><td>Degree of female dominance</td><td>-0.17</td><td>0.49</td><td>-0.97</td><td>0.82</td><td></td><td></td></tr><tr><td>Sex ratio<sup>§</sup></td><td>-1.24</td><td>0.19</td><td>-1.87</td><td>-0.69</td><td>38.41</td><td><strong>&lt;0.001</strong></td></tr><tr><td>Group size<sup>§</sup></td><td>-0.88</td><td>0.23</td><td>-1.58</td><td>-0.26</td><td>15.70</td><td><strong>&lt;0.001</strong></td></tr><tr><td>Female dominance * dyad type (FM)</td><td>-0.18</td><td>0.10</td><td>-0.53</td><td>0.15</td><td>5.31</td><td>0.070</td></tr><tr><td>Female dominance * dyad type (MM)</td><td>-0.29</td><td>0.13</td><td>-0.71</td><td>0.12</td><td></td><td></td></tr><tr><td rowspan="8">2b</td><td rowspan="8">Did the conflict comprise an aggressive signal (Y/N)</td><td>Intercept</td><td>-1.22</td><td>1.51</td><td>-4.74</td><td>1.76</td><td></td><td></td></tr><tr><td>Dyad type (FM)</td><td>0.41</td><td>0.13</td><td>0.01</td><td>0.77</td><td></td><td></td></tr><tr><td>Dyad type (MM)</td><td>-0.95</td><td>0.23</td><td>-1.54</td><td>-0.37</td><td></td><td></td></tr><tr><td>Degree of female dominance</td><td>-0.87</td><td>0.51</td><td>-1.88</td><td>-0.06</td><td></td><td></td></tr><tr><td>Sex ratio<sup>§</sup></td><td>-0.05</td><td>0.22</td><td>-0.72</td><td>0.67</td><td>0.04</td><td>0.848</td></tr><tr><td>Group size<sup>§</sup></td><td>0.49</td><td>0.27</td><td>-0.24</td><td>1.20</td><td>3.23</td><td>0.072</td></tr><tr><td>Female dominance * dyad type (FM)</td><td>0.22</td><td>0.13</td><td>-0.13</td><td>0.60</td><td>6.85</td><td><strong>0.033</strong></td></tr><tr><td>Female dominance * dyad type (MM)</td><td>0.57</td><td>0.19</td><td>0.08</td><td>1.05</td><td></td><td></td></tr><tr><td rowspan="8">2d</td><td rowspan="8">Did the conflict comprise a submissive signal (Y/N)</td><td>Intercept</td><td>-4.81</td><td>1.83</td><td>-9.34</td><td>-1.11</td><td></td><td></td></tr><tr><td>Dyad type (FM)</td><td>0.19</td><td>0.45</td><td>-1.02</td><td>1.27</td><td></td><td></td></tr><tr><td>Dyad type (MM)</td><td>1.20</td><td>0.88</td><td>-1.06</td><td>3.09</td><td></td><td></td></tr><tr><td>Degree of female dominance</td><td>2.90</td><td>0.79</td><td>1.87</td><td>4.23</td><td></td><td></td></tr><tr><td>Sex ratio<sup>§</sup></td><td>0.46</td><td>0.41</td><td>-0.32</td><td>1.34</td><td>1.18</td><td>0.278</td></tr><tr><td>Female dominance * dyad type (FM)</td><td>-0.56</td><td>0.27</td><td>-1.34</td><td>0.18</td><td>11.08</td><td><strong>0.004</strong></td></tr><tr><td>Female dominance * dyad type (MM)</td><td>-0.48</td><td>0.50</td><td>-1.61</td><td>0.76</td><td></td><td></td></tr></tbody></table>

Results from Model 2c explaining the probability of using submissive acts are not shown here as this model did not differ from the null model. Since all the continuous variables were standardized to a mean of 0 and a standard deviation of 1, the intercepts and corresponding main effects are indicated for an average degree of female dominance, sex ratio and group size. For all the estimates of the "Dyad type" fixed effect, female-female dyads are the reference category. SE indicates the standard error of the estimate for each predictor. <sup>§</sup>Indicates control predictors. Significant *p*-values (*p* < 0.05) are indicated in bold and trends (*p* < 0.1) in italics. CI<sub>low</sub> and CI<sub>high</sub> indicate the lower and upper limits of the 95% confidence intervals for the estimates of each predictor. The sample size for each model is N<sub>interactions</sub> = 11492, N<sub>dyads</sub> = 2908, N<sub>individuals</sub> = 508.

