The decision to apply a behavioural framework that exists already and is grounded in theory is generally recommended (Groeneveld et al. 2017, Schlüter et al. 2017). In particular, it facilitates the comparison and re-use of models (Groeneveld et al. 2017), leading to consolidation and improvements of the results (Bell et al. 2015). Moreover, it fosters communication between modellers and enhances theory development. When modelling human behaviour, the most commonly used behavioural framework derives from the Expected Utility Theory (EUT), initially proposed by Bernoulli (1954). This framework’s fundamental assumptions are that humans are selfish, have stable and transitive preferences, have an unlimited cognitive capacity to evaluate every behavioural option available and base their decisions exclusively on the utility deriving from those. Being the standard in the economics discipline and being easily formulated mathematically, this framework is prevalent (Schlüter et al. 2017). In contrast, numerous empirical studies refuted the critical assumptions of the EUT in different domains (e.g. Siebenhuner (2000), van den Bergh and Gowdy (2000), Bocquého et al. (2014), Levine et al. (2015)). Consequentially, many other frameworks, mainly from psychology, have been proposed to fill the gap between the EUT and observed human behaviour. Groeneveld et al. (2017), Schlüter et al. (2017) comprehensively describe these frameworks.

Here, the approach to modelling the farmer’s behaviour follows the Bounded Rationality framework (Simon 1955, Simon 1997). Bounded rationality states that, when making decisions, humans (or farmers, in our case) do not set out complex optimisation procedures; instead, they mediate between constraints regarding time, knowledge and cognitive abilities. More specifically, as Jones (2003) explained, four distinct facets concerning the human decision-making must be considered. These are:

1. humans encounter difficulties in evaluating and planning long behavioural sequences, given by their limited, or “bounded”, cognitive capacity and the inherent complexity of their environment;
2. people tend to set aspirational levels related to specific goals;
3. they work on goals sequentially and not simultaneously;
4. their search strategy is aimed at satisfaction rather than optimisation.

A vital aspect of the bounded rationality framework is called “ecological rationality” (Gigerenzer and Selten 2001). This concept underlines how decisions are strongly influenced by the environment, intended as the parts of the context, both physical and social, relevant to agents’ goals and needs. According to the bounded rationality framework, the definition of ecological rationality and environment both account for the agent’s context when defining the system’s boundaries in a bottom-up modelling approach aimed at replicating realistic human decision-making. The environment becomes part of the limitations to human-comprehensive rationality (Simon 1997). From another perspective, the ability of individuals to understand and adapt to the environment could determine their success in satisfying their goals (Gigerenzer and Selten 2001).

The approach used to model the interaction amongst farmers in this model is the opinion dynamic. This specific branch of the more general social network analysis framework has gained attention for its potential application in social and political science (Sun and Müller 2013). The opinion dynamic studies the evolution of individuals’ views as the result of the interactions between a network of individuals. In other words, it assumes people influence each other, describes the interaction process from an individual point of view and produces results emergent from those interactions, pooled for the population. The seminal works of this discipline are the study conducted by French Jr. (1956) and its revision and formal elaboration by Degroot (1974). Their model, also known as the French-DeGroot model, focuses on consensus and the conditions that lead to a consensus amongst individuals. Since then, many other opinion dynamic models have been developed (e.g. Toscani 2006, Düring and Wolfram 2015, Tian and Wang 2018).

