Agricultural landscapes are quintessential socio-ecological systems, places where social and environmental factors co-exist and interact in inherently complex ways. When modellers try to reproduce these systems, farmers’ behaviour is of paramount importance. Crop choice, the application of certain agricultural practices and the adoption of innovations are actions that ripple through the economy, social sustainability and environmental sustainability of an agricultural landscape. Agent-based models, computational representations that focus on the atomistic parts of a system and describe their behaviour and interactions in a bottom-up approach, have become the tool of choice for capturing these dynamics. Yet while models involving farmers’ behaviour are now quite numerous, relatively few studies explicitly account for social interactions. GeSoN was designed precisely to fill this gap, recreating the farmers’ social context relevant to their decision-making process.

The theoretical heart of the model is the bounded rationality framework, first articulated by Herbert Simon. Bounded rationality states that, when making decisions, humans do not set out complex optimisation procedures; instead, they mediate between constraints regarding time, knowledge and cognitive abilities. Four distinct facets of human decision-making must be considered: humans encounter difficulties in evaluating and planning long behavioural sequences given their limited cognitive capacity and the inherent complexity of their environment; people tend to set aspirational levels related to specific goals; they work on goals sequentially rather than simultaneously; and their search strategy is aimed at satisfaction rather than optimisation. A vital aspect of the framework is ecological rationality, the insight that decisions are strongly influenced by the environment, both physical and social, relevant to agents’ goals and needs. This stands in deliberate contrast to the Expected Utility Theory, whose assumptions of selfishness, stable transitive preferences and unlimited cognitive capacity have been refuted by numerous empirical studies in different domains.

To model the interaction amongst farmers, the researchers turned to opinion dynamics, a branch of social network analysis that studies the evolution of individuals’ views as the result of interactions within a network. The approach 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. GeSoN belongs to the family of models in which opinions are continuous variables, usually ranging between 0 and 1, following the seminal work of Deffuant and colleagues and of Hegselmann and Krause. The major constraint applied is bounded confidence: influence during an interaction occurs only when a specific condition regarding the similarity between opinions is met. The underlying assumption is that opposite opinions have little or no influence on each other, a principle grounded in the observation that people with similar attitudes are more likely to interact and that there is a lack of understanding between persons with substantially different views.

What sets GeSoN apart is its multi-layer network structure, built on the concept of geographical specificity. The model generates connections between farmers using different criteria, forming a multi-criteria web of channels through which farmers interact. The first and major component is the Geographical Network, which represents the influence over the landscape of so-called nodal farmers, those that create the highest number of connections with others and hence significantly influence the agricultural landscape. This network uses a modified gravity model, an empirical economic model originally inspired by Newton’s law of gravitation and primarily applied to international trade studies. The two main assumptions are that closer farmers are more likely to interact and that larger farms, in terms of farm size, have more influence over their neighbours than smaller ones. The strength of the link connecting Farmer i with Farmer j is computed as the size of Farmer j divided by the physical distance between the two farms. After computing the force connecting them, all farmers hold a ranked list of the other farmers in the landscape, ordered by that force, and choose a predetermined number of neighbours from the top of the list when interactions take place.

Two further layers complete the structure. The Associative network simulates the presence, in a landscape, of groups of cooperating farmers, such as members of the same cooperative, a producer organisation or similar farmers in terms of agricultural production. This layer matters because farmers are strongly affected in their decision-making by being part of such groups. The Virtual network captures the non-agricultural connections between farmers, like friendship or parenthood, incorporating a determined level of stochasticity into the structure. Both of these layers are exogenous and predetermined at the beginning of a simulation. Together, the three layers evolve beyond the purely mathematical random connection rules of the seminal Watts-Strogatz and French-DeGroot models, forming a genuine socio-economical network in which economic and social criteria shape agents’ connections.

