Dynamics of cooperative networks associated with gender among South Indian Tamils

Abstract

Helping behaviour is thought to play a major role in the evolution of group-living animals. Yet, it is unclear to what extent human males and human females use the same strategies to secure support. Accordingly, we investigate help-seeking over a 5-year period in relation to gender using data from virtually all adults in two Tamil villages (N = 782). Simulations of network dynamics (i.e. stochastic actor-oriented models) calibrated to these data broadly indicate that women are more inclined than men to create and maintain supportive bonds via multiple mechanisms of cooperation (e.g. reciprocity, kin bias, friend bias, generalized exchange). However, gender-related differences in the simulated dynamics of help-seeking are modest, vary based on structural position (e.g. out-degree), and do not appear to translate to divergence in the observed structure of respondents' egocentric networks. Findings ultimately suggest that men and women in the two villages are similarly social but channel their sociality differently. This article is part of the theme issue 'Cooperation among women: evolutionary and cross-cultural perspectives'.

Keywords: India; complex systems; cooperation; social networks; social support; stochastic actor-oriented models.

Figure 1.

Stylization of sex-homogeneous one-degree (i.e. one-step) egocentric networks. Stylization is based on evolutionary theorizing of male and female sociality as, respectively, ‘dyadic’ and ‘group-based’ [17,18,23]. Arcs (i.e. directed connections) indicate hypothetical aid relationships—i.e. to whom does one turn for help?—and are coloured based on relationship type. Dark-blue arcs emanate from kin, light-blue arcs emanate from friends, and yellow arcs emanate from in-group 'strangers' (i.e. associates who are neither kin nor friend). Red vertices (i.e. nodes) indicate ego. Vertices for ego's alters are coloured to reflect social status relative to ego—where darker-coloured vertices are more high-status than ego (i.e. the focal actor), white vertices are more low-status, and grey vertices are of a similar status. (a) Theorized female egocentric network characterized by low absolute size, low interconnectivity, a large degree of status homogeneity and no supportive bonds with non-kin and non-friends. (b) Theorized male egocentric network characterized by large absolute size, high interconnectivity, a large degree of status heterogeneity and multiple supportive bonds between kin, friends, non-kin and non-friends. Lengths of arcs, placement of vertices and spacing between arcs and vertices are purely aesthetic.

Figure 2.

Stylization of ‘change’ in a stochastic actor-oriented model (SAOM) vis-à-vis network-formation mechanisms. Note the two outgoing ties in a transitive triad—both of which are under the control of the focal actor i (ego) and only one of which is eligible to be changed at a time. Also, note that mechanisms are not always mutually exclusive. For example, transitive closure is related to popularity bias (n.b., the incoming ties of the actors with whom i can connect). We are grateful to anonymous reviewer 2 for proposing this schematic.

Figure 3.

Network dynamics investigated with stochastic actor-oriented models (SAOMs) vis-à-vis hypotheses alongside key network-structure-related controls. Formulae are used to calculate the network statistics s_k,i(x)—i.e. the covariates in our SAOMs (see also electronic supplementary material, table S6). Network statistics generally take the form of actor-specific counts over all network members j to which some focal actor i is tied. Note the two outgoing ties in a transitive triad—both of which are under the control of i and only one of which is eligible to be changed at a time. We are grateful to anonymous reviewer 2 for proposing this schematic.

Figure 4.

Parameter estimates $\hat{\beta }$ from the three stochastic actor-oriented models (SAOMs) of social support within and across Tenpaṭṭi and Alakāpuram. SAOMs fit using standardized scores (i.e. Z-scores) of age (mean = 44.01; s.d. = 14.70), household wealth (i.e. Log_e INR; mean = 12.62; s.d. = 0.94), social standing (i.e. $\sqrt{\mathrm{General}\hspace{0.17em}\mathrm{Reputation}}$; mean = 2.28; s.d. = 1.97), and pairwise geographic distance (i.e. Log_e metres + 1; mean = 5.69; s.d. = 1.36). Log- and square-root transformations taken prior to standardization. s.d. = standard deviation.

Figure 5.

