Hub-and-spoke social networks among Indonesian cocoa farmers homogenize farming practices

Smallholder farms support the livelihoods of 2.5 billion people and their decisions on fertilizers use have profound sustainability implications. We investigated if and how social inuence exerted through peer-to-peer information exchange affect the use of fertilizer among 2734 Indonesian cocoa farmers across 30 different villages. Results show that the structures of these village-based social networks strongly relate to farmers’ use of fertilizer. In villages with highly centralized networks (i.e. where one or very few farmers holds disproportionately central position in the village network), a large majority of farmers report the same fertilizer use. By contrast, in less centralized networks, fertilizer use varies widely. The observed community-level distributions of fertilizer use are consistent with complex contagion mechanisms in which social inuence is only exerted by opinion leaders that are much more socially connected than others. Our ndings suggest signicant policy implications for development programs targeting smallholder farming communities.


Opinion Leadership And Social Networks
Existing research suggests that much of what we do is in uenced by our peers in social networks [14,17].
However, in uence within social networks is typically unevenly distributed and not all network relationships are consequential for our behaviour [18,19]. One of the factors differentiating social in uence is social status [20]. Peers of a higher status are more in uential than others [21]. Peer status and in uence can be de ned as two sides of the same coin, i.e. being in uential means that you have high status and vice versa [22]. Furthermore, the phenomenon where high status individuals have large and very disproportionate effects on decisions of others is at the core of studies of "opinion leadership" [23]. This phenomenon is routinely leveraged in the design of social interventions, education, training, marketing, as well as development programs that build on peer-to-peer information sharing and in uence [24]. High status individuals are here targeted to promote innovation and entice others towards adopting desirable practices and behaviours who, in turn, are expected to in uence their peers in their networks [25]. A caveat that needs to be considered is, however, that although high-status opinion leaders can in uence crucial decisions of many others, this does not mean that they are the most informed individuals in their networks or engaged in the particular issues of interest to intervention organizers, nor that their advice and opinions are bene cial or relevant for everyone else [26][27][28].
Social status can be both a consequence and a driver of social network structure. Firstly, social status can be re ected and derived from prominent (i.e. central) positions in social networks [29,30]. Secondly, social status can be self-reinforcing --actors in visibly central positions are typically perceived as having higher status, competence, and desired social capital and therefore are more attractive network partners [31]. This is called the "Mathew effect" or "preferential attachment" [32,33]. These feedback mechanisms imply that opinion leadership is not only a phenomenon that can be isolated to the whereabouts of some speci c individuals, rather opinion leadership shapes the ways all peers in the network are communicating with each other. The presence of strong opinion leaders drives network centralization -which is a macro-level property of a network where some individuals are signi cantly more central than others [34].
Although opinion leaders uphold these prominent positions, they nonetheless tend to be aware of, and act in line with, norms and expectations that prevail in their communities (in other words, opinion leaders are in general not unconstrained in what they can promote and enforce) [35]. This implies there is a risk that centralized network structures, in which the sources of in uence are limited to a few prominent actors who in turn might tend to observe and follow the trends of the majority, could hamper members' abilities to freely deliberate and address complicated problems [36]. Studies from laboratory experiments, student and research teams, and Western corporate teams have accordingly suggested that a dominance of a small number of highly in uential individuals in a network sti es learning autonomy and decrease "the wisdom of crowds", knowledge exploration, creativity, and experimentation of their collectives [37][38][39].
Whether these ndings are valid outside the laboratories and online platforms, and in particular, in contexts such as smallholder farming in remote villages in low-and middle-income countries is, however, largely untested. Nonetheless, centralized in uence exerted by opinion leaders, potentially sti ing learning and change, could have far-reaching consequences especially in contexts where informal social networks are the most readily-available channel for accessing information about essential practices to sustain one's living [40].
To examine the mechanisms of network centralization, opinion leadership, and social in uence in agrarian communities, we analyse social networks and fertilizer use among smallholder cocoa farmers in 30 Indonesian villages by drawing on data originally collected by development organizations Koltiva/Swisscontact. We corroborate these analytical results with agent-based simulations replicating possible peer-to-peer social in uence processes to test the hypothesis that farmers in highly centralized (so called hub-and-spoke) social networks characterised by the presence of high-status opinion leaders are more likely to be locked in the same agricultural practices across the entire network. The hypothesis is based on available evidence that smallholders' decisions to use a fertilizer partially depend on fertilizing practices of other farmers in their village and the structure of networks through which information and preferences in uencing these choices are shared [11,41]. Consistently with literature from other contexts, we hypothesise that centralized network structures will be associated with lower levels of farmers' exploration of, exposure to, and experimentation with locally less-prevalent (and potentially more productive) practices than what most other farmers apply. Further, we hypothesize that the practice being preferred by the most in uential network member is also the most commonly applied practice.

