Introduction

Farm household systems are agro-ecosystems in which rural households are a central component. Diverse and integrated farm household systems are often associated with sustainable agro-ecosystems (Dalsgaard and Oficial 1997), because diversity and integration enable the realisation of complementarities between different activities and may improve resource use efficiencies. Diversity in farming activities may increase income stability and reduce income risks of resource-poor households (Ellis 2000; Niehof 2004). Integrated farm household systems use the outputs of one activity as inputs in another activity, which may reduce adverse effects to the environment and decrease the dependency on external resources through recycling (Edwards et al. 1993; Vereijken 2002). Cycling of energy and nutrients are considered two of the most important features that confers stability to ecosystem functioning (Allesina and Ulanowicz 2004).

In practice, diversity and integration are still poorly defined and, although there have been several studies that focus on integrated agro-ecosystems (Prein 2002; Pant et al. 2005), there is no practical method to characterise, quantify, and assess integration of diverse agro-ecosystems. We define integration in agro-ecosystems as the degree to which the compartments (or activities in such systems) are interconnected by flows of material. In agro-ecosystems that are diverse, the number of options for flows of material is larger than in relatively simple, often specialised non-diverse agro-ecosystems. We introduce and apply network analysis (NA) to quantify the degree of integration and diversity of farm household systems using a set of indicators. NA is basically an input–output analysis originally developed in economics (Leontief 1951) that was introduced into ecology by Hannon (1973) to quantify relationships within ecosystems (Fath and Patten 1999). Leontief developed input–output analysis to estimate the amount of materials needed to produce a certain quantity of goods. It is applied in systems analysis, which conceptualizes systems as networks of interacting compartments exchanging resources. In farm household systems, it may be used to analyse input–output relationships among different compartments or household activities. The flow analysis of Finn (1980), belongs to the early developments of NA where it was used to study throughflow of nutrients or energy, and cycling in ecosystems. The Shannon index, derived from communication theory (Shannon 1948), was introduced in ecology by MacArthur (1955) to evaluate flow patterns in ecosystems. Later, Rutledge et al. (1976) introduced another measure of communication theory, i.e. the average mutual information (AMI) to study the organisation of nutrients and energy flows in ecosystems. AMI has been proposed by Ulanowicz (1980, 1997, 2001) to measure systems organisation, and how the structure of the flows in an ecosystem is refined to increase autocatalysis (Odum 1969). Since the earlier developments of NA, there have been several applications to study ecosystem properties (e.g. Baird and Ulanowicz 1993; Christian et al. 1996; Heymans et al. 2002), but seldom to study agro-ecosystems (e.g. Fores and Christian 1993; Dalsgaard and Oficial 1997; Groot et al. 2003).

The objective of this study was to assess the potentials and limitations of NA to evaluate integration of diverse agro-ecosystems, specifically indicators of flow analysis (throughflow, throughput and cycling) and indicators from communication theory (i.e. measures of organisation and diversity) are addressed. We introduce the method, the system conceptualisation and the indicators using theoretical examples to illustrate their meaning. Then we present a case study from the highlands of Northern Ethiopia where the method was applied, and the consequences of different management options for the degree of integration and diversity were explored. We end the article with conclusions on the appropriateness of the indicators to characterise diversity and integration of agro-ecosystems.

Materials and methods

Network analysis of nutrient flows

The NA uses matrices built with the resource flows of the systems under study, and a number of indicators. The resource flows characterise the organisation of the system. In this study, we use flows of nitrogen (N) to perform the NA because this resource is often the most limiting production factor in low-input agriculture, and it can—to a large extent—be managed by farm households. The selection of the system boundary depends on the purpose of the study. In the application presented later the system definitions were defined by the resource base of the farm household, which consists of a number of compartments that interact. We used one year as the temporal unit of analysis, because this is a common time horizon for agricultural production.

Conceptualising the system

After having defined the boundaries of the system/network, the next steps in NA are to define the n compartments, and to quantify their interactions (N flows). For farm households, compartments are defined as farming activities that contribute directly (e.g. provide food) or indirectly (e.g. through cash income) to the consumption of the farm household and have an impact on the N resources (Langeveld et al. 2008). Farming activities can be characterised in terms of N inputs and N outputs of which the latter can be used in other farming activities or can be exported from the system.

