Comparing measures of social complexity: larger mountain gorilla groups do not have a greater diversity of relationships

Abstract

Social complexity reflects the intricate patterns of social interactions in societies. Understanding social complexity is fundamental for studying the evolution of diverse social systems and the cognitive innovations used to cope with the demands of social life. Social complexity has been predominantly quantified by social unit size, but newer measures of social complexity reflect the diversity of relationships. However, the association between these two sets of measures remains unclear. We used 12 years of data on 13 gorilla groups to investigate how measures of social complexity relate to each other. We found that group size was a poor proxy for relationship diversity and that the social complexity individuals experienced within the same group varied greatly. Our findings demonstrate two fundamental takeaways: first, that the number of relationships and the diversity of those relationships represent separate components of social complexity, both of which should be accounted for; and second, that social complexity measured at the group level may not represent the social complexity experienced by individuals in those groups. These findings suggest that comprehensive studies of social complexity, particularly those relating to the social demands faced by individuals, may require fine-scale social data to allow accurate comparisons across populations and species.

1. Background

Complex social systems have been hypothesized as a key driver in the evolution of brains [1–3], communication [4], multilevel social structure [5] and cooperation [6–8]. Animals that live in more complex societies are proposed, for example, to require larger brains and more sophisticated cognitive abilities [1,3,9]. Social complexity has even been suggested to enable greater ecological success, thus explaining the prevalence of taxa such as humans, hymenoptera and termites across a wide variety of environments [10]. Correctly quantifying the complexity of social systems is therefore of utmost importance to our ability to test these predictions and to advance our understanding of social evolution. While the complexity of social systems has often been assessed intuitively, comparisons across populations and species require quantifiable measures [11]. Yet how best to quantify social complexity remains unclear.

Social complexity is most often measured in one of two ways: (i) the number of relationships in a social unit or (ii) the diversity of social relationships within that social unit [9,10,12,13]. The idea that groups with a greater number of relationships are more socially complex assumes that each additional relationship comes with its own social demands. Quantifying realized relationships, as can be done using the social network measures of degree or density [14], requires extensive social data, limiting its feasibility as a measure in large cross-species comparisons. As a result group size has been used extensively as a proxy of relationship number in studies of social complexity due to the wide availability of these data across study sites and species [15]. Alternatively, social complexity has been proposed to be greater in groups with a larger number of differentiated relationships of different type [9]. Each additional relationship that is of a different type to all other relationships results in a more complex social environment. Measures of relationship diversity therefore do not focus on the total number of relationships or potential relationships, but on the number of different types of relationship (usually distinguished by association strength), and the distribution of relationships across those types. The greater the number of different types of social relationship and the more evenly spread relationships are across those types, the more complex a social system [12,13].

Group size and the diversity of types of social relationship within groups are expected to be tightly linked at small group sizes because small groups have a small maximum number of potential relationship types. However, beyond this, group size and relationship diversity may represent fundamentally different components of social complexity [10]. For example, a large colony of eusocial insects without individual recognition may have a fairly low diversity of social relationships if relationships are based on a small number of different castes [16]. By contrast, large groups of primates could have a high diversity of social relationships if relationships are individual-specific and based on factors such as past interactions, dominance and kinship [17]. If each individual has a clearly differentiated relationship with each other individual in the group, group size could provide just as much information about social complexity as relationship diversity [1,9]. Yet the extent to which group size correlates with relationship diversity remains unknown for any taxa or species.

Because social complexity is believed to drive the cognitive demands experienced by individuals [9], it is also important to verify whether group-level measures of social complexity adequately reflect the experience of individuals or whether they mask important individual-level variation [18] (figure 1). A mismatch between group-level and individual-level measures may be one reason for the often conflicting evidence for a relationship between social complexity (measured as group size) and brain size [15,19–24]. Attributes such as sex may also be important determinants of the complexity an individual experiences in its social environment. This complexity could also change throughout an individual's life, for example, as an individual ages. To investigate the processes of social evolution, we therefore also require a greater understanding of whether group-level metrics reflect the social complexity experienced by individuals.

Figure 1.

