Organic agriculture, labour exchange, and social networks: a case study of smallholder farming in Bhutan

We examine the informal exchange of labour in farming villages with the successful adoption of labour-intensive farming practices. Previous studies have characterised the network pattern of labour exchange to relate such cooperative behaviour to the community’s social structure. We use network patterns from the literature and recreate the internal network structure of the labour exchange in selected Bhutanese villages to determine the type of social enforcement mechanisms used. Results show that labour exchange networks in these villages are characterised by a high prevalence of triad closure as an underlying social structure. These are completely connected structures within the labour exchange network in which any two farmers exchanging labour have a common farmer with whom both share labour. The results from our random graph modelling imply that villages with well-functioning labour exchange institutions may be most suitable for being promoted as “organic villages” as they can adapt to the high labour requirement that comes with organic farming. Future research should analyse how villages with different network structures produce different farm outcomes and how the village and farm-specific attributes affect their social enforcement mechanisms.


Introduction
In most farming societies in low-income countries, the majority of day-to-day farming activities are still predominantly performed manually. The absence of formal labour markets and scarce labour supply means farmers cannot rely upon the use of contract labour; instead, family farms depend on labour exchange arrangements (Erasmus 1956;Jackson et al. 2012;Gilligan 2004). In such an agricultural context, farmers agree to engage in joint action by participating in labour exchange among themselves, because this type of cooperative behaviour produces mutually beneficial outcomes for all involved parties (Dasgupta 2005;Gilligan 2004; Kirinya et al. 2013).
In low-income countries, it is a burden for labourintensive farming systems when communities fail to Abstract We examine the informal exchange of labour in farming villages with the successful adoption of labour-intensive farming practices. Previous studies have characterised the network pattern of labour exchange to relate such cooperative behaviour to the community's social structure. We use network patterns from the literature and recreate the internal network structure of the labour exchange in selected Bhutanese villages to determine the type of social enforcement mechanisms used. Results show that labour exchange networks in these villages are characterised by a high prevalence of triad closure as an underlying social structure. These are completely connected structures within the labour exchange network in which any two farmers exchanging labour have a common farmer with whom both share labour. The results from our random graph modelling imply organise labour exchange. Evidence shows that the promotion of labour-intensive farming systems in smallholder farming has failed in farming communities where labour exchange has disappeared (Natcher et al. 2018). Without well-functioning labour exchange institutions, communities also resort to herbicides and farm inputs that have devastating effects on the environment (ICIMOD and MoAF 2018; Bajgai and Yeshey 2014). In mountainous regions, subsistence farmers vulnerable to climate change are encouraged to transition to sustainable farming practices and abandon the use of mineral fertilizers and herbicides (ICIMOD and MoAF 2018;RGoB 2021). However, the transition can be challenging due to its implications on labour to replace external inputs. But, for progressive communities with well-functioning labour exchange institutions, the transition would be easier (Kinga 2010). Although labour exchange was predicted to disappear from peasant societies by early studies (Erasmus 1956;Moore 1975), Kranton (1996) shows that it can persist alongside formal labour markets and does not show signs of disappearance. The persistence of labour exchange arrangements implies that farming societies are still benefiting from it, making labour exchange still an important institution.
Labour cost plays an important role in the production and profitability of organic farming. Crowder and Reganold (2015) compared conventional and organic farms and found that the global average cost of organic farming exceeds the corresponding cost of conventional farming by 7-13%. Such discrepancies arise mainly from more labour used to control pests, manage weeds, apply manure, and perform a wide diversity of work (Crowder and Reganold 2015;Lampkin and Padel 1994;Pattanapant and Shivakoti 2013;Suwanmaneepong et al. 2020;Tashi and Wangchuk 2016). Labour exchange institutions can help organic smallholders to cope with the burden of labour and keep the cost of labour uniform across households and constant across time.
Many scholars have been intrigued to study communities with well-functioning labour exchange and to investigate how they foster cooperative behaviours through social networks (Dasgupta 2005;Jackson et al. 2012). They have studied the use of different forms of social norms and culture to informally enforce cooperation. Some have even formulated models providing a theoretical foundation of informal enforcement mechanisms in labour-sharing arrangements (Gilligan 2004;Jackson et al. 2012;Krishnan and Sciubba 2009). They have argued that labour-sharing networks carry network patterns that characterise the network structure generated by the informal enforcement of cooperation (Gilligan 2004;Jackson et al. 2012;Krishnan and Sciubba 2009). They further argue that the network structure explains the type of social enforcement used by the community (Gilligan 2004;Jackson et al. 2012;Krishnan and Sciubba 2009).
