Can We Estimate Farm Size from Field Size? an Empirical Investigation of the Field Size to Farm Size Relationship.

CONTEXT: Farm size is a key indicator associated with environmental, economic, and social contexts and outcomes of agriculture. Farm size data is typically obtained from agricultural censuses or household surveys, but both are usually only available in infrequent time intervals and at aggregate spatial scales. In contrast, spatially explicit and detailed data on individual fields can be accessed from cadastral information systems or agricultural subsidy applications in some regions or can be derived from Earth observation data. Empirically exploring the field-size-to-farm size relationship (FFR) is a lever to enhance our understanding of spatial patterns of farm sizes by assessing field sizes. However, our currently limited empirical knowledge does not allow for the characterization of the FFR over large spatial extents. OBJECTIVE: We analyze the FFR using data from the Integrated Administration and Control System (IACS) for Germany. The IACS manages agricultural subsidy applications in the European Union; therefore, the data include spatial information on the extent of all fields and farms for which farmers have applied for subsidies. METHODS: We developed a Bayesian multilevel model and a machine learning model to estimate farm size based on field size, controlling for contextual factors such as crop types, state boundaries, topography, and neighborhood effects. RESULTS AND CONCLUSIONS: We found that farm size generally increased with field size for almost all federal states and crop type groups, but the FFR varied considerably in magnitude. Farm size predictions were accurate for medium-sized and large farms (50-7,000 ha, representing 66% of the data) with mean absolute percentage errors of 40-114%, but estimates for smaller farms had higher errors. To evaluate the relationship at the landscape level, we spatially aggregated the predictions into hexagons with a diameter of 15 km. This resulted in more accurate predictions (mean absolute percentage errors of 37%) than at the field level. SIGNIFICANCE: Our study presents the first empirical insights into the FFR, opening future research directions towards producing spatially explicit farm size predictions at scale. Such information is key for monitoring scale transitions in agricultural systems, facilitating the design of timely and targeted interventions, and avoiding undesired outcomes of such processes.