In order to capture the diversity among farms considering AEI practices, 120 farm households were selected in a first round of interviews using the snowball and maximum variation sampling approach. Thus, farmers and/or key informants were interviewed to identify very and less diverse farms in their neighborhoods to capture the conventional as well as rarely adopted AEI practices. In total, 60 households each were visited in Lwamata sub-county in Kiboga district, and Rugaaga sub-county in Isingiro district. During the interviews, a preliminary questionnaire was used, to collect both qualitative and quantitative information on farm, farm location, and household and farm management, including the farm, household and livestock size, number of cultivated crop species, number and type of applied agro-ecological practices, and the production orientation, constraints and objectives.

Sixteen potential key variables were selected to cluster the farms according to their AEI level (Table 1). As in Alvarez et al. (2018), multivariate statistics, executed in R (version 3.5.1), were used for the typology construction. By drawing pairs plot, boxplots and histograms, the data were checked for missing values and possible outliers, which were subsequently removed. In addition, key variables with a non-normal distribution were transformed to a more normal distribution. Out of the 120, 112 households were retained and the logarithm (log₁₀) and square root function applied to the variables “farm size” and “tropical livestock units,” respectively. Tropical livestock units (TLU) were calculated according to FAO guidelines (Otte and Chilonda, 2002), using the conversion factors : cattle = 0.70, pigs = 0.20, sheep and goats = 0.10, and chickens = 0.01. These factors were multiplied by the number of each animal species present on farm and summed up to come up with the final TLU value. The transformed variables are represented by the codes area2 and tlu2, respectively.

In order to reduce the number of key variables into non-correlated dimensions, the Factor Analysis of Mixed Data (FAMD) was executed with the packages “factoextra” (version 1.0.5) and “FactoMineR” (version 1.41). However, highly correlated key variables resulted in a poor outcome of the factor analysis. Therefore, key variables with the lowest contribution to the dimensions were omitted during several rounds of analysis, until only seven variables were kept for the final grouping. These variables included five quantitative (farm size, tropical livestock units, number of cultivated crop species, number of applied AEI practices, number of agroforestry species) and two qualitative variables (farm location and farmer's objectives). To determine the number of dimensions kept in the analysis the Kaiser criterion was used, to keep only the dimensions with an eigenvalue larger than one. The remaining dimensions were used for further analysis to classify the farms into different groups.

The clustering analysis was performed by the HCPC function (Hierarchical Clustering on Principal Components) from the “FactoMineR” package (version 1.41). This function starts with assigning every observation to its own cluster and subsequently merges the two most similar clusters until only one cluster is left (Crawley, 2013). The optimal number of clusters was found by using Ward's method, which maximizes both intra-cluster homogeneity and inter-cluster heterogeneity (Murtagh and Legendre, 2014). In order to identify the variables that characterized the different clusters, boxplots were drawn for the quantitative variables and statistical significances between the different clusters were detected with the pairwise Wilcoxon test. Moreover, a classification tree was built using the R package “rpart” (version 4.1–13). The Margalef index (M), representing species richness, and Shannon index (H), representing both species richness and evenness, were calculated for each identified cluster, based on the following formulas, respectively:

where S is the number of crop species present on farm, A the total farm area (m²) and p_i the area proportion of crop i.

In order to calculate the performance of each farm type and reveal windows of opportunities for farm optimization, we used the FarmDESIGN model (Groot et al., 2012; Ditzler et al., 2019). Three farms from every cluster, identified by the farm typology, were selected for a second round of interviews. This selection was based on the willingness of the farmer to participate and on the quality of the information provided by the farmer during the previous interview. Additionally, farmers as close as possible to the cluster centers, as identified by the HCPC analysis, were selected. Then, a more detailed questionnaire was used, which captured necessary input variables for the FarmDESIGN model, including household and herd composition, and for each crop, crop yield, product destination, cultivation costs, labor requirements and market prices. Additional information such as, data on environmental and crop characteristics, like soil type and climatological conditions, N fixation and nutrient composition was obtained from secondary data available within the FarmDESIGN model or from literature (Gutteridge and Shelton, 1994; Groot et al., 2012; Kongkijthavorn, 2017; de Jager, 2018; HarvestPlus, 2018; USDA, 2018; World Agroforestry Centre, 2018a,b,c).

Besides being able to calculate the performance of the original farm, the FarmDESIGN model can explore redesigns that outperform the original farm by using a multi-objective Pareto-based Differential Evolution algorithm. Considering as well-objectives as constraints, the performance of Pareto-optimal redesigns cannot be improved without compromising one of the other objectives (Groot et al., 2007). For every run, the number of iterations was set at 1,000. We wanted to maximize operating profit, dietary energy yield, vitamin A yield, iron yield and to improve the farm sustainability by minimizing N losses and soil erosion (objectives). Constraints were set so that the total crop area could not increase and that each fruit species could occupy maximally 0.4 ha. Redesigns varied in the area allocated to each (mixture of) crop(s) and destination of the crop products and residues (decision variables). A summarizing table listing the objectives, decision variables and constraints used for the FarmDESIGN model is given in Table S1. In addition, two scenarios were created, in which Calliandra calothyrsus (as hedge row) and Mucuna pruriens (as cover crop) were each separately introduced on farm to evaluate the effect on farm performance.