Our objective in this article is to examine whether these social structures reported in the literature are also prevalent in the labour exchange network data from our study sites and whether they can characterise the social mechanisms for enforcing cooperative behaviour. In examining this, our aim is to illustrate how labour relationships in a society must be organised to cope and adapt to labour-intensive farming systems (Jackson et al. 2012). Specifically, we first want to analyse how a farmer's decision to engage in labour exchange is influenced by the network pattern of behaviour of other actors in the community. Secondly, using the social structures found in the selected villages, we aim to identify a set of properties that illustrate the social enforcement mechanisms in the studied Bhutanese villages. In this way, we show that tools from social network analyses can be used to identify appropriate villages in which labourintensive farming is feasible. This also implies that the functioning and preservation of such networks are a prerequisite for a successful conversion to labourintensive organic farming. Our network formation analysis combines economics and graph theory and offers a unified framework to understand the why and how of labour exchange network formation.
While the European organic farming movement has been a bottom-up initiative, farmers receive substantial support under the Common Agricultural Policy (CAP) (Jaime et al. 2016;Buitenhuis et al. 2020;Runowski 2021;Feuerbacher et al. 2018). On the contrary, organic farming in Bhutan is a top-down initiative (ICIMOD and MoAF 2018), and providing large subsidies is not possible because of budgetary constraints. Thus, the issue of whether a society like the Bhutanese one, which primarily relies upon the farming sector, can adapt to a more labour-intensive farming system is important to address. Although 66% of farmers in Bhutan use labour exchange arrangements (MoAF 2019), it has not yet been analysed how this informal sector is used and benefits smallholders. Besides our understanding of labour arrangement as a culture and social norm in the country, no study provides a careful examination of this institution. In this respect, considering that certified organic farming is relatively new in Bhutan, and only a few traditional farming 1 villages have converted to this comparatively more labour-intensive farming system, our analysis can serve as an example on how smallholder farming can adopt farming systems that can provide a sustainable future even with a relatively high labour burden.
This article is structured as follows: "The role of social networks in labour exchange" section presents the theoretical foundations and concepts from social network analyses along with a brief literature review. Next, a description of our data and of the methods used is given in the section "Data and methods". Finally, the "Results" section is followed by a "Discussion" and a "Conclusion" section.

The role of social networks in the labour exchange
Theory of network formation A simple network formation theory guides our social network analysis of labour exchange. The network formation theory postulates that individuals can choose with whom to form labour relationships and make efforts to maintain them if they perceive them as beneficial and dissolve those labour ties that are not considered useful (Jackson et al. 2020;Jackson 2006;Krishnan and Sciubba 2009). The choice of labour links among farmers then results in patterns of interactions between them, leading to social networks (Barnes 1954). The network formation theory predicts that some distinctive network patterns will emerge, forming the underlying micro-configuration of the social network under study (Jackson et al. 2020;Jackson 2006). They are considered the building blocks or mechanisms through which society fosters cooperation among the farmers (Jackson et al. 2012;Jackson 2006). Different processes can result in varying network patterns for dissimilar communities, characterising the form of the specific social enforcement mechanism used to informally enforce cooperation.
While we do not formulate new network patterns that emerge from our labour exchange networks, we use two specific social structures described in the literature that capture strategic network formation theory. According to this theory, forming and dissolving labour-sharing relations involves strategic decision-making and communities capable of fostering cooperation in informal labour exchanges show the prevalence of certain social structures (Jackson 2006; Krishnan and Sciubba 2009). The social structures emerging from this strategic decision-making can be characterised in one of two ways. They are either homophilious, wherein labour exchange ties are more common among homogenous farmers with similar characteristics (Krishnan and Sciubba 2009). Or they show a triad closure, in which labour exchange ties between two farmers are always supported by a common farmer with whom they both share a labour tie (Jackson et al. 2012).
Further, a theory outlining the effects of endowment (with land and machinery) on the formation of labour exchange ties between farmers is also used in our analysis to capture the effects of farmers' attributes (Gilligan 2004). We use these theoretically founded social structures to identify which micro-configurations of the labour network are (most) important in our study villages. This helps to disentangle the why behind the network formation and gain insights into the incentives or costs and benefits of the links formed (Jackson 2006).
We use random graph theory to disentangle the how behind the network formation (Jackson 2006). Social network analysis for network formation is now possible with the graph theory developments, specifically the exponential random graph model (Robins et al. 2007). This technique makes it possible to model the formation and dissolving of ties as a stochastic process (Robins et al. 2007). This helps to trace the overall labour network to the social structures used to informally enforce cooperation and enables us to understand the underlying network formation process (Jackson 2006). In the following sections, we present the relevant empirical evidence on the above-mentioned social structures in the literature.

