In ﬂ uence of maternal kinship on association network structure in a long-term study of spider monkeys ( Ateles geoffroyi )

Maternal kinship can structure social relationships in mammals, as demonstrated in species characterized by female philopatry. In these species, females tend to be closely related and interact more often with maternal relatives. However, there is limited evidence indicating a role of maternal kinship in species characterized by male philopatry. To increase our understanding of the role of maternal kinship on the social structure of these species, we explore how maternal kinship in ﬂ uences the structure of association networks in a group of wild Geoffroy's spider monkeys, Ateles geoffroyi , over 24 years. Using 53 546 instantaneous scan samples collected from 1997 to 2020 (mean ± SD ¼ 2231 ± 890 per year), we built yearly association networks using the simple ratio index to establish links among 93 individuals observed over the study period. We used generalized linear mixed models (GLMMs) and vector generalized linear models (VGLMs) to examine whether edge weight, network modularity and eigenvector and betweenness centrality were related to ﬁ ve maternal kin categories, four age-difference classes, three sex classes and matriline membership. We found that among individuals of similar age difference, maternal kin had higher edge weight and higher probabilities of being assigned to the same module in the association network than nonmaternally related individuals; maternal brothers, maternal sisters and maternal female e male siblings associated more than nonmaternally related individuals; and matriline membership in ﬂ uenced the eigenvector and betweenness centrality of its members, resulting in higher centrality values within certain matrilines. Matriline size was positively associated with eigenvector centrality, indicating that members of larger matrilines tended to be better integrated into the overall network through close connections with their maternal kin. Our results suggest that, in addition to age and sex, maternal kinship plays a signi ﬁ cant role in structuring association networks even in a species characterized by male philopatry. © 2024 The Authors. Published by Elsevier Ltd on behalf of The Association for the Study of Animal Behaviour. This is an open access article under the CC BY license (http://creativecommons.org/licenses/ by/4.0/).

Maternal kinship can structure social relationships in mammals, as demonstrated in species characterized by female philopatry.In these species, females tend to be closely related and interact more often with maternal relatives.However, there is limited evidence indicating a role of maternal kinship in species characterized by male philopatry.To increase our understanding of the role of maternal kinship on the social structure of these species, we explore how maternal kinship influences the structure of association networks in a group of wild Geoffroy's spider monkeys, Ateles geoffroyi, over 24 years.Using 53 546 instantaneous scan samples collected from 1997 to 2020 (mean ± SD ¼ 2231 ± 890 per year), we built yearly association networks using the simple ratio index to establish links among 93 individuals observed over the study period.We used generalized linear mixed models (GLMMs) and vector generalized linear models (VGLMs) to examine whether edge weight, network modularity and eigenvector and betweenness centrality were related to five maternal kin categories, four age-difference classes, three sex classes and matriline membership.We found that among individuals of similar age difference, maternal kin had higher edge weight and higher probabilities of being assigned to the same module in the association network than nonmaternally related individuals; maternal brothers, maternal sisters and maternal femaleemale siblings associated more than nonmaternally related individuals; and matriline membership influenced the eigenvector and betweenness centrality of its members, resulting in higher centrality values within certain matrilines.Matriline size was positively associated with eigenvector centrality, indicating that members of larger matrilines tended to be better integrated into the overall network through close connections with their maternal kin.Our results suggest that, in addition to age and sex, maternal kinship plays a significant role in structuring association networks even in a species characterized by male philopatry.
© 2024 The Authors.Published by Elsevier Ltd on behalf of The Association for the Study of Animal Behaviour.This is an open access article under the CC BY license (http://creativecommons.org/licenses/ by/4.0/).
Preferential social behaviour towards kin can occur when kin are available and can be recognized from nonkin (Silk, 2021).Opportunities for interaction with kin are enhanced by philopatry, which refers to an individual's tendency to remain in its natal group instead of dispersing into another group.In several femalephilopatric mammals, groups are composed of females of different generations clustered into matrilines, with maternal kin interacting more closely than nonmaternal kin and nonkin (Cape bushbuck, Tragelaphus sylvaticus: Apio et al., 2010;fringe-lipped bat, Trachops cirrhosus: Flores et al., 2020; Japanese macaque, Macaca fuscata: Kawamura, 1958;reviewed in Clutton-Brock & Lukas, 2012).For example, blue monkeys, Cercopithecus mitis, preferentially groom, feed and rest in proximity to maternal kin (Cords & Nikitopoulos, 2015).In spotted hyaenas, Crocuta crocuta, maternal half-siblings are more likely to play, associate and form coalitions than nonkin and also tend to associate more with one another than do paternal half-siblings (Wahaj et al., 2004).Male philopatry is less common than female philopatry in mammals (Lawson Handley & Perrin, 2007), occurring in a variety of taxa, such as bats (Günther et al., 2017), primates (Ishizuka et al., 2018;Moore et al., 2015;Strier et al., 2011) and marsupials (Walker et al., 2008).It is expected that philopatric males interact frequently with their paternal kin (Silk, 2021).However, it has been documented that males preferentially form affiliative and cooperative relationships with maternal kin even when paternal kin are available (Bray & Gilby, 2020;Mitani, 2009;St€ adele et al., 2016).For example, male chimpanzees, Pan troglodytes, affiliate and cooperate with maternal brothers more often than with paternal brothers (Langergraber et al., 2007).Similarly, in Geoffroy's spider monkeys, Ateles geoffroyi, maternal kinship influences the quality of social relationships between group members (Rebecchini et al., 2011).Kin recognition is also a prerequisite for preferential interaction towards kin (Silk, 2021).Maternal kin recognition may arise via familiarity, because of the proximity with their mother, older siblings and the mother's relative social network (Charpentier et al., 2007;Silk, 2021).However, paternal kin recognition requires other mechanisms such as age-mediated proximity, father-mediated proximity or phenotype cues (Schülke et al., 2013;Widdig, 2007).
Regardless of the philopatric sex, maternal kinship is important in structuring mammal social relationships and behaviour (Diaz-Aguirre et al., 2018;Silk, 2009;Smith, 2014;Widdig et al., 2016).Most evidence about the influence of maternal kinship on social behaviour patterns comes from female-philopatric species characterized by well-differentiated relationships among females and matrilineal social structure (Kapsalis, 2004).Our understanding of the role of maternal kinship in the social behaviour of species with male philopatry is still limited.In male-philopatric species, males are not only exposed to paternal kin, but also to maternal kin, including their mother, brothers and sisters, before dispersal (Silk, 2021).Additionally, in certain male-philopatric species, females may occasionally remain and reproduce within their natal group (chimpanzees: Pusey et al., 1997;muriquis, Brachyteles hypoxanthus: Strier et al., 2011), enabling individuals to co-reside with additional categories of maternal relatives.Altogether, individuals may gain direct fitness benefits from establishing stronger and long-lasting social relationships with maternal relatives (Bray & Gilby, 2020;Langergraber et al., 2007;Mitani, 2009).For example, association with maternal kin allows philopatric males to increase reproductive success (Strier et al., 2011;Surbeck et al., 2019).Thus, one might expect that maternal kin would play an important role in structuring social relationships in malephilopatric species.
To enhance our understanding of how maternal kinship influences social behaviour patterns in male-philopatric species, we studied Geoffroy's spider monkeys, which live in multifemale/ multimale groups with a high degree of fissionefusion dynamics (Aureli & Schaffner, 2008).Males are largely philopatric; females normally disperse from their natal groups when they reach sexual maturity and do not engage in secondary dispersal (Shimooka et al., 2008).As a result, males should be more genetically related to one another than females, as reported for a population of white-bellied spider monkeys, Ateles belzebuth (Di Fiore, 2009), but not for a population of Geoffroy's spider monkeys, in which male immigration occurs (Aureli et al., 2013).Sex and age differences in affiliative behaviours are particularly characteristic features of spider monkeys, with males exchanging more affiliative behaviours with other males than females (Aureli & Schaffner, 2008;Slater et al., 2009), and same-age males reciprocating embraces (Schaffner et al., 2012).Additionally, young adult males have stronger associations with females than they do with older males, but as they mature, they associate more with older males than with females (Ramos-Fern andez et al., 2009).Furthermore, in spider monkeys, kinship plays a role in co-feeding (Pastor-Nieto, 2001), allomaternal care (Matisoo-Smith et al., 1997) and relationship quality (Rebecchini et al., 2011).However, we still know little about the role of maternal kinship on their social structure.Therefore, we used social network analysis to examine the influence of maternal kinship on the structure of association (i.e.being in the same subgroup) networks in a group of wild Geoffroy's spider monkeys.
Social network analysis is a powerful tool to quantify interaction patterns and measure aspects of social structure (Whitehead, 2008).Previous applications of social network analysis on animal sociality include studies examining the influence of kinship on the position and role of individuals.For example, individuals from larger matrilines occupy more central positions in the network due to preferentially socializing with kin partners, which are available in a larger number (Beisner et al., 2020;Bret et al., 2013).Furthermore, kinship can influence the composition of tightly connected subsets of individuals (i.e.modules), which are composed of closely related individuals (Diaz-Aguirre et al., 2019, 2020;Reisinger et al., 2017;Wilkinson et al., 2019).For instance, studies with a social network analysis approach have revealed that kin interact or associate more frequently in affiliative networks than nonkin (Bret et al., 2013;Gazes et al., 2022;Hirsch et al., 2012;Wey & Blumstein, 2010;Wikberg, Ting, & Sicotte, 2014;Wilkinson et al., 2019).
We hypothesized that maternal kinship influences the structure of spider monkey association networks, particularly the distribution of associations, modularity and centrality patterns.We predicted (1) higher associations between maternal kin than between nonkin, (2) that maternal kin would have a higher probability of being assigned to the same association network module than nonkin and that this module assignation would persist across years, (3) that individuals within the same matriline would have similar centrality scores and that larger matrilines would have higher centrality values.