The opinion dynamic approach focuses on the individual elements of the network and requires the specification of several key elements. These are the network identification, the opinions definition and the formulation of an interaction mechanism. The first step in defining the network is to determine whether the network has a specific topology or is completely random and, ultimately, determine who interacts with whom and in which order. The opinions definition involves its mathematical representation; there are two main types. The first type represents opinions as discrete variables; examples are the voter model (Clifford and Sudbury 1973) and the Snajzd model (Sznajd-Weron and Sznajd 2000). The second type models the opinions as continuous variables; usually, the opinion range values lie between 0 and 1. This type includes the Deffuant model (Deffuant et al. 2000) and the French-DeGroot model. The present study belongs to the second type. The interaction mechanism describes how agents respond to the interaction with others. This involves the formula determining the magnitude of the influence and any constraints added to the interaction. The major constraint used in the model presented here is bounded confidence. Models developed applying this constraint assume that influence amongst interacting agents does not always occur. This means there is influence during an interaction only when a specific condition regarding the opinions (usually similarity between opinions) is met. Thus, the assumption underlying bounded confidence is that opposite opinions have little or no influence on each other.

The concept of geographical specificity (Namatame and Chen 2016) has been applied to model the links enabling the connection between agents. The geographical specificity must be considered an attribute of the agents that creates higher levels of heterogeneity in the population and ultimately affects the interaction rules by explicitly defining the possible interactions amongst agents. As a result, a multi-layer network was defined following the geographical specificity. Different network configurations were defined with different linking properties, each influencing the same explicit structure where the opinion dynamic takes place. This allows feedback mechanisms to alter the overall network dynamics due to inter- and intra-network interactions. The criteria behind the multi-layer network formation are different. Examples are the physical location and agents’ economic attributes. This approach evolves from the random connection formation rule, used in the seminal models of Watts-Stogatz and French-DeGroot and that is a purely mathematical network. Instead, applying economic and social criteria to agents' connections forms a socio-economical network (Namatame and Chen 2016). Other examples of this approach can be found in Chen et al. (2006), Yang et al. (2022) A detailed explanation of this process is given in the Overview of the processes section.

Decisions about what to include or not to include influence the model’s flexibility, results and predictive power (Topping et al. 2015). In the modellers’ opinion, the processes included in GeSoN were the most relevant in capturing the essential dynamics emerging from the social interaction amongst farmers. Nonetheless, some processes were intentionally left outside the model's system boundaries to maintain an adequate level of model parsimony, simplicity and feasibility. At this stage of development, farmers are the only type of agent represented in the model. In real scenarios, some other entities, like agricultural advisors, food processing industries or institutions, may mediate the interaction amongst farmers and influence the diffusion of innovation. The inclusion of those actors is planned for future developments of the model. Second, although the theoretical approach used in the model accounts for the socio-psychological characteristics of the farmers, the inclusion of every personal psychological sphere is outside the scope of the model. Notably, farmers’ emotions were intentionally left outside of the system boundaries. As pointed out by Huber et al. (2018), emotions are rarely included in farmer behaviour models and a more consistent inclusion of these aspects should be considered in future works. Third, the agricultural land market is not taken into consideration. The decision to keep the land market outside the model was taken so as not to over-complicate the model and because of its relatively small effect on determining farmers’ social interaction. Fourth, the farmers’ position in the landscape is assumed to be located in their farm centre. The location has a major influence on the farmers’ social network. Still, farmers’ physical movements are not reasonably predicted; therefore, the assumption of the same location between farms and farmers has been made.

An important aspect left outside the model’s system boundaries is the other sources of influence affecting farmers’ opinions. At this stage of the development of the model, a focus on only the endogenous influence of farmers’ opinions best fits the study’s aim. Nonetheless, the model structure allows the integration of other sources of influence, like economic and environmental shocks causing a generalised shift in the farmers’ opinions, such as their risk aversion.

The GeSoN model has two main components that are strictly related and work together while representing different aspects of the social context of farmers. These are the farmers’ social network and the interaction amongst farmers. The former is the structure that represents the connections between farmers. The latter is the process of interaction between farmers. In the following sections, both components are described in detail. The farmer social network is the process of forming connections between farmers. Different factors, such as the geographical distance between farms, regulate the formation of ties. The Network structure is composed of three distinct layers, forming a multi-criteria web of channels through which farmers interact. The interaction between farmers generates the model influence farmers have on each other when interacting. The influence considers farmers’ opinions, like risk aversion or sustainability concerns. The farmer network forms the structure over which the interaction between farmers occurs. Those interactions are not random, but based on neighbourhood. The specific morphology of the landscape and the farmers’ characteristics strongly influence the outcome of these interactions and the results of applying the network structure.

