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Page 8 of 20 Corsini et al. Carbon Footprints 2026, 5, 34

associated with smaller size or irregular geometry, are more exposed to external influences and therefore,
exhibit a smoother decay curve (lower β). Conversely, larger or more compact habitats show steeper
attenuation of pressure (higher β). In these formulations, β acts as a modulator of the response, reflecting the
degree of ecological resilience or susceptibility of the landscape to external stress.

Operationally, beta is obtained from two independent components:

(i) a shape-based circularity index (CI), representing geometric exposure to edge effects; and

(ii) an area-based resistance factor (k), representing the buffering effect of fragment size.

• Circularity index (CI)
Fragment shape is quantified using the CI, a dimensionless metric that relates area to perimeter and provides
a proxy for edge susceptibility . Shape metrics are strongly linked to fragmentation and edge exposure . CI
[45]
[33]
measures how closely a fragment approximates a perfect circle, which minimizes edge length for a given area.

4 A (6)
CI = p 2

Where:
• CI is the circularity index, unitless;

• A is the project area, expressed in square meters;
• p is the project perimeter, expressed in meters.

CI ranges from 0 to 1. Values approaching 1 indicate compact geometries with low edge exposure, while
values near 0 indicate elongated or irregular shapes with high edge density and increased susceptibility to
external disturbance.

• Area factor (k)
Fragment size influences degradation dynamics primarily through the proportion of interior (core) habitat
because no standardized size index exists at the single-fragment level . We defined an area factor (k) that
[41]
captures the buffering capacity associated with fragment size. The relationship between area (A) and factor
(k) is monotonically increasing and non-linear in nature—that is, larger areas have higher k values, but with
decreasing growth (smaller marginal gains as A increases). This behavior is represented using a smooth,
continuous function derived from monotonic cubic Hermite interpolation by segments (splines) ,
[46]
following established approaches for preserving monotonicity in ecological scaling . k(A) is defined as the
[47]
continuous function interpolated in logarithmic space, from previously defined anchor points.

k(A) = 10 f(log 10 A) (7)

Where:

• k(A) is the area factor, unitless;

• A is the project area, expressed in the same units used to define the anchor points;

• f is a monotonic cubic Hermite spline function fitted to predefined anchor points in log-area space.