Node attribute (endowment) effect
While there are studies that predict that labour exchange will disappear under conditions of outmigration of surplus labour from agriculture (Lewis 1954), low population density (Boserup 1965) and certain social and economic conditions (Erasmus 1956;Moore 1975), recent evidence shows otherwise (Gilligan 2004;Jackson et al. 2012;Kranton 1996;Krishnan and Sciubba 2009). Gilligan (2004) shows that a farmer's decision to engage in labour exchange decreases with improvement in his endowment level measured in terms of bigger farm size, household size, and asset holding. Other researchers analysed the relation between formal labour market imperfections and the prevalence of an informal labour market (Carter and Zimmerman 2000;Eswaran and Kotwal 1986;Feder 1985). Gilligan (2004) used plot-level data from Indonesia to show that better-endowed households are autarkic and that the probability that they will participate in labour exchange is low.
In network terms, the effect of a farmer's endowment on labour exchange is called the node attribute effect (Fig. 1a). In our study, we use ownership of a power tiller and area under cultivation as measures of the endowment to test the effect of the endowment on enforcing labour exchange. We hypothesize the following: Hypothesis 1: Farmers are less likely to engage in labour exchange when they own a power tiller. Hypothesis 2: Farmers are less likely to engage in labour exchange with an increasing size of their cultivated area.
Homophily Some literature has shown how similar farmers prefer to form links in informal labour-sharing relations (Krishnan and Sciubba 2009;Udry and Conley 2005), referring to the common social phenomenon of "birds of a similar feather flock together" (Glueck and Glueck 1950). In network terms, this social structure that can informally enforce cooperation in laboursharing is called the homophily effect (Fig. 1b). It also received interest in the studies of informal enforcement mechanisms (Galeotti et al. 2006;Johnson and Gilles 2003;Haller and Sarangi 2005).
Homophily indices are constructed using different farm-level characteristics to study how homophily can explain participation in labour exchange. Udry and Conley (2005) used both binary (similar religion, matrilineage, gender, soil type, generation, origin If the attribute in question is the ownership of machinery, then nodes 2, 3 and 4 own machines and have fewer labour links, while node 1 has more links since it does not own a machine. b Example for Homophily: nodes 5 and 6 are homo-philious and share a link because they have the same number of labour links with other farmers. c Example for Triad Closure: nodes 8 and 9 share labour when they are connected to node 7 (with whom they both share a labour link). Node 7 cooperates and exchanges labour with nodes 8 and 9 because when not participating in the group, node 7 would lose two links from the same region) and continuous (absolute difference of age, wealth, plot distance) categories of farm and household level characteristics. Based on labour exchange data from four villages in Ghana, Udry and Conley (2005) showed that homophily defined as 'farmer's origin from a similar region' has a high odds ratio of 9.73 in enforcing labour exchange, with similarly high effects from the same religion, matrilineage, and gender. Krishnan and Sciubba (2009) constructed a simple homophily index using the number of labour exchange links. They used labour exchange data from 15 villages in rural Ethiopia to show that farmers with a similar number of links are more important in enforcing labour exchange cooperation and contribute highly to labour network formation.
We construct an index similar to Krishnan and Sciubba (2009) to test the informal enforcement of labour exchange from homophily, which leads to our third hypothesis: Hypothesis 3: Farmers are less likely to engage in labour exchange when the difference in the number of labour exchange ties increases.

Triad closure
One social structure that has received much attention in enforcing cooperation in labour exchange is clustering (Coleman 1988;Dasgupta 2005;Krackhardt 1996;Simmel 1950). It measures "the number of pairs of friends that have some friends in common" (Jackson et al. 2012). In the context of labour exchange, it counts the number of pairs of farmers which overlap when exchanging labour. In network terms, this network structure is called triad closure (Fig. 1c).
The common farmer to whom a pair of farmers is connected has different terms throughout the literature: support (Jackson et al. 2012), mutual enforcement (Dasgupta 2005), and closure (Coleman 1988). Jackson et al. (2012) show that 80% of all pairs of labour exchange ties between two farmers have a common farmer with whom they have exchanged labour. To test the effect of triad closure on labour exchange network formation, we specify our final hypothesis as: Hypothesis 4: Two farmers are more likely to engage in labour exchange when they have a common farmer with whom they share labour exchange.