Groups with the same diversity of relationships at the group-level (group-level S) can have drastically different levels of social complexity at the individual-level (mean individual-level S). Grey circles represent individuals in the group, arrows represent their relationships. Group-level S is based on the total number of relationship types in a group. For (a) and (b) this is 1.07: 5 weak relationships (light), three intermediate relationships (medium) and five strong relationships (dark). Individual-level diversity of relationships (reported within grey circles) is based on the relationships that each individual has, e.g. 0 when all their relationships are of the same type or 1.1 when they have three relationships, each of a different type. The mean individual-level diversity for a group is therefore the mean of all individuals' values: 0.21 for group (a) and 0.81 for group (b). (Online version in colour.)

One way to investigate links between measures of social complexity is to use cross-species data. However, for many species, this level of fine-scale data is not available, and where it is, considerable differences in the habitats, sampling methods and species-specific social behaviours have the potential to obscure or drive these links [14]. Another method is to use intra-specific data in study systems with lots of variation in group size. Mountain gorillas (Gorilla beringei beringei) provide an ideal study organism in which to do this. Their groups vary considerably in size (2 to 65 individuals) and numerous such groups have been the subject of long-term consistent monitoring in the wild [25]. We use social behaviour and demographic data from 13 wild mountain gorilla groups collected by the Dian Fossey Gorilla Fund over 12 years. We quantify social relationships using proximity data due to the documented importance of proximity within the gorilla social system [26–28], and the potential for proximity-based measures to be compared across primates [29–32] and other social species [13]. We test whether group size predicts the diversity of social relationships within groups. We also investigate social complexity at the individual level, testing whether individual-level measures reflect group-level metrics, and can be predicted by sex and age. Finally, we test whether the diversity of social relationships is influenced by variation in socio-sexual factors (adult sex ratio and mating strategy).

Unlike western gorillas, which primarily live in groups with a single dominant adult male, mountain gorillas form both single-male and multi-male groups [33], resulting in groups that vary in size, as well as levels of reproductive competition and mating strategy. Variation in socio-sexual parameters additionally enables tests of the hypotheses that increased male sexual competition or changes in mating system can lead to higher levels of social complexity [22,34]—hypotheses of purported importance in human social evolution. Numerous transitions in social structure and mating system are thought to have occurred during human evolution, and the ancestral social structure of humans remains hotly debated [5,35,36]. However, little is known about what such transitions may have meant for the social complexity of early human populations. Modern human populations also show wide variation in mating patterns, despite the universality of marriage in human societies, with promiscuity, monogamy, polyandry and polygyny all observed [37]. Similarities in the variation expressed in the mountain gorilla social system [38] may be valuable to understanding our own highly flexible social system, providing key information on how elements of the social system can influence social complexity and the potentially very different pressures of group living experienced when these elements change.

2. Methods

(a). Behavioural and demographic data collection

Habituated mountain gorilla (Gorilla beringei beringei) groups were monitored for up to 4 h daily by the Dian Fossey Gorilla Fund's Karisoke Research Center in the Volcanoes National Park (VNP), Rwanda. We used data collected over 12 years between 2004 and 2015. During this time, the number of groups monitored varied between 3 and 11 (annual mean = 7.78 groups). All gorillas were individually identified by physical characteristics. Behavioural data were collected on each group member via 50 min focal sampling, with scan sampling completed every 10 min to record all gorillas within 2 m of the focal individual. Group composition was monitored daily. Groups that remained stable across a given year (did not form, merge, fission or disintegrate) and contained at least three individuals that were present for the entirety of a year were used in analyses.

(b). Quantifying social complexity—group size

For each group in each year that was analysed (n = 72), the size, adult sex ratio and mating strategy of the group for that year were recorded. Group size was the total number of individuals present in the group for at least 11 months of the year and over the age of 1 at the start of the year. All individuals over the age of 8 by the midpoint of the year were classified as adults. Adult sex ratio was the proportion of adults in the group that were male. Mating strategy was classed as multi-male if a group contained more than one sexually mature silverback male over the age of 16—the median age of male dispersal [28] and the estimated age at onset of adulthood for males [39] (see electronic supplementary material).

