ELIA model
ELIA is an energy-information-landscape integrated analysis resulting from a mathematical model (see 24 for a detailed methodological description, and Annex B inSupplementary Information ). It combines the landscape functional structure (L ) with the interlinking pattern of energy flows driven by farming (E ) and the information carried by them (I ), as a proxy of the potential biodiversity located in cultural landscapes. ELIA allows to interrelate the three indicators (E , I , L ) accounted in a spatial-explicit manner in each unit of analysis (i.e. transects) of digital land cover maps, to then relate them with georeferenced biodiversity data (Fig. 4 ).
Agroecosystem’s energy storage (Fig. 5a ) is seen as the harnessing of dissipation thanks to the farmers’ activity that generates and increases energy loops (30 ). Farmers’ energy reinvestment (E ) also means that this energy looping does not occur randomly across space and time, because it is driven by information (I ). Depending on the information delivered by farmers, the energy flows are redistributed in one or another way with different intensities across the agroecosystem. It is because energy carriers flow across different land uses following a deliberate pattern that they ‘imprint’ a specific land cover mosaic (L ) that we recognize as a cultural landscape (Fig. 5b ). The resulting mathematical model (24 ) allows calculating a three-dimensional relationship among E ,I and L (Fig. 5c ), starting from the interaction between metabolic fluxes and land-uses which give rise to specific human-transformed landscapes. It can be expressed combining the landscape functional structure with the complexity of the interlinking pattern of energy flows (their ‘loopiness’) and the information carried by them (49 ), taken as a biodiversity predictor in cultural landscapes:
\begin{equation} \text{ELIA}=\left(\frac{\left(EI\right)\text{\ L}}{\max\left\{\text{EI}\right\}a}\right)^{1/3}\nonumber \\ \end{equation}
Where E is the energy storage, I is the information carried by the network of energy flows and L is the energy ‘imprint’ in the landscape functional structure (24 ). Lis measured as the landscape pattern (land-cover heterogeneity) and improved including the landscape processes (ecological connectivity). According to the ELIA model,\(\max\left\{\text{EI}\right\}e=0.6169\ \)(Annex B ). Once we have the maximum \(EI\) to structure the landscape, we can add the landscape functional structure (L ). ELIA values theoretically range from 0 to 1.
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The socio-metabolic analysis is based on an energy flow-fund approach of agroecosystems (50 ) of the BMR, using data from the Spanish Ministry of Agriculture and the Catalan Statistics Institute (44 ). The landscape composition and configuration has been calculated from the 2009 Land Cover Map of Catalonia (www.creaf.uab.es/mcsc/).