Data and methods
Context, study location, and data collection Although organic farming faced minimal support in the past, the current Bhutanese government invested a relatively high budget in the 12th Five-Year Plan. 2 The organic support provides farmers with seeds, training, electric fencing, machinery, and in a few cases, the construction of farm roads and access to water. Development partners also aid Bhutan in building resilient communities against climate change by helping communities with the transition to organic farming 3 . The National Organic Programme (NOP) provides training in certification procedures and access to the local certification system (LOAS) without administrative cost to improve the market access to organic produce in the local market. The LOAS also ensures the credibility of organic production within Bhutan and is supposed to incentivize organic 'mass conversion' (NOP 2019a). It ensures that food production follows the Bhutan Organic Standard (BOS) (NOP 2019b). BOS is adapted to the traditional agricultural system and is not in conflict with the norms of IFOAM-Organics International and Codex Alimentarius Guidelines. It is characterised by promoting traditional farming practices that are still practised by farmers and do not contradict the core organic principles. For instance, farmers are obliged to continue using farm-yard-manure in place of mineral fertilizers and to apply only manual weeding instead of herbicides to control weeds. Bhutanese farmers also cultivate a wide diversity of crops, which is also encouraged under the BOS. In addition to the traditional farming practices still allowed under BOS, the NOP introduces new farm management practices such as organic pest management, new improved organic seeds, crop protection, etc. Although LOAS requires the whole land of farmers to be certified and to grow diverse crops, the government identifies each village with specific crops to increase production under the 'One Gewog One Product (OGOP)' policy.
Our study sites are based on the list of registered and certified organic producers provided by NOP. Hence, the organic villages selected were comprised of households that were certified organic. Khatoed gewog (a subdistrict administrative block consisting of five villages) and Berti village fulfilled this criterion and were selected for the survey. Khatoed focuses on potato and garlic, and Berti on watermelon and paddy. Our network analysis uses nine villages situated in different agroecological zones under different farming systems (Table 1). Besides Khatoed and Berti, our village list includes three traditional farming villages, which are "villages that use no or minimal external inputs" (NOP 2019a).
Our study site consists of different villages from diverse AEZ with a large diversity of farming systems (NEC 2022). A farming system in the humid subtropical zone (600-1200 m above sea level (masl)) receives more rainfall and is characterised by higher temperatures. The wetlands are used for main crops like wheat and paddy, while hilly cropland is cultivated with commercial crops like vegetables, legumes, citrus, etc. In the dry subtropical zone (1200-1600 masl), farmers receive moderate rain, and the temperatures are warm. Farmers grow diverse baskets of crops like paddy, maize, mustard, legumes, and vegetables. A moderately warm climate with winter frost is characteristic of the warm temperate zone (1800-2600 masl). Farmers use wet and dry land to grow crops like paddy, wheat, potato, fodder, and vegetables. Farmers in the cool temperate zone (2600-3600 masl) engage in livestock rearing as a common activity and also partake in dryland farming. They grow potatoes, buckwheat, mustard, and barley.
Paddy is grown as a subsistence crop for livelihood in all the selected villages except for Khatoed, where only a few farmers have access to wetland for growing paddy. Farmers depend on monsoon rain to irrigate their fields. In Khatoed, farmers grow garlic and carrot, while potatoes are cultivated as cash crops in both Khatoed and Lingmukha. Only in Berti, do farmers grow watermelon as a cash crop. Chilli is a common vegetable grown in all the study villages after the harvest of major crops. While, in Berti, the harvest of watermelon is followed by plantations of paddy, in Lingmukha, potato harvest is followed by paddy. In Khatoed, garlic harvest is followed by the harvest of potatoes. Farmyard manure is used as the main source of soil fertilization in all the villages.
For smallholder farming, during a typical crop season, work in the field begins with land preparation, followed by plantation. For a few months of the crop calendar, farmers are engaged with weeding, which is usually conducted two-to-three times, separated by 4 to 5 weeks apart, and is ultimately followed by the harvest. In all these field activities, farmers depend on labour exchange. In traditional villages, weeding is often replaced by herbicides, especially for paddy and potatoes. Weeding is a major field activity in organic villages, even during land preparation. In both the organic and traditional villages, farmers use power tillers only during land preparation to plough the field, and almost all remaining work on the field is completed manually. The complete list of the households was requested from the Gewog office. In each village, the enumerator asked: "With whom among them [names of the village members read out to the respondent] did you engage in labour exchange during the specific crop [name of the crop coinciding with the data collection period] season?" This method enables a complete enumeration of names associated with labour exchange instead of asking half of the village farmers to nominate a few with whom they exchange labour (Jackson et al. 2012;Krishnan and Sciubba 2009;Udry and Conley 2005). Additional information on social, economic, and agricultural variables was gathered. The villages given in Table 1 consist of smallholdings with very small areas under cultivation, and with satisfactory use of machinery, like power tillers. The average area under cultivation for paddy (Berti (P), Lingmukha, Drachukha, Hebisa) is higher than for cash crops like watermelon (Berti (W)) and potato (Khatoed). In all the studied villages, more than half of the village population owned a power tiller except for Berti.