Indicators from network analysis to assess integration

In this section the indicators used to assess size, activity and cycling in ecosystems (Finn 1980) are explained using a theoretical example of a simple network, i.e. a system with two compartments (H1 and H2), for which storage (x 1, x 2) and flows are quantified (y 01, z 10, f 12, f 21, y 02, z 20) (Fig. 1). This system is characterised by the following elements: H i is the compartment i, \( \dot{x}_{i} \) is the change in the storage of compartment H i , y oi is the outflow from compartment H i to the external environment, z io is the inflow from the external environment to compartment H i , and f ij is an internal flow from compartment H j to compartment H i . The flows are expressed in kg N year−1, and storage and the size of the compartments in kg N. Nitrogen flows move from one compartment (j = 0, …, n) to another (i = 1, …, n, n + 1, n + 2), where n + 1 accounts for usable exports (e.g. grain, milk) and n + 2 accounts for losses (e.g. animal excreta in pastures, human excreta). Here compartment j = 0 is used to keep track of the imports. We use the convention of usable (n + 1) and unusable export or losses (n + 2) from Hirata and Ulanowicz (1984). Storage in a compartment is an estimation of the amount of N contained in the total human and animal mass (expressed as kg N per compartment) while for cropping activities or field compartments storage is an estimation of the amount of N contained in the top soil layer (e.g. 0–30 cm), also expressed in kg N per compartment.

Fig. 1
figure 1

System representing a network with two compartments H1 and H2, and their respective storages x 1 and x 2, the internal flows f 12 and f 21, and exchanges from (z10 and z20) and to the external environment, (y01 and y02). The rectangular box defines the system boundaries. Source: Finn (1980)

Based on this conceptualisation of the network, Finn (1980) developed a number of indicators that characterise N flows in the system:

Imports (IN) is the amount of N that is imported from the external environment into the system (Eq. 1).

$$ {\text{IN}} = \sum\limits_{i = 1}^{n} {z_{{i{\text{o}}}} } $$
(1)

Total inflow (TIN) into the system is the sum of N flows from external inputs (z) into all n compartments plus the amount of N contributed to the system total flows by the storage of all compartments \( \left( {\dot{x}_{i} } \right) \), i.e. negative changes in the storage (Eq. 2).

$$ {\text{TIN}} = \sum\limits_{i = 1}^{n} {z_{{i{\text{o}}}} - \sum\limits_{i = 1}^{n} {\left( {\dot{x}_{i} } \right)_{ - } } } $$
(2)

These definitions take the input perspective (Finn 1980), and are used to assess whether a network accumulates or loses material.

Throughflow (T i ) is the total flow from other compartments to compartment i (f ij ) plus the inflow from the exterior (z) and the N flows contributed by the storage of compartment H i (the negative changes in storage \( {\dot{x}_{i} } \)) (Eq. 3). This definition takes the input perspective.

$$ T_{i} = \sum\limits_{j = 1}^{n} {f_{ij} } + z_{{i{\text{o}}}} - \left( {\dot{x}_{i} } \right)_{ - } $$
(3)

Total system throughflow (TST) is the sum of all the T i in the system (Eq. 4). It represents the N pool within the system that contributes to the production or activity. The ratio IN/TST is an indicator of dependency of the system on external inputs.

$$ {\text{TST}} = \sum\limits_{i = 1}^{n} {T_{i} } $$
(4)

Path length (PL) is the average number of compartments that a unit of inflow passes through (Eq. 5). It is a measure of the cycling intensity within the system. Part of the nutrients entering the system may flow through one or more compartments and leave the system, while another part may be recycled repeatedly before leaving the system.

$$ {\text{PL}} = \frac{\text{TST}}{\text{TIN}} $$
(5)

Throughput (T ..) is the sum of all flows in the system (Eq. 6).

$$ T_{..} = \sum\limits_{i = 1}^{n+2} \sum\limits_{j = 0}^{n}{T_{ij} } $$
(6)

Each flow f ij can be expressed as a fraction \( q_{ij}^{ * *} \)of the total flow (T j ) leaving the compartment H j , then throughflow can be expressed as:

$$ T_{i} = \sum\limits_{j = 1}^{n} {q_{ij}^{ * *} T_{j} } + z_{{i{\text{o}}}} - \left( {\dot{x}_{i} } \right)_{ - } $$
(7)