(c). Quantifying social complexity—relationship diversity at the group level

Despite living in cohesive social groups, rates of social interaction are extremely low in adult mountain gorillas. For example, Stoinski et al. [28] found that most subordinate silverbacks had no affiliative or aggressive interactions with the dominant silverback over a year, but subordinate silverbacks that later dispersed tended to spend less time in close proximity to the dominant silverback. They suggest that, similarly to western gorillas [27], proximity may be a better indicator of relationship quality in this species. We therefore used proximity data to assess the social relationships present within mountain gorilla groups. Proximity data (within 2 m) from focal sampling was extracted for all individuals that were present in the group at least 11 months of the year and were greater than 1 year old at the start of the year. Weighted social networks were constructed from proximity data for each group in each year. Edge values of the networks were calculated using the simple ratio index (SRI) of association [40]. These values represented the proportion of time two individuals were within 2 m of each other, such that a value of 1 would indicate that the two individuals were within 2 m of each other every time they were observed, while 0 would indicate that they were never observed within 2 m of each other.

We used mixture models to cluster the SRI values from each network into categories following Weiss et al. [13]. Mixture models were run with varying numbers of categories to identify the number of categories of relationship type that best fit the distribution of SRI values (figure 2; electronic supplementary material, figure S1) using integrated completed likelihood (ICL). This data-driven approach enabled each dyadic relationship to be categorized into a given relationship type. The diversity of social relationships within each network was then extracted from the best fitting model using Shannon's index [13], taking into account both the number of different types of relationship and the distribution of dyadic relationships across these categories. We repeated this analysis using only data on adults.

Figure 2.

Density histogram (blue bars) and distribution (black lines) of relationship types (T1–5) as distinguished by mixture modelling based on the strength of association from the simple ratio index for proximity (proportion of time pairs of individuals were within 2 m). Plot excludes SRI values of 0 for visualization purposes. See electronic supplementary material, figure S2 for frequency histogram of full dataset. (Online version in colour.)

(d). Quantifying social complexity at the individual level

We estimated the diversity of social relationships for individuals each year by running mixture models on a single dataset combining all SRI values from all 72 networks across years and groups. This assigned all SRI edge values into categories of relationship type. The best-fitting model (number of relationship types that best fit the data) included five types of relationship across the population (figure 2). As this value was lower than the number detected in some groups in certain years, simulations were run to demonstrate that rare relationship types, only present in a small number of the total groups, were unlikely to be detected when analysing the population as a whole. While this suggests that individual relationship diversity may be slightly underestimated in a small number of cases, this approach enables the direct comparison of individuals across the population and across multiple years (electronic supplementary material).

Following this population-wide classification of relationship types, all the relationships that an individual was involved in within a given year were extracted, and the diversity of these relationships calculated using Shannon's diversity [12,13]. This resulted in a single social diversity score for each individual in each year (n = 1007, 166 individuals sampled across a mean of 6.67 years). This value represented only the diversity of relationships that a specific individual was involved in. The mean of this for a group was therefore different to the diversity of relationships across that group (figure 1).

(e). Testing the association between group-level measures of social complexity

We used generalized additive mixed models (GAMMs) to determine if the diversity of social relationships in a group was predicted by group size following linear or polynomial relationships. This analysis was repeated with only adult relationships, using the number of adults instead of group size. Group identity was included as a random factor to account for sampling the same group over different years. The mean sampling effort for all relationships in a group in a given year was included as a smoothing term in the model to account for differences in sampling. This was particularly important as relationships in smaller groups tended to be better sampled due to a smaller number of individuals on which to collect data. We additionally tested adult sex ratio and mating strategy as predictors of relationship diversity using GAMMs to assess how well socio-sexual structure predicted relationship diversity.

(f). Testing the association between group-level and individual-level measures of social complexity

GAMMs were run to investigate whether individual-level social complexity was predicted by group-level estimates of social complexity (the diversity of social relationships in a group and group size). As plots demonstrated a potential polynomial relationship, both linear and polynomial predictors were investigated. Models included the year of data collection nested within group and individual as random factors, with sampling effort as a smoothing term. All continuous variables were z-transformed to aid comparison. To investigate variation in social complexity within and between individuals, the mean, minimum and maximum variance of an individual's relationship diversity across multiple years was calculated for all individuals present across more than one year (n = 153). This was compared with the mean, minimum and maximum variance between individuals within a group in a given year (n = 72) and the total variance observed across the entire sample.