Network data of labour exchange were collected for the crop season in which the survey was administered to enable high recollection of the names with whom the surveyed households were engaged in labour exchange. The data collection time coincided with paddy cultivation for most of the villages (Berti, Lingmukha, Drachukha, Hebisa), potato (Khatoed), and watermelon (Berti). The data collected is a binary-directed network, where each household indicated in a list the names of the households with whom labour exchange was performed. All the networks are one-mode in that only information related to labour exchange between households was used in the adjacency matrix. The adjacency matrix is a social matrix that records the labour exchange tie between households. We represent this data in network form (Fig. 2).
Labour exchange networks were plotted, and descriptive statistics for average ties (average number of farm households with whom a farmer exchanged labour) and network densities (ratio of actual ties over potential ties) were estimated for organic farming villages. In Khatoed, the average number of labour exchange ties was 6.84 with a density of 13.95% (Table 1); in Berti, the average tie was 7.33 with a density of 31.88% during watermelon season, and 18.70 with a density of 84.98% during paddy season ( Table 1). The procedure was repeated for traditional farming villages. In Lingmukha, the average number of labour exchange ties was 7.05 with a network density of 39.18%; in Drachukha the average tie was 8.32 with a network density of 46.19%; in Hebisa the average tie was 11.18, and the network density amounted to 53.24% (Table 1).

Graph modelling and conditional dependence
Graph theory is used to model labour exchange network formation as the result of the given social structure measured using different network structures. These social structures are the micro-configuration of the underlying network that explains the formation of the network under study. One of the advantages of using graph modelling is its ability to account for dependency in nodes connected by edges (Fig. 1). When two farmers exchange labour, they create a dependency between them conditional on the rest of the network. This feature of network modelling is called conditional dependence. Our analysis accounts for dependency between nodes and, unlike previous studies (Gilligan 2004;Jackson et al. 2012;Krishnan and Sciubba 2009;Udry and Conley 2005), uses endogenous network formation modelling. It is unrealistic to model network formation under assumptions of conditional independence. An Exponential Random Graph (ERG) model, belonging to a class of random graphs, was designed to analyse the dependent data (Lusher et al. 2013;Frank and Strauss 1986;Wasserman and Pattison 1996). The ERG model estimates a set of parameters for each of the micro-configurations (chosen by the researcher) to show their effect on the formation of the network. The magnitude (high or low) of the parameters should be interpreted as whether the micro-configurations could have occurred more or less likely by chance. The parameters are estimated using an iterative procedure called Markov Chain Monte Carlo (MCMC) maximum likelihood estimation (MLE). This model first estimates a provisional parameter. Next, using this parameter as a basis, many networks (graphs) are simulated for which network statistics for each configuration in the sampled networks are compared with the statistics of the observed network. The parameters in the simulated network are then adjusted to get the means of the network statistics closer to the observed network statistics. When this happens, the model is said to have achieved convergence. In addition to convergence, ERG needs to achieve significant goodness of fit. In this procedure, after thousands of networks are simulated using the estimated parameters, a random sample of statistics of the micro-configurations (social structures) is compared with those of the observed network. When the ratio of the difference between the simulated and the observed data and the standard deviation of the simulated network is less than 0.1, the model is treated as a good representation of the observed data.

ERG model specification
The Exponential Random Graph (ERG) model allows for treating a labour exchange network as a dependent variable (Lusher et al. 2013;Frank and Strauss 1986;Wasserman and Pattison 1996). The dependent variable N ij is a variable that shows the potential ties between individual farmers i and j that take a value of 1 if a labour exchange tie exists and 0 in the case it does not. The matrix N of these random variables will represent all the potential ties in the network. However, this type of modelling is based on several assumptions of which randomness and dependencies of ties are primal. ERG models for any social network assume that networks result from micro-level processes (Lusher et al. 2013). Network n is one such observed network among many potential labour exchange networks. The observed network n could be a result of certain dominant micro features like the prevalence of closed triads, and it would look completely different in another form if closed triads were not prevalent. Under the influence of different microlevel structures, different configurations of n can exist within the population of possible networks represented by N ij . In the most general sense, ERG models estimate the probability of observing the observed network of labour exchange as a function of its underlying micro network structure, represented by the network statistics S (n) describing our network n concerning micro-level features. Such features include node attribute effects, homophily, and triad closure. The network statistics are simply the count of those micro features. For example, an observed network might have 10 edges, 4 homophily ties, and 20 triad closures. The corresponding coefficients S are the parameters to be estimated for each network statistic according to Eq. (1): This probability is expressed as a sum over all the network possibilities C, which is difficult to estimate. As such, the ERG can be reformulated using logistic regressions, which will represent the likelihood ratio between two hypothetical networks. They differ only by a single dyad value in which a hypothetical network A will have the relation N ij = 1 and the network B has N ij = 0. The estimated probability will be the probability that farmers i and j have a labour exchange tie with each other conditional on the rest of the network N c ij The network statistics S (n) measure the amount by which a potential tie between i and j will change the underlying network statistics (the considered tie, for instance, may change the homophily cases by a certain number), which are modelled as the independent variables. The coefficient S is to be interpreted as the change in the log odds when the particular labour exchange tie existed and if the formation of this tie changed the corresponding network statistics by one unit (Goodreau et al. 2009). The coefficients are to be interpreted exactly like in logistic regression.

