Social support drives female dominance in the spotted hyaena

Abstract

Identifying how dominance within and between the sexes is established is pivotal to understanding sexual selection and sexual conflict. In many species, members of one sex dominate those of the other in one-on-one interactions. Whether this results from a disparity in intrinsic attributes, such as strength and aggressiveness, or in extrinsic factors, such as social support, is currently unknown. We assessed the effects of both mechanisms on dominance in the spotted hyaena (Crocuta crocuta), a spe-cies where sexual size dimorphism is low and females often dominate males. We found that individuals with greater potential social support dominated one-on-one interactions in all social contexts, irrespective of their body mass and sex. Female dominance emerged from a disparity in social support in favour of females. This disparity was a direct consequence of male-biased dispersal and the disruptive effect of dispersal on social bonds. Accordingly, the degree of female dominance varied with the demographic and kin structure of the social groups, ranging from male and female co-dominance to complete female dominance. Our study shows that social support can drive sex-biased dominance and provides empirical evidence that a sex-role-defining trait can emerge without the direct effect of sex.

Full text

Articles
https://doi.org/10.1038/s41559-018-0718-9
Social support drives female dominance in the
spotted hyaena
ColinVullioud 1,2,4, EveDavidian 1,4, BettinaWachter1, FrançoisRousset3, AlexandreCourtiol 2,4
and OliverP.Höner 1,4*
1Department of Evolutionary Ecology, Leibniz Institute for Zoo and Wildlife Research, Berlin, Germany. 2Department of Evolutionary Genetics, Leibniz
Institute for Zoo and Wildlife Research, Berlin, Germany. 3Department of Evolutionary Genetics, ISEM, Université de Montpellier, CNRS, IRD, EPHE,
Montpellier, France. 4These authors contributed equally: Colin Vullioud, Eve Davidian, Alexandre Courtiol, Oliver P. Höner *e-mail: hoener@izw-berlin.de
SUPPLEMENTARY INFORMATION
In the format provided by the authors and unedited.
NATURE ECOLOGY & EVOLUTION | www.nature.com/natecolevol

This file contains:
Supplementary Notes
Supplementary Figures 1-6
Supplementary Tables 1-6
Supplementary Notes
Why the social support proxy ‘supporter-proximity’ is unlikely to be confounded by
residency
In this study, we tested whether the probability of a spotted hyaena to win an agonistic
interaction against a hyaena of another clan was influenced by a disparity in the proximity to
potential supporters (that is, members of the clan), as deduced from the distance between the
location of the interaction and the current core areas of activity of the clan. In territorial
species such as the spotted hyaena, the winning probability may also be influenced by
residency if the interaction takes place inside the territorial boundaries of one individual (the
resident) but not the other (the intruder)1,2. For interactions at such locations, the residency
hypothesis predicts that the resident has a higher winning probability because it perceives the
territory as a resource of higher value and thus has a higher motivation to defend it1,2. At
these locations, the potential effects of social support and residency might be confounded
because the resident usually is closer to its supporters than the intruder. In contrast, at
locations where both hyaenas are intruders (in a third clan’s territory), or both are resident
(where two neighbouring territories overlap3), social support and residency are not
confounded because the residency hypothesis predicts that both have similar motivation and
winning probabilities.
To disentangle the effects of social support and residency, we thus studied interactions
that took place at a location closer to a third clan’s current core area of activity. This revealed
that, similar to the overall analysis (Fig. 1, black square and dot in panel Social support), the
individual that was closer to its clan’s current core area of activity won the majority (71%) of
interactions (n = 105). This confirms that the winning probability is influenced by social
support and that the effect of residency is likely to be small.