To better describe the GeSoN structure, the connections between agents are mapped using the network science’s concepts of nodes and links. For example, in Fig. 1, the basic features of the GeSoN structure are shown. Farmers and other agents (note that, in the current version of the GeSoN, only farmers are considered) form the nodes distribution. Arrows represent the links between nodes and indicate the connections between agents. Both nodes and links have attributes (or features, characteristics). Nodes’ attributes are size, position and the number of connections with other nodes. Links’ attributes are direction and strength.

Figure 1.  

Example of network elements. Coloured dots represent nodes and arrows represent links. The dots’ colour, size and position represent the nodes’ attributes. The colour and direction of the arrows indicate the strength and direction of the connections.

The network represents the sum of relevant ties connecting farmers in the same agricultural landscape. These connections resemble the channels through which communication takes place. Amongst all the possible and only partially predictable relationships between farmers, only a few of those are modelled here. Although the farmers’ social context involves numerous actors (e.g. their family, agricultural advisors operating in the area and local food industries), in this first development of the GeSoN, the connections between farmers are made only between farmers. In other words, GeSoN does not consider the influence of those actors directly, but leaves the possibility to involve those in future developments. In the past, the network’s topology (i.e. the position of the nodes and links between those) was most often separated from sociological questions (Will et al. 2020). Examples are the random network (Erdös and Rényi 1959), the small-world networks (Watts and Strogatz 1998) and scale-free networks (Albert-László and Réka 1999). On the other hand, the network’s topology reflects socio-economics phenomena and is highly dependent on the agricultural landscape. Nonetheless, a certain level of stochasticity is incorporated in the formation of the ties. The different criteria forming the links between agents are intended to be separate and interacting layers, each shaping the individuals’ social network. Hereafter, the specification of the rationale behind the connection between farmers is given.

The ties formation process involves different features, each forming a specific sub-section of the GeSoN. In the first instance (Geographical Network), the geospatial configuration of the landscape is what most influences the network’s structure. Farmer agents’ primary connections are based on the farms’ specific location across the landscape. The basic concept is that, as demonstrated by literature (Neal and Neal 2014, Will et al. 2020), farmers are highly influenced by their peers’ behaviour. Physical distance, or proximity, between farmers partially determines their connection. Moreover, the economic size of the farmer also affects the possibility of creating links and larger farms are assumed to influence other farmers more frequently than others. Innovative and more influential farms are usually economically significant (Just and Zilberman 1983, Sunding and Zilberman 2001, Daberkow and McBride 2003). As a second connected parallel network, a set of links is formed to simulate the presence, in a landscape, of groups of cooperating farmers (the Associative network). These can be members of the same cooperative, members of a producer organisation or only similar farmers in terms of agricultural production. The third network set of ties is generated to capture the non-agricultural connections between farmers. These can be various, like friendship or parenthood (the Virtual network). The sub-model section describes these three sets of links in more detail.

The Geographical Network is the major component of the GeSoN; it represents the influence over the landscape of “nodal” farmers. As described by Poudel et al. (2015), nodal farmers create the highest number of connections with others and, hence, significantly influence the agricultural landscape. The Geographical Network uses a modified gravity model to shape farmer connections. The gravity model is a well-known empirical economic model, originally developed by Newton’s law of gravitation (Anderson 2011), first used by Isard (1954) and primarily applied to international trade studies (e.g. Brun et al. (2005), Carrère (2006)). A modified gravity model has been used for three reasons. First, although there is a lack of connection with the economic theory, the gravity model has been proven to have an important explicatory predictive power (Anderson 2011); second, it is a parsimonious model; third has already been applied to ABM regarding farmers network (Yang et al. 2022). The two main assumptions behind the application of this model are: 1) closer farmers are more likely to interact and 2) larger farmers (in terms of farm size) have more influence over their neighbours than smaller farmers. In the Geographical Network, the links between agents are weighted and directional. This means that Farmer i can be linked strongly or weakly with Farmer j, independent of how Farmer j is linked with Farmer i. The resulting formula behind the formation of links between farmers under the Geographical Network is:

\(F_ {ij}= {M_j \over D_{ij}}\)

where \(F_ij \) is the strength of the link that connects Farmer i with Farmer j. \(M_j\) is the Farmer j size (note that only the size of Farmer j is taken into consideration) and \(D_ij\) is the physical distance between Farmer i and Farmer j, i.e. between the two farms. After computing the force connecting them, all farmers have a ranked list of all the other farmers in the landscape, ordered by the force. A graphical example is given in Fig. 2. Note that the ordered list varies amongst farmers; in the example, farmer i has its strongest link with Farmer j, while Farmer j is linked primarily with Farmer z. When the interactions take place, farmers will choose a predetermined number of neighbours from the top part of the ranked list in the same order they are listed. The number of neighbours is one of the state variables of the model.

Figure 2.  

Graphical example of the spatial distribution of farmers and their ranked list of neighbours under the geographical network.

The concept governing the Associative network’s formation of ties between farmers is the potential to incorporate information about the farmer’s membership of cooperatives, corporations or producer organisations. It is important to add the influence of these types of organisations on the network since farmers are strongly affected in their decision-making by being part of one of these groups (Franks and Mc Gloin 2007). The Associative network is exogenous and predetermined at the beginning of the simulation. If information about farmers’ membership to cooperative-like associations is available, scenarios with cooperatives associating similar farmers may give interesting results.The Virtual Network’s primary purpose is to incorporate unpredictable connections between farmers. Those can be of various types, like normal friendships, family relationships or social network friendships. This additional layer completes the network structure involving a determined level of stochasticity. As with the Associative network, the Virtual network is exogenous.

Once the link between agents is formed, different kinds of information can travel through it. Here we focus on the diffusion of opinions. These are risk aversion and sustainability concerns and form parameters in the farmers’ decision-making process. Opinions have been modelled as continuous variables ranging from 0 to 1, with 1 excluded, as proposed by Deffuant et al. (2000) and Hegselmann and Krause (2002). As underlined by Weisbuch et al. (2002), an explicit role of the actor-uncertainty regarding personal opinions is fundamental. Hence, every farmer has his/her personal opinion and a certain level of uncertainty. Uncertainty is modelled as a continuous variable, ranging from 0 to 0.6. A graphical example is given in Fig. 3. The farmer’s opinion is the uncertainty's central point or mean value. The values 0 and 1 are the opposite extreme opinions. During the simulation, farmers interact with their neighbours and adjust their opinion according to the neighbours’ one. The interaction follows the principle of bounded confidence, which implies that an agent is not influenced by distant positions (Xia et al. 2011). The rationale is that people with similar attitudes are more likely to interact (Neal and Neal 2014) and that there is a lack of understanding between persons with substantially different opinions (Deffuant et al. 2002). The minimum distance, or threshold, to enable the influence of one opinion over the other is represented by the uncertainty associated with the influenced agent’s opinion (Weisbuch et al. 2002). Fig. 4 shows when an influence of opinions occurs and when it does not, accordingly to the distance of opinions between agents. In the model, time is discrete and divided into time steps in which the farmers can interact. Every farmer has a list of neighbours, ranked by the force of the link under the geographical network. A certain number of neighbours is taken from this list. To these, other neighbours coming from the other networks may be added. Each farmer then interacts with the chosen neighbours and updates their opinion after interacting with all the selected neighbours. It is important to emphasise that farmers upload their opinions after every other farmer has interacted with their respective neighbours. In this way, it is avoided that the starting order of farmers makes a difference in the results. The magnitude of the influence is controlled by the mobility parameter. The mobility value is fixed for all the agents and set at the beginning of the simulation. The resulting formula controlling the influence is:

Figure 3.  