Ethical Note
This research adhered to the laws of Mexico and complied with protocols approved by environmental Mexican laws (SEM-ARNAT), under research permits from the Direcci on General de Vida Silvestre (00910/13, 02716/14, 10405/15 and 03005/19).These permits authorized our research on a wild population of Geoffroy's spider monkeys (an endangered species) within a protected area in Mexico for the duration of our study.The study also adhered to the ASAB/ABS Guidelines for the ethical treatment of nonhuman animals in research.Data collection was exclusively observational; therefore, none of the researchers had any direct interaction with the studied animals that could cause disturbance.The study group was continuously studied from 1997 through 2020, and thus, the researchers were a normal presence for all the study animals.

Study Site and Group
We conducted our study in the Otoch Ma'ax yetel Kooh protected area (5367 ha) near the village of Punta Laguna in the Yucatan peninsula (Mexico; 20 38 0 N, 87 38 0 W).The area is composed of a semi-evergreen forest with different successional stages (Ramos-Fern andez et al., 2018).The mean annual temperature in the region ranges from 20.1 C in January to 26.9 C in August.The dry season spans from November to April, and the rainy season spans from May to October (Spaan et al., 2021).
We studied a well-habituated wild group of Geoffroy's spider monkeys continuously from 1997 to 2020 (Ramos-Fern andez et al., 2018).We classified group members according to their age into the following classes: adults (>9 years), subadults (5e9 years), juveniles (3e5 years) and infants (0e3 years; Shimooka et al., 2008;Smith-Aguilar et al., 2019).For individuals born in the group, data collection began between ages 2 and 3.During the study period, females that immigrated into the group were assumed to be 6 years old, which is the mean age at which natal females emigrated (estimated based on 19 females born in the group during the study period; range 4.8e8.1).Females that were already in the group when the study began in 1997 were considered adults (at least 9 years of age) as they had offspring.All group members were individually identified by facial marks and unique body features.
We used data collected between 1997 and 2020 by well-trained field assistants, researchers and students.The overall size of the study group varied between 18 (11 females and 7 males) and 51 (32 females and 19 males) individuals.Demographic variation resulted from 73 births, 28 immigrations, 26 female emigrations, 40 disappearances (including those of any male of any age, any female younger than 48 months old, and any non-natal female, with or without offspring, residing in the group for at least 1 year) and 9 confirmed deaths.In total, we analysed the yearly association patterns of 93 group members (63 females and 30 males) that were observed at least once in a given year.

Data Collection
Monkey subgroups were followed for 4e8 h per observation day.We determined subgroup composition using a 30 m chainrule, in which individuals within 30 m of any subgroup member were considered to belong to the same subgroup (Croft et al., 2008;Ramos-Fernandez, 2005).We used instantaneous scan samples (Altmann, 1974) every 20 min to record the identity of all subgroup members.We collected a total of 53 546 scan samples over 3554 observation days, with a mean (± SD) of 2231 ± 890 scan samples per year.

Maternal Kinship
We established maternal kinship based on continuously updated demographic records collected for the study group since 1997, including the identity of all mothers and their newborns.Therefore, we knew maternal kinship for all group members except for immigrants, who were assumed not to be maternally related to any group member apart from their own offspring.Hence, all dyads (i.e.pairs of individuals) of group members that were related over the maternal line (i.e.individuals maternally related to a female who started the maternal line) were considered maternal kin.One female did not disperse and reproduced successfully in the study group.This female had four female offspring who coexisted during the study period with their grandmother and some uncles and aunts (Fig. 1).Although this is an infrequent scenario, it provided an opportunity to analyse the influence of additional maternal kin categories.We therefore classified maternal kin into seven categories: (1) siblings (femaleefemale, femaleemale and maleemale dyads that shared the same mother), (2) mothereinfant offspring (dyads including females and their infant son or daughter), (3) motherejuvenile offspring (dyads including females and their juvenile son or daughter), (4) motheresubadult offspring (dyads including females and their subadult son or daughter before dispersal), (5) mothereadult offspring (dyads including females and their adult sons or the daughter who remained in the group), ( 6) grandmotheregrandoffspring (dyads including a female and the offspring of her daughter who remained in the group), (7) aunt/ uncleeniece (dyads including sisters or brothers of the female who remained in the natal group and this female's four daughters).We categorized all dyads of group members not belonging to the maternal line of females who reproduced in the group as nonmaternally related individuals (hereafter nonkin).We excluded mothereinfant or motherejuvenile dyads from our analysis related to predictions 1 and 2 because individuals of these dyads were always together in the same subgroup, thereby possibly masking any effect of maternal kinship on the association patterns of other types of dyads.We analysed a total of 1732 dyads that were observed in the same subgroup at least once over the study period.Most of these dyads consisted of nonkin (1619), 39 dyads corresponded to motheresubadult offspring, 7 to mothereadult offspring, 49 to siblings, 4 to grandmotheregrandoffspring and 14 to aunt/uncleeniece.We identified 15 matrilines, each composed of two or more related individuals through maternal lines for which there was available data (Fig. 1).One matriline was not considered because the three offspring disappeared before data collection began for them.Additionally, offspring from any matriline born in the group that died or disappeared before the onset of data collection for them were excluded from the analysis.The size of the matrilines varied between 2 and 10 individuals during the study period (Fig. 1).We also classified dyads into two categories according to matrilineal membership: dyads belonging to the same matriline and dyads belonging to different matrilines.