As there was high variance within groups and individuals, we also explored whether the age and sex of individuals predicted the diversity of social relationships at the individual-level. Due to the polynomial appearance of the relationship between age and an individual's relationship diversity, we ran GAMMs with increasingly higher degree polynomials for age (e.g. age, then age + age², then age + age² + age³…) until the addition of a further polynomial did not improve the adjusted r-squared. This resulted in a model that included age polynomials up to the fifth degree (age + age² + age³ + age⁴ + age⁵), sex and their respective interactions predicting how male and female gorillas' relationship diversity changed as they aged. Models included year nested within group and individual as random factors. As each individual was monitored over an average of 6.19 years, by including individual as a random factor we could investigate how relationship diversity changed within an individual as they aged. The sampling effort for the group was again included as a smoothing term and all continuous variables z-transformed.

All GAMMs were run using the GAMM4 package [41] in R version 3.6.1 [42]. Model diagnostic plots were generated to verify that model assumptions were not violated [43].

3. Results

(a). Larger groups do not have a greater diversity of social relationships

Up to 7 types of social relationship were detected within gorilla groups (mean = 4.51, min = 2, max = 7; see electronic supplementary material, figure S1 for examples), with the diversity of social relationships ranging from 0.43 to 1.87 (mean = 1.29). Although there was not a linear relationship between group size and the diversity of social relationships within a group, there was a significant polynomial relationship between these variables (table 1). Very small or very large groups had lower levels of relationship diversity, while mid-size groups showed the highest diversity (figure 3). These results were the same when all group members were included, and when analyses were restricted to adults. These results also remained when the one unusually large group, PAB, was removed, but only when all group members were included (electronic supplementary material, table S1).

Table 1.

GAMMs demonstrate a polynomial relationship between group size and both the diversity of social relationships in a group and the diversity of adult relationships in a group. Italics indicate significance at p < 0.05.

model	variable	full group		adults only
		t-value	p	t-value	p
linear	group size	1.662	0.211	1.568	0.121
R2 . (adj) = 0.136 (full) and 0.125 (adults)
polynomial	group size	2.091	0.040	1.698	0.094
R2 . (adj) = 0.303 (full) and 0.286 (adults)	group size2	−4.503	<0.001	−4.818	<0.001

Figure 3.

Relationships between group-level measures of social complexity. (a) The diversity of social relationships within groups against group size and (b) the diversity of social relationships among adults within groups against the number of adults, for all study groups across all years. Group indicated by colour. Significant relationships indicated by black curve with shaded area indicating standard error bounds. (Online version in colour.)

(b). Traits influencing the diversity of relationships in a group

Adult sex ratio followed a polynomial relationship with the diversity of social relationships within a group (figure 4). There was a lower diversity of relationships when adult group members were either mostly male or mostly female, and highest diversity when around 40% of adult group members were male. However, no such relationship was found when analyses were restricted to the diversity of adult social relationships (table 2; electronic supplementary material, figure S3). The mating strategy of the group did not influence the diversity of social relationships (electronic supplementary material, table S2). That is, groups in which multiple mature males had the opportunity to mate with females did not have a greater diversity of relationships than groups where only one mature male did (t = 1.228, p = 0.224).

Figure 4.

The relationship between adult sex ratio and the diversity of social relationships within the group, for all study groups across all years. Mating strategy (MM: multi-male or SM: single male) indicated by circles and triangles, respectively. Group indicated by colour. Significant relationship indicated by black curve with shaded area indicating standard error bounds. (Online version in colour.)

Table 2.

