Enumerators collected the field data from farms in selected areas of Indian Sundarbans, which are constituted of 19 community development blocks (CDB) (Supplementary Figure S1). We randomly selected one CDB each from 13 CDBs of South 24 Parganas district and six CDBs of North 24 Parganas District in the West Bengal State of India. From each CDB, we selected one Gram Panchayat (GP) (village self-governing body) randomly. Fifty-two farms from the selected GP of South 24 Parganas and 88 farms from the selected GP of North 24 Parganas representing nearly 15% of the farm families in those GPs—were randomly selected from a list of farms prepared in consultation with the local stakeholders of agricultural development. We selected farms below the size of two ha to maintain a normative classification of the agricultural census. But, because of the extremely small size of farms, all farms (except for two) were less than one hectare in size.

There are six agro-climatic zones—based on climate, soil, and physiography—in the state of West Bengal in India, and the Sundarbans region comes under the coastal saline zone (Gajbhiye and Mandal, 2000). The Indian part of Sundarbans consists of 4,200 km² of reserved forest and 5,400 km² of non-forest areas, and it is intersected by large numbers of rivers, rivulets, and tidal waterways. Fifty-four islands are inhabited by over 4.4 million people (World Bank, 2014). River embankments guard the boundaries of islands in the upstream areas, but tidal saline water often intrudes into the embankments and floods farmlands. Soil salinity increases in dry months to render the soil uncultivable. The region is vulnerable to cyclonic storms and prolonged inundation. Rice is the main crop grown over different land terrains and seasons. Spring paddy, sesame, and green gram in the early wet season; jute and aman rice in the wet season; maize, different oilseeds and pulses; and vegetables in the winter season are the important crops. Apart from agriculture, a large portion of the population depends on non-timber forest products and migrates to urban centers of India and abroad. Population density has risen rapidly over the past decade and is well above the national and state average. Sustainable use of natural resources is critical to managing livelihoods in the region. Nearly half of the region's population live below the poverty line, and limited employment opportunity creates conflict between livelihoods and environmental sustainability. Nearly all farmers are living marginally, having less than one hectare of land, and sustaining households using small parcels of land within the context of socioeconomic; environmental vulnerability is a great challenge to support smallholders in Sundarbans.

We collected field data through face-to-face interviews with a pre-tested standardized interview schedule (RKMVERI/NDP/EC/RG/Fulb/2018-19) and farm-level measurements. The interview schedule consisted of respondents' background information, livelihood assets, household income and expenditure, details on farming practices, and resource interaction on the farm. The data collection instrument had all the sustainability assessment indicators. The draft instrument was piloted on non-sampled integrated farms in the study areas and modified based on piloting experience. The enumerators stayed in the villages before collecting data, and the actual field data were collected on 140 farms from March-June 2018. Observations and measurements were made on the farms during the interview itself. Summarily, we collected field data to (a) delineate farm types and characterize them, (b) assess the farm's sustainability, and (c) assess farm resource interaction.

Since the smallholder system is heterogeneous in terms of evolution, resource endowments, and vulnerabilities, the smallholder farmers are expected to employ different resource intensification strategies and might pursue different trajectories of sustainability outcomes (Tittonell, 2014b). Different types of farms employ different mechanisms of RI to achieve sustainable livelihoods. Hence, typology delineation for small farms is a pragmatic step to simplify the diverse farming systems before studying the interrelationship of RI and farm sustainability. Based on representative literature (Netting, 1993), we selected 18 potential indicators (Supplementary Table S1) to define the smallholder system in the study region. To reduce the multicollinearity of the data, we used principal component analysis (PCA) to extract six principal components (PCs). These PC scores were then used in hierarchical cluster analysis and K-means cluster analysis to arrive at five distinct farm types (Supplementary Tables S2–S4). Once we classified the farms based on these six PCs, we characterized them in terms of a set of background variables (Supplementary Table S5). We tested whether the five farm types differed in terms of this set of background variables. Significant variables in the one-way ANOVA and Chi-square tests suggested the efficacy of our classification. For quantitative variables, we used post-hoc tests after the one-way ANOVA to identify the distinctly high or low farm types for the individual variables (Supplementary Table S6). Mostly, these distinct high and low values of indicators were used to characterize different farm types. When the mean value of a variable for a farm type was highest and significantly higher than the other farm types in the post-hoc test, we called it “high”. Similarly, the statistically significant lowest value of a variable was called “low”. Anything in between was called “moderate”. A qualitative description of the delineated farm types is given in Supplementary Table S7.