Once the links are formed, opinions travel through them. In GeSoN, opinions such as risk aversion and sustainability concerns are modelled as continuous variables ranging from 0 to 1, with 1 excluded. Crucially, every farmer carries not only a personal opinion but also a level of uncertainty, modelled as a continuous variable ranging from 0 to 0.6, with the farmer’s opinion sitting at the uncertainty’s central point. The minimum distance required to enable the influence of one opinion over another is represented by the uncertainty associated with the influenced agent’s opinion. The magnitude of influence is controlled by a mobility parameter, fixed for all agents and set at the beginning of the simulation. The governing formula is a weighted mean of the influenced farmer’s opinion and the central part of the influencing farmer’s shared opinion, with weights given by the mobility parameter and its inverse, both scaled by a factor indicating the difference in the farmers’ uncertainties. This factor makes the influence between farmers with unequal uncertainties asymmetrical: when two farmers with high and low uncertainty respectively interact, the effect is stronger on the farmer with high uncertainty. Time is discrete, and farmers upload their opinions only after every other farmer has interacted with their respective neighbours, ensuring that the starting order of farmers makes no difference to the results.

The researchers demonstrated the model’s behavioural capabilities with a prototype implementation in Python, running simulations over both real and simulated landscapes. In a scenario based on the real Danish landscape of Himmerland, with 190 farmers whose locations and sizes were extracted from the EU’s Land Parcel Identification System database, initial opinions drawn from a uniform distribution evolved over 100 time steps into a double peak distribution, with the more prominent peak slowly forming from around the sixtieth time step. In a striking comparison, two simulations with identical input values but different network structures produced substantially different results: applying all three networks showed polarisation of opinions around two values, roughly 0.3 and 0.7, while applying just the Geographical Network showed consensus around the mean opinion value of about 0.5. This indicates that a single simple network would give erroneous results if the other networks were active in the real world. A second experiment on a simulated landscape of 214 farmers revealed further emergent behaviour, with two peaks forming rapidly and the larger peak drifting towards higher values, driven by the peculiar initial spatial configuration in which clusters of small farms remained uninfluential and uninfluenced.

The model’s peculiarity lies in the conjunction of bounded confidence opinion dynamics with the bounded rationality behavioural framework and geographical specificity, together with a multifactorial asymmetrical interaction function unique to this model. In the seminal Deffuant-Weisbuch model, by contrast, the formula governing the interaction is symmetrical and uncertainty is not taken directly into consideration. The asymmetrical function has a double consequence: farmer interactions are independent, so exchanges are not guaranteed to be mutual, and the influence one farmer has on another may differ in magnitude. This allows for the formation of different roles during a simulation, with farmers holding the most connections and low uncertainty playing the role of leaders or nodal farmers. The prototype results, characterised by consensus, polarisation and fragmentation, display non-linearities indicating the emergence of interesting, complex dynamics.

GeSoN has clear limitations at this stage of development. Farmers are the only type of agent represented, although agricultural advisors, food processing industries and institutions may mediate interactions in real scenarios and are planned for future developments. Farmers’ emotions were intentionally left outside the system boundaries, as were the agricultural land market and other sources of influence such as economic and environmental shocks. The continuous representation of opinions also ignores the intricacies related to one’s personal views. Nonetheless, the model presents flexibility and adaptability to be incorporated into more complex simulation systems, and the team plans to integrate it as a module of the ALMaSS agent-based modelling platform, where farmers’ decision-making is handled through the CONSUMAT conceptual framework. The practical payoff could be considerable: ex-ante policy analysis could benefit from the model in predicting farmers’ responses to specific measures, and predicting the adoption rate of voluntary enrolment measures in the EU agricultural policy framework could lead to higher efficiency and effectiveness, avoiding sub-optimal budget allocation when adoption cannot be precisely foreseen. As the model matures within richer simulations, the different configurations of inputs, diverse populations of farmers and varied agricultural landscapes are expected to generate complex emergent properties that can inform the real world.

Subject of Research: Socio-ecological simulation

Article Title: GeSoN: A Geo-Social Network model applying bounded rationality to farmers in socio-ecological simulations

Article References: Paparella, A., Cembalo, L., & Topping, C. (2023). GeSoN: A Geo-Social Network model applying bounded rationality to farmers in socio-ecological simulations. Food and Ecological Systems Modelling Journal, 4, Article e100714. https://doi.org/10.3897/fmj.4.100714

Image Credits: AI Generated

DOI: 10.3897/fmj.4.100714

Keywords: agent-based modelling, bounded rationality, opinion dynamics, socio-ecological systems, agricultural networks, farmer behaviour, gravity model, bounded confidence, GeSoN, Geo-Social, Network, model