Why the social support proxy ‘tenure’ is unlikely to be confounded by age
In our study, we found that the probability of winning an agonistic interaction in the context
of intraclan interactions between two immigrant males was influenced by the number of
potential supporters, as estimated by the proxy ‘tenure’. Because tenure increases with age,
effects of tenure on the winning probability could reflect effects of age rather than social
support.
To discriminate between the effects of age and tenure, we studied interactions in
which one immigrant male was older but shorter tenured than the other. Immigrant males can
be older but shorter tenured than other immigrant males when they undertake breeding
dispersal after spending time in their first chosen clan4. These older, shorter tenured males
should be more likely to win against younger, longer tenured males than vice versa if age had
a stronger effect on the outcome than tenure. Contrary to this prediction, we found that
immigrant males that were older and shorter tenured than the immigrant male they interacted
with won only 38% of interactions (n = 143). This indicates that tenure (and social support)
has a stronger effect on dominance establishment than age.
Why our results on dominance establishment are unlikely to be confounded by
winner-loser effects
Winner and loser effects refer to a self-reinforcing process whereby an individual’s past
experience of winning or losing a dyadic interaction will affect its physiological or
psychological state, and influence its probability of winning subsequent interactions; winners
will reinforce their probability of winning whereas losers will reinforce their probability of
losing, independently of disparities in intrinsic attributes or other differences in competitive
ability such as the amount of social support5,6. The reinforcement mechanism of winner-loser
effects may involve a process of generalisation; the outcome of past interactions will
influence future winning probabilities against any other individual and in different social
contexts5,7. Winner-loser effects have been proposed as an alternative to the intrinsic attribute
hypothesis to explain the emergence of linear social hierarchies6. The two hypotheses
however are not mutually exclusive and disentangling winner-loser effects from effects of
intrinsic attributes and social support on dominance establishment can be challenging5,8. Our
results are unlikely to be confounded by a generalised reinforcement emerging from winner-
loser effects for three main reasons.

First, we incorporated in our models a random factor that considered the identity of the
interacting individuals and correlation between interactions involving the same individual(s).
The random factor thereby largely captured the effects of individual-level traits other than
those accounted for in our model and effects of repeated interactions by a given individual or
dyad that may be attributed to winner-loser effects. By discarding the realisation of the
random effect for the computation of model predictions, the strong predictive power
associated with the model predictions shows that disparities in the amount of social support
the individuals can expect to receive – and not winner-loser effects – were the main predictor
of dominance establishment between pairs of individuals.
Second, in the spotted hyaena system, individuals spend most of their time within their
clan territory and mainly interact with members of their own clan. According to the winner-
loser hypothesis, an individual’s winner or loser experience within its clan should strongly
influence its winning probability in the context of interclan interactions. In contrast to this
prediction, we found that the winning probabilities in interclan interactions were primarily
determined by asymmetries in social support as quantified by the individuals’ proximity to
the core area of activity of their respective clan. Thus, an individual’s competitive ability (and
winning probability) in the context of interclan interactions was independent of its experience
as winner or loser in the context of intraclan interactions.
Third, according to the winner-loser hypothesis, an individual’s competitive ability
should be independent of the identity of its interactor. Here, we quantified social support in
social contexts that involved two members of the same clan (intraclan-native and intraclan-
mixed) based on decision rules that considered the relatedness and ancestry relationships
between the two interactors and any bystander. These rules assume that the identity of one
interactor influences the number of supporters of the other. When we applied these rules, the
outcome of intraclan interactions was correctly predicted in the great majority of cases
(Supplementary Table 3). This confirms that generalised winner-loser effects were unlikely to
be at play in these social contexts and unlikely to have confounded our results.
Although winner-loser effects do not seem to be the main determinant of dominance
establishment in spotted hyaenas, they may still play a role in maintaining the stability of
social hierarchies within a clan. For example, individuals that occupy a high social rank are,
by definition, likely to win most of their social interactions. High-ranking individuals may in
turn become more prone to initiate interactions and to participate in coalitionary social
support and may thereby reinforce their social dominance within their clan.

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Supplementary Figure 1
Algorithm to calculate the number of clan members supporting a spotted hyaena in a dyadic interaction with another clan member. a,
The algorithm combines decision rules that consider the origin (native or immigrant) of individuals as well as the relatedness and ancestry
relationships between the interacting parties and any bystander. Shaded boxes show the decisions of the bystander. b, c, Maternal links between
two interacting individuals (A and B) and a bystander (C) involved in two exemplary interactions. Boxes shaded in orange and green show the
decisions of the bystanders in the two exemplary interactions.
C neutral
Is C native?
Is C kin of A and B?
Is C ancestor of A?
Is A ancestor or descendant of B?
Is Ax > Bx?
Are A and B native? Is C kin of A and/or B?
C supports kin
Is C ancestor of B?
Is Cz ≥ Bz?
C supports A
C supports A
C neutral
Is Cy ≥ Ay? C supports B
C supports B C neutral
C neutral Is B ancestor of A?
Is C ancestor of B?
C supports A Is Cz ≥ Bz?
C supports A C neutral
Is C ancestor of A?
C supports B Is Cy ≥ Ay?
C supports B C neutral
A, B interacting parties
C bystander
Ax daughter of common ancestor of A and B in line of A
Bx daughter of common ancestor of A and B in line of B
Ay daughter of common ancestor of A and C in line of A
Cy daughter of common ancestor of A and C in line of C
Bz daughter of common ancestor of B and C in line of B
Cz daughter of common ancestor of B and C in line of C
= is twin or same individual
> is older than
yes
no
C neutral Is C kin of A or B?
C supports kin C neutral Is Ax = Bx?
a
B
Bx, Bz
A
Ax, Cz
C
Ay
Cy
Time at birth
b
past
present
C
Cy, Cz
A
Ax, Ay
Bx, Bz
B
c past
present