Independent variables
The goal of ERG modelling is to describe the global network of labour exchange we observe with a set of local structures or micro configurations as shown in Table 2 (column 1). These social structures enter our ERG model similar to how we specify independent variables in logistic regression. For Nodeofactor, ERG estimates the effect of outgoing ties of a farmer who owns a power tiller (Fig. 1a); for Nodeocov, ERG estimates the effect of outgoing ties of a farmer for different levels of cultivated area (Fig. 1a). For Absdiff, ERG estimates the effect of the absolute difference of tie numbers between two farmers (Fig. 1b).
The ERG model term uses a geometrically weighted edgewise shared partner (GWESP) to estimate the effect of triad closure (Goodreau 2007;Hunter et al. 2008;Robins et al. 2007). Two farmers are said to have edgewise-shared partners if they are connected simultaneously, and each one is connected to a third farmer (Hypothesis 4). This term counts the number of triangles in which all the farmers in the network are connected to everyone in the triangle (Fig. 1c).

Results
We examined labour exchange networks and analysed which distinctive social structures emerge as microconfigurations out of the network formation process to explain how the surveyed Bhutanese communities informally enforce cooperation in the organic and traditional farming systems. The social structures that are statistically significant in the model hint at the properties of the labour exchange network that emerged as effective in enforcing cooperation. They should be interpreted as the relevant key features of the informal mechanism that drives the cooperative behaviour observed in our study sites. These results highlight the role of social network structures in fostering cooperation to pool labour inputs and cope with the burden of labour.
The results from the ERG model estimation are presented in Table 3. To show that the surveyed communities are suitable, we check for social structures that informally enforce cooperation in labour exchange. As outlined above, we formulated four hypotheses based on previous literature and tested them together but separately for different villages. While the results from organic farming villages allow us to understand how farmers adapt to labourintensive farming, results from traditional farming villages enable us to understand similar behaviour for comparable labour-intensive traditional farming.
The edge term can be interpreted as how the probability of a labour exchange tie between two farmers is affected by existing ties in the network. This term is similar to an intercept in regression. The estimates regarding the endowment effect (Hypotheses 1 and 2) failed to show any conclusive result for the predictions made by the endowment theory. We found only one village (Model 5) with the predicted sign and significance for power tiller endowment, and none of the villages showed a significant expected effect on the cultivated area.
For the homophily effect (Hypothesis 3), we found that five out of six models have the expected sign, but only three show a significant effect. The homophily effect is more pronounced than the endowment effect, which is not supported by our data.
We found the most conclusive result for triad closure as the social structure feature that can explain best how farmers informally enforce cooperation in labour exchange. A non-ERGM analysis of labour exchange formation would not detect this effect. We found the expected sign and significant results for Hypothesis 4: the tendency for two farmers to form a labour exchange when they have a common farmer with whom they exchange labour. The odds are very high, especially for networks with a high density of labour exchange (Models 3 and 6). We found this effect for all villages studied, indicating its power in explaining how farmers informally enforce cooperation.
An important element in ERG analyses is to assess the goodness of fit. Table 4 shows p-values for differences in network statistics (columns) between observed and a sample of simulated networks for different models (rows) for the ERG estimates in Table 3. Table 4 shows that all the model specifications are good fits for the data generated in different farming villages. Figure 3 shows an example of the goodness of fit plots for one of the models estimated. The boxplots show statistics for simulated networks, which are compared with observed network statistics illustrated by the solid line. The figures show that the observed network statistics are within the simulated confidence intervals and do not deviate too much.