Association Networks
We defined the association between two individuals as their presence in the same subgroup in a given instantaneous scan sample.We estimated association between two individuals using the simple ratio index (SRI; Cairns & Schwager, 1987).For each dyad of individuals A and B, SRI was calculated as follows: where N AB corresponds to the number of scan samples during which A and B were present in the same subgroup, N A is the number of scans containing A and N B is the number of scans with B. The index can range from 0 (two individuals were never observed together) to 1 (the individuals were always observed together).We used the annual SRI values as the weight of nondirectional links between individuals in annual association networks.Package 'asnipe' (Farine, 2013) for R (R Core Team, 2023) was used to estimate SRI and construct the networks.
For each of the 24 yearly networks, we calculated modularity, including the module assignment for each node.Modularity is the degree to which a network contains substructures, corresponding to sets of nodes more closely connected to each other than to others within the network.Module assignment has been used to assess whether individuals belonging to the same module have a higher degree of genetic relatedness than individuals from different modules (Best et al., 2013;Diaz-Aguirre et al., 2018;Reisinger et al., 2017;Wilkinson et al., 2019).To identify modules in the yearly association networks, we tested four community-detection algorithms for weighted networks: edge betweenness, fast-greedy, Louvain and walktrap (Csardi & Nepusz, 2006).We used Newman's (2004) modularity coefficient Q to quantify how clearly partitions were detected using each algorithm.The Q coefficient is the  1997e2020).Each matriline is composed of the mother (black lines) and her offspring (females: orange lines; males: blue lines).Mother lines begin the year of immigration into the group (except those for the mothers of the first six matrilines that were in the group at the beginning of the study).Offspring lines begin in the year of their birth except for those from the first six matrilines, the line of which begins in 1997 because they were in the group at the start of the study.LI, from matriline M3, is the only offspring born in 1997.All lines end in the year of an individual's disappearance or confirmed death.The arrows indicate individuals who were still in the group when the study ended.Letters represent identity codes for each individual.LO from matriline M1 is the only female that was born and reproduced in the study group (thick orange line in matriline M1).
proportion of the total SRI (i.e. the sum of all edge weights of the network) corresponding to the weights for all dyads belonging to the same module, minus its expected proportion if dyads associated at random in the network (Newman, 2004;Whitehead, 2008).The Q coefficient ranges from 0 to 1 with a value close to 1 indicating more dense connections within than between modules (Newman, 2006;Shizuka & Farine, 2016) and values above 0.3 are often used as evidence of the presence of modules in the network (Newman, 2004).After testing the four algorithms, we selected the module assignment from the algorithm that maximized the values of Q.
Since fast-greedy and Louvain produced identical Q values in all years, and both achieved the highest Q values over 17 yearly association networks (Appendix, Table A1; Fig. A1), we arbitrarily chose the modules rendered by the fast-greedy algorithm.
Because we were interested in module assignment rather than the modularity of the network itself, instead of using the Q coefficient, we assessed the robustness of module assignment.We did so by running the fast-greedy algorithm over 1000 bootstrapped replicates of the observed network and estimating the community assortativity measure r com , which is a measure of the degree to which the empirical community assignment of nodes agrees with the community assignment in bootstrap replicates (Shizuka & Farine, 2016).Values of r com range from À1 to 1, where a value of 1 indicates that bootstrap replicates result in the exact same module assignments as the observed modules, values close to 0 indicate bootstrapped networks produce random network module assignment relative to the original data and values close to À1 indicate that the modules of the bootstrap replicates are formed by different nodes in contrast with the original network.An r com value >0.5 suggests that the network is highly structured by modules, reflected by the consistency of module assignment across different bootstrap replicates (Shizuka & Farine, 2016).We calculated r com with the package 'assortnet' (Farine, 2014) for R (R Core Team, 2023).We used the same bootstrap procedure to generate bootstrapped confidence intervals for our empirical modularity measure (Q).We also estimated the proportion of all bootstrapped replicates in which dyads were assigned to the same module (henceforth 'module assignment certainty').
We calculated two centrality metrics for the nodes: betweenness and eigenvector centrality.Each metric was estimated for each individual each year.Centrality metrics reflect how well nodes are connected within the network; we used them to assess whether an individual's position resulted from preferential interactions with kin (Abell et al., 2013;Bret et al., 2013;Ramos et al., 2019;Sosa, 2016;Sueur et al., 2011).Eigenvector centrality accounts for the number and strength of an individuals' direct connections and those of close neighbours.Individuals with high eigenvector centrality are either connected to many individuals or to others that are themselves highly connected (Whitehead, 2008).Betweenness measures the total number of shortest paths between other group members passing through an individual.Individuals with high betweenness values are likely to connect different modules of the network.The removal of high-betweenness individuals tends to fragment networks into separate components (Whitehead, 2008).The two centrality metrics were calculated using the 'igraph' package (Csardi & Nepusz, 2006) for R (R Core Team, 2023).

Data Analysis
Yearly association networks included an average (± SD) of 23 ± 3.6 individuals (range 15e36).Considering that age homophily is an important factor for social behaviour, we calculated pairwise differences in age by subtracting the estimated age in years between individuals.We then used four age-difference categories (0e3, 3e5, 5e9 and >9 years of age difference) to examine the modulating effect of age homophily in our analyses.
We used generalized linear mixed models (GLMMs) to assess the effect of maternal kinship on edge weights (SRI values) (prediction 1) and betweenness and eigenvector centrality (prediction 3).Additionally, we used vector generalized linear models (VGLMs) to assess the effect of maternal kinship and matrilineal membership on module assignment certainty (prediction 2).Regression models such as GLMMs and VGLMs have been shown to appropriately account for the nonindependence of social network data (Hart et al., 2022).In each analysis, we built separate models for each age-difference category.We did not include age-difference categories in the models as an interaction with maternal kinship due to the heavily unbalanced number of maternal kin categories present within each age-difference category.