Results And Discussion
Although the gathered data focuses only on farmers of the same produce in the same part of Indonesia, we nd 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 in uential individual and no one else ( Fig. 1, right). These differences in network structures can be quanti ed 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 signi cantly 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). Speci cally, very few people adopt fertilizers in such communities. Further, as a general trend the predominant community practice correlates with the practice of the most in uential individual (the Pearson's correlation between a dummy variable indicating the most in uential individuals' fertilizer adoption choice in each village, counted as 0.5 for villages with two most in uential 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 signi cant (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 coe cient [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 coe cients are < 0.37), but not the clustering coe cient and centralization (Pearson correlation coe cient is -0.85). Hence, to avoid multicollinearity, we did not include the clustering coe cient in the regression model (a different model where both centralization and the clustering coe cient were included is presented in the Supplementary Material, however the results from that model showed the clustering coe cient not to be signi cant while centralization remained signi cant). In summary, all our ndings 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 multi nality. Centralization levels above this threshold are unanimously associated with low fertilizer adoption.
Mechanisms other than in uence exerted by opinion leaders that could potentially cause the observed results also need to be considered. In network terms, if in uence coming through a relationship is dependent on other peers, it may be referred to as "complex contagion" (e.g., an individual may be in uenced 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 in uence 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 in uenced by a certain other if that other is much more socially connected than other individuals in the network).
To test alternatives to our social in uence through opinion leader hypothesis mimicking a process of complex contagion, we rst 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 in uence mechanism being at focus (in uence is conditional on peers' degree centrality, which is indeed an example of complex contagion), we test cognitive dissonance mechanism (the probability of being in uenced is proportional to the number of peer adopters), threshold mechanism (following the practice of the majority of peers), echo-chamber mechanism (in uence is much stronger if all peers use the same practice), and random peer in uence mechanism (in uence 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. Speci cally, the sudden homogenization of practice for networks above a critical level of centralization could be replicated only in ABMs in which the actors were in uenced 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 in uence may be exerted only by exceptionally connected actors (who are present only in centralized communities). Thus, those who exert in uence through their relationships are also those who have in uence 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 eld assistants of the local partner organizations who have substantial experience of working across various Indonesian farming villages. The eld 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 signi cant 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.

Conclusion
Smallholder farmers' choice of agricultural practices has consequences for livelihoods and food security of billions of people. Better understanding of the sources of in uence on their practices is thus a matter of life and death for many. This study attempted to shed light on how social in uence plays out in in this context, and we found that in highly centralized (or "hub-and-spoke") social networks, farmers not only tend to apply the same practice, but that practice is typically to avoid using fertilizers.
The analytical ndings combined with our simulations suggest that this is because farmers in centralized villages are disproportionately in uenced by a small number of high-status opinion leaders. Our results are consistent with a complex contagion model in which measurable in uence is exercised only through relationships to peers of degree centralities above certain thresholds.
However, the results are entirely different in villages with centralization levels below a certain threshold (around 40%). Fertilizer use varies widely across these decentralized villages, and neither the analyses nor the simulation models suggest any tendencies of peer-to-peer in uence in such context. Peer-to-peer social in uence thus appears to be exerted only by exceptionally connected high-status actors in centralized villages, which can explain why some villages appear as if collectively locked in sub-optimal practices, while villages without extremely highly connected high-status actors appear to be able to leverage the "wisdom of crowds" of diversity of opinions and transition away from the long-held status quo of not using fertilizers.
While a lot remains unanswered about the drivers of social in uence in the examined networks because of the inherent limitations of cross-sectional observational research (and the many di culties in gathering reliable data in these remote contexts), we can clearly state that we found no evidence of simple contagion. While models re ecting epidemiological processes have always been in uential in social science (and arguably our general awareness has become even more saturated with epidemiological metaphors and diffusion curves since the Covid19 pandemic), our research in this context is in line with studies from Western industrialized settings demonstrating that simple contagion processes might not adequately describe the contagion processes that steer if and how social in uence plays out across many different contexts. One practical policy implication arising from these ndings is the need for more caution when implementing intervention policies, and in particular exerting extreme caution when elevating a small number of key program participants above others in ways that stimulate social network centralization in the targeted communities.