Expressed in matrix form:

$$ T = Q^{**} T + z - \left( {\dot{x}_{i} } \right)_{ - } $$
(8)

where Q** is a matrix with the \( q_{ij}^{**} \) elements, T is a column vector of throughflows, z is a column vector of inflows and (x i ) is a vector of negative state derivatives. Solving for T gives:

$$ T = [I - Q^{**} ]^{ - 1} \left[ {z - (\dot{x}_{i} )_{ - } } \right] $$
(9)

where I is the identity matrix, the matrix [I−Q**]−1 is called N**, whose i, j element indicate the flow in H i due to an unit of flow starting in H j . Cycling efficiency (RE i ) (Eq. 10) is the fraction of throughflow (T i ) that returns to the compartment H i , and it can be found by examining the diagonal of matrix N**. The element n** ii represents the flows generated by a unit of flow that started in H i .

$$ {\text{RE}}_{i} = \frac{{n_{ii}^{**} - 1}}{{n_{ii}^{**} }} $$
(10)

The Finn’s cycling index (FCI) is the proportion of TST that is recycled (Eq. 12) within the system. FCI is calculated by dividing the relative cycling efficiency of all compartments (TSTc) (Eq. 10) by the total TST (Eq. 11). It yields values between 0 and 1, indicating either no recycling or complete recycling.

$$ {\text{TST}}_{\text{c}} = \sum\limits_{i = 1}^{n} {{\text{RE}}_{i} T_{i} } $$
(11)
$$ {\text{FCI}} = \frac{{{\text{TST}}_{\text{c}} }}{\text{TST}} $$
(12)

See Finn (1980) for more details on the calculation of the flow analysis indicators. We use the indicators FCI, PL and the relationship between IN/TST to assess integration in agro-ecosystems, because according to our definition (see “Introduction”) a more integrated system shows more internal recycling and less dependency from the external environment. Additionally, the ratio of TST/T .. can be used to characterise the role of the storage in the compartments to the system total flow.

The analysis focused on N flows associated with management decisions and controlled by farmers, such as the imports of N through fertilisers or food and the exports to the market in harvested products. We did not estimate the size of flows such as N leaching, volatilisation, runoff, wet deposition, N2-fixation or redistribution of nutrients at the farm and landscape level. Information related to the size of these flows is difficult to obtain at the farm scale. The assumption was made that these flows do not largely differ for the studied farm households. Clearly, omission of these flows may affect the contribution from and to the soil N storages, and losses to the environment.

Illustration of integration indicators

Here, we present examples of different systems with four compartments to illustrate the calculations of the indicators and to facilitate their interpretation (Fig. 2A, B). Systems A and B receive both inputs from the external environment (IN). For system A the total inflow (TIN) is five, and for network B it is four. Comparing IN and TIN allows to assess whether a system accumulates or loses material because TIN combines the external input (IN) with the changes in compartment storage needed to support the total network flow. In these systems TIN and IN are the same because the compartment storages do not contribute to the network flows. Both systems do not accumulate or lose material; they are in a steady-state as storage x i  = 0 and total inflows (TIN) and imports (IN) are equal. The ratio IN/TST shows that system A depends more on imports to support the system activity (TST) than system B. The total system throughflow (TST) is the sum of all material flowing through the system compartments, while the T .. sums all inputs and outputs flowing from and to all system compartments. System B differs from system A in that imports are smaller and recycling is larger. As a result, the ratio TST/T.. is larger for B than for system A, which means that the storage compensates for the difference between inputs and outputs. As an example the detailed calculations of FCI (Eqs. 112) for system A (Fig. 2) are presented in Table 1.

Fig. 2
figure 2

Examples of four systems with four compartments to illustrate the calculations of the indicators and to explain their interpretation. Flows are represented by the arrows and storage is indicated between brackets. N flows in systems A and B are in steady-state with no change in storage (\( {\dot{x}_{i} } = 0\)) and total inflows (TIN) and imports (IN) are equal. Systems C and D are not in steady state with a negative change in storage (\( {\dot{x}_{i} } < 0\)), imports (IN) = 0 and differ from total inflows (TIN) which are supported by the change in storage (see “Illustration of integration indicators” for further explanation)

Table 1 Flow matrix for the network shown in Fig. 2A

Systems C and D are not in steady-state and the change in storage is negative in all compartments. External inputs (IN) are zero and the total inflows (TIN), which are supported by the change in storage, are in both cases four. These systems export material to the external environment. System D recycles more material than system C, which increases the ratio TST/T.. because part of the activity in the network is supported by cycling and not only by the change in storage. An increase in PL is associated with an increase of cycling (Fig. 2C, D).