of missing dyads was included as a control factor in our models and did not yield a significant effect on the correlation between the two hierarchies. In addition, there are species and sex differences in the dynamics of hierarchies that are not accounted for here, and which may influence hierarchical properties, especially transitivity. Specifically, the methods used here to build hierarchies ignore temporal changes in hierarchies, whereas other methods continuously adjust and update a hierarchy over time when it is characterized by high temporal dynamics (e.g., use of the dynamic Elo- ranking methods: Neumann et al., 2011). Static approaches may be suitable in some cases, such as the stable, linear and heritable hierarchies of female cercopithecines, but less so for unstable male hierarchies in seasonal breeding species where most males are not permanent group members, as in mandrills (Brockmeyer et al., 2015) and rock hyraxes (Barocas et al., 2011), or species where males move frequently between groups, as in crested macaques (Neumann et al., 2011; Marty et al., 2016). The moderate correspondence between intra- and intersexual hierarchies may thus reflect the social dynamics in these species, which may occur over

the course of a year (i.e., the time frame used here to derive hierarchies).

Different dominance styles in male- and female-dominated societies

We finally investigated whether the relative importance of agonistic acts vs. signals and of aggressive vs. submissive behavior varies across the spectrum of interspecific variation in intersexual dominance. This analysis highlighted at least two important results. First, the relative frequencies with which different agonistic behaviors were used followed the same pattern in relation to the degree of female dominance for male- male, female-female, and male-female dyads. Second, and most noticeably, an increase in the degree of female dominance was related to a steep increase in submissive signals during contests and a modest decrease in the use of aggressive acts. This pattern suggests that in societies where dominance is biased toward females, signals are particularly important for structuring social life and likely limit the use of direct aggression during conflicts,
<figure><img src="image_6.png" /><figcaption>FIGURE 4</figcaption></figure>

Influence of the degree of female dominance (Index 1a) and dyad type (FM, FF, MM) on the likelihood for conflicts to comprise aggressive acts (A), aggressive signals (B), submissive acts (C), or submissive signals (D). Each dyad type is depicted using a different color and symbol: Red square: female-female dyads (FF), orange circle: female-male dyads (FM) and blue triangle: male-male dyads (MM). Each dot represents one dyad type of a study group on a given year and dot size is proportional to the log number of dyads. Log scale was chosen here because the number of dyads in each dyad type in the largest groups were orders of magnitude larger than in smallest groups. The red, orange and blue lines depict the predicted relationship between the degree of female dominance and the likelihood of each act or signal to occur for FF, FM, and MM dyads respectively. These lines are derived from Models 2a (panel A), 2b (panel B), 2c (panel C), and 2d (panel D). Please note that for Model 2c the full model did not significantly differ from the null model and the corresponding lines do not represent meaningful statistical relationships but are used for illustration.

compared to societies dominated by males. Nonetheless, the intensity and frequency of agonistic acts or signals can vary even between species that are positioned alongside on intersexual dominance spectrum. For example, across macaque societies, which are all largely male-dominated, there are well-described differences between species in the ratio of contact aggression and non-contact aggression, which are typically related to a species' "dominance style," which characterizes dominance relationships from most egalitarian to most despotic (Thierry, 2007).

The relationship between the degree of female dominance and the differential use of aggression and submission might partly reflect a reduction in male aggressiveness across the female dominance gradient, along with a decreasing magnitude of sexual dimorphism. Indeed, in several species where females dominate males, their body size or levels of aggressiveness and androgens resemble those of males – as in many lemurs (Jolly, 1984; Petty and Drea, 2015; Grebe et al., 2019), spotted

hyenas (McCormick et al., 2021), rock hyraxes (Koren et al., 2006), and meerkats (Davies et al., 2016), and ongoing research confirms that the degree of sexual dimorphism is a strong predictor of the outcome of intersexual agonistic interactions across primates (Huchard et al., unpubl. data). In addition, species-specific patterns of agonistic interactions (Supplementary Figure 2) suggest that the general, interspecific relationship is largely driven by spotted hyenas and sifakas, which stand out by using fewer aggressive acts than other female-dominant species. In contrast, the increased use of submissive signals in female-dominant species is robust and involves most populations where dominance is largely female-biased, except for bonobos. Overall, female-biased dominance appears associated with a higher ratio of submissive signals to aggressive acts, a result that needs verification with a larger number of species, as well as using analyses that control for phylogenetic proximity between species. Controlling for
phylogeny was here complicated by the low number of species involved, coupled with a heterogeneous phylogenetic coverage comprising a disproportionate number of primates as well as a couple of other, distantly related species.