GAMMs to predict the diversity of social relationships in a group from the adult sex ratio (ASR) demonstrate a polynomial relationship only when both adults and immature individuals are included. Italics indicate significance at p < 0.05.

	variable	full group		adults only
		t-value	p	t-value	p
linear	ASR	−1.262	0.249	0.251	0.802
R2 . (adj) = 0.040 (full) and 0.022 (adults)
polynomial	ASR	−0.917	0.362	−0.035	0.972
R2 . (adj) = 0.177 (full) and −0.022 (adults)	ASR2	−2.444	0.017	−1.038	0.303

(c). Individuals in larger groups do not have a greater diversity of relationships

We identified a high diversity of relationships (S = 1.493) across the population as a whole, detecting five types of intra-group social relationship. The strongest relationships (relationship types 4 and 5) were primarily mother–offspring and maternal–kin relationships, but relationship types were not determined purely by the kinship or age–sex classes of the individuals involved (electronic supplementary material, figure S4, and table S3). We found a positive linear relationship between the diversity of an individual's relationships and the total relationship diversity in their group (GAMM (n = 1107): R² (adj) = 0.094, t = 3.574, p < 0.001; figure 5a). The diversity of an individual's relationships declined with group size (table 3). However, this pattern was driven by the unusually large PAB group and disappeared when they were excluded from the analysis. A polynomial model better explained the relationship between individual-level diversity and group size (table 3, figure 5b). The diversity of an individual's relationships increased with group size up to 25, before decreasing steeply with group size beyond this. The significant polynomial relationship between individual-level diversity and group size remained after the removal of the PAB group demonstrating that this relationship was not driven by the unusually high group size values of PAB alone (although it peaked at a lower group size) (table 3).

Figure 5.

Social complexity (diversity of relationships) at an individual-level plotted against (a) the group-level measure of diversity of social relationships and (b) group size. Group means for a given year are represented by filled points, individual values represented by unfilled points. Group membership indicated by colour. The shapes of significant relationships are indicated by solid lines. Shaded area indicates standard error bounds. (Online version in colour.)

Table 3.

GAMMs to examine the association between an individual's diversity of social relationships and group size demonstrate a significant negative linear relationship and a polynomial relationship. Only the polynomial relationship holds when excluding the unusually large PAB group. Italics indicate significance at p < 0.05.

model	variable	all groups		without PAB
		t-value	p	t-value	p
linear	group size	−2.315	0.021	1.875	0.0612
R2 . (adj) = 0.094 (all groups) and −0.033 (without PAB)
polynomial	group size	−2.137	0.033	−0.338	0.736
R2 . (adj) = 0.168 (all groups) and 0.117 (without PAB)	group size2	−5.087	<0.001	−3.665	<0.001

Despite the overall relationships between group-level and individual-level measures, there was nonetheless notable variation in the diversity of social relationships for individuals from the same group (figure 5). The mean variance of relationship diversity for the same individual over multiple years was 0.049 (min = 0, max = 0.360), while the mean variance between individuals within a group in a given year was 0.065 (min = 0, max = 0.285). This was only marginally less than the variance observed across the entire sample (total variance = 0.082). This suggests that while group-level relationship diversity explains a significant amount of variance in individual-level diversity between groups, there is a large amount of unexplained variation in the relationship diversity of individuals within the same group. Between-individual variation was only slightly greater than within-individual variation, demonstrating that the social complexity an individual experiences can change considerably year to year.

(d). Age and sex predict individual-level social complexity

The diversity of relationships at an individual level was significantly predicted by sex and age, and changed differently between the sexes as gorillas aged (figure 6; electronic supplementary material, table S4). Overall, individual-level social complexity declined with age and was lower in males. For males, relationship diversity declined until roughly 14 years of age, when it began to increase again. In females it declined more gradually with age before plateauing during the age range of roughly 12–25, before a slight decline after the age of 25.

Figure 6.

Individual-level social complexity (diversity of relationships) changes differently with age in male and female gorillas. Significant polynomial relationship indicated by solid curves (y = poly(x, 5)). Shaded area indicates standard error bounds. (Online version in colour.)

