296
All statistical and social network analyses were performed using R (R Development 297
Core Team 2012). Social network analyses were conducted using the suite of packages 298
developed in ’statnet’ (Handcock et al. 2003): ‘sna’(Butts 2006), ‘network’ (Butts 2008) and 299
‘ergm’ (Hunter et al. 2008). I worked on four networks: (i) undirected and weighted for the 300
association and kinship networks, (ii) directed and weighted for the dominance network and 301
(iii) undirected un-weighted for the breeding group membership network. In a weighted 302
network, the edges are associated with the frequency of associations or interactions between 303
nodes. All networks were computed using the package ’statnet’. 304
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Correlations between networks
305
I tested whether relatedness and breeding group membership structured the associations 306
and the agonistic interactions observed at the feeder for each of the eight colonies monitored 307
in this study. Each colonial group included the same individuals across the different networks 308
(i.e. kinship, membership, association and agonistic interaction networks). I ran Multiple 309
Regression Quadratic Assignment Procedure (MRQAP) with 5000 permutations to assess 310
correlations between the association or the dominance networks with kinship and breeding 311
group membership networks in two ways (Dekker et al. 2007): First, I included all individuals 312
for which behavioural data were available. Second, I tested males only, because the kin 313
structure is stronger between males than between females within colonies while males 314
dominate females. Consequently the correlations between kinship and association or between 315
kinship and dominance are likely to be less pronounced when including both females and 316
males. QAP regression is a type of Mantel test allowing the regression of a single matrix against 317
multiple explanatory matrices. When parameterizing a continuous dependent matrix, the 318
MRQAP regression examines and controls for all multiple predictors, so that the results can be 319
interpreted similarly to those of standard regression procedure (Dekker et al. 2007; Mann et al. 320
2012). I combined probabilities from QAP analyses of eight colonies using a Fisher’s omnibus 321
test to assess the overall significance of both predictor networks (kinship and group 322
membership) together and their individual effects, on the association network or on the 323
dominance network (Madden and Clutton-Brock 2009; Madden et al. 2012). When I had 324
different directions of relationship between groups for the networks correlation, I used the 325
procedure developed by Madden et al. (2009; 2012) to assess the mean correlation coefficient 326
and the overall p-values. 327
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Centrality, phenotypic attributes and cooperative contribution
328
I obtained centrality metrics for 134 individuals (52 females, 76 males and 6 individuals 329
of unknown sex). Based on the undirected, weighted association networks, I calculated the 330
following centrality metrics for each individual within their colony: degree, betweenness and 331
closeness. Based on the directed, weighted networks of dominance, I calculated an individual’s 332
indegree within its colony. Centrality metrics were normalized to allow comparison between 333
colonies (Croft et al. 2006). 334
I used a Bayesian mixed model approach (package ‘MCMCglmm’; Hadfield 2010) to 335
evaluate inter-individual variation in centrality metrics in all the models because network data 336
are intrinsically not independent so that classic least squares regression procedure cannot be 337
performed. Parameter estimates, 95% confidence intervals and p-values were estimated using 338
Markov-Chain-Monte-Carlo randomization method as follows: 100000 iterations, a thinning 339
of 100 and a burn-in of 1000 to ensure convergence. The minimal models were obtained by 340
removing non-significant predictors according to a stepwise downward model selection 341
procedure. In all models, colony identity nested in the year of observation was included as the 342
random factor. 343
For 87 breeders and helpers, I first tested whether dominance, the average relatedness 344
to the colony, sex, breeding status (i.e. breeder or helper) and minimum age predicted central 345
positions (betweenness, degree and closeness) within the association network while controlling 346
for body size (tarsus length) and body mass (i.e. body condition). I also included the 347
interactions between dominance and breeding status, dominance and sex, and between breeding 348
status and sex as well as the interactions between the average degree of relatedness and 349
dominance, sex or breeding status. 350
I then focus on helpers only to assess whether centrality in the network is predicted by 351
cooperative contributions as contributions in mobbing, nestling provisioning and communal 352
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thatch building are all true cooperative acts for helpers but may not be for breeders (i.e. nestling 353
provisioning is an act of parental care for breeders). I did not include relatedness in this analysis 354
for two reasons. First, I had helpers not genotyped yet so the inclusion of relatedness would 355
decrease drastically a sample size already limited (exclusion of 8 helpers). Furthermore, as seen 356
in Chapter 5, cooperative contributions may depend on different levels of relatedness 357
depending on the task considered (e.g. both high level of relatedness to the father and low level 358
to the mother predict high provisioning). For instance, thatch building is not influenced by 359
average relatedness to the colony (Chapter 5) but by local relatedness to the members 360
occupying the nest chambers embedded in the preferred area of building (van Dijk et al. 2014). 361
Therefore, I focused here on whether dominance, sex, minimum age and contributions in 362
mobbing, feeding and communal thatch building predicted helpers’ network centrality (N = 363
27). As males are dominant over females, I also included the interaction between sex and 364
dominance. I controlled for body size and body mass and included colony identity as a random 365
factor. 366
In order to test whether helpers that contributed less to cooperative tasks suffered from 367
higher level of aggressions, I examined whether an helper’s indegree (based on the dominance 368
network, N = 27) was predicted by its cooperative contributions (i.e. mobbing, nestling 369
provisioning and communal thatch building) while controlling for dominance, sex, minimum 370
age and body size and the interactions between dominance and the cooperative contribution for 371
each task and the interaction between dominance and sex. The average relatedness to the colony 372
was not included for the same reasons mentioned above. 373
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6.4
Results
374