To assess smallholder farms' sustainability, we scouted a suite of indicators following relevant assessment frameworks of local and global importance (Scoones, 1998; Rao and Rogers, 2006; FAO, 2014; Goswami et al., 2017). Our framework is grounded on the sustainable livelihoods framework and guided the selection of indicators (Supplementary Figure S2), the coverage of social, economic, and ecological dimensions of sustainability, access and availability of related data sources, cost of measurement, time involved, and understanding of the indicator by the respondents (Dasgupta et al., 2017). Thus, we identified 39 indicators covering social (16), economic (12), and ecological (11) dimensions of sustainability (Supplementary Table S8). We incorporated these 39 indicators in a data collection instrument and pre-tested them on non-sampled integrated farms before the final data collection on 140 integrated farms. These indicators were standardized using max-min standardization, winsorized (to manage outliers), weighted, and aggregated to develop a composite sustainability index (SI) (OECD, 2008; Goswami et al., 2017). We employed principal component analysis on the dataset and used factor loadings of the principal components for weighing individual indicators. Finally, we aggregated the weighed indicators linearly to develop a composite sustainability index. The index value ranged from 0 to 100, “0” being the lowest and “100” being the highest possible value (Supplementary Section S3; see Supplementary Table S9 for comparison of sustainability indicators across farm types).

Farm families of the study locations identified 10 types of distinct resources/farm components, namely Rice field (R), Vegetable plots (V), Cattle (C), Poultry (PL), Pond (PN), Homestead (H), Tree (T), Kitchen (K), Common property resources (CP), and Fallow land (F) before the actual data collection. We considered the presence of a resource interaction (RI) on the farm when a perceived flow of energy or matter or sharing of space between any two of these 10 resources existed. We ascertained such existence in consultation with the respondents coupled with farm visits and measurements. We recorded the RI in a 10x10 binary matrix for all 140 farms. Thus, there were 140 RI networks and 140 binary matrices. In graph-theoretic parlance, a node in the RI network represents a resource/farm component, and a directed tie represents the interaction between two nodes. Based on the matrices, we generated two types of network information for individual farms: First, we identified the linkage, reciprocal linkage, triads, and presence of a resource/farm component at the core of the RI network (Borgatti and Everett, 2000) to understand the structural composition of the farm resource interaction. Second, we computed different network properties of individual farms, namely density, component ratio, connectedness, fragmentation, compactness, dependency ratio, Weiner index, closure, transitivity, clustering coefficient, and arc reciprocity, to understand the nature of resource interaction in the farms (Supplementary Table S10). We used UCINET for Windows software (Borgatti et al., 2002) for matrix manipulation and analyses of the farm RI's structural composition, i.e., the ties, reciprocal ties, triads, and presence at the core. We used the same software for the computation of the network properties of RI. The structural compositions were then related to farm sustainability and farm types in a graph-theoretic layout using NetDraw software (Borgatti, 2002). NetDraw was also used for the visualization of the co-occurrence of RI.

We examined the relationship between RI and farm sustainability following two approaches. First, we developed a two-mode network (network involving both the resources and individual farms) of 140 RI networks and visualized it in the graph-theoretic layout. This helped to identify the RI motifs associated with highly sustainable farms. Then, to study the co-occurrence of RI motifs on individual farms we converted the two-way networks into one-way networks (considering RI motifs as the nodes) and visualized them in a metric multi-dimensional layout. The proximity of RI motifs denoted their higher tie strength and thus a higher probability of co-occurrence. The RI motifs that were associated with highly sustainable farms and co-occurred on the same integrated farms were identified as the critically important motifs for achieving farm sustainability.

Second, we used two extracted principal components from 11 network properties of 140 farms to explain their sustainability score (Supplementary Tables S11, S12). Using SPSS Modeler 18.1 (IBM_Corp, 2016), we employed 12 models together, and the output is based on the three best-performing models in terms of their correlation value and relative error (Supplementary Table S13). The relationship was also examined separately for all five farm types to examine whether it held across farm types.

We identified five farm types using a sequence of principal component analysis (PCA) and hierarchical cluster analysis (CA) to reduce the heterogeneity of smallholder systems and created socio-ecological boundaries within which resource management could be understood better (Kansiime et al., 2018) (Supplementary Information details the typology delineation and characterization in Supplementary Tables S1–S6, Supplementary Sections S1, S2). Farm type-1 (22 no., 15.71% of farms) were resource-rich extended families who employed low-to-moderate input intensity and demonstrated moderate-to-high system yield and system profitability in their farms. Farm type-2 (28 no., 20% of farms) were resource-poor extended families, who achieved high system yield by employing high input intensity and family labor. Farm type-3 (33 no., 23.57% of farms) were resource-poor feminized subsistence farms that diversified with livestock and non-farm incomes, used low input intensity in farming, and received moderate system yield and low system profitability. Farm type-4 (35 no., 25% of farms) was predominated by resource-poor and marginalized tribal nuclear families, who survived on off-farm wages, used low input intensity on their farms, and achieved moderate system yield and low system profitability. Farm type-5 (22 no., 15.71% of farms) was resource-poor, profit-oriented nuclear families, which diversified with livestock, earned little or no off-farm income and employed moderate management intensity to maintain moderate system yield and profitability. A summarized qualitative description of farm types is given as Supplementary Information (Supplementary Figure S3; Row 1, Supplementary Table S7).