4. Discussion

We found that group size was not a straightforward proxy for metrics of social complexity based on the diversity of social relationships. Neither the diversity of relationships within a group nor an individual's relationship diversity followed a positive linear relationship with group size. This provides quantitative support for the hypothesis that group size and the diversity of social relationships represent fundamentally different elements of social complexity [10], bringing into question the use of any single metric as an estimate for social complexity. Both the diversity of social relationships within a group and individual relationship diversity followed an n-shaped polynomial relationship with group size. Such a pattern may be expected where the number of potential relationship types increases with group size in smaller groups, but no longer influences the diversity of social relationships once a group includes most, or all, of the potential relationship types. However, the decrease in the diversity of social relationships in larger groups was unexpected and may reflect strategies to reduce the cognitive demands of larger than average group sizes.

Yellow-bellied marmots establish fewer social connections than are possible in larger groups, with closeness and betweenness centrality decreasing with group size [44]. If this pattern occurs in mountain gorillas, it could result in a less even distribution of relationships across relationship types, with the majority falling into the weakest category when groups are particularly large, reducing the overall diversity (electronic supplementary material, figure S1). This also fits with research on human and other hierarchical mammalian societies [45,46], including gorillas [38], where the number of relationships of a given type increases exponentially from the strongest to weakest relationship categories. This scaling pattern, with larger numbers of progressively weaker relationships, is hypothesized to be due to cognitive or time constraints on the number of relationships that can be maintained at a given strength [45]. Small groups could therefore have low relationship diversity when not all types of relationship are present. Diversity could then peak in mid-sized groups where all types are present with a fairly even distribution across categories. In the largest groups, this diversity could then decline again as cognitive or temporal demands prevent the addition of further relationships to the strongest categories, and the distribution of relationships across the categories becomes less and less even.

Adult sex ratio predicted the diversity of social relationships present in a gorilla group following an n-shaped curve, peaking when roughly 40% of adults were male. However, this relationship was not observed when investigating only adults, suggesting that it is not driven by reproductive competition. Instead, it appears to be primarily driven by relationships involving immature individuals. Since the types of relationships gorillas form were influenced by their age and sex, it's likely that the presence or absence of individuals at certain ages could influence group-level relationship diversity (electronic supplementary material, figure S4). Groups with low adult sex ratio could have formed more recently, and include a single dominant male and multiple females but no adult and few immature offspring, reducing the total diversity of relationships. Diversity may peak when a dominant male is midway through their tenure and groups contain offspring at a wide variety of different ages, including males greater than 8 years old, increasing the adult sex ratio. As dominant males reach the end of their tenure, females may begin to leave the group if there is no clear successor [47], increasing the adult sex ratio further and leading to groups with fewer females and fewer young offspring, again reducing the diversity of relationships [48]. However, further research is required to investigate sex ratio changes across dominant male tenures and how this may differ between one-male and multi-male groups. It is also clear that the composition of groups is not the only factor influencing the diversity of relationships within them as there is considerable variation in the strength of association and type of relationship within dyadic age–sex classes (electronic supplementary material, figure S4).

Mating strategy did not affect the diversity of social relationships present in a group. This suggests that mating system transitions between polygynandry and polygyny may not inherently lead to changes in social complexity. However, in mountain gorilla groups with multiple sexually mature males, mating remains biased towards the dominant male, siring 47–85% of offspring [33,49]. This is a greater proportion than has been observed for the highest-ranking males in many promiscuous mating systems, such as the 30.3% observed in chimpanzees [50]. While mating strategy varies considerably within mountain gorillas it still may not cover the complete variation present in a species transitioning from polygynandry or promiscuity to polygyny. We therefore cannot rule out that more extreme changes in mating system could influence social complexity.

Group-level and individual-level metrics of social diversity were positively correlated. This suggests that within mountain gorillas, relationship diversity at the group level may be a valid proxy for relationship diversity at the individual level. However, our results show mountain gorilla relationships were strongly predicted by the age and sex of the individuals involved, influencing how different types of relationship are distributed within groups. These social rules are likely to apply consistently within this species but unlikely to apply consistently across many different species. When the rules that shape the distribution of relationship types between individuals change, this is likely to break the correlation between group-level and individual-level social complexity. This will cause difficulties in cross-species comparisons, where group-level and individual-level approaches may lead to conflicting conclusions [18]. While group-level relationship diversity was a valid estimate for the average experience of gorillas within each group, there was extremely high variance around this mean, such that the social environments individuals were experiencing and the potential cognitive demands of those social environments could vary greatly. A far greater depth of information is therefore available for investigating the differing demands of group living (e.g. as individuals age) through this individual-level approach. This approach would also enable consistent cross-species comparisons of social complexity and its associated cognitive demands faced by individuals.