Gender-based differences in the simulated micro-level dynamics of help seeking. Each hypothesis-specific linear combination ${\hat{\beta }}_{\mathrm{Linear}\hspace{0.17em}\mathrm{Combination}}$ denotes the total contribution to the evaluation function—i.e. the overall ‘attractiveness’ [70] of creating and maintaining a single outgoing tie x_ij—for a focal actor i (ego) who is either a woman (blue bullets) or man (orange bullets) with identical characteristics (e.g. average age and average wealth) and identical structural positions. Each bullet is a linear combination. The linear combinations themselves are sums of key parameter estimates ${\hat{\beta }}_k$ from Model 3 (Social Constraints) and artificial change statistics Δ_k,ij(x, x^±ij) (see electronic supplementary material, table S8). The change statistics indicate the difference in network statistics s_k,i (electronic supplementary material, table S6) representative of some status-quo network state x and some new network state x^±ij induced by i's addition/subtraction of a single tie x_ij to/from x. Linear combinations represent artificial status quo networks x wherein i's out-degree varies from zero to 32, i's in-degree is fixed at six, the in-degree of those to whom i is tied is fixed at six, j's in-degree varies from zero to 64, and j's out-degree is ignored. There are 2145 (33 × 65) linear combinations for the average man and the average woman for each cooperative mechanism (H1–H7) or 4290 per sub-plot. Tiny bullets (e.g. H1, top-left) are for linear combinations that have a p-value ≥ 0.001—where each p-value (two-tailed) is associated with the test statistic $z_{{\hat{\beta }}_{\mathrm{Linear}\hspace{0.17em}\mathrm{Combination}}}={\hat{\beta }}_{\mathrm{Linear}\hspace{0.17em}\mathrm{Combination}}÷s.e{.}_{{\hat{\beta }}_{\mathrm{Linear}\hspace{0.17em}\mathrm{Combination}}}$. The standard error (s.e.) for each linear combination was obtained with the procedure of Ripley et al. [, pp. 95–97]. Using Reciprocity as an example, linear combinations generally take the form: ${\hat{\beta }}_{\mathrm{Out}-\mathrm{degree}}\left({\mathrm{\Delta }}_{\mathrm{Out}-\mathrm{degree},\hspace{0.17em}ij}\right)+{\hat{\beta }}_{\mathrm{Woman}}\left({\mathrm{\Delta }}_{\mathrm{Ego}-\mathrm{Activity}:\hspace{0.17em}\mathrm{Gender},\hspace{0.17em}ij}\right)+{\hat{\beta }}_{\mathrm{Reciprocity}}\left({\mathrm{\Delta }}_{\mathrm{Reciprocity},\hspace{0.17em}ij}\right)+{\hat{\beta }}_{\mathrm{Woman}\hspace{0.17em}\times \hspace{0.17em}\mathrm{Reciprocity}}({\mathrm{\Delta }}_{\mathrm{Ego}-\mathrm{Activity}:\hspace{0.17em}\mathrm{Gender},\hspace{0.17em}ij}\times$ ${\mathrm{\Delta }}_{\mathrm{Reciprocity},\hspace{0.17em}ij})+{\hat{\beta }}_{\mathrm{Out}-\mathrm{degree}\hspace{0.17em}\mathrm{Activity}}\left({\mathrm{\Delta }}_{\mathrm{Out}-\mathrm{degree}\hspace{0.17em}\mathrm{Activity},\hspace{0.17em}ij}\right)+{\hat{\beta }}_{\mathrm{In}-\mathrm{degree}\hspace{0.17em}\mathrm{Activity}}\left({\mathrm{\Delta }}_{\mathrm{In}-\mathrm{degree}\hspace{0.17em}\mathrm{Activity},\hspace{0.17em}ij}\right)+{\hat{\beta }}_{\mathrm{In}-\mathrm{degree}\hspace{0.17em}\mathrm{Popularity}}\left({\mathrm{\Delta }}_{\mathrm{In}-\mathrm{degree}\hspace{0.17em}\mathrm{Popularity},\hspace{0.17em}ij}\right)+{\hat{\beta }}_{\mathrm{Woman}\hspace{0.17em}\times \hspace{0.17em}\mathrm{Out}-\mathrm{degree}\hspace{0.17em}\mathrm{Activity}}$ $({\mathrm{\Delta }}_{\mathrm{Ego}-\mathrm{Activity}:\hspace{0.17em}\mathrm{Gender},\hspace{0.17em}ij}\times {\mathrm{\Delta }}_{\mathrm{Out}-\mathrm{degree}\hspace{0.17em}\mathrm{Activity},\hspace{0.17em}ij})+{\hat{\beta }}_{\mathrm{Woman}\hspace{0.17em}\times \hspace{0.17em}\mathrm{In}-\mathrm{degree}\hspace{0.17em}\mathrm{Activity}}({\mathrm{\Delta }}_{\mathrm{Ego}-\mathrm{Activity}:\hspace{0.17em}\mathrm{Gender},\hspace{0.17em}ij}\times {\mathrm{\Delta }}_{\mathrm{In}-\mathrm{degree}\hspace{0.17em}\mathrm{Activity},\hspace{0.17em}ij})+{\hat{\beta }}_{\mathrm{Woman}\hspace{0.17em}\times \hspace{0.17em}\mathrm{In}-\mathrm{degree}\hspace{0.17em}\mathrm{Popularity}}({\mathrm{\Delta }}_{\mathrm{Ego}-\mathrm{Activity}:\hspace{0.17em}\mathrm{Gender},\hspace{0.17em}ij}\times$ ${\mathrm{\Delta }}_{\mathrm{In}-\mathrm{degree}\hspace{0.17em}\mathrm{Popularity},\hspace{0.17em}ij})$, where ${\hat{\beta }}_k({\mathrm{\Delta }}_{\mathrm{Reciprocity},ij})={\hat{\beta }}_{\mathrm{Reciprocity}}$ $(s_{\mathrm{Reciprocity},i}(x^{\pm \hspace{0.17em}ij})-s_{\mathrm{Reciprocity},i}(x))$. Note, H6 concerns a one unit increase in the absolute difference between the Z-score of ${\sqrt{\mathrm{General}\hspace{0.17em}\mathrm{Reputation}}}_i$ and ${\sqrt{\mathrm{General}\hspace{0.17em}\mathrm{Reputation}}}_j$ (i.e. Δ_{Abs. Diff.: General Rep.,ij}(x, x^±ij) = 1 − 0). Thus, the linear combinations for H6 summarize the attractiveness of x_ij for two actors with a one-standard-deviation difference in $\sqrt{\mathrm{General}\hspace{0.17em}\mathrm{Reputation}}$, where H6 implies higher levels of attractiveness for men in relation to this difference.