Discussion
We studied labour-intensive farming villages in Bhutan, intrigued by their ability to enforce cooperation in forming labour exchange to reduce the burden of labour on their farm. We examined the micro-configurations of these labour exchanges that emerge out of the network formation process to explain the mechanisms used by farmers to enforce cooperation in these villages informally. We used social structures identified in prior literature to interpret why farmers may decide to form certain links. We then used an exponential random graph model to show how the network formation process generates the labour network we have observed. Our objective was to characterise the informal enforcement mechanism of cooperative behaviour in a labour-intensive farming system of a low-income country. Previous work on the role of social structures in fostering cooperation in informal exchanges has suggested that certain network patterns emerge in these networks that can be used to characterise and predict consistency within data (Coleman 1988;Dasgupta 2005;Gilligan 2004;Jackson et al. 2012;Krishnan and Sciubba 2009). However, with few exceptions, empirical evidence has remained largely scant in the informal labour exchange still prevalent in lowincome countries (Gilligan 2004;Jackson et al. 2012;Krishnan and Sciubba 2009). Our research contributes to the literature by providing empirical evidence for the consistency of the network patterns of labour network formation theory. We use multiple theoretical   Table 4 foundations from this research to characterise the social network of labour-sharing arrangements in our labour-intensive farming villages. When modelling different structures of informal enforcement mechanisms used in the selected villages, both organic and traditional farming villages show significant effects of triad closure in enforcing cooperation (Coleman 1988;Jackson et al. 2012). Jackson et al. (2012, page 1857 use social ostracism as an argument to explain why this structure emerges in most labour-sharing arrangements: "any two individuals interact too infrequently to sustain exchange, but such that the social pressure of the possible loss of multiple relationships can sustain exchange". They further argue that this social ostracism leads to "treelike unions of completely connected subnetworks (in which) any two individuals exchanging favours have a common friend" (Jackson et al. 2012). Coleman (1988) uses closure within a similar network structure, arguing that groups of farmers can easily monitor and exert pressure on other farmers to behave in the interest of the group.
The literature has focused only on explaining why farmers engage in cooperative labour-sharing behaviour and has remained short in explaining how the labour network formation process results in the network patterns. Our work combines both approaches used for explaining the network formation theory to provide a unified approach and explain the why and how of labour exchange networks. We use a recent development in the random graph theory called ERG modelling and test multiple social structures from the literature to determine which network patterns emerge among the Bhutanese farmers. Past studies do not consider this feature and assume only one structure underlying the social enforcement mechanism. Our analysis assumes that multiple social structures can exist. One social structure could lead to the formation of another structure through an endogenous process. This kind of modelling is still a novelty in the literature on labour network formation. The evidence for other network patterns we tested is mixed in our analysis. Two explanations come to mind. One, villages have differing underlying social structures, and some network patterns are relevant only in a certain context. This feature could be useful in differentiating labour exchange institutions in future work. Two, farmers tend to work in more constellations than in groups of two. However, the predictions made by some theories make sense only for dyad relationships between farmers. For instance, the first three hypotheses are only based on dyad-level network structures. But in the field, we found that group dynamics are often more prevalent, which might have provided consistent predictions for triad closure as a network pattern in all the villages.
In drawing our recommendations, we emphasize that projects and policies should consider villages with well-functioning labour exchange to promote organic farming. When smallholders adopt organic farming practices this can have huge implications on labour. This holds especially true in low-income countries, where farm infrastructure is weak, and where labour exchange can play a critical role in meeting increasing labour demands. While labour exchange may play an important role in mitigating labour problems in organic farming, it will face limitations if problems of out-migration from villages are not considered a policy priority in Bhutan. In general, the farming systems in Bhutan are highly labourintensive (Feuerbacher et al. 2020), and a decrease in the pool of available labour could have an impact on the labour exchange system, with further implications for the promotion of organic farming. Although our research did not analyse such issues, network structures are susceptible to changes in the underlying conditions (Jackson et al. 2012). Further research in this area could help policymakers intervene with necessary measures to ensure well-functioning labour exchange systems.
While our data from 'organic' and 'traditional farming' villages are from Bhutan, caution is necessary for generalizing the results beyond Bhutan's country context. However, it must be reiterated here that the network patterns used in predicting the consistency were test-based in other low-income countries. One finds relevance across the board, implying that some social enforcement mechanisms may be common across different contexts. Our analytical approach can serve as a tool for policymakers and project partners to identify suitable villages to promote organic farming. As governments in lowincome countries usually face serious budgetary constraints, choosing suitable villages when implementing organic farming to promote policies and projects matters. For instance, over 66% of the farmers in Bhutan use labour exchange (MoAF 2019). Our analysis can be used to characterise which villages are most suitable for implementing labour-intensive farming practices. Although our argument of a suitable farming community for promoting organic or other labour-intensive farming is based on the existence of a well-functioning labour exchange system, a similar network analysis using ERG could be performed to describe and explain other informal institutions like the ones that govern the exchange and use of credit, seed, machinery, water, etc., which constitute other forms of resource sharing mechanisms in low-income countries. A report by ICIMOD and MoAF (2018) showed that over 98% of Bhutanese farmers use seed networks to meet seed demand. Surprisingly, the Bhutanese government does not currently take advantage of such networks.
