Remote sensing enables the quantification of tropical deforestation with high spatial resolution1,2. This in-depth mapping has led to substantial advances in the analysis of continent-wide fragmentation of tropical forests1,2,3,4. Here we identified approximately 130 million forest fragments in three continents that show surprisingly similar power-law size and perimeter distributions as well as fractal dimensions. Power-law distributions5,6,7 have been observed in many natural phenomena8,9 such as wildfires, landslides and earthquakes. The principles of percolation theory7,10,11 provide one explanation for the observed patterns, and suggest that forest fragmentation is close to the critical point of percolation; simulation modelling also supports this hypothesis. The observed patterns emerge not only from random deforestation, which can be described by percolation theory10,11, but also from a wide range of deforestation and forest-recovery regimes. Our models predict that additional forest loss will result in a large increase in the total number of forest fragments—at maximum by a factor of 33 over 50 years—as well as a decrease in their size, and that these consequences could be partly mitigated by reforestation and forest protection.
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Achard, F. et al. Determination of tropical deforestation rates and related carbon losses from 1990 to 2010. Glob. Change Biol. 20, 2540–2554 (2014)
Hansen, M. C. et al. High-resolution global maps of 21st-century forest cover change. Science 342, 850–853 (2013)
Haddad, N. M. et al. Habitat fragmentation and its lasting impact on Earth’s ecosystems. Sci. Adv. 1, e1500052 (2015)
Chaplin-Kramer, R. et al. Degradation in carbon stocks near tropical forest edges. Nat. Commun. 6, 10158 (2015)
Storch, D., Marquet, P. A. & Brown, J. H. Scaling Biodiversity (Cambridge Univ. Press, 2007)
Marquet, P. A. et al. Scaling and power-laws in ecological systems. J. Exp. Biol. 208, 1749–1769 (2005)
Sornette, D. Critical Phenomena in Natural Sciences. Chaos, Fractals, Selforganization and Disorder: Concepts and Tools (Springer, 2006)
Turcotte, D. L. & Malamud, B. D. Landslides, forest fires, and earthquakes: examples of self-organized critical behavior. Physica A 340, 580–589 (2004)
Bak, P. How Nature Works. The Science of Self-Organized Criticality (Copernicus, 1996)
Stauffer, D. & Aharony, A. Introduction to Percolation Theory (Taylor & Francis, 1994)
Christensen, K. & Moloney, N. R. Complexity and Criticality Vol. 1 (Imperial College Press, 2005)
Le Quéré, C. et al. Global carbon budget 2014. Earth Syst. Sci. Data 7, 47–85 (2015)
Wright, S. J. Tropical forests in a changing environment. Trends Ecol. Evol. 20, 553–560 (2005)
Lewis, S. L., Edwards, D. P. & Galbraith, D. Increasing human dominance of tropical forests. Science 349, 827–832 (2015)
Houghton, R. A. The worldwide extent of land-use change. Bioscience 44, 305–313 (1994)
Laurance, W. F. et al. The fate of Amazonian forest fragments: a 32-year investigation. Biol. Conserv. 144, 56–67 (2011)
Saberi, A. A. Recent advances in percolation theory and its applications. Phys. Rep. 578, 1–32 (2015)
Milne, B. T. et al. Detection of critical densities associated with piñon-juniper woodland ecotones. Ecology 77, 805–821 (1996)
Drossel, B. & Schwabl, F. Self