We assessed the sustainability of 140 farms by a composite index built on 39 indicators covering social, economic, and ecological dimensions of sustainability (Supplementary Table S8). The mean sustainability score for FT-1 was highest, followed by FT-2, FT-5, FT-3, and FT-4 (Figure 1A). The resource-rich large families (FT-1) fared better than other farms in terms of multifunctionality, balanced soil reaction, contact with extension functionaries, lower cost of production, availability of cereals, and adoption of sustainable agricultural practices (Figure 1B). FT-2 closely followed FT-1 in all the above indicators and came next to highest in terms of women's engagement as family labor, family dependency ratio, women's access to farm resources, use of family labor in farming, lesser soil salinity, tree species diversity, per-capita income, the proportion of irrigated land, system profitability, use of organic manure, and rice equivalent yield. FT-5 followed FT-1 or FT-2 in terms of several indicators and emerged next to the highest in livestock index and distance to the road. FT-3 fared best in terms of Nitrogen, Phosphorus, and Potassium (NPK) use, pesticide use, distance to market, access to financial institutions, use of indigenous knowledge and per-capita food availability, apart from being second best in terms of livestock index, training, availability of cereals, and soil fertility. FT-4 fared well in terms of income diversity and soil fertility; they emerged second best in terms of distance to market, NPK use, pesticide use, and use of indigenous knowledge. An explanatory note on the rationale of abovesaid characterization (Supplementary Section S2, Supplementary material) and a summarized description (Row 2, Supplementary Table S7) are given as Supplementary material. An explanatory scheme shows sustainability regimes of different farm types concerning their assets and capabilities for a better comprehension of the readers (Supplementary Figure S4).

We examined the abundance of four types of RI motifs, namely linkage, reciprocal linkage, triad, and presence (of a resource) at the core (see definitions in Supplementary Table S10) in five identified farm types (Figure 2) to characterize them in terms of these interactions. The heatmap cells represent the proportion of farms under individual farm types having a specific RI motif. Both FT-1 and FT-2 are characterized by R- (Rice->Cattle), H-(Homestead->Tree), and V (Vegetables->Poultry) based linkages, R-based reciprocal linkages (Rice <->Cattle), R- and V-based triads (ΔRice <->Cattle <->Homestead), and presence of R and V (R, V, and C for FT-2) at the core of RI network. Although the abundance of RI is similar in FT-1 and FT-2, the difference primarily exists in the magnitude of their abundance. Also, in FT-2, the importance of C and the use of CP and F are unique. Unlike FT-1 and FT-2, FT-3 is characterized by linkages involving diverse resources such as R, H, V, PL, PN, and C; predominantly H, PL, PN, and V-based reciprocal linkages; R, V, PN, PL, and H-based triads; and the presence of H and V at the core of the RI networks. FT-4 shows fewer linkages, reciprocal linkages, and triads, and features the presence of H at the core of the networks. FT-5 is characterized by a smaller number of diverse linkages involving R, H, and C, very few reciprocal linkages and triads, and the presence of R, V, and C at the core of the RI networks. Overall, FT-1 and FT-2 employed similar resource integration strategies centering around R, H, and V, with FT-2 integrating C and V slightly more than FT-1. FT-3 used diverse resources for interaction—centering around H—that could spatially accommodate V, PN, PL, C, and K due to their physical proximity. For FT-4, the paucity of resources and dependence on off-farm income might have resulted in a lack of resource interaction on their farms. FT-5, on the other hand, showed a diverse but non-predominant nature of resource interactions centering on rice fields (R), homesteads (H), and cattle (C) (see Row 3, Supplementary Table S7 for a typology-wise detailed description).

