Mapping forest restoration costs using a spatial–economic framework for fractal deforestation patterns

This work addresses a fundamental limitation in current forest restoration strategies: degraded landscapes are highly fragmented, yet investment decisions are rarely guided by spatially explicit economic indicators. As a result, restoration efforts often depend on voluntary actions and fail to alter the spatial configurations that allow deforestation to persist and spread. We present a framework that integrates fractal theory¹, landscape topology², and economic reasoning to convert the geometry of deforested areas into measurable restoration costs at the pixel level.

Using ecological skeletons² and critical thresholds of natural capital, we derive a spatial–economic metric that assigns an intervention cost to every degraded patch. This leads to investment and priority maps that explicitly show where action should be taken, the expected financial effort required, and the order in which patches should be restored. By turning sophisticated fractal diagnostics into practical decision-support tools, this work provides a quantitative foundation for allocating public and private funds to restoration actions that maximize impact per unit of investment.

¹ Urgilez-Clavijo, A., Rivas-Tabares, D. A., Martín-Sotoca, J. J., & Tarquis Alfonso, A. M. (2021). Local fractal connections to characterize the spatial processes of deforestation in the Ecuadorian Amazon. Entropy, 23(6), 748.

² Urgilez-Clavijo, A., Rivas-Tabares, D. A., Gobin, A., Tarquis Alfonso, A. M., & de la Riva Fernández, J. (2025). Understanding local connectivity and complexity in the skeleton of deforestation. Scientific Reports, 15(1), 18192.