The generality of this phenomenon across all dyad types may be compatible with the idea that agonistic interactions are ruled by convention-based norms that are shared by group members across age-sex-classes. These norms might possibly be socially transmitted, or flexibly influenced by prior experience, such as winner-loser effects (Tibbetts et al., 2022). Regardless of the underlying mechanism, these results suggest that female-dominated societies may rely less on aggression than male-dominated ones. This constitutes an important finding to identify the consequences of intersexual power for individual health, welfare and fitness, as well as for social dynamics and population demography. Our findings may also have ramifications for a better understanding of variation in the level of intra- and intersexual violence across past and contemporary human societies (Gómez et al., 2016; Glowacki et al., 2020).

Other patterns are more discrete. The use of aggressive signals also covaried with the degree of female dominance in female-female and intersexual dyads, with fewer threats observed in societies where ritualized submissive signals limit the use of direct aggression; threats may therefore lose their intimidating function when they are not reinforced by direct aggression. Alternatively, it is possible that either aggressive or submissive signals are needed to maintain a dominance hierarchy (Tibbetts et al., 2022), but that both are functionally redundant and rarely co-exist. Male-male dyads, in contrast, hardly use any threats across the continuum, possibly because it is risky to threaten a rival in male-dominant societies where male-male competition is often intense and contest-based, while threats are uncommon in female-dominant societies for the reasons discussed above. Finally, the slight (non-significant) decline of submissive acts along the female dominance gradient likely reflects the decline of aggressive acts, probably because submissive acts represent responses to aggressive acts. In contrast, aggressive acts are not systematically followed by a submissive act, which may explain why the decline is less pronounced for submissive than aggressive acts.

## Conclusions and Recommendations

This study provides important insights and key methodological tools to study intersexual dominance relationships in mammals, and perhaps in other vertebrates. First, we show that several distinct quantitative indices of intersexual dominance are equally successful at ordering groups from several populations and species along an intersexual gradient ranging from strict male to strict female dominance. Second, we show that intersexual hierarchies are meaningful

emergent properties of interactions occurring within and between the sexes. These hierarchies arise from merging male and female hierarchies, where individuals retain their intrasexual rank, but can be outranked by a variable number of opposite-sex group members. Third, we found continuous variation in patterns of agonistic interactions across species, characterized by less direct aggression and more ritualized submissions in female-dominant societies, which have apparently developed potent mechanisms of conflict mitigation that promote peaceful interactions and inhibit aggression. This work provides important foundations for future studies of intersexual dominance across mammals to uncover determinants and consequences of variation in intersexual dominance comprehensively, using standardized, quantitative measures within and across societies.

## Data availability statement

The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found below: Data deposited in Figshare: https://figshare.com/articles/dataset/Dataset_for_Sex_and_Dominance_How_to_Assess_and_Interpret_Intersexual_Dominance_Relationships_in_Mammalian_Societies-/19583215.

## Ethics statement

This study uses data from nine different species coming from countries with different regulations. All details regarding permits and authorizations have been provided in the relevant section of the manuscript.

## Author contributions

The manuscript was conceived collectively based on shared discussions among co-authors during a workshop that took place in 2020 in Leiden (Netherlands), co-organized by CH and PK. PK, EH, and CG-B drafted the manuscript. CG-B performed the data analyses. All authors contributed critically to writing, either collected, curated, and/or analyzed the behavioral data (from their respective study population).