Figure 6.

No substantial differences in the structure of men's and women's egocentric networks. Each bullet point (i.e. the middle of each Edward-Tufte-style box plot) indicates the median difference in the gender-specific averages of an ego-net statistic across networks simulated at the end of the observation period (2017). The mean of an ego-net statistic for men is subtracted from the mean of that statistic for women. Positive values indicate that the ego-nets of women have, on average, more of a statistic relative to the ego-nets of men. For example, Out-degree indicates that, in 2017, the observed difference (dashed horizontal line) between the average size of men's out-ego-nets and women's out-ego-nets is roughly zero. However, the median difference in the average across the 10 000 networks simulated under the Baseline model is roughly 0.6. The gaps immediately above and below the bullet points indicate the interquartile range (i.e. the values between the 75th and the 25th percentile). And the lines denote the whiskers—where the terminus of each whisker indicates the maximum/minimum of the distribution of values. Statistics capture ego's number of supportive alters that: (i) do not rely on ego (Out-degree); (ii) also rely on ego (Reciprocal Out-degree); (iii) are considered a friend by ego (Supportive Friends); (iv) are kin (Supportive Kin); and (v) are the same gender as ego (Same Gender Patrons). Transitive Triads and Three Cycles are, respectively, counts of the number of out-bound two-paths [i → h → j] and the number of in-bound two-paths [i ← h ← j] closed by ego's outgoing ties. General Reputation is the sum of the absolute value of the differences between the Z-score of the square root of the generation-reputation nominations of ego and each of their alters. That is, General Reputation is given by $\sum _j{x}_{ij}\left|{\sqrt{\mathrm{General}\hspace{0.17em}\mathrm{Reputation}}}_i-{\sqrt{\mathrm{General}\hspace{0.17em}\mathrm{Reputation}}}_j\right|$, where x_ij = 1 if i seeks help from j. This sum is averaged across all men and all women and then compared. We are grateful to anonymous reviewer 1 for proposing this comparison of ego-net statistics.