Supplementary Figure 2
The decrease in cumulative relatedness experienced by dispersing male spotted hyaenas.
Cumulative relatedness was the sum of relatedness coefficients between an individual and all
other clan members through the maternal line. Time at 0 represents the date at which males
dispersed (n = 165 immigrant males) or started to be reproductively active in the natal clan (n
= 32 native males), respectively. Thin lines depict individual trajectories; thick lines and
shaded areas represent means ± CI95%.
0
2
4
−2 0 2 4
Time (years)
Cumulative relatedness
Immigrant male
Native male

Supplementary Figure 3
The effect of dispersal and age on the social rank of spotted hyaenas. Ranks were
standardised by distributing them evenly between the highest rank (standardised rank +1) and
lowest rank (standardised rank -1), with the median rank scored as zero. For immigrant males
(n = 248), ranks were calculated one year before and after dispersal; for native males (n =
30), one year before and after the onset of reproductive activity; for females (n = 345), one
year before and after the mean dispersal age of males of 3.5 years. Boxes indicate the
interquartile range around the median (horizontal bar), and vertical bars represent cumulative
relatedness values that lie within 1.5 times the interquartile range.
−1.0
−0.5
0.0
0.5
1.0
Social rank
Immigrant males
Native males
Females
1yr before dispersal
1yr after dispersal
1yr before onset of
reproductive activity
1yr after onset of
reproductive activity
2.5 yrs of age
4.5 yrs of age

Supplementary Figure 4
The probability of an individual to be actively supported in a polyadic interaction as a
function of the distance to its clan’s core area of activity. The predicted probability was
calculated using a logistic regression mixed-effects model considering as response variable
the binary outcome for the support (0 = supported by no one, 1 = supported by at least one
clan member) during polyadic interactions (n = 506 interacting parties), as fixed-effect
predictor the distance to the clan’s current core area of activity, and as random effect the
individual identity. The shaded area depicts the CI95%.
0.00
0.25
0.50
0.75
0 5 10 15 20
Distance to clan's current core area of activity (km)
Probability to be supported

Supplementary Figure 5
Relationship between the difference in cumulative relatedness and the difference in
potential social support between two interacting individuals. The Pearson correlation
coefficient was 0.62. The data points were jittered to reduce overlap.
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−40
0
40
−8−4 0 4
D Cumulative relatedness
D Social support

Supplementary Figure 6
The body mass of female and male spotted hyaenas as a function of age. Lines represent
the predictions from the additive model for repeated measurements of 77 females and 90
males. Shaded areas depict the CI95%.
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0
20
40
60
0 2 4 6 8 10
Age (years)
Body mass (kg)
●
●
Female
Male

Supplementary Table 1
Main hypotheses and predictions for the determinants of the establishment of
dominance relationships in spotted hyaenas
Hypothesis
Details
Prediction
Social support
The amount of social support an individual can
rely on affects its assertiveness and competitive
ability
The winning probability of the individual with
greater potential social support is higher (higher
than 50%) than that of its interactor, in all social
and sexual contexts
Intrinsic attributes:
Body mass
Larger body mass confers a competitive
advantage over an opponent
The winning probability of the heavier individual is
higher (higher than 50%) than that of its lighter
interactor, in all social and sexual contexts
Intrinsic attributes:
Sex-related
Females are more aggressive than males or differ
in other traits that provide them with a competitive
advantage over males
The winning probability of a female is higher
(higher than 50%) than that of her male interactor,
in all social contexts
Docile male
Male aggression against females impairs fitness.
To increase their chances to be chosen as mates,
males concede dominance to females when they
become reproductively active
The winning probability of an immigrant and a
reproductively active native male is lower (lower
than 50%) than that of his female interactor in all
social contexts
Ontogenetic switch
Dispersal is accompanied by ontogenetic socio-
behavioural changes; immigrants are less
aggressive and more submissive than before
emigration from their natal clan
The winning probability of an immigrant is lower
(lower than 50%) than that of his native interactor,
in all social and sexual contexts