Methods
The data was collected by a non-governmental development organization Swisscontact and their partner Koltiva. Funded mainly by international governments and food productions companies, the organizations have been surveying cocoa farmers in Sulawesi as a part of the support they channel to them through from their sponsors in effort to understand the barriers to adoption of productive and sustainable farming practices. The average cultivated land area was 0.9ha and cocoa yields of these farmers were under 500kg/ha, which are levels considered well below potential and have been linked in Sulawesi to fertilizer misinformation and mismanagement [46]. While serious environmental damage can be done by uninformed application of fertilizers [47], replenishing nutrients, whether by organic or inorganic fertilizers, is always necessary in agricultural soil [48]. Appropriate use of fertilizers has profound implications on yield, soil health, water pollution, and greenhouse gas emissions [49]. Further characteristics of the sample are discussed in more detail in Supplementary Information.
In 2018, the survey included the question "Please mention people outside of this household, where you get advice, you can learn from, or who can provide information and knowledge related to farming practices, especially about cocoa". The farmers have provided written consent that their data may be used for research. For the purpose of this study, the authors have obtained a completely anonymized subset of the secondary data with the approval of the human research ethics committee at the University of [anonymised]. The data required extensive cleaning, which is described in detail in the SI, and the implication of decisions made in the cleaning process did not substantially affect the main characteristics of the analysed subsample in relation to the acquired dataset. The cleaned data used in this paper include 30 villages varying in size between 31 and 365 farmers, with mean size 91 and median 75; 2353 respondents, who reported between 1 and 4 peers as their agricultural information sources, with mean 1.3 and median 1 (the total number of farmers in the village networks was 2774, meaning that some farmers in the networks were not interviewed, but still included in the networks since they were nominated by at least one respondent). Fertilizer adoption rates varied from 0-78% between villages. The number of connections farmers have (i.e. network degree) varies from 1 to 55 (only accounting for links to farmers in the same village), with mean 2.29.
We tested our hypothesis by OLS regression, with and without logarithmic transformation (logtransformation was used to create more evenly distributed numerical values of the Freeman degree centralization metric), with and without accounting for heteroscedascity using robust standard error estimations, without and without all combinations of the following controls: network size, mean degree of centrality, and level of modularity (i.e. clustering -measured by the global clustering coe cient). In all cases, the relationship between high homogeneity of fertilizer use and high centralization was statistically signi cant. The relationship between centralization and prevalence of fertilizer adoption was, however, not smooth. By exploring the distribution of residuals, we can observe qualitatively different patterns of the outcome dispersion for networks above and below centralization levels of approximately 0.4. We compare and con rm the difference in terms of the fertilizer adoption outcomes for these two groups of networks by an unpaired two-samples Wilcoxon test.
To test whether the observed patterns of fertilizer use can be explained by simple contagion, we analyse the networks with heterogeneous fertilizer outcomes with Autologistic Actor Attribute Models (ALAAMs) [50]. ALAAM are used for cross-sectional network data to test, by Markov chain Monte Carlo maximum likelihood estimations, if certain network patterns can explain nodal attributes. Here ALAAM was used to test whether pairs of connected nodes are more likely to have the same value on the nodal binary attribute using fertilizer or not (more in SI).
To test alternative complex contagion mechanism, we ran simple agent-based models on two empirical networks (one centralized and one decentralized village network), in which the agents' probability of becoming in uenced by their network peers is dependent on their other peers (i.e. complex contagion, i.e. exerted social in uence is different from the algebraic sum of in uences exerted through individual pairs of actors). If a certain complex contagion mechanism was able to reproduce networks with similar distributions of fertilize uses as in the highly centralized and decentralized empirical networks, we deemed is as a potentially relevant mechanism. These evaluations were not intendent to single out what mechanisms are explaining the observed data, but rather to evaluate if a given mechanism could have possibly given rise to the observed results.
The presented qualitative insights come from 1-hour interviews and subsequent open-ended discussions and email exchanges with 5 members of the local partner organizations who conducted the data gathering in the eld, and have decades of experience of working inside Indonesian cocoa communities and implementation of agricultural programs.  Network centralization and fertilizer adoption. The tted curve to the left is based on a linear regression of fertilizer ratio based on log(centralization). The grey area is 95% con dence interval of the t. The colour of the dots depicts the practice of the individual with the largest number of links in the village: green means that the individual does not use a fertilizer, red means that they use fertilizers. Blue villages have two individuals with the same maximum number of links in the village, one of them uses fertilizers, one of them does not. Grey dots are villages with incomplete data. The diagram to the right shows the dispersion of the residuals of the tted regression model. The dispersion declines rapidly for centralization levels above approximately 40%.

Figure 3
Fertilizer adoption ratios in villages below and above 40% Freeman degree centralization scores. Points depicting fertilizer ratios for villages in each category are horizontally jittered for visibility. Point colours are as in Fig. 2. The middle horizontal lines represent the means of the respective groups and the top and bottom lines delimit the range of one standard deviation from the means.

Supplementary Files
This is a list of supplementary les associated with this preprint. Click to download. SupplementaryInformation20210306.docx