Prediction 1: effect of maternal kinship on edge weight
In each GLMM testing the effect of maternal kinship on SRI, we entered edge weight as the dependent variable, maternal kin category as the predictor variable, the dyad sex combination (femaleefemale, femaleemale, maleemale) as a fixed control factor and dyad identity and year as random effects.We used the gamma distribution and a log link function in each GLMM because the dependent variable did not have normally distributed errors.We repeated the analysis excluding all dyads including the adult female who did not disperse and reproduced in the group and her four daughters (i.e.mothereadult daughter, grandmotheregrandoffspring, aunt/uncleeniece).This allowed us to assess the influence of maternal kinship on edge weights for the most frequent maternal kin categories.
We also explored the influence of sex class combination on the relationship between maternal kinship and edge weight.To do so, we used two GLMMs with edge weight as a dependent variable, maternal kin category, sex class combination and their interaction as predictor variables and dyad identity and year as random effects.In one model, maternal kin category consisted of siblings and nonkin dyads, while sex class combination comprised three types of dyads (femaleefemale, femaleemale, maleemale).In the other model, maternal kin categories included mothers with subadult offspring and nonkin dyads with similar age (adultesubadult) and the sex class combination included two types of dyads (femaleefemale, femaleemale).We did not analyse the interaction effect of sex and maternal kin categories on edge weights for each age-difference category due to the limited sex category combinations for each maternal kin category within each age-difference category.All of these analyses were done without considering the data of the exceptional cases of mothereadult offspring, grandmotheregrandoffspring and aunt/uncleeniece dyads.

Prediction 2: effect of maternal kinship on module membership
To assess the effect of maternal kinship and matrilineal membership on module assignment certainty, we used VGLMs because module assignment certainty did not fit to a gamma or Gaussian distribution.Instead, it exhibited a U-shaped distribution with a high frequency of values of 0 and 1 and a low frequency of values greater than 0 and less than 1 (Appendix, Fig. A2a).Therefore, considering that frequency of values, module assignment certainty was used as a categorical variable with three levels.Dyads with a value of 1 were classified as 'high certainty of assignment to the same module'; dyads with a value of 0 were classified as 'high certainty of assignment to different modules'; and all other dyads with values greater than 0 and less than 1 were classified as 'low certainty of assignment to different or same module' (Appendix, Fig. A2b).In each VGLM, this categorical variable was considered Please cite this article in press as: Jasso-del Toro, C., et al., Influence of maternal kinship on association network structurein a long-term study of spider monkeys (Ateles geoffroyi), Animal Behaviour (2024), https://doi.org/10.1016/j.anbehav.2024.05.006 as multinomial and was entered as the dependent variable, with either maternal kin category or type of matriline membership (dyads belonging to the same or different matriline) as the predictor variable and sex class combination as a fixed control factor.

Prediction 3: the effect of maternal kinship on centrality
For the analysis of the effects of maternal kinship on betweenness and eigenvector centrality, each GLMM contained one of the centrality metrics as the dependent variable, matrilineal membership as the predictor variable, sex class combination as a fixed control factor and individual identity and year as random effects.We used a negative binomial distribution with log link function for betweenness centrality models and a Gaussian distribution with identity link function for eigenvector centrality.We ran Pearson's correlation test in R (R Core Team, 2023) to test the association between centrality values and matriline size.
We performed GLMM using the 'glmmTMB' package (Brooks et al., 2017) and VGLM using 'VGAM' package (Yee, 2015) in R (R Core Team, 2023).In all the models, we ran post hoc Tukey's tests using the 'multcomp' package (Hothorn et al., 2008) with singlestep adjusted P values in R (R Core Team, 2023) to determine which levels of either the predictor variables or the interaction effects differed significantly.

RESULTS
Prediction 1: Effect of Maternal Kinship on Edge Weight GLMM results indicated that maternal kin categories were significant predictors of edge weight in each age-difference class (Table 1).Maternal kin with similar age differences associated more than nonkin.In particular, siblings and aunt/uncleeniece dyads had higher association values than nonkin with the same age difference both in dyads with 0e3 years of age difference and in dyads with 3e5 years of age difference (Fig. 2a, b).However, the SRI values and the results for aunt/uncleeniece dyads with an age difference of 3e5 years and >9 years should be interpreted with caution due to the limited sample size, with only three data points (Fig. 2b) and one data point (Fig. 2d), respectively.Motheresubadult offspring dyads with an age difference of 5e9 years associated more than aunt/ uncleeniece dyads and nonkin with the same age difference.Siblings with an age difference of 5e9 years associated more than nonkin with the same age difference (Fig. 2c).Grandmotheregrandoffspring, siblings and motheresubadult offspring dyads with an age difference of >9 years had higher association values than nonkin with the same age difference (Fig. 2d).
We found similar results when excluding the exceptional maternal kin categories and the philopatric adult female (Appendix, Table A2).Siblings with 0e3 and 3e5 years of age difference had higher association values than nonkin with the same age difference (Appendix, Fig. A3a and b).Motheresubadult offspring dyads with an age difference of 5e9 and >9 years associated more than nonkin (Appendix, Fig. A3c and d).