Supplementary Table 2
Predicted winning probability of female and male spotted hyaenas during dyadic interactions as derived from the main hypotheses
tested in the study. Bold font indicates contexts for which predictions differ between at least two hypotheses and hypotheses can be
discriminated.
Hypothesis
Social
Intrinsic attributes (IA)
Docile
Ontogenetic
Social context
Sexual context
support (SS)
Body mass
Sex
male (DM)
switch (OS)
Discriminable hypotheses
Interclan§
intersex
FN = MN
FN = MI
FN > MN
FN > MI
FN > MN
FN > MI
FN = MN#
FN > MI
FN = MN
FN > MI
SS ↔ IA
SS ↔ IA
SS ↔ DM
SS ↔ OS
IA ↔ DM
IA ↔ OS
intrasex
FN = FN
MN = MN
MN = MI
MI = MI
FN = FN
MN = MN
MN = MI
MI = MI
FN = FN
MN = MN
MN = MI
MI = MI
FN = FN
MN = MN
MN = MI
MI = MI
FN = FN
MN = MN
MN > MI
MI = MI
SS ↔ OS
IA ↔ OS
DM ↔ OS
Intraclan-Mixed§
intersex
FN > MI
FN > MI
FN > MI
FN > MI
FN > MI
Intrasex
MN > MI
MN = MI
MN = MI
MN = MI
MN > MI
SS ↔ IA
SS ↔ DM
IA ↔ OS
DM ↔ OS
Intraclan-Native
Intersex
FN = MN
FN > MN
FN > MN
FN = MN#
FN = MN
SS ↔ IA
SS ↔ DM
IA ↔ DM
IA ↔ OS
Intrasex
FN = FN
MN = MN
FN = FN
MN = MN
FN = FN
MN = MN
FN = FN
MN = MN
FN = FN
MN = MN
Intraclan-Immigrant§
Intrasex
MI = MI
MI = MI
MI = MI
MI = MI
MI = MI
Interclan specific†
Intersex
FN < MI
FN > MI
FN > MI
FN > MI
FN > MI
SS ↔ IA
SS ↔ DM
SS ↔ OS
Intrasex
MN < MI
MN = MI
MN = MI
MN = MI
MN > MI
SS ↔ IA
SS ↔ DM
SS ↔ OS
IA ↔ OS
DM ↔ OS
FN, native female; MN, native male; MI, immigrant male; §assumes that immigrants are males; †interactions between immigrant males who were closer to their clan’s current core area of
activity and natives from a different clan; #assumes that native males are not reproductively active in their natal clan (reproductively active native males would be predicted to submit to – and
thus have lower winning probability than – females).

Supplementary Table 3
The winning probabilities (in %) of the focal individuals as predicted by the models and
observed (raw) for the social support and intrinsic attributes (body mass, sex)
hypotheses. The focal individual is the individual with greater social support, the heavier
individual, and the female, respectively.
Social support
Body mass
Sex
Social context
Sexual context
n
predicted
raw
predicted
raw
predicted
raw
Interclan
intersex
200
85 (77-91)
83
57 (40-73)
62
62 (46-75)
62
intrasex
302
95 (89-98)
88
47 (23-73)
50
NA
NA
Intraclan-Mixed
intersex
421
98 (96-99)
97
79 (67-87)
83
98 (96-99)
97
intrasex
180
96 (86-99)
90
30 (08-69)
42
NA
NA
Intraclan-Native
intersex
488
76 (69-81)
67
45 (35-56)
49
50 (38-62)
52
intrasex
1313
85 (80-88)
80
31 (22-41)
43
NA
NA
Intraclan-Immigrant
intrasex
1229
93 (90-95)
85
58 (52-65)
64
NA
NA
Interclan specific§
153
97 (85-99)
88
NA
NA
NA
NA
Numbers in brackets are CI95%; n, number of interactions; NA, not applicable. Results in bold are consistent with the hypothesis
(see Supplementary Table 1). Predicted and raw probabilities differ because the model fits control for the identity of the
interacting individuals and thus remove bias from unbalanced representation. §Interactions between immigrant males who were
closer to their clan’s current core area of activity and natives of both sexes of a different clan.