Although our work is focused on examining informal labour-sharing systems, it will be valuable in future work when analysing the association between networks and economic outcomes. Past work has emphasised that not only the number of labour exchange links but also the structure of the network matters when estimating the effects of labour exchange on farm productivity (Krishnan and Sciubba 2009). It has shown that high-ability farmers tend to form links with similar high-ability farmers and that these farmers are unavailable to low-ability farmers. It has further been shown that this structural behaviour leads to productivity differences on the farm. Our analysis shows that other social structures are also relevant (and partly statistically significant) in addition to triad closure as a common social structure. A careful observation of our analysis shows that all the surveyed villages are structurally different. This implies that economic outcomes from these villages should also be different, which could be explored in future work.
In our view, labour exchange has always been seen as an old-age custom passed down from generation to generation. We think this view is somewhat misleading because this resource gap-filling institution is assumed being available to everyone in the village and makes the adoption of labour-intensive farming systems easy for farmers. Together with previous researchers, we highlight the existence of strategic decision-making, leading to network structures with specific characteristics. This implies that labour exchange is not a norm where a labour contribution from all members of the community is expected. Instead, it involves careful decision-making concerning with whom to form links. Farmers engage in labour exchange not because they want to contribute to the community's well-being but, according to the triad closure hypothesis, for fear of losing other links if they do not exchange with farmers in the connected links (Jackson et al. 2012). Alternatively, it could be that another farmer has machinery that can be useful (Gilligan 2004) or that the other is of high ability compared to the farmer close to his house (Krishnan and Sciubba 2009). In short, although labour exchange is common in most villages in Bhutan, its specific 'micro-configurations' might differ, implying that the social mechanisms used for enforcing cooperation are different.
Although smallholder subsistence farmers are among the most vulnerable groups concerning climate change, they also display the ingenuity and capacity to adapt to climate change through their community dynamics (Nazir and Das Lohano 2022; Tshotsho 2022). Because smallholder farming produces relatively high yields and engages in a high diversity of crops, it is also enshrined in future sustainable agriculture development policies (Ricciardi et al. 2021). Policymakers should recognize the role of communities in building resilient farming systems. However, smallholders also need the state and external support to improve the outcomes of resilient communities (Ahmed 2022; Shafeeqa and Abeyrathne 2022).

Conclusion
We presented the case of labour-intensive farming villages that are capable of coping with the burden of labour through the use of labour exchange institutions. While examining these informal institutions, we found that farmers engage in joint action of sharing labour, which seems to provide a mutually beneficial outcome to managing the burden of labour. We modelled our social network data using an exponential random graph model to characterise the underlying social structure. We identified one major network pattern that emerges from the network formation process: triad closure. This social structure seems to be a labour exchange arrangement that can help to identify other communities that may be suitable for further promotion of labour-intensive (organic) farming systems in Bhutan and other low-income countries. Our network formation analysis combines economics and graph theory and offers a unified framework to understand the why and how of labour exchange network formation.
Our analysis has relevance for organic development policies for three reasons: first, a society like the Bhutanese one that, to a large extent, relies upon the farming sector, can thus better adapt to a more labourintensive farming system; second, the functioning and preservation of labour exchange is even to be seen as a prerequisite for successful conversion to labourintensive organic farming; third, public spending in suitable communities assures successful implementation justifying public funding for providing seeds, training, machinery support, electric fencing, road and water connectivity, and market support. This article provides insight into whether the transition from one agricultural system to another may be possible without major difficulties for the farmers studied here and in the broader context of the country.
The analysis of organic farming villages provides a starting point in recognizing the role of labour exchange in managing labour requirements in organic farming. As more farm households convert to organic farming, future research should focus on collecting network data from more villages before and after conversion to organic farming. It should study if labour exchange institutions are successfully carried over as the farming system undergoes conversion and whether communities can still informally enforce cooperation. Future research should also extend beyond labour and look at other important informal exchanges for farm inputs like seed, credit, machinery, advice, water use, etc. Future work on the role of labour exchange systems may conduct comparative analyses investigating to what extent labour exchange systems with different enforcement mechanisms increase the uptake of labour-intensive farming practices. Future studies can also use the specific properties of labour exchange to investigate the economic outcomes of the farms under different farming systems. For instance, one could study the yield gap in different farming systems with different mechanisms used for enforcing cooperation in labour exchange.
Author contribution CL and TT were involved in the formulation and evolution of the research goals and aims. Data collection, formal analysis, methodology, software, visualization, and writing of the article was carried out by TT. CL and AF provided critical review and revisions on earlier drafts of the manuscript. All authors read and approved the final manuscript.
Funding Open Access funding enabled and organized by Projekt DEAL. We are grateful to the German Academic Exchange Service (DAAD) who supported our research work by awarding a scholarship for PhD studies to the corresponding author.

Competing interests
The authors declare no competing interests.
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