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Corsini et al. Carbon Footprints 2026, 5, 34 Page 9 of 20

Figure 2. Continuous relationship between project area (A) and area factor (k). The curve of the equation and the graphic were generated
in R, from ggplot package.

This formulation yields a continuous, analytically tractable estimate of k for each project, avoiding
discontinuities at class boundaries, and allows recalibration if additional reference points are introduced
[Figure 2].

• Estimation of beta
The parameter β integrates the effects of fragment size and shape into a single structural control on
degradation propagation. This combination allows β to reflect both a fragment's intrinsic capacity to dampen
disturbances (area factor) and its geometric propensity to amplify edge effects (CI), resulting in a biologically
significant and landscape-responsive parameter in the exponential degradation model.

Beta is calculated as:

= 1 − e (−k∗Cl) , = 1 m -1 (8)
0
0
Where:

• β is the decay rate of the exponential model, expressed in m ;
-1

• β 0 is a scaling coefficient to preserve dimensional consistency, expressed in m ;
-1

• k is the Area Factor, unitless;

• CI is the circularity index, unitless.