Maternal Kinship and Social Network Metrics
Prediction 2: effect of maternal kinship on module membership For prediction 2, we explored modularity using the following approaches.First, we calculated modularity (Q) for each of the 24 yearly networks to identify substructures (modules) within the network and determined whether the modules contained maternal kin.Second, using a bootstrap procedure, we assessed the robustness of the assignment of individuals to modules for each network using the community assortativity measure (r com ).Third, we estimated module assignment certainty to determine the degree of certainty that maternal kin dyads tended to belong to the same module in contrast with nonkin.Finally, we analysed the effect of maternal kinship on module assignment certainty.
Modularity values (Q) ranged between 0.05 and 0.56 across the 24 years (Table 2).On average (± SD), we detected 4 ± 1.2 (range 2e6) modules in each yearly association network.Specifically, the association network for 1998 exhibited the lowest Q value, detecting four modules, while the network for 2018 had the highest Q value and identified five modules (Fig. 4a, c).
The bootstrap procedure showed that the assignment of individuals to modules was robust since yearly values of community robustness fell above 0.67 (r com mean ± SD: 0.91 ± 0.09; Table 2).The mean number of modules detected in the bootstrapped yearly networks was 4 ± 0.88 (range 2e6).Notably, the networks from 2015, 2017 and 2018 exhibited high values of modularity (Q) and community robustness (r com ) (Table 2), indicating a modular structure and high module fidelity with a low propensity of association between individuals from different modules (Shizuka & Farine, 2016).In contrast, the remaining annual networks with lower Q values also presented high r com values (close to 1) (Table 2), suggesting a robust assignment of individuals to modules despite a weaker distinction between modules (i.e.smaller difference between intramodule versus intermodule links; Shizuka & Farine, 2016).The results of the bootstrapped modularity analysis for 1998 and 2018 are shown in Fig. 4b, d.These networks differ from the yearly association networks because edges represent the module assignment certainty (the proportion of bootstrap replicates for which the dyad was assigned to the same module).The module certainty network for 1998 showed lower robustness in assignment of individuals to each module (r com ¼ 0.7) compared to the module certainty network for 2018 (r com ¼ 0.98) that showed a more robust assignment of individuals in each module.
The modules in each annual network had an assortment of different categories of matrilineal kin dyads (mothereadult offspring, motheresubadult offspring, siblings, grandmotheregrandoffspring,  aunt/uncleeniece) and sex class combination (femaleefemale, femaleemale, maleemale; for example, see Fig. 4), as well as nonkin.Maternal kin dyads tended to be assigned to the same module across different years (Fig. 5).Among all maternal kin dyads assigned to the same module in a given year, 56% of mothereoffspring dyads, 28% of sibling dyads, 29% of aunt/uncleeniece dyads and 75% of grandmotheregrandoffspring dyads were assigned to the same module for !3 years.For instance, in matriline M1, mother CH and her son JO were assigned to the same module for 4 years (1998e2000, 2002), whereas CH and her daughter LO were assigned to the same module over 17 years (2004e2020).Maternal siblings such as KO and MS from matriline M1 or LI and CO from matriline M3 were also assigned to the same module for 7 years (2015e2020) and 3 years (1997e1999), respectively (Fig. 5).We also observed distant maternal relatives belonging to the same module in matriline M1.For example, grandmother CH and her granddaughter VA were assigned to the same module across 5 years (2013e2017) and aunt TK and her niece VA were assigned to the same module over 3 years (2015e2017) (Fig. 5).
According to the VGLM, maternal kin category and sex class combination were significant predictors of module assignment certainty.Maternal kinship influenced module assignment certainty in all age-difference classes (Table 3).We also performed a VGLM, grouping all maternal kin categories into one category due to the limited amount of data available for some categories (i.e.aunt/uncleeniece and grandmotheregrandoffspring), revealing that maternal kinship impacted module assignment certainty in three age-difference classes (0e3, 3e5, >9 years) but not in 5e9 years age difference (Table 3).Specifically, maternal kin with age differences of 0e3 and >9 years had a higher probability of belonging to the same module with high certainty (versus assignment to different modules with high certainty or assignment to the same or different module with low certainty) than nonkin (Fig. 6aed).Maternal kin with age differences of 3e5 years had a higher probability of belonging to the same or a different module with low certainty (versus belonging to a different module with high certainty) than nonkin (Fig. 6e).Considering all maternal kin categories, we found that maternal kin, including siblings (b ¼ 1.87, SE ¼ 0.40, P 0.001) and aunt/uncleeniece dyads (b ¼ 2.00, SE ¼ 0.49, P 0.001) with an age difference of 0e3 years, mothers with their subadult offspring with an age difference of 5e9 years (b ¼ 1.92, SE ¼ 0.58, P 0.001) and >9 years (b ¼ 1.21, SE ¼ 0.33, P 0.001) as well as mothers with adult offspring with an age difference of >9 years (b ¼ 1.30, SE ¼ 0.40, P 0.001) had a higher probability of being assigned to the same module with high certainty (as opposed to assignment to a different module with high certainty) than nonkin (Fig. 7aec).Siblings (b ¼ 1.32, SE ¼ 0.43, P ¼ 0.002) and aunt/uncleeniece dyads (b ¼ 1.37, SE ¼ 0.56, P ¼ 0.01) with 0e3 years of difference and mothers with their subadult offspring and grandmotheregrandoffspring dyads with age differences of >9 years had a higher probability of being part of the same module with high certainty (versus the same or a different module with low certainty) than nonkin (Fig. 7d, f).Siblings with age differences of 3e5 years had a higher probability of being in the same or a different module with low certainty (versus a different module with high certainty) than nonkin (b ¼ 1.08, SE ¼ 0.40, P ¼ 0.007; Fig. 7e).
We found that the type of matriline membership influenced module assignment certainty across all age-difference classes (Table 4).In particular, dyads belonging to the same matriline with an age difference of 0e3 years and >9 years had a higher probability of assignment to the same module with high certainty (versus a different module with high certainty or the same or a different module with low certainty) than dyads of a different matriline based on the b coefficient corresponding to the same module versus a different module with high certainty (0e3 years of difference: b ¼ 1.45, SE ¼ 0.24, P 0.001; >9 years of difference: b ¼ 1.41, SE ¼ 0.22, P 0.001) and for the same module with high certainty versus low certainty (0e3 years of difference: b ¼ 0.87, SE ¼ 0.25, P 0.001; >9 years of difference: b ¼ 1.38, SE ¼ 0.28, P 0.001).Dyads of the same matriline with 0e3, 3e5 and 5e9 years of difference had a higher probability of assignment to the same or a different module with low certainty (versus a different module with high certainty) than dyads of a different matriline (0e3 years of difference: b ¼ 0.58, SE ¼ 0.24, P ¼ 0.01; 3e5 years of difference: b ¼ 1.22, SE ¼ 0.38, P 0.001; 5e9 years of difference: b ¼ 0.69, SE ¼ 0.26, P ¼ 0.01).Dyads of the same matriline with 5e9 years of difference had a higher probability of assignment to the same module with high certainty (versus a different module with high certainty) than dyads of a different matriline (b ¼ 0.79, SE ¼ 0.29, P ¼ 0.01).

Prediction 3: the effect of maternal kinship on centrality
We found that matriline membership significantly influenced eigenvector centrality of its members (Table 5), so that members of the same matriline had similar centrality values.Individuals belonging to matrilines M1, M2 and M8 had the highest eigenvector centralities, whereas those from matriline M13 had the lowest eigenvector centralities (see Fig. 8a for pairwise comparisons among matrilines).Matriline size was positively correlated with eigenvector centrality, meaning that the larger the matriline, the higher the eigenvector centrality value of its members (r ¼ 0.27, P < 0.001) (Fig. 9).Matriline membership also influenced the betweenness centrality of its members (Table 5), with individuals in matriline M8 having higher betweenness centralities than those in matriline M1 (Fig. 8b).

DISCUSSION
We examined how maternal kinship impacts the structure of association networks in a group of wild spider monkeys considering a large data set spanning 24 years.Our findings support our predictions on how maternal kinship plays a role in the structure of the association networks.Maternal kin had overall higher association indices and a higher probability of belonging to the same module than nonkin of similar age differences.Association patterns of maternal kin varied among sex class combinations.Individuals belonging to the same matriline had more similar centrality scores than individuals of different matrilines.