Each time the FarmDESIGN model was run, it generated 800 Pareto-optimal redesigns. Those redesigns which outperformed the original farm in all objectives were selected. As trade-offs between objectives made it impossible to reach the best performance for each indicator simultaneously, objectives had to be ranked to select the most optimal redesign. In this study, profitability was prioritized, followed by soil quality and nutritional yield improvement. As postulated by Kansiime et al. (2018), it is believed that higher incomes allow on-farm investments, which in turn can lead to increased soil quality, if the right investments are made, and hence improved sustainability.

The operating profit was calculated by subtracting both variable (for labor, manure, fertilizer and other inputs) and fixed costs (for land) from the crop and animal product revenues. To calculate the nutritional yield, expressed in persons/ha/year, the nutrient supply of the products, annually produced on one ha of land, was compared with the recommended daily reference intake multiplied by 365 days. The N balance was computed by considering both N inputs (symbiotic and non-symbiotic N fixation, atmospheric N deposition, and the N content of green manure, animal manure and fertilizers) and outputs (N content of exported crop and animal products, soil erosion and N volatilization) (Groot et al., 2012). Erosion levels were determined for each crop by the soil erosion C factor, defined as the ratio between soil losses on bare soil and those on land cultivated by every specific crop (FAO, 2001). Therefore, soil erosion C factors are dimensionless, ranging from zero to one, whereby low values are assigned to crops which cause limited soil erosion.

Due to time constraints, the outcome of the model runs was discussed with the interviewed farmers in Kiboga only during two focus group discussions. The best redesigns and scenarios were presented to the farmers with slides each representing the composition of the modeled farm, after which farmers opinions were asked.

LI farms were the least intensified of the three farm types. On average, 11.0 out of the 34 AEI practices (Table S2) such as intercropping, integration of agroforestry species, application of kitchen and household waste and manual control of pests and diseases were applied in these farms (Figure 3). Additionally, LI farms were the smallest (1.41 ha; 6.3 household members), with the smallest number of cultivated crop species (11.1) including banana, coffee, maize, beans, cassava and groundnuts. Annual species covered about 49% of the land. Perennials mainly comprised banana and coffee. However, 10% of the land was allocated to trees, i.e., 7% agroforestry species and 3% fruit species (Table S3). While the fruit species [i.e., Artocarpus heterophyllus (jackfruit), Mangifera indica (mango), Persea americana (avocado)] were mainly grown as an additional food source for the farm household, agroforestry species (i.e., Eucalyptus grandis, Maesopsis eminii, Albizia coriaria, Erythrina abyssinica, and Syzigium cuminii) were valued for shade, fodder, mulch, firewood and timber. Hedges, in contrast, were not abundant. If present, hedges were used as a mulch, fodder and/or firewood source. LI farms had a Margalef index, indicating species richness, of 2.32. An index of 0 represents monocultures, while larger indices indicate more species in a determined area or the same amount of species on a smaller area. The Shannon index, a measure of both species richness and evenness mainly ranging from 1.5 to 3.5, reached a level of 2.12, indicating that the relatively high number of species were more or less evenly distributed on farm. Few animals, like chickens and pigs were on farm, resulting in the lowest TLU of 0.45 amongst all farm types. While chickens were free ranging, pigs were tethered in the farmyard. These least intensified farms were mainly located in Kiboga (83.3%) and managed by subsistence farmers who mainly produced for home consumption.

In MI farms, defined as the moderately intensified farms, 13.0 AEI practices were on average applied (Figure 3). Unlike farm type LI, MI farms were the largest (7.57 ha; 7.8 household members). Although about 80% of the total land area was covered by banana, many crop species (18.8), like beans, maize, groundnut and millet, were cultivated mainly as monocrops. Crops grown for home consumption only, such as eggplants, leafy vegetables and pumpkins, were found on a very small to negligible scale, consisting of one or two plants per species and this was reflected by the species indices. The Margalef index was the smallest for all farm types and reached a level of 1.32. Moreover, the relatively small number of species was not evenly distributed (Shannon index = 0.92). Perennials other than banana occupied 1% of the land and included Carica papaya (papaya), Ricinus communis and Eucalyptus grandis. While the former two species were grown within the banana fields, the latter was allocated to a separate field to avoid possible competition for water, soil nutrients and solar radiation with the cultivated crops. Cattle, goats and chickens were managed by the farm household (TLU = 3.32). While cattle and goats were on communal grazing areas during day time and kept in kraals overnight, chickens were found in the farmyard. This resulted in a large availability of animal excreta, which was applied on the banana field(s). In addition to application of farmyard manure on banana fields, kitchen and household waste, mulch and external cow dung were applied and soil and water retention ditches dug. These farms were mainly (98%) located in Isingiro, where farmers had commercial objectives.

