Although the gathered data focuses only on farmers of the same produce in the same part of Indonesia, we find a large variation in the way agricultural information exchange networks are structured in the studied 30 villages, ranging from communities with widely distributed numbers of information-sharing links among their members and no single centre (Fig. 1, left) to an extreme case of a community in which everyone is connected to the most influential individual and no one else (Fig. 1, right). These differences in network structures can be quantified with the Freeman degree centralization metric [42]. The metric is based on the difference in the number of links of the node with most links in a network and the number of links of every other node, and varies from 0 to 1 (0-100% centralization). While the number of reported information links by a respondent varied between 1–4 (all respondents were prompted to provide at least one tie), the number of nominations an individual received by others as their agricultural information source goes up to 76. Such highly sought peers were present only highly centralized communities where the number of links to the vast majority of other community members was significantly lower (Fig. 1 for illustration, see Supplementary Information for descriptive statistics of all networks). Similarly to centralization, the prevalence of fertilizer use in the villages varies highly (between 0–78% of the village members were using fertilizers).
Ordinary least square regression results show that the prevalence of fertilizer use in a village is strongly associated with the structure of village-based social networks (The Pearson’s correlation between log(centralization) and fertilizer adoption ratio is -0.54 (p = 0.002). In highly centralized communities, where one farmer holds a very prominent position in the information-sharing network of the village, the community as a whole to grow their produce with almost no fertilizer (Fig. 2). Specifically, very few people adopt fertilizers in such communities. Further, as a general trend the predominant community practice correlates with the practice of the most influential individual (the Pearson’s correlation between a dummy variable indicating the most influential individuals’ fertilizer adoption choice in each village, counted as 0.5 for villages with two most influential individuals with opposite practices, and the fertilizer adoption rate in the village is 0.69, p < 0.001).
This pattern is contrasted in less centralized networks where fertilizer adoption rates are more dispersed (there is a threshold at around 40% centralization as shown in Fig. 2). The difference between means of village-level fertilizer use rates below and above 40% centralization threshold (24% versus 4%, Fig. 3) is highly statistically significant (unpaired two-samples Wilcoxon test gave p < 0.015).
To control for other important network characteristics size, density, and clustering (measured as number of farmers, average number of ties per farmer, and the global clustering coefficient [43], we include these variables in a multivariate regression model. The number of farmers in a network and the average number of ties per farmer are uncorrelated with each other and the village-level centralization (Pearson correlation coefficients are < 0.37), but not the clustering coefficient and centralization (Pearson correlation coefficient is -0.85). Hence, to avoid multicollinearity, we did not include the clustering coefficient in the regression model (a different model where both centralization and the clustering coefficient were included is presented in the Supplementary Material, however the results from that model showed the clustering coefficient not to be significant while centralization remained significant).
Table 1
The relation between network structure and fertilizer adoption at the village level
Network structure
|
Coefficients
(SE in parenthesis)
|
Centralization (Freeman degree, log)
|
-0.1800
(0.0507)**
|
Network size (number of nodes)
|
0.8300*10− 4
(3.160*10− 4)
|
Network density (mean degree)
|
0.0199
(0.0778)
|
Multivariate linear regression with the dependent variable indicating village-level fertilizer adoption rates (0–1). N = 30. **Significance at p < 0.01. To account for heteroscedasticity, the reported standard errors are based on the White-Huber sandwich estimator of variance (i.e. ‘robust’ standard error). Adjusted R-squared is 0.218.
In summary, all our findings are consistent with an asymmetric effect of network centralization on fertilizer adoption. Until a certain threshold (around 40% of maximum possible Freeman degree centralization), the effect of village network centralization on fertilizer usage is either weakly negative or on par with multifinality. Centralization levels above this threshold are unanimously associated with low fertilizer adoption.
Mechanisms other than influence exerted by opinion leaders that could potentially cause the observed results also need to be considered. In network terms, if influence coming through a relationship is dependent on other peers, it may be referred to as “complex contagion” (e.g., an individual may be influenced by its peers only if a certain proportion of its peers are in agreement)[44]. Complex social contagion is different from “simple contagion”, such as a viral spread (whether a virus transmission from one individual to another during close physical contact does not depend on other links these individuals may have to others) [45]. The differentiated influence that we elaborate here represent complex contagion, albeit from the sender’s point of view and not from the receiver’s point of view (an individual is only being influenced by a certain other if that other is much more socially connected than other individuals in the network).
To test alternatives to our social influence through opinion leader hypothesis mimicking a process of complex contagion, we first examine whether the observed patterns of fertilizer adoption across communities could be explained by a model of simple social contagion. If simple contagion was present, we would expect a relatively higher-probability of similar practice among any interconnected pair of farmers, possibly resulting in clusters (subgroups) of similar practices. We applied Autologistic Actor-Attribute models (ALAAM) to all villages with heterogeneous fertilizer use, but found no evidence of simple contagion in any of them (ALAAM cannot be applied in cases where fertilizer use is homogenous due to lack of variability, see Supplementary Materials).
Next, we tested a set of complex contagion mechanisms using agent-based simulation models (ABM; Supplementary Material). In addition to the status-based influence mechanism being at focus (influence is conditional on peers’ degree centrality, which is indeed an example of complex contagion), we test cognitive dissonance mechanism (the probability of being influenced is proportional to the number of peer adopters), threshold mechanism (following the practice of the majority of peers), echo-chamber mechanism (influence is much stronger if all peers use the same practice), and random peer influence mechanism (influence is exercised only by one randomly selected peer at any given time). The only mechanism that qualitatively reproduced the empirically observed patterns was the high-status model of opinion leaders. Specifically, the sudden homogenization of practice for networks above a critical level of centralization could be replicated only in ABMs in which the actors were influenced only by exceptionally highly central peers (2–4 standard deviations above the mean degree of the village). Even though we were experimenting with sliding parameters in all simulation models, the other tested mechanisms for complex social contagion did not consistently reproduce the situation of homogenous adoption outcomes in centralized networks and heterogeneous outcomes in decentralized networks.
The combination of the analytical results and the simulation results thus demonstrate that peer-to-peer social influence may be exerted only by exceptionally connected actors (who are present only in centralized communities). Thus, those who exert influence through their relationships are also those who have influence over many others, which leads to community-wide homogenous fertilize usage in those networks were such individuals are present.
Two remaining and interrelated questions are how the high-status opinion leaders emerged, and why some village networks become so different from others? While we cannot use our dataset to answer such questions, we can draw some insights from qualitative interviews with research field assistants of the local partner organizations who have substantial experience of working across various Indonesian farming villages. The field assistants consider the existence of the exceptionally connected actors to be a legacy of previous external agricultural interventions that were delivered via a small number of selected local farmers (often being the leaders, or becoming the leaders, of externally-required local farmer groups for channelling interventions and subsidies), which as a side effect increased their prominence within their communities. Even though significant time has passed since then, the observed highly centralized networks (and their subsequent effects on fertilizer use) appear as imprinted into the social structures of these villages. This interpretation raises concerns regarding unintended long-term side effects of agricultural and environmental interventions and call for considerable caution before implementing any major programs that may alter social structures and processes in villages like the ones we studied here.