Prediction 1: The Effect of Maternal Kinship on Edge Weight
In support of prediction 1, that maternal kin would show higher associations than nonkin, we found that maternal siblings and mothers with their subadult offspring associated more than nonkin with similar age differences.This preferential association between close maternal relatives occurs in other mammals such as European bison, Bison bonasus (Ramos et al., 2019), and African elephants, Loxodonta africana (Archie et al., 2006), and in other primates, particularly in species characterized by female philopatry: whiteface capuchin monkeys, Cebus capucinus (Perry et al., 2008), rhesus macaques, Macaca mulatta (Albers & Widdig, 2013;Kapsalis & Berman, 1996), and blue monkeys (Cords & Nikitopoulos, 2015).In male-philopatric primates like chimpanzees, males prefer to affiliate and cooperate with maternal over paternal brothers (Langergraber et al., 2007;Mitani, 2009) and females associate with close maternal kin more frequently than with nonkin (Foerster et al., 2015).Similarly, in hamadryas baboons, Papio hamadryas, both sexes establish and maintain relationships with maternal kin (St€ adele et al., 2016).Our findings provide support for our hypothesis that maternal kinship plays an important role in structuring association networks in spider monkeys.Our result is consistent with a previous study on Geoffroy's spider monkeys conducted at the same study site, in which maternal kin exhibited higher levels of association than nonkin (Rebecchini et al., 2011).
The preferential association with maternal kin found in our study could be attributed to the close association between mothers and their offspring, even after weaning.Indeed, we found higher association between mothers and their subadult offspring than similarly matched nonkin dyads.
Our study includes the infrequent presence of mothereadult daughter, aunt/uncleeniece and grandmotheregrandoffspring dyads in a group of spider monkeys.It is well documented that male spider monkeys are philopatric, while females typically disperse from their natal group as subadults (Shimooka et al., 2008).This female dispersal usually impedes co-residence with maternal relatives.Therefore, the kin network in a male-philopatric system is typically formed by patrilineal kin as well as the mother and maternal brothers (Chapais, 2016;Silk, 2021).However, our study documented an interesting exception since LO, the daughter of CH (from matriline M1), did not emigrate and successfully reproduced in the group.Throughout our study, LO had four female offspring that had the opportunity to associate with maternal relatives like their sisters, grandmother, uncles and aunts.Similar sporadic cases occur in other male-philopatric primate species such as muriquis (B.hypoxanthus: Strier et al., 2011) and chimpanzees (Pusey et al., 1997), allowing individuals to co-reside with a wider network of maternal kin.Hence, female dispersal exceptions in spider monkeys enable individuals to associate with otherwise unavailable maternal kin, with potential benefits to individuals (see below), but these are complementary to the regularly present maternal relatives (mothers and brothers).Another factor that may contribute to association among maternal kin is parallel dispersal, in which individuals immigrate together into groups or immigrate alone into groups containing related individuals (Pusey & Packer, 1987;Wikberg, Jack, et al., 2014).However, there is no evidence of parallel dispersal in our study group or in any other Geoffroy's spider monkey groups (Dell'Anna et al., 2024;Melin et al., 2020).Considering these exceptional maternal kinship categories, our results support preferential association among maternal relatives beyond the conventional mothereoffspring and sibling relationships as we found higher association among aunt/uncleeniece dyads with up to 5 years of age difference, as well as grandmotheregrandoffspring dyads with >9 years of age difference, compared to nonkin.Despite the relatively low number of 1 9 9 7 1 9 9 8 1 9 9 9 2 0 0 0 2 0 0 1 2 0 0 2 2 0 0 3 2 0 0 4 2 0 0 5 2 0 0 6 2 0 0 7 2 0 0 8 2 0 0 9 2 0 1 0 2 0 1 1 2 0 1 2 2 0 1 3 2 0 1 4 2 0 1 5 2 0 1 6 2 0 1 7 2 0 1 8 2 0 1 9 2 0 2 0  dyads in the aunt/uncleeniece and grandmotheregrandoffspring categories, the data suggests a clear pattern of preferential maternal kin association.The preferential association between mother and offspring likely promotes familiarity and interaction between infants and other maternal relatives available in the group such as siblings, grandmothers, aunts, uncles, nephews, nieces and cousins (Silk, 2009(Silk, , 2021)).Despite the interesting case of matriline M1, it is worth noting that our findings are not conditioned on the relationships resulting from the philopatric female, as evidenced by the patterns observed for mothereoffspring and sibling pairs.In fact, our results remained consistent when we excluded aunt/ uncleeniece, grandmotheregrandoffspring and mothereadult daughter categories from the analyses.We also found that the effect of maternal kin on association patterns varied among sex class combinations, consistent with findings from studies on male-philopatric species.For instance, in chimpanzees, males prefer to affiliate and cooperate with maternal brothers (Langergraber et al., 2007;Mitani, 2009) while females associate and groom close maternal kin (their mother and sisters) more frequently than nonkin (Foerster et al., 2015).Conversely, muriquis had weak affiliative relationships or social associations among maternal brothers (Strier et al., 2002).In our study, maternal brothers as well as sisters and femaleemale siblings associated more than nonkin, and maternal sisters associated more than maternal femaleemale siblings.This provides evidence of the importance of maternal kin and sex shaping associations in spider monkeys, which could be attributed to the familiarity resulting from a shared mother and the fitness benefits of associating with maternal kin.
We also found that mothers associated more with their subadult daughters than with their subadult sons.This pattern has been documented in other male-philopatric species in which mothers associated more with their older daughters than with their older sons (Tolentino et al., 2008).These low levels of association among mothers and their subadult sons could be because subadult males tend to spend more time with adult males than they do with their mothers (Ramos-Fern andez et al., 2009;Vick, 2008).

Prediction 2: The Effect of Maternal Kinship on Modularity
The bootstrap procedure demonstrated a robust assignment (r com ) of individuals to modules even when the modularity (a) ( .Frequency of maternal kin dyads in age-difference categories where we detected significant differences between kin and nonkin: high certainty of assignment to the same module; high certainty of assignment to a different module; low certainty of assignment to either module (same or different module).The significant comparisons between kin and nonkin were in terms of high certainty of assignment to the same module versus high certainty of assignment to the different module (a, b), high certainty of assignment to the same module versus low certainty of assignment to either module (c, d), as well as high certainty of assignment to the different module versus low certainty of assignment to either module (e).
coefficient values (Q) were low in some annual networks.Q values are influenced by how clearly the network has a modular structure (i.e.how clear the existence of modules is where individuals within the same module tend to associate more with each other than with individuals from different modules in the network), while r com relies on the robustness of the assignments of individuals to specific modules (Shizuka & Farine, 2016).Therefore, the high values of r com paired with low Q values in certain annual networks suggest a robust assignment of individuals to modules despite the weak partition of the network into modules (Shizuka & Farine, 2016).We found the presence of modules formed by maternal relatives with similar age differences lasting over 3 years.This result supports prediction 2, that maternal kin would have a higher probability of being assigned to the same social network module than nonkin and that the pattern would persist across years.Our finding of a significant relationship between modularity and maternal kinship extends existing results on maternal kin association bias (a tendency for individuals to preferentially associate with maternal relatives) (Diaz-Aguirre et al., 2019, 2020;Reisinger et al., 2017;Wilkinson et al., 2019).Although most modules comprise maternal kin and nonkin individuals, maternal kin with similar age differences were assigned to the same module with higher certainty than nonkin.Moreover, individuals belonging to the same matriline showed a higher probability of assignment to the same module than individuals belonging to different matrilines.These patterns reflect how matriline acts as a structuring factor of association networks, with modules being formed in part through preferential associations between maternal kin.Likewise, studies on other mammal species, such as Burrunan dolphins (Diaz-Aguirre et al., 2018), killer whales, Orcinus orca (Reisinger et al., 2017), eastern grey kangaroos, Macropus giganteus (Best et al., 2013), wild boar, Sus scrofa (Podg orski et al., 2014), and bats (9 species from the families Emballonuridae, Phyllostomidae, Thyropteridae and Vespertilionidae: Wilkinson et al., 2019), have found clusters of individuals consisting primarily of kin.Similarly, clustering of related individuals into subsets occurs in macaques (Macaca spp.: Sueur et al., 2011) and sperm whales, Physeter macrocephalus (Konrad et al., 2018).In particular, our results indicate that maternal siblings with up to 3 years of difference in age and motheresubadult offspring and mothereadult offspring dyads with up to 9 years of difference in age have a higher probability of assignment to the same module, which can be attributed to maternal care that fosters an association between a mother and her offspring and her offsprings' siblings (Silk, 2021).Mothereoffspring pairs maintained close proximity, which in turn may generate stronger association among siblings that are close in age (Bray & Gilby, 2020;Silk, 2009).The early association among mothereoffspring dyads and the age similarity among individuals may provide opportunities to recognize and associate with other maternal kin such as older siblings, aunts and grandmothers (Silk, 2009(Silk, , 2021)).This may explain why maternal kin who are close or distant in age (e.g.siblings or aunt/uncleeniece dyads with an age difference of up to 3 years, grandmotheregrandoffspring dyads with an age difference of >9 years, individuals of the same matriline with an age difference up to 3 years and from 5 years to >9 years of age difference) have a high probability of belonging to the same module.These results contribute to our understanding of factors that shape social networks.It is widely recognized that sex plays a crucial role in modularity in spider monkeys, with individuals of the same sex often belonging to the same module (Ramos-Fern andez et al., 2009;Smith-Aguilar et al., 2019).In addition to sex, our study suggests that individuals also cluster based on maternal kinship, adding another important factor structuring social networks.We also found that maternal kin dyads were consistently assigned to the same module over multiple years, indicating that strong associations among maternal kin persist over time.According to Ramos-Fern andez et al. (2009), associations between adultejuvenile pairs of spider monkeys are typically strong during the first year, but after 3 years, these associations become indistinguishable from random.However, we observed long-lasting associations, particularly in mothereoffspring dyads since they were consistently assigned to the same module for more than 3 years.In some cases, these associations began when the offspring were infants and continued through subadult or adult life.In Geoffroy's spider monkeys, long-term associations between mothers and their offspring have also been observed, reflected by high support during attack episodes, travelling or foraging together even after their offspring reach maturity (Vick, 2008).In chimpanzees, outside mothereoffspring dyads, maternal siblings are the first nonmother social partners, and they can also form long-lasting social bonds (Mitani, 2009).Older siblings often affiliate with their younger sibling as a result of the proximity with the mother (Lonsdorf et al., 2018).This could also be why, in spider monkeys, maternal sibling dyads of different ages were also consistently assigned to the same module for more than 3 years.Similarly, distant maternal relatives, such as grandmother, grandoffspring, niece, aunt and uncle, also belonged to the same module for more than 3 years.Our findings are consistent with previous research on other group-living species documenting long-lasting social relationships among maternal kin (wild boar: Podg orski et al., 2014;yellow baboons, Papio cynocephalus: Silk et al., 2006).Our results suggest that maternal kin can have long-term influence on association patterns.However, maternal kinship is not the only relevant factor, as we found dyads of individuals from different matrilines belonging to the same module for at least 3 years, probably pointing to the influence of other factors (e.g.reciprocal altruism or mutualism; Clutton-Brock, 2009), including sex and paternal kinship, on association patterns.

