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Page 14 of 20 Corsini et al. Carbon Footprints 2026, 5, 34

might propagate, while β quantifies the structural resistance governing the rate of decay. As shown in our
results, these parameters adjust intuitively across contrasting landscapes, emerging as functional descriptors
of well-established ecological principles.

Recent empirical studies [14,49] show fragmentation-driven degradation represents a large and persistent carbon
loss that is often comparable to, or exceeds, emissions from deforestation itself, providing strong support for
our conceptual foundation. For example, persistent collapse of edge biomass in the Amazon between 2001
and 2015 amounted to 947 Tg C—nearly one-third of the carbon emitted through deforestation during the
same period . This indicates that fragmentation-driven degradation is a large and persistent carbon flux,
[14]
often invisible to deforestation-only accounting frameworks. Complementing this Amazonian evidence,
observations using GEDI LiDAR showed that canopy height and structural deficits extend 1-1.5 km, and up
to 7 km in repeatedly disturbed tropical forests . In our model, however, the parameter α is not the
[49]
penetration depth of edge effects in the same sense as that study. Instead, α defines the maximum range over
which degradation risk is allowed to be non-zero, after which the function is truncated to zero. The effective
“depth” of the gradient inside that range is governed by β. Crucially, the thresholds used in Bourgoin et al.’s
study (95% structural recovery) map conceptually onto the β-derived decay distances in the RACZ model
[49]
(e.g., distances at which R(d) declines to 1%-5% of edge influence), suggesting that the model’s decay
function captures the same underlying ecological gradients observed across global tropical forests.

Growing evidence further reinforces the generality of this edge-driven deforestation pattern. Edge forests
have been shown to undergo chronic structural degradation, becoming more vulnerable to fire, drought, and
other disturbances than intact interiors . A global synthesis found that negative edge effects on above-
[12]
[50]
ground biomass occur in 97% of the world’s forests, with average biomass deficits of ~16% near edges. A
recent study further adds that small patch sizes and irregular geometries dramatically exacerbate biomass
loss, showing how structural vulnerability accelerates forest degradation in highly fragmented landscapes .
[51]

Collectively, these empirical studies converge on a fundamental pattern: degradation is a spatially extensive,
structurally mediated, and pressure-dependent process, rather than a localized or binary phenomenon (e.g.,
arbitrarily defined edge strips). The mechanisms they document—microclimatic changes, shifts in species
interactions, increased tree mortality, fire susceptibility, and biomass decline—behave like diffusion
processes traveling from disturbance sources into forest interiors. This is directly compatible with the
exponential decay kernel adopted in RACZ, which is grounded in mathematical ecology and diffusion
theory [35,42] . Through the α-β decomposition, RACZ captures both: (i) the potential extent of influence (α),
reflecting the cumulative burden of external anthropogenic forces; and (ii) the resistance-based attenuation
(β), reflecting structural susceptibility. In this sense, RACZ not only mirrors but formalizes and quantifies the
ecological mechanisms that have been described qualitatively for decades.

The integration of external pressure and internal susceptibility is particularly relevant for carbon crediting,
where traditional methodologies assume that carbon benefits derive solely from the avoidance of
deforestation. These approaches neglect the large and growing body of evidence showing that intact forests
adjacent to deforestation edges experience significant carbon losses via degradation. By restricting crediting
to areas within the RACZ envelope—that is, where degradation risk is empirically and theoretically
supported—the model improves the environmental integrity of carbon credits. It prevents over-crediting in
low-pressure landscapes where risk is minimal and appropriately recognizes larger vulnerable areas in highly
pressured, fragmented forests. In doing so, RACZ aligns carbon-accounting practices with contemporary
scientific understanding of forest degradation, promoting transparency, defensibility, and ecological realism.