Intercropping, integration of agroforestry- and hedge species, application of kitchen and household waste, mulch, manure and even mineral fertilizers were some of the 16.4 AEI practices applied on HI farms (Figure 3). These highly intensified farms had, on average, a size of 2.59 ha (7.6 household members), of which 45% was allocated to annual crop species, such as maize, sweet potato, cassava, beans and tomato. Coffee and banana occupied together about 50% of the total area. Half of the remaining land was covered by agroforestry/hedge species while the other half with fruit tree species (i.e., jackfruit, mango and avocado). Additionally, these farms were characterized by the highest diversity of agroforestry and hedge species, with on average 19.9 and 1.0 species, respectively. The five most occurring agroforestry species were Markhamia lutea (96%), Albizia coriaria (92%), Maesopsis eminii (92%), Ficus natalensis (85%), and Vernonia amygdalina (85% of HI farms). Hedges occurred on 50% of the farms and were used by 77% of these households as a fodder, mulch and/or firewood source. Especially Calliandra calothyrsus and Morus spp. were used for these production objectives. HI farms were highly diverse with a Margalef index of 3.12. Additionally, the relative high number of species were equally divided among the available land (Shannon index = 2.49). As for all farm types, animals were kept on farm. Here, livestock mainly consisted of goats, pigs and chickens, resulting in a TLU of 1.25. While the former two were mainly zero grazed, chickens were free ranging in the farmyard. This type of farmers were all located in Kiboga district, defining themselves as subsistence farmers.

In order to improve the farm performances (profitability, productivity and/or sustainability), redesigns of each farm type were generated by multi-objective optimization by first varying the area allocated to every species, already present on the farm and, hence, without introducing new species. As an illustration, out of the clouds of redesigns, one Pareto-optimal redesign which outperformed the original farm in terms of all objectives was chosen for each farm type (Table 3A). Unlike for farm type MI, whereby all objectives could be enhanced, farm composition changes did not profoundly improve the N balance in farm type LI, while in farm type HI N balance improved but still remained negative. Nevertheless, profits could be doubled and even quadrupled. Also, the nutritional parameters were improved.

To obtain these performances, perennials seemed to be important, covering 54% to 88% of the total farm area (Table 3B). While for farm type LI and MI, banana was the main perennial on farm, agroforestry tree species and other perennials comprised the largest area allocated to perennials on farm type HI. Erythrina abyssinica, Pennisetum purpureum, and Maesopsis eminii were the most prominent perennial species here, comprising each 86%, 4% and 3% of the total area under perennial species other than banana, respectively (data not shown). Considering annuals, cassava occupied the largest area in all redesigns (56, 22, and 43% of the total area under annuals on farm type LI, MI, and HI, respectively). The rest of the area was mainly allocated to maize, tomato, peas and cabbages. The detailed composition of the original farm types and the best redesigns can be found in Tables S3, S4, respectively.

For a given farm type, the model generated a wide range of redesigns (Table 4A), allowing farmers to choose a redesign in line with their own preferred ranking of objectives. However, trade-offs between objectives impeded the existence of compositions which performed better for all objectives simultaneously than the original farm composition. Increased nutritional yield, for instance, was related to a reduced N balance. Likewise, a positive N balance on farm type HI was associated with a lower operating profit. Moreover, the variation of the performance was not equally large for all farm types. For farm type LI, only three better performing but similar redesigns were identified by the model.

Similar to the best performing composition (Table 3) perennials accounted for more than 50% of the total farm area in these redesigns (Table 4B), with at least 80% of land allocated to banana on farm types LI and MI. In contrast, agroforestry tree species, specifically E. abyssinica accounted for the largest area under perennials on farm type HI. To increase the area under perennials, the area under annuals had to decrease in most cases. Major annual crops were cassava, maize and beans on farm type LI, cassava, tomato, groundnuts, beans and peas on farm type MI and cassava and cabbages on farm type HI (data not shown).

Besides changing the compositions of the initial components, new species, which potentially reduce the dependency on external inputs, can be added to the model to investigate their effect on the farm performance. In a first scenario Calliandra calothyrsus, a N fixing species with high biomass production (8.5 tons DM/ha/year; Kongkijthavorn, 2017), was integrated as a hedge around farmers' fields in the model. Explorations by the FarmDESIGN model revealed that with exception of the N balance for farm type LI, all redesigns with C. calothyrsus outperformed the original farm type for all objectives considered (Table 5A). Again, perennials played a key role (Table 5B): i.e., banana on farm type LI and MI, occupying 80% and 87% of the total area, respectively, and other agroforestry species on farm type HI, covering 52% of the total area. Here, E. abyssinica was the most prominent, comprising 91% of the area allocated to agroforestry species. Important annuals were cassava on farm type LI, tomato and Solanum potato on farm type MI and cabbages and sweet potato on farm type HI, covering 69, 27, 13, 18, and 18% of the area allocated to annuals, respectively (data not shown).

In a second scenario, the N fixing cover crop Mucuna pruriens was integrated below the banana canopy on farm type MI. This introduction alone, without changing any of the current farm components, reduced soil erosion and farm profitability by 5% and tripled the N balance.