Supplementary Table 4
The predictive power of models predicting the probability that a hyaena wins an
interaction
Model name
Focal individual
Fixed-effect model structure
logLik
df
AIC
Tjur's D
Intersex interactions
social_inter_fullfit
most support
social_context * (body_mass_bin + sex)
-411.91
9
841.82
0.51
social_inter_nosex
most support
social_context * body_mass_bin
-413.36
6
840.72
0.51
social_inter_nomass
most support
social_context * sex
-414.65
6
841.29
0.51
social_inter_null
most support
social_context
-417.78
3
843.57
0.50
mass_inter_fullfit
heaviest
social_context * (social_support_bin + sex)
-411.91
9
841.82
0.51
mass_inter_nosex
heaviest
social_context * social_support_bin
-413.36
6
840.72
0.51
mass_inter_nosupport
heaviest
social_context * sex
-481.51
6
977.01
0.36
mass_inter_null
heaviest
social_context
-576.84
3
1161.67
0.15
sex_inter_fullfit
female
social_context * (body_mass_bin + social_support_bin)
-411.91
9
841.82
0.51
sex_inter_nosupport
female
social_context * body_mass_bin
-481.51
6
977.01
0.36
sex_inter_nomass
female
social_context * social_support_bin
-414.65
6
841.29
0.51
sex_inter_null
female
social_context
-484.60
3
977.21
0.36
Intrasex interactions
social_intra_fullfit
most support
social_context * body_mass_bin
-1010.96
6
2039.91
0.54
social_intra_null
most support
social_context
-1027.58
3
2065.17
0.54
mass_intra_fullfit
heaviest
social_context * social_support_bin
-1010.96
6
2039.91
0.54
mass_intra_null
heaviest
social_context
-1364.04
3
2738.08
0.05
The predictive power was expressed as AIC and Tjur's D. AIC measures the accuracy of a model at predicting new samples from
the (unobserved) true model. A low (high) AIC indicates high (low) predictive power. Predictive powers can only be compared
within the same sexual context, that is, within intersex or intrasex interactions. Tjur's D measures the accuracy of the fitted model
at predicting the fitted data. D is defined by the average difference between the winning probabilities of the individuals that did
actually win and the individuals that did actually lose. The predictive power increases with increasing D and a D of 0.5 represents
a substantial difference in winning probabilities. Equivalences of model results are expected because defining the focal according
to a predictor or using a covariate as a binary predictor is equivalent (see methods). +, additive effects alone; *, additive effect
together with interactions. Variables ending with the suffix _bin are binary and took 1 if the focal individual had a larger trait value
than the non-focal individual, and 0 otherwise. The variable sex also contains two levels (M/F or F/M in intersex interactions, and
M/M or F/F in intrasex interactions; with the format focal/opponent). An example of the summary output of a full model fit is
provided in Supplementary Table 6.