The diversity of social relationships experienced by individual gorillas was high for both males and females as infants. This declined rapidly in males, reaching the lowest levels at around 14, when males show many characteristics of sexual maturity but are 1–2 years away from full sexual maturity. This is also the period when males are most likely to disperse from their natal group [28]. Males may therefore be socially distancing themselves in the lead-up to their dispersal. Relationship diversity then rapidly increased for young males that remained with the group, when many gain in dominance status [28,51]. By contrast, females' relationship diversity decreased more gradually, plateauing around age 10, when they are likely to first give birth [52]. It then declined again gradually from around 25 to 35, when female fertility is thought to decline [52]. Both sexes showed a slight increase in relationship diversity at their oldest ages. However, estimation at this end of the age range is limited by lower numbers of surviving individuals and may also be biased by differences in those that survive (and remain with the group) to this late age.

While this study investigates social complexity from a variety of perspectives, quantifying and comparing all elements of social complexity within the mountain gorilla social system is beyond the scope of a single study. One important component we have not investigated is relationship stability and how changes in social relationships over time may contribute to their diversity [53]. In gorillas, with long-term stable groups, this is likely to be low in comparison with species that exhibit fission–fusion dynamics. However, our analyses have largely removed this element by excluding unstable groups, as well as individuals that died or changed group in a given year. Another element of complexity not addressed is social relationships between neighbouring groups [38,54]. While these represent an important part of gorilla social structure, they make up a small proportion of gorilla social interactions. We detected five types of social relationship within gorilla groups. Given that inter-group relationships have been shown to be influenced by kinship, group familiarity and threat level [54], it is likely there are also multiple types of inter-group relationship in the gorilla social system. While excluding these elements of gorilla social complexity and relying solely on proximity as an estimate of social relationships have enabled clearer comparison of group-level social complexity, we must acknowledge that we are not quantifying the full extent of social complexity in mountain gorillas.

5. Conclusion

Our findings demonstrate considerable variation in estimates of social complexity at both the group level and the individual level in mountain gorillas, and that these estimates of social complexity are not good linear proxies of each other. While group size contains information on the number of individuals group members may regularly encounter, it is just one component of social complexity. Studies relying solely on group size as a measure of social complexity may therefore be limited, especially when it comes to understanding the cognitive demands experienced by individuals. Conversely, this also implies that the diversity of social relationships alone may not fully describe social complexity. Maintaining five types of social relationship with five partners may not be equivalent to maintaining five types of relationship with 50 partners. Both the abundance and diversity of social relationships may need to be taken into account.

While the development of a single metric for measuring social complexity would aid cross-species comparisons, the creation of a metric that was valid across species would be extremely difficult. Rather than attempting to quantify social complexity as a single metric, it may be more beneficial to view it as consisting of multiple components including the number, diversity and stability of relationships, all of which contribute to the demands of social life within a social system. The increasing availability of fine-scale social data across a broad range of taxa, combined with recently developed metrics of relationship (or association) diversity, may provide an important opportunity to revisit many fundamental hypotheses on the evolution of social behaviour. Taking into account multiple components of social complexity and tailoring, the metrics used (whether at group level or individual level) to the specific hypothesis being tested will be vital to improving our understanding of social evolution and the innovations driven by the demands of social life.

Ethics

All applicable international, national and institutional guidelines for the care and use of animals were followed. All data collection (observational monitoring of mountain gorillas) was approved by the Rwandan Development Board.

Data accessibility

This article has no additional data.

Authors' contributions

R.E.M. conceived the project with advice and feedback from T.S.S., W.E. and L.J.N.B. Data collection and cleaning was overseen by W.E. Data analysis was carried out by R.E.M. with advice from T.S.S., W.E. and L.J.N.B. R.E.M. wrote the manuscript with feedback, advice and final approval from all authors.

Competing interests

We declare we have no competing interests.

Funding

We received no funding for this study.