Indicators to assess diversity

Diversity in farm household systems may be assessed straightforwardly from the number of farming activities, equivalent to assessing species richness in ecosystems. This is, however, rather limited because different compartments/activities use different types and amounts of resources (e.g. land, fertilisers) to produce plant or animal products that contribute differently to the household consumption.

The Shannon index (Shannon and Weaver 1949) is the most common index used to assess (bio) diversity (Clergue et al. 2005) (Eq. 13).

$$ S = - \sum\limits_{i} {p_{i} \log_{2} \left( {p_{i} } \right)} $$
(13)

where p i is the fraction of flow \( \frac{{T}_{i}}{{T}_{..}} \). The Shannon index (Eq. 13) sums over all ith linkages in the system, and it quantifies the diversity of the network connections. When a flow T i is a large proportion of T .. then log (p i ) is close to zero, and the contribution of that flow to the system diversity is small. This happens in systems with few compartments, where the flow of one compartment dominates T ... Such systems have a low diversity in their flows network.

The Shannon index was further elaborated to study how the pattern of flows is refined or organised in a network (Rutledge et al. 1976; Ulanowicz 1980). The diversity in network connections is not necessarily used to its full extent. Mageau et al. (1998) defined the AMI as: “… a measure of the information we have regarding the exchange of material within the system. If material from any compartment had the equal chance of flowing into any other compartment, then we have no information regarding the flow in the network. If all material from one compartment was transferred to only one of the potential recipients, we would have complete information regarding the flow structure”. AMI quantifies the organisation of the flows in the network (Eq. 14). In the log part of Eq. 14, the conditional probability that a flow entering i comes from j is quantified. That probability is the fraction of the flow T ij to all flows that enter T i , divided by the product of the fraction of T i to total flows T .. and T j to total flow T ... Each of these conditional probabilities are weighted by the joint probability of that flow (T ij /T ..), and these weighted ‘constraints’ are summed over all combinations of i and j in the network. For example, in a system where the total flow is divided equally among all compartments, and all compartments are connected, AMI will be zero or very close to zero. If few flows, which are a large proportion of T .., connect few compartments, the value of AMI will approach its upper boundary.

$$ {\text{AMI}} = k\sum\limits_{i = 1}^{n + 2} {\sum\limits_{j = 0}^{n} {\frac{{T_{ij} }}{T_{..}}} \log_{2} \frac{{T_{ij} T_{..}}}{{T_{i.} T_{.j} }}} $$
(14)

Statistical uncertainty (H R) is the upper boundary for AMI, it is the Shannon-diversity (Eq. 13) of flows given a certain value of T .. (Eq. 15). When the contribution of the flow out of a compartment (T .j ) to total system T .. is small and different across compartments, diversity increases. H R increases when T .. is partitioned among a greater number of flows.

$$ H_{\text{R}} = - \sum\limits_{j = 0}^{n} {\frac{{T_{.j} }}{T_{..}}\log_{2} \frac{{T_{.j} }}{T_{..}}} $$
(15)

AMI/H R is the proportion of diversity that is reduced by the actual pattern of flows. This may be used to evaluate the organisation of N flows to total diversity of the network connections. The units of AMI and H R are bits and the scalar k = 1 for AMI. For more detail on AMI and its derivation we refer to Ulanowicz (2001) and Latham and Scully (2002).

Illustration of diversity indicators

In Fig. 3 two groups of three systems are presented to show the meaning of AMI and H R . T .. is kept constant to show differences in organisation of the flows reflected in changes in AMI, and in diversity shown in changes in H R. In the first group (Fig. 3A–C), the diversity of flows changes slightly because the contribution of each of the flows (T .j ) to T .. changes little from system A to system C. However, AMI increases considerably from A to C, reflecting a selection of flow paths from almost all connections possible in system A to very few in system C. This happens when e.g. the most efficient path is selected for nutrient flows.

