The evolution of social ties is crucial to understanding sociality. Alexander (1974) highlighted the rarity of social animals due to the lack of automatic benefits and the prevalence of drawbacks like conflict and disease. Sociality evolves when ecological conditions provide significant fitness benefits outweighing these costs; resource access and defense being a primary driver (Shen et al., 2017). Early human history involved global expansion (Boyd et al., 2011), necessitating new skills for survival (Boyd et al., 2011). Mastering all necessary skills is costly (Kaplan et al., 2009; Dyble et al., 2016), leading to social dependence on others with complementary skills (Kaplan et al., 2009; Dyble et al., 2016). Humans, as a highly cultural species, demonstrate social dependence driven by skill and knowledge diversification (Boyd et al., 2011; Hill et al., 2011). Skills can be interconnected; for example, "fishing" and "sailing" or "mathematics" and "computer programming". This suggests a network structure of skills and knowledge (Arthur, 2009; Yeh et al., 2019; Phoa et al., 2020), where diversification changes the network structure. The study explores how this diversification influences social dependence.

Extensive theoretical work in behavioral ecology, particularly social foraging theory (Giraldeau and Caraco, 2000), uses evolutionary game theory to analyze sociality emergence during resource competition. This includes research on group foraging (Clark and Mangel, 1986), producer-scrounger games (Vickery et al., 1991; Ohtsuka and Toquenaga, 2009; Afshar and Giraldeau, 2014), resource-patch exploitation (Pyke, 1984), and social learning (Rendell et al., 2011; Nakahashi et al., 2012; Hoppitt and Laland, 2013). These models focus on resource sharing, distribution, accessibility, and exploitation, but rarely consider the relationships between resource patches. This study models resource patches as a network to investigate how network structure impacts competing strategies, simulating solitary and social learning processes to determine which is favored under different skill diversification levels.

The simulation model includes M patches (each with Q resources) and N actors. A square matrix X (M x M) represents the patch network, where x_ij = 1 if patches i and j are connected. A square matrix Y (N x N) represents the actors' social network, with y_ij = 1 if actors i and j are connected. Two actor types exist: solitary actors (move between patches, acquire resources randomly) and social actors (behave like solitary actors, but with probability p, utilize social ties to acquire resources from friends' neighboring patches). A simulation experiment involves several generations (T time steps each), ending when the population consists of a single actor type. Initially, 10% of actors are social. Each generation involves: (1) constructing the patch network with link density D, (2) constructing an empty actors' social network, (3) iterating through time steps, randomly selecting an actor, and executing procedures for solitary or social actors, (4) at the end of each generation, calculating resource accumulation for each type, determining the proportion q of social actors for the next generation (based on resource accumulation), and removing actors to create a new generation. The model explores how parameters p (probability of using social ties), T (generation time), and D (link density of the patch network) affect the outcome. A null model (p=0) tests the significance of social strategy's success using p-values (cutoff at 0.05).

The study investigated model behavior in the T-p parameter space for various D values. Figures 4 and 5 show that as D increases (network shifts from localized to complete graph), social strategies are less likely to outcompete solitary strategies. In densely connected networks, solitary strategies are advantageous as actors quickly access unvisited patches. Social strategies waste time establishing connections. Figures 4 and 5 demonstrate that social strategies, especially those heavily reliant on social ties (high p), are detrimental when the patch network is densely connected. Social strategies are only successful when T (generation time) is long (Figure 4). Short generation times favor solitary strategies (Figure 5). Increasing the number of patches (M) favors social behavior (Figures 6 and 7), while increasing the number of actors (N) favors solitary behavior (Figures 8 and 9). Solitary behavior is favored when resource abundance (Q) increases (Figures 10 and 11). Social behavior is less advantageous when the proportion of shared resources (S) going to the actor using social ties decreases (Figures 12 and 13). The model is robust to different initial conditions (Figures 14 and 15). Figure 16 shows that as the patch network becomes more localized (D decreases), the average number of social ties increases, the number of social groups decreases, and the size of the largest social group increases.

The findings suggest social ties are advantageous when resources are distributed in a highly localized patch network (highly diversified skills and knowledge). The model shares similarities with producer-scrounger models (Afshar and Giraldeau, 2014; Vickery et al., 1991; Ohtsuka and Toquenaga, 2009) and social learning models (Boyd and Richerson, 1985; Laland et al., 1993; Henrich, 2016; Feldman et al., 1996; Wakano and Aoki, 2006; Smolla et al., 2015; Lee et al., 2016). Long generation times (low turnover rates) and weak competition favor social actors. The results relate to the social brain hypothesis (Brothers, 1990; Dunbar, 1998; Dunbar, 2011), suggesting skill diversification could be an ecological condition for complex social behavior. The model also aligns with social exchange theory (Homans, 1958; Emerson, 1976) and social resource theory (Lin, 2001) and weak tie hypothesis (Granovetter, 1973). The model has potential applications in industrial sectors and business competition.

The study demonstrates that resource diversification favors social ties, but only when resources are scarce and generation times are long. Purely social strategies are outcompeted by solitary strategies. Future research could improve the model by allowing multiple resources per patch, incorporating realistic social network structures, and incorporating dynamic skill and knowledge networks. Adding behavioral mutation would enhance model realism.

The model simplifies several aspects of human social interaction. The assumption of a fixed actor type throughout their lifetime is unrealistic. The social network generation mechanism is simplistic. The model's parameters may not fully capture the complexities of real-world resource distribution and social dynamics.