## Funding

EH was funded by the ANR ERS-17-CE02-0008, 2018-2021 during the write-up of Tsaobis Baboon Project. Kokolopori Bonobo Research Project is funded by the Harvard University, Max-Planck Society. Project Mandrillus is funded by the SEEG
Lekedi and LIA (INEE-CNRS) to MC, Agence Nationale de la Recherche (ANR SLEEP 17-CE02-0002 to MC and ANR ERS-17-CE02-0008, 2018-2021 to EH), Deutsche Forschungsgemeinschaft (DFG, KA 1082-20-1) to PK and MC, as well as by the State Scholarships Foundation (IKY) under the scholarship program from the proceeds of the “Nic. D. Chrysovergis” bequest to NS. Inkawu vervet project is funded by the Fyssen Foundation (granted to CC) and the Swiss National Science Foundation (31003A_159587 and PP00P3_170624) along with the Branco Weiss Fellowship in Science (granted to EW). Macaca nigra Project is funded by the German Research Council within the Emmy-Noether programme, the Federal Ministry for Economic Cooperation and Development and the German Academic Exchange Service (to Antje Engelhardt), by the Volkswagen Stiftung (to JD) and the University of Portsmouth (to JM). Ein Gedi rock hyrax sociality project was funded by the Israel Science Foundation and United States-Israel Binational Science Foundation (2015088). Ngorongoro Hyena Project is funded by the Leibniz Institute for Zoo and Wildlife Research; Werner Dessauer Stiftung.

## Acknowledgments

We would like to thank colleagues who contributed ideas or suggestions during the various discussions and exchanges that led to the setup of the study, as well as two referees for their constructive comments, and Christof Neumann for fruitful discussions. The Kokolopori Bonobo Research Project thanks the ICCN, Bonobo Conservation Initiative and Vie Sauvage for their support of the study, the Ministry of Scientific Research and Technology in the Democratic Republic of the Congo for the permission to work in the DRC, the people of the villages of Bolamba, Yete, Yomboli, and Yasalakose for granting access to their forest, all local and international field assistants for their support in the field, as well as Harvard University and the Max-Planck Society for funding the project. The Tsaobis Baboon Project is grateful to the volunteers from 2013 and 2014 for collecting behavioral data. This research was carried out with the permission of the Ministry of Environment and Tourism, the Ministry of Land Reform, and the National Commission on Research, Science, and Technology. We further thank the Tsaobis beneficiaries for permission to work at Tsaobis, the Gobabeb Namib Research Institute and Training Centre for affiliation, and Johan Venter and the Snyman and Wittreich families for permission to work on their land. This article is n° ISEM 2022-144. The Mandrillus Project is grateful to the past and present field assistants who collected behavioral data and to the SODEPAL-COMILOG society (ERAMET group) for their long-term logistical support. This is a Project Mandrillus publication number 27. This study was approved by an

authorization from the CENAREST institute (permit number, AR0060/18/MESRS/CENAREST/CG/CST/CSAR). The Inkawu Vervet Project (IVP) thanks the van der Walt family for permission to conduct the study on their land and the whole IVP team for their help and support in the field. The Macaca Nigra Project in Tangkoko thank all team members, especially Antje Engelhardt and Jan-Boje Pfeifer. We thank Joko Pamungkas from the Primate Research Centre, Muhammad Agil and Perwitasari Farajallah from the Institute Pertanian Bogor University for supporting our stay in Indonesia. We gratefully acknowledge the permission of the Indonesian Institute of Sciences, the Directorate General of Forest Protection and Nature Conservation and the Department for the Conservation of Natural Resource, North Sulawesi, particularly Pak Domingus and Pak Yunus, to conduct research in the Tangkoko Reserve. The Kirindy Forest Lemur Project thanks the Malagasy Ministry of the Environment, the University of Antananarivo and the CNFEREF Morondava for authorizing our work, and the Kirindy field assistants for help with data collection. The Ein Gedi rock hyrax sociality project is grateful for the hospitality and logistic support from the Ein Gedi Field School and the Ein Gedi Nature Reserve. The Ngorongoro Hyena Project thanks the Tanzania Commission for Science and Technology, the Tanzania Wildlife Research Institute, and the Ngorongoro Conservation Area Authority for permission to conduct the study, and Bettina Wachter and Philemon Naman for long-term behavioral and demographic monitoring of the eight spotted hyena clans.

## Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

## Publisher's note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

## Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fevo.2022.918773/full#supplementary-material
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