Fig. 3
figure 3

Examples of six systems with four compartments to show how simplification of flow patterns decreases diversity and increases the information content in networks. Flows are represented by the arrows, and the size of the flows is indicated next to the arrow, except for system A, where all flows equal one. From system A to C, flows become less random and therefore organisation increases. From system D to F diversity decreases, and because the flow network is simple, AMI approaches H R. (See Sect. “Illustration of diversity indicators”)

In the second group of systems (Fig. 3D–F), the diversity of flows in the system changes due to differential contribution of each compartment to total flows. System D is less diverse than system A (each compartment contributes similar amounts to total flows), but the network of flows is more constrained, many flows of system A are eliminated in system D, and therefore the value of AMI increases. In system E, the contribution of the compartments to total flows is not uniform, diversity decreases and AMI is relatively high because of the limited number of connections between the compartments. In system F, diversity decreases further, and because the total flows are dominated by one compartment, i.e. the ratio of AMI/H R is high.

In practice, AMI and H R can be used to assess nutrient allocation between activities and resulting efficiencies. It is expected that in specialised systems, H R will be relatively low and AMI will be close to H R. These adapted systems use the most efficient paths. In less specialised and more diverse systems AMI will be smaller. These systems are more adaptable, and may keep several (more inefficient) network connections active as a risk management strategy.

Application to mixed farm household systems in Ethiopia

In this section, we aim at gaining understanding on how the diversity in flow patterns relates to integration by using the proposed indicators.

The study area

The method was applied to farm household systems of the village Teghane (13°45′N, 39°41′E), Atsbi Wonberta district in Northern Ethiopia. Average farm size is about 0.5 ha and most households grow cereals for subsistence and legumes (faba beans, common beans). Steep slopes, stony soils, frost-risk during part of the year and seasonal rainfall constrain agricultural production. Average annual rainfall is 540 mm, of which most is concentrated in a period of only 75 days (from June to September). Livestock (dairy and beef cattle, donkeys, and sheep) graze on communal pastures and are fed crop residues and other grasses cut and carried to the farm.

Data collection and processing

During the 2002 growing season, a farm household survey was conducted in Teghane as part of the research programme ‘Policies for Sustainable Land Management in the Ethiopian Highlands’ sponsored by the Dutch ministry of foreign affairs (DGIS). During a rapid diagnostic appraisal, farmers in Teghane (n = 50) identified three household wealth classes based on land, livestock and labour (Mulder 2003; Abegaz 2005). The poor households had no or few livestock and little land, the medium wealth households had at least one ox, one donkey and few sheep, and usually a labour surplus, the wealthier households had several oxen, some cattle, donkeys and sheep and they were most of the time food self-sufficient. We used three farm households, each representing a typical wealth class (Table 2).

Table 2 Main characteristics of three types of farm household systems from Teghane, Ethiopia representing three different wealth classes, i.e. poor, medium wealth and wealthy

Detailed information on household composition and consumption, farm and fields characteristics, input use to different activities, flows between activities, crop yields, animal production, sales and input and output prices were collected using the participatory NUTrient MONitoring (NUTMON) approach (De Jager et al. 1998; Van den Bosch et al. 1998). The combination of farm household surveys, field observations and measurements, and simple models provided the basis for the NA application. Intake and excretion of the livestock was estimated using a model that uses as inputs animal type, size, grazing time and feed availability (Vlaming et al. 2001). To quantify N flows we used conversion coefficients obtained from analysis of plant and soil samples taken during the survey and for those flows that were more difficult to quantify we used conversion coefficients from the literature (Table 4 in Appendix). A more detailed description of the farming systems and data used can be found in Rufino et al. (2008) and Langeveld et al. (2008).

Exploring the effect of management options

NA indicators for the three farm household types were calculated for the situation at the moment of the survey (baseline scenario), followed by an exploration of the consequences of farm management changes for the indicator values (improved management scenario). IN, TIN, TST, T .. and TSTc were expressed on a per capita basis to allow comparison of N use of the different farm household types. The management changes included increased yields of barley from its current value of 2 to 3 t ha−1, and faba-beans from 1 to 2 t ha−1, these yield levels were recorded in similar agro-ecosystems in the highlands of Ethiopia (Agegnehu et al. 2006). It was assumed that the associated increase in the availability of crop residues was subtracted from the feed imported from common pastures. More manure N was retained on-farm because of improved management within feasible ranges as reported by Rufino et al. (2006). We assumed that in the improved management scenario, 70% of the manure available for recycling on-farm was conserved contributing to higher application rates to crops, and resulting in higher crop yields.