A representation of farmers’ personal opinions.

Figure 4.  

In the upper part, example of similar opinions producing an interaction. In the bottom, example of different opinions not producing an interaction.

\(x_{A,t+1}=x_{A,t}*(1-{u_A\over{(u_A+u_B)}}*q)+m_{u_{overlap}}*({{u_A } \over {(u_A+u_B)}}*q) \\Where: \\x_{A,t} = Farmer \:A \:opinion, at\: time\: t \\ x_{B,t} = Farmer \:B \:opinion, at\: time\: t \\ u_A= Farmer \:A \:uncertainty\\ u_B= Farmer \:B\:uncertainty \\u_{overlap}=overlapping \:between \:u_A \: and \:u_B\\m_{u_{overlap}}=central\:point\:of\:u_{overlap}\\ q= mobility\)

The formula is a weighted mean of the influenced farmer's opinion and the central part of the influencing farmer's shared opinion. The weights given to the two elements are the mobility parameter and its inverse, both scaled by a factor indicating the difference in the farmers' uncertainties. This factor results in the influence between farmers with unequal uncertainties being asymmetrical. Thus, when two farmers with high and low uncertainty respectively influence each other, the effect is stronger on the farmer with high uncertainty.

In Fig. 6, a real configuration of farms from a Danish landscape is shown, Himmerland (DK). The dots represent the farms and the size of the dots represents the area covered by each farm. In this landscape, the farms are distributed relatively evenly across the space and there are no particular clusters of large or small farms. Data regarding the farms’ location and size have been extracted from the Land Parcel Identification System (LPIS) database for Denmark. LPIS is an IT system based on satellite orthophotos used by the EU to monitor land use and provide farmers with the proper income support. This database is managed at the regional level, making the availability and quality of those data highly region-dependent.The actualisation of the Geographical Network is shown in Fig. 7. Again, the position of the dots represents the actual position of the farms in the landscape and their size represents the actual farm size. The links between the nodes indicate the strongest connections a farmer has. The colour of the dots indicates the number of connections. Hence, dark blue dots indicate farmers strongly embedded in the network, eventually influencing numerous other farmers.

Figure 6.  

The spatial distribution and size of farms from the Himmerland landscape in Denmark. The dots represent the farms and the size of the dots represents the area covered by each farm.

Figure 7.  

The network structure for the Himmerland (DK) landscape. The links between the nodes indicate the strongest connections a farmer has. Only the top three edges are shown. Edges are coloured differently to indicate the edges’ order in strength.

To provide a less balanced example in terms of farm size and location, we have generated hypothetical landscapes where this information was simulated. Figs 8, 9, 10 show three different examples of the Network implementation over simulated landscapes. The landscapes were produced by forming clusters of farms and with a degree of correlation between farm size and farm location. The resulting network of links differs substantially and, as shown in the next section, will produce different emerging system dynamics.

Figure 8.  

Implementation of the network over a simulated landscape. Here, farms are centred on one cluster and farm size and location are positively correlated. Hence, larger farms are more likely to occupy a central position.

Figure 9.  

Implementation of the network over a simulated landscape. Here, farms are centred on two clusters and farm size and location are positively correlated. Hence, larger farms are more likely to occupy a central position.

Figure 10.  

Implementation of the network over a simulated landscape. Here, farms are centred on four clusters of different sizes. Farm size and location are independent.

We created a prototype implementation of the model in Python to demonstrate its behavioural capabilities. The results below are derived from simulations of real and simulated landscapes and using different network structures.