Prediction 3: The Effect of Maternal Kinship on Centrality
Our results support prediction 3, that individuals within the same matriline would have similar centrality scores and that larger matrilines would have higher centrality values.Therefore, matriline membership can influence centrality patterns in the association network given individual preferences to associate with maternal kin.These findings contribute to our understanding of the factors that influence the position of individuals in spider monkey social networks.Previous research in spider monkeys has revealed the influence of sexeage classes on differential central positions within the network.For instance, Smith-Aguilar et al. (2019) reported that adult males and females tend to occupy more central positions, while subadult females exhibit lower centrality in a multiplex network.Additionally, adult males play a central role in connecting the network.Ramos-Fern andez et al. (2009) found that adult females are more central in the network and that young males played a central role in connecting males and females.The reproductive  The box plots' central line represents the median, box limits represent the 25th and 75th percentiles, whiskers represent the maximum and minimum range of the data within 1.5 times the interquartile range, and black dots shows values outside 1.5 times the interquartile range.Significant differences between matrilines are shown with horizontal lines on top of the plot.Differences are indicated between the group marked with the short vertical line and those marked with arrows and asterisks (P 0.05).For example, matrilines M1, M2 and M8 had higher eigenvector centralities than those in matrilines M10, M11, M12, M13 and M14.
Please cite this article in press as: Jasso-del Toro, C., et al., Influence of maternal kinship on association network structurein a long-term study of spider monkeys (Ateles geoffroyi), Animal Behaviour (2024), https://doi.org/10.1016/j.anbehav.2024.05.006 status of females is another factor that may influence network centrality (Shimooka, 2015).Lactating females tend to occupy a more central position in the network, being well connected with other members of the group (Shimooka, 2015).Such connections may benefit lactating females by mitigating the risk of infanticide or predation or by providing increased socialization opportunities for their offspring (Shimooka, 2015).Our study adds maternal kinship as another component that influences network centrality in spider monkeys.We found that certain matrilines had higher eigenvector centrality than others and that individuals within the same matriline tended to have similar centrality values.Our results suggest that individuals from matrilines with higher eigenvector centrality were better and more strongly connected with the members of their own matriline than were individuals from matrilines with a lower eigenvector centrality and that higher centrality was associated with larger matriline size.Similar patterns occur in other primate species, where individuals within the same matrilines have similar centrality values (Sosa, 2016), or individuals are more central in kin-related groups than in groups formed by nonkin (Sueur et al., 2011).And, as in our study, higher centrality has been linked to matriline size (Beisner et al., 2020;Bret et al., 2013;Sosa, 2016), because individuals from larger matrilines have more kin partners with whom to interact than do individuals from smaller matrilines (Beisner et al., 2020), given that individuals associated more with maternal kin than with nonkin.Individuals related through maternal kinship often engage in affiliative interactions, cooperate and form coalitions (Cords & Nikitopoulos, 2015;Langergraber et al., 2007;Wahaj et al., 2004).Therefore, individuals from larger matrilines like M1 have opportunities to interact affiliatively, cooperate or form coalitions with a greater number of partners, which may contribute to stronger relationships and subsequently increase individuals' centrality in that matriline.In terms of betweenness centrality, we found that individuals of certain matrilines had higher values than others.Individuals with higher betweenness centralities are important for group cohesion (Whitehead, 2008) and social network stability (Abell et al., 2013).For example, individuals from matriline M8 showed significantly higher betweenness centralities than individuals from matriline M1, which suggests that individuals with high betweenness centrality serve as connecting bridges between matrilines and may have a key role in promoting group cohesion.
Paternal kinship is expected to influence social structure in male-philopatric species since individuals tend to live and interact frequently with their paternal kin (Chapais, 2016;Silk, 2021).Notably, we are missing information on paternal kinship, which may also be fundamental in shaping relationships, particularly among males (Aureli & Schaffner, 2008;Di Fiore, 2009;Shimooka et al., 2008).In our study, many paternal kinship relations were likely grouped with nonkin.Future steps should examine the influence of both types of relationships (maternal and paternal) and overall kinship on association patterns.Genetic studies are needed to investigate potential sex differences in kin bias and the role of paternal kinship in association patterns of spider monkeys characterized by male philopatry.This will enable tackling questions such as whether males (philopatric sex) or females (dispersing sex) exhibit stronger associations towards maternal or paternal relatives.Additionally, it would be valuable to explore how association preference for maternal kin and matriline membership influence fitness costs and benefits.