Sensitivity analysis

The objective of the partial sensitivity analysis was to evaluate the effect of changes in the underlying data used to estimate N flows, and the conceptualisation of the system on the NA indicators. We used only the wealthier farm household for the sensitivity analysis. First, all parameters associated to plant and animal products and fertilisers were changed to their maximum and minimum values (Table 4 in Appendix). Second, parameters related to management were changed to their maximum and minimum. Third, we compared three network configurations of the same farm household system to evaluate the impact of (dis)aggregation of compartments on NA indicators, i.e. (1) the baseline configuration with 12 compartments (Fig. 4), and (2) a configuration with four compartments where all animal compartments were aggregated into one livestock compartment and all cropping activities into one crop compartment, and (3) a configuration with 14 compartments where two crop compartments were each split into two compartments, i.e. fields were divided into two plots.

Fig. 4
figure 4

Flow diagrams of three different farm household types, i.e. poor with seven compartments/activities, medium with ten compartments/activities and wealthier with 12 compartments/activities. Dashed lines are relatively small flows, solid lines are large N flows

Results

The farm households as a network of N flows

The poor, medium and wealthier farm household were each conceptualised as networks of N flows in Fig. 4.

The poor farm household had 0.3 ha of land, cattle, sheep and few chickens. Livestock fed mainly with biomass from communal land and with on-farm produced crop residues. No feed was purchased to support animal production. Manure from the corral was used only as household fuel. Most milk was sold and only a small portion was used for household consumption. Two crops were grown, i.e. (irrigated) barley (Hordeum vulgare L.) and prickly pear (Opuntia spp.). Part of the barley harvest was exchanged for labour and traction by means of share-cropping. Mineral fertilisers were applied exclusively to the irrigated barley crop. A large amount of food was imported because on-farm production could not meet the household requirements (see Table 5 in Appendix). A significant amount of cash came from off-farm employment of the family head. There were no other important sources of income.

The medium wealth farm household had 0.7 ha with rainfed and irrigated barley, faba beans (Vicia faba L.), cattle, a mule, a donkey, sheep, and chickens. Animals were fed on communal land, crop residues produced on-farm, and purchased feed. Manure was collected from the corral, composted in heaps and used as fertiliser. Milk was partly sold and partly consumed by the household members while eggs were sold. Mineral fertilisers were exclusively applied to the irrigated barley crop. Some food was purchased, but most household consumption was met by on-farm production (see Table 6 in Appendix). Cash was generated mainly through the sale of honey, eggs, sheep hides, and leasing out the mule.

The wealthier farm household had 2.4 ha with common wheat (Triticum spp.), buckwheat (Fagopyrum esculentum), barley and faba beans, cattle, sheep, donkeys and chickens. The animals were fed on communal land, with crop residues produced on-farm, and with purchased supplements. Manure from the corral was partly used as fertilisers and partly as fuel. Neither manure nor fertilisers were applied to the rented land. Milk was used for home consumption. Half of the grain production of the rented land was used to pay this rent. Mineral fertilisers were applied only to the irrigated plots. Household food requirements were met by on-farm production and the food surplus was marketed (see Table 7 in Appendix). The N flow within each of the three farm households was dominated by the N supply to the household and the livestock. The largest N inflow was the result of the livestock grazing in the common pastures. The collected livestock excreta was recycled and used as fertiliser and fuel for cooking. A part of the crop residues was used to feed livestock but their contribution to the total N flow in the system was relatively small.

Indicators to assess integration and diversity

Baseline scenario under current management

All farm households depended largely on imported N (IN) to support the system throughflow (TST) (Table 3). IN represented between 66 and 70% of TST for the three farm types. IN comprised N fertilisers, feed N and food N. Fertiliser N use was limited in all three farms. The poor farm household used more fertiliser N on a per hectare basis, and imported more feed N per tropical livestock unit (TLU) than the other types. The medium and wealthier farm households applied manure N (109 and 30 kg ha−1, respectively) while the poor farm household used manure mainly as fuel. Imported feed N represented the largest proportion (78–92%) of IN, with a daily average of 100–150 g N per TLU. Purchased food N as grain accounted for about 3 kg N per capita per year in the poor and medium wealth farm households.