We examined the relationship of RI with farm sustainability by examining the proximity of discrete RI (squares) with the sustainable farms (larger circles, area scaled by farm sustainability score) in a graph theoretic layout of the two-mode RI-farm network (see Supplementary Figures S5a–S5d; an explanatory description is given in Section S4) and identified the discrete RI associated with highly sustainable farms (Row 4, Supplementary Table S7). Scrutiny of the farms in the ninth decile of the sustainability score provided a hint of how the highest sustainability was achieved, irrespective of farm types, by using specific RI motifs and not others (Figures 3A–D; Row 1, Table 1). Scrutiny of Row 1 in Table 1 and Row 4 in Supplementary Table S7 (and Figures 3A–D and Supplementary Figures S5a–S5d) shows a high commonality of RI associated with sustainable farms. This indicates that higher sustainability was achieved by a small number of unique RI motifs in individual farm types. Summarily, we found that farms achieved higher sustainability by having R-, V, C-, PN-, PL-, H-, and K-based linkages; R- and PN-based reciprocal linkages; R-, V-, PN-, K-, and H-based triads; and presence of R, V, C, K, PN, and PL at the core.

We also studied the co-occurrence of RI motifs, meaning the simultaneous occurrence of RI motifs on the same farm. We performed the co-occurrence study for two reasons—first, the co-occurrence of resource interaction on a farm is expected to be more stable because of its possible interdependence tested by the farmers. Hence, studying them gives us an idea of what RIs go together and stabilize in smallholder systems of a region as a response to the internal and external stimulus of change to the farming systems. Second, in the absence of panel data on farm RI or empirical study on the evolution of regional farming systems, the study of the co-occurrence of RI motifs could suggest the possible evolutionary stage of RI in smallholder systems. Despite the limitation of snapshot data, we can still examine how these co-occurrence patterns of RI gravitated toward highly-sustainable farms. We segregated the co-occurrence of RIs for farms of the ninth decile of sustainability (Figures 4A–D; Row 2, Table 1). These farms, irrespective of their farm types, featured 35 co-occurring linkages, 11 co-occurring reciprocal linkages, 28 co-occurring triads, and the presence of R, V, and PN at the core in terms of their high tie strengths (Row 2, Table 1). This means that these RIs are more closely linked and likely to co-occur on the same farm to achieve high farm sustainability. Summarily, we found that farms achieved higher sustainability by having R-, V-, C-, PN-, H-, PL- and K-based linkages; R- and PN-based reciprocal linkages; R-, V-, PN-, K-, and H-based triads; and presence of R, C, and K at the core. The co-occurrence network for all 140 farms is given as supplementary information (Supplementary Figures S6a–S6d). Notably, a high proportion of co-occurrences (recorded on 140 farms) are retained by the highly-sustainable farms of the highest decile.

Finally, we identified 32 linkages, 11 reciprocal linkages, 21 triads, and three core elements (Row 3, Table 1) that occurred and co-occurred in the highly sustainable farms (of the highest decile), and thus most critical to contribute to farm sustainability. Concrete examples of these critical RI motifs are given in Table 2.

We also explained the sustainability of the sampled farms by the properties of the individual farm's RI networks. We computed 11 network properties (Supplementary Table S10) for all the farms' RI networks and reduced their multicollinearity to two principal components (PC)—“connectedness” (PC1) and “reciprocity and transitivity” (PC2), and used them as the predictors of farm sustainability score. After examining 12 models, we found a model explaining 88.7% of the variance in farm sustainability scores (Figure 5A). We also examined how the model performs within different farm types (Figure 5B) and found the linear correlation for the five farm types to be 0.809, 0.715, 0.638, 0.727, and 0.86. These findings imply that resource interaction within a farm when expressed in terms of its network properties, can explain the farm sustainability measured by 39 multi-dimensional indicators, and this holds significantly true for all farm types.

We also examined the nature of this relationship at different values of PC1 and PC2 separately (Figures 6A, B). We found that farm sustainability increased monotonically with increased PC1 and found two areas of stacked points (farms) (Figure 6A), roughly the boundary of PC1 for one or more type/s of farms. While the first stack is the boundary of PC1 for FT-3 and FT-4, the second stack is the boundary for all other farm types. This indicated that RI, as a result of increased connectedness, could not be advanced by those groups of farms beyond a specific limit, although differential sustainability was achieved by farms of the same type with that same level of connectedness. These boundaries suggest a resource-limiting condition for a large number of resource-poor farms. We also found that PC2 enhanced farm sustainability up to a point and declined after that (Figure 6B). Here, also we find two stacks of farms—first, the highly-sustainable farms of FT-1, FT-2, and a few farms from FT-5; second, the poorly-sustainable farms of FT-3 and FT-4. We anticipate that highly-sustainable farms do not need to engage in many reciprocal and transitive RI on their farms since they could achieve substantial sustainability with one-way connectedness and do not need to move further toward the right of the x-axis. On the other hand, the second stack of farms has limited resources, which are located close to each other and easily linked resources (enhancing their reciprocity and transitivity). However, this could lift only a smaller proportion of farms above-median sustainability (Figure 6B).