Supplementary Table 5
The variation in female dominance due to clan demography in spotted hyaenas
Example 1
Example 2
Example 3
Example 4
Example 5
Clan
Shamba
Lemala
Munge
Engitati
Triangle
Date
1998-09-22
2005-01-01
2005-01-01
2003-07-01
1999-01-01
N females
1
32
20
15
7
N males
4
16
21
15
6
Sum ranks females
3
736
368
178
29
Sum ranks males
12
440
493
287
62
U females
2
304
262
167
41
U males
2
208
158
58
1
Max U
4
512
420
225
42
Female dominance
0.5
0.59375
0.62381
0.74222
0.97619
Rank 1
male (N)
female (N)
female (N)
male (N)
female (N)
Rank 2
male (N)
male (N)
female (N)
male (N)
female (N)
Rank 3
female (I)
male (N)
male (N)
female (N)
female (N)
Rank 4
male (I)
male (N)
female (N)
female (N)
female (N)
Rank 5
male (I)
female (N)
male (N)
male (N)
female (N)
Rank 6
male (N)
male (N)
female (N)
female (N)
Rank 7
female (N)
female (N)
female (N)
male (N)
Rank 8
female (N)
female (N)
female (N)
female (N)
Rank 9
female (N)
male (N)
female (N)
male (I)
Rank 10
female (N)
female (N)
female (N)
male (I)
Rank 11
female (N)
male (N)
male (N)
male (I)
Rank 12
female (N)
male (N)
female (N)
male (I)
Rank 13
female (N)
female (N)
male (N)
male (I)
Rank 14
female (N)
male (N)
female (N)
Rank 15
female (N)
male (N)
female (N)
Rank 16
female (N)
female (N)
female (N)
Rank 17
male (N)
male (N)
female (N)
Rank 18
female (N)
female (N)
female (N)
Rank 19
male (N)
male (N)
female (N)
Rank 20
female (N)
female (N)
female (N)
Rank 21
male (N)
female (N)
male (I)
Rank 22
female (N)
female (N)
male (I)
Rank 23
female (N)
male (N)
male (I)
Rank 24
female (N)
female (N)
male (I)
Rank 25
female (N)
female (N)
male (I)
Rank 26
female (N)
male (N)
male (I)
Rank 27
female (N)
female (N)
male (I)
Rank 28
male (N)
female (N)
male (I)
Rank 29
female (N)
female (N)
male (I)
Rank 30
male (N)
female (N)
male (I)
Rank 31
female (N)
female (N)
Rank 32
female (N)
female (N)
Rank 33
female (N)
male (I)
Rank 34
female (N)
male (I)
Rank 35
female (N)
male (I)
Rank 36
female (N)
male (I)
Rank 37
male (N)
male (I)
Rank 38
female (N)
male (I)
Rank 39
female (N)
male (I)
Rank 40
female (N)
male (I)
Rank 41
female (N)
male (I)
Rank 42
female (N)
Rank 43
male (I)
Rank 44
male (I)
Rank 45
male (I)
Rank 46
male (I)
Rank 47
male (I)
Rank 48
male (I)
Female dominance was calculated using the standardised Mann-Whitney U statistic of the social ranks of female and male clan
members that were >1 year of age. N, native; I, immigrant.

Supplementary Table 6
Model parameter estimates for a full model fitting the intersex interactions
Fixed effects
Term
Estimate
Cond. SE
t-value
Intercept
-1.021
0.411
-2.479
Social_context (Mixed)
1.792
0.709
2.528
Social_context (Native)
0.005
0.493
0.010
Sex (M/F)
-0.897
0.781
-1.149
Social_support_bin (TRUE)
3.556
0.552
6.444
Social_context (Mixed) : Sex (M/F)
-2.930
1.302
-2.250
Social_context (Native) : Sex (M/F)
0.518
0.924
0.561
Social_context (Mixed) : Social_support_bin (TRUE)
NA
NA
NA
Social_context (Native) : Social_support_bin (TRUE)
-1.375
0.646
-2.129
Random effects
Term
Variance
PairsID
3.841
Estimates are for the model mass_inter_fullfit (see Supplementary Table 4), where the heavier individual is considered as focal
for each interaction. For fixed effects, columns give the name of the model parameter (Term), its estimate (Estimate), the
standard error on parameter estimates conditional on other parameters being considered at their best estimate (Cond. SE), and
the ratio between the estimate and the standard error providing an effect size (t-value). The intercept is the estimate of the log-
odds of the winning success for a female that is heavier but less socially supported than its male competitor during an interclan
interaction. Other estimates correspond to departure from this baseline situation (also on the logit scale) with the factor level
under consideration indicated between parentheses (for the social context: Mixed or Native each contrasted to the baseline Inter;
for sex: M/F, indicating that the focal is a male and that the opponent is a female, contrasted to the baseline F/M, indicating the
reverse situation; for the social support: TRUE, indicating the focal is more supported than the opponent, is contrasted to the
baseline FALSE, indicating the reverse situation). The row with NA indicates that the corresponding parameter was not fitted
because no immigrant male was more socially supported than its native female opponent. For the random effects, the variance is
given on the logit scale. PairsID are the levels of the random effect correlated among dyadic interactions sharing one or both
individuals (see methods). This model produces the same fit as the models social_inter_fullfit and sex_inter_fullfit (see
Supplementary Table 4) but in contrast to these other models, its parameterisation illustrates both the effect of social support and
sex.