Conclusion
In general, our study contributes to the understanding of maternal kinship as a structuring factor of association networks of a species characterized by female dispersal and male philopatry.Our results revealed that preferential association with maternal kin can extend beyond mothereoffspring and young siblings, encompassing other maternal relatives like adult siblings, or even aunts, uncles and nieces, or grandmother and grandoffspring, when they occasionally occur.Preferential associations among maternal kin influence the formation of distinct clusters composed of maternal relatives that persist over years.The association patterns among maternal kin and the presence of modules formed by maternal relatives suggest that spider monkeys may recognize maternal relatives, although the mechanisms that drive the association patterns require further study.Our analyses revealed centrality patterns within spider monkey social networks, which go beyond our earlier understanding of the roles of age and sex by introducing maternal kinship as a determining factor.Being part of a certain matriline can determine the costs and benefits faced by individuals regarding group living.For example, individuals from a matriline with low centrality can potentially have less access to information about resources or predator vigilance than individuals from matrilines with higher centralities, which could be tested in further studies.

Figure 1 .
Figure1.Fifteen matrilines (M1eM15) identified throughout the study period (1997e2020).Each matriline is composed of the mother (black lines) and her offspring (females: orange lines; males: blue lines).Mother lines begin the year of immigration into the group (except those for the mothers of the first six matrilines that were in the group at the beginning of the study).Offspring lines begin in the year of their birth except for those from the first six matrilines, the line of which begins in 1997 because they were in the group at the start of the study.LI, from matriline M3, is the only offspring born in 1997.All lines end in the year of an individual's disappearance or confirmed death.The arrows indicate individuals who were still in the group when the study ended.Letters represent identity codes for each individual.LO from matriline M1 is the only female that was born and reproduced in the study group (thick orange line in matriline M1).

Figure 2 .Figure 3 .
Figure 2. Edge weights (simple ratio index, SRI, values) for maternal kin categories and for each age-difference class: (a) 0e3 years of difference; (b) 3e5 years of difference; (c) 5e9 years of difference; (d) >9 years of difference.In each graph, the SRI mean for each maternal kin category is represented by an orange point; error bars show ± SE of the mean.The horizontal lines with an asterisk indicate significant differences (P < 0.05, based on post hoc tests) between two maternal kin categories, with one category located at the beginning of the line and the other one located at the end of the line.Mo_SA: motheresubadult offspring; Mo_A: mothereadult offspring; AUN: aunt/uncleeniece.

Figure 4 .
Figure 4. Graphic representation of the association networks for (a) 1998 and (c) 2018 and module certainty networks for (b) 1998 and (d) 2018.The networks show the four and five modules identified for 1998 and 2018, respectively, by the fast-greedy algorithm.In all cases, nodes represent individuals, with males as squares and females as circles.Node colour indicates the matriline to which an individual belongs.In (a) and (c), edge width is proportional to the association index for each dyad; in (b) and (d), edges represent the proportion of bootstrap replicates where individuals were assigned to the same module (i.e.thicker edges indicate more consistency in assignment to the same module).

Figure 5 .
Figure 5. Visual representation of individuals assigned to modules detected in each annual network.In every year, each circle represents an individual and its colour, the matriline (M1eM15).Circles connected by lines across years represent the same individual.Two-letter identity codes of certain individuals are located at the beginning of their line for description purposes (see text).Grey rectangles group individuals assigned to the same module.NM (no matriline) refers to immigrants who did not belong to any matriline during the study period (including one female whose offspring disappeared/died before they were 3 years old).
Figure6.Frequency of maternal kin dyads in age-difference categories where we detected significant differences between kin and nonkin: high certainty of assignment to the same module; high certainty of assignment to a different module; low certainty of assignment to either module (same or different module).The significant comparisons between kin and nonkin were in terms of high certainty of assignment to the same module versus high certainty of assignment to the different module (a, b), high certainty of assignment to the same module versus low certainty of assignment to either module (c, d), as well as high certainty of assignment to the different module versus low certainty of assignment to either module (e).

FrequencyFigure 7 .
Figure7.Frequency of maternal kin and nonkin dyads for age-difference classes where we detected significant differences among maternal kin categories: high certainty of assignment to the same module; high certainty of assignment to a different module; low certainty of assignment to either module (same or different module).The significant comparisons were in terms of high certainty of assignment to the same module versus high certainty of assignment to the different module (a, b, c), high certainty of assignment to the same module versus low certainty of assignment to either module (d, f), as well as high certainty of assignment to the different module versus low certainty of assignment to either module (e).The horizontal lines with an asterisk indicate significant differences (P < 0.05) between maternal kin categories in terms of module assignment certainty.Mo_SA: motheresubadult offspring; Mo_A: mothereadult offspring; AUN: aunt/uncleenieces.

Figure 8 .
Figure 8.(a) Eigenvector and (b) betweenness centrality values for each matriline (M1eM15).The box plots' central line represents the median, box limits represent the 25th and 75th percentiles, whiskers represent the maximum and minimum range of the data within 1.5 times the interquartile range, and black dots shows values outside 1.5 times the interquartile range.Significant differences between matrilines are shown with horizontal lines on top of the plot.Differences are indicated between the group marked with the short vertical line and those marked with arrows and asterisks (P 0.05).For example, matrilines M1, M2 and M8 had higher eigenvector centralities than those in matrilines M10, M11, M12, M13 and M14.

Figure 9 .
Figure 9. Relationship between eigenvector centrality and matriline size.Each point corresponds to an individual present in each of the study years.Correlation line in orange with 95% confidence intervals in light grey.

Figure A3 .
Figure A3.Edge weights (simple ratio index, SRI, values) for maternal kin categories (without exceptional cases) and for each age-difference class: (a) 0e3 years of difference; (b) 3e5 years of difference; (c) 5e9 years of difference; (d) >9 years of difference.In each graph, the SRI mean for each maternal kin category is represented by an orange point.Error bars show ± SE of the mean.The horizontal lines with an asterisk indicate significant differences (P < 0.05, based on post hoc tests) between two maternal kin categories, with one category located at the beginning of the line and the other one located at the end of the line.Mo_SA: motheresubadult offspring; Mo_A: mothereadult offspring

Table 1
GLMM results on the effect of maternal kinship on edge weight for each agedifference class

Table 2
Number of modules and modularity coefficient (Q) of the yearly networks with confidence intervals (CI) and community robustness (r com ) values from the bootstrap analysis Please cite this article in press as: Jasso-del Toro, C., et al., Influence of maternal kinship on association network structurein a long-term study of spider monkeys (Ateles geoffroyi), Animal Behaviour (2024), https://doi.org/10.1016/j.anbehav.2024.05.006

Table 3 VGLM
results on the effect of maternal kin on module assignment certainty in 1000 bootstrap replicates, for each age-difference class Please cite this article in press as: Jasso-del Toro, C., et al., Influence of maternal kinship on association network structurein a long-term study of spider monkeys (Ateles geoffroyi), Animal Behaviour (2024), https://doi.org/10.1016/j.anbehav.2024.05.006

Table 4
VGLM results on the effect of the type of matriline membership (dyads belonging to the same or different matriline) on the module assignment certainty for each agedifference category

Table A1 Modularity
org/10.1016/j.anbehav.2024.05.006Q values generated from four community-detection algorithms and the number of individuals in each year of the study