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The parameters CI and k are descriptors of the area’s structure and do not carry spatial units. Their role in
the model is to modulate the rate at which the influence of external pressure decays across space. The
dimensional component of the decay parameter is provided by β 0. This formulation allows the model to
maintain dimensional consistency while preserving its ecological interpretation as a measure of its
susceptibility to degradation.

Mathematically, the equation ensures that β decreases with both a decrease in project area and an increase in
shape irregularity (i.e., lower CI). Conversely, beta increases as the project area grows and CI increases.
Consequently, lower decay rates are produced in structurally susceptible areas, while higher rates are
produced in more stable areas.

Application of the model
The RACZ framework was applied to two contrasting case-study landscapes to demonstrate model behavior
under differing disturbances. In both cases, land-cover data were reclassified into a binary deforestation
matrix, from which Euclidean distance-to-deforestation surfaces were generated and used as inputs to the
exponential degradation model.

The first case represents a low-pressure landscape, characterized by limited surrounding deforestation and
weak fragmentation dynamics. The second represents a high-pressure frontier landscape, where extensive
deforestation generates strong spatial gradients of degradation risk. Together, these cases demonstrate the
flexibility, scalability, and structural sensitivity of the RACZ framework.

Case study 1: low anthropogenic pressure
Case study 1 [Figure 3] is a tropical forest called Kokolopori Bonobo Natural Reserve, located between the
provinces of Tshuapa and Tshopo in the Democratic Republic of Congo, within the Congo Basin tropical
rainforest, part of the Afrotropical moist broadleaf forest biome. The region lies in the Af classification of the
Köppen-Geiger system and is characterized by high precipitation, consistently high temperatures, and the
absence of a dry season. These conditions sustain dense evergreen forests with high biomass and complex
vertical structure, forming part of one of the largest contiguous tropical forests in the world.

Case study 2: high anthropogenic pressure
Case study 2 [Figure 4] is located within the Brazilian Amazon and falls under the Am classification of the
Köppen-Geiger climatic system, characterized by uniformly high temperatures, a pronounced wet season,
and a short dry period. The area corresponds to the indigenous land Parakanã in Pará, an officially
recognized Indigenous Territory containing extensive tracts of mature evergreen forest. Although these
conditions support the functional integrity of dense tropical forests, with their high levels of biomass
accumulation and year-round ecological productivity, the project area is located within an expanding
agricultural frontier and is subject to persistent deforestation due to logging, the expansion of ranching and
regional infrastructure. These conditions generate high edge exposure and strong spatial gradients of
degradation risk along the project boundary.

RESULTS
Application of the RACZ framework to the two similar-sized while contrasting landscapes produced distinct
spatial extents and configurations of degradation risk [Figure 5], indicating differences in surrounding
deforestation pressure and landscape structure. The RACZ areas ranges from 1,150 ha in the low-pressure
landscape to 337,985 ha in the high-pressure one, confirming the sensitivity of the exponential decay model
to fragment geometry and external pressure [Table 1].