Table 3 Network analysis of annual N flows for three farm household types from Teghane, Ethiopia, i.e. poor, medium wealth and wealthier

The amount of N recycled (TSTc) was small for all three systems (between 1 and 2.5 kg N per capita) as compared with the total system throughflow (TST), and therefore FCIs and path lengths (PL) were also relatively small. Statistical H R showed that diversity in the network connections (N flows) increased from the poor to the wealthier farm households, but differences were small. The relatively more diverse and wealthier farm households (H R = 2.4) did not recycle more N (FCI = 2.2–2.6%) than the relatively less diverse (H R = 2.2) and poor farm household (FCI = 2.9%). Since the three farm households manage their N resources similarly, the degree of integration in the poor, medium and wealthier farm households was also similar.

Scenario under improved management

In the alternative management scenario the integration of farming activities increased (FCI ranged from 4.2 to 7.7%, see Table 3) because the amount of N recycled (TSTc) more than doubled. The dependency on external N inputs decreased (IN/TST) from 66–70 to 53–58%, while PL increased only slightly. N flows of the improved management scenario are shown in Tables 5, 6, and 7. The diversity in the N flow pattern also increased somewhat (H R = 2.4–2.6 vs. 2.2–2.4 in the baseline) because the size of internal flows increased. AMI was slightly reduced because the N flows were more homogeneously distributed.

Sensitivity analyses

The change of parameters associated to plant and animal products and fertilisers to the maximum and minimum values found in the literature caused a relative change of 26–29% in IN, TIN, TST, 10–15% in TSTc and FCI and practically no change in the other indicators (Fig. 5A). Changes in the conversion coefficients alter the size of the N flows, and therefore all the indicators related to system size, activity and cycling. The change in TSTc and FCI is different than for the other indicators because there are few cycling flows in the network, i.e. the change in TSTc is relatively smaller than the change in TST. PL does not change as it depends much on the number of activities which was not altered.

Fig. 5
figure 5

Fractional changes in the indicators IN, TIN, TST, TSTc, FCI, PL, AMI, and H R for three situations: A changes in conversion coefficients for N concentrations, dry matter and energy values of plant and animal products; B changes in management related parameters; C changes in the indicator values as a result of aggregating (n = 4) or disaggregating compartments (n = 14) as compared to the observed situation (n = 12). The fractional changes refer to the observed values in Table 3 and were obtained by using the maximum and the minimum of the ranges presented in Table 4

The change in management parameters had a relatively greater effect on the integration indicators (TSTc, FCI and PL) (Fig 5B) than the change in conversion coefficients of plant and animal products and fertilisers. PL changed because of the changes in TIN and TST. Management parameters determine the amount of N retained in the system resulting in a much larger effect on TSTc, FCI and PL (Fig. 5B). The conceptualisation of the system has a large effect on the recycling indicators (TSTc, FCI and PL) and on the structure/organisation related indicators (AMI, H R) (Fig. 5C), and relatively no or little effect on the system size related indicators (IN, TIN and TST). By removing compartments, the amount of N cycled increased because we aggregated the flows of several compartments into one. The total flow in the system did not change due to the aggregation, and therefore the largest effects were observed in TSTc and FCI. The aggregation also had an effect on the diversity of N flows because the indicator sums the contribution of each compartmental flow to obtain the system diversity.

Discussion

In order to study N flows within agro-ecosystems the relevant sub-systems or compartments need to be identified (Hirata and Ulanowicz 1986). NA is sensitive to the system definitions, a common issue in using systems analytical tools to study ecological systems (Fath et al. 2007), and even more so in agro-ecosystems where biophysical and socio-economic aspects interact (Stomph et al. 1994). The aim of the study determines the system boundaries and its compartments. Only explicit definition of the system characteristics allows comparison across different studies. Furthermore, sensitivity analysis of aggregating compartments is helpful to assess the consequences on indicators as illustrated in “Sensitivity analyses” and Fig. 5C. This analysis showed that some indicators are more (TSTc, FCI), and others are less (IN, TIN and TST) affected by changes in the conceptualization of the system. Similarly, effects can be assessed of neglecting resource flows because of the difficulty to measure or quantify them accurately. In any analysis technique, the accuracy of the results is as good as the data available (Fath et al. 2007). The uncertainty in parameter values (conversion coefficients) affecting the indicator values (cf. Fig. 5a) can be addressed by improving the accuracy of parameters and flows size estimations. Estimation of flows (e.g. feed intake from grasslands, crop residues removal from fields) and system processes represent a major challenge, one in which we can build experience, and that should not prevent us from using NA to characterise the integration of agro-ecosystems.

The indicators of organisation are useful to compare diversity and organisation of the flows across farm household systems. AMI and H R provide information on the configuration and diversity of the network of flows resulting from the management by the farm household. These measures can be used to compare systems within a region but also across environments. AMI will approach its upper boundary when a few flows dominate the total flow in a system for a given system size (T ..) as shown in Fig. 3. The three farm households types evaluated in this study did not differ much in diversity and organization of the flows (cf. Table 3). Probably differences in these indicators would be evident in systems with different production structure, or when comparing systems across regions of different agroecology. Using NA the impact of technologies aimed at intensifying crop or livestock production on the whole farm household can be evaluated ex post in terms of integration and dependency of external inputs. This allows to assess properties that are otherwise not evident from direct observation or measurements from individual compartments of the system, and offers opportunities to test configurations of flow patterns resulting in more efficient use of resources which may be confronted with economic indicators.

The NA indicators showed that the farm households were different in size (TST), but equally small in recycling and dependency on large N imports from common pastures to support livestock production. According to the analyses of this study, N cycling in farm household systems is much smaller compared to natural ecosystems (Finn 1980) since the principal aim of agro-ecosystem is to produce food and other products that are exported from the system. The three farm types hardly differed in organisation of flows and diversity although the poor household appeared to be somewhat less diversified than the wealthier household. On-farm production of fodder crops could substitute or supplement the feeds from common pastures, and add to the opportunities to increase recycling. However, household objectives and limitations imposed by other farm resources (e.g. labour constraints) determine whether this strategy could improve integration.

In the case study, collected excreta contributed to the manure heap, but most urine from livestock was lost reducing the amount of recycled N (TSTc). In addition to mineral fertilisers, nitrogen input of crop activities comprised household waste and (a part of) human excreta. Both N sources contribute to the recycled N (TSTc), and the cycling index of the systems (FCI). The number of animals largely determined the amount of imported N, because most of the feed requirements were met with biomass from communal grazing land. Wealthy and medium households imported relatively large amounts of N for feeding livestock, but at least half of the N excreta returned to the common pastures during grazing. The amount of recycled N could increase considerably if the animals were fed with fodder produced on-farm, but this may compete for land, labour and other resources.

Integrated systems which use nutrients efficiently and reduce the dependency on external inputs should be aimed at, especially in situations where farmers have no or limited access to external inputs. In marginal environments such as Northern Ethiopia, where the availability of external inputs is uncertain (Abegaz et al. 2007), recycling of nutrients for crop and livestock production may increase the adaptability and reliability of farm household systems (López-Ridaura et al. 2002).

NA can be used ex ante to compare farm household systems across environments. In this study the farm household system was the unit of analysis but NA may be applied at other aggregation levels (e.g. village or watershed), requiring a different conceptualisation of the system. In the quantification of N flows within the farm household systems we did not include losses of N through leaching, and gaseous losses. Provided data is available these flows can be included in the NA, although estimation of their importance is highly problematic (Faerge and Magid 2004). Linking integration indicators with farm economic indicators may enable the identification of synergies and trade-offs and the design of more resource use efficient and robust farming systems. Evaluating the relative importance of different flows into and within the systems and comparing systems across regions will be the focus of further research.

Conclusions

NA provides a tool to analyse the degree to which household activities are integrated. Diversity of farm household activities does not necessarily lead to integration of these activities through increased exchange of nutrient resources. Conceptualising and measuring processes and flows remain a major challenge in agro-ecosystems studies, but this should not prevent us from applying NA that assist us in quantifying integration and diversity of agro-ecosystems. N cycling indicators of farm household systems are much lower than those calculated for natural ecosystems due to export of food and other products from these systems. The relative large amounts of N that are withdrawn limit opportunities for recycling within farm household systems. But still opportunities to increase N cycling in farm household systems can be indentified using NA. Increasing the input use to increase harvests, also increase the amounts of nutrients prone to losses. To our view, farming system (re)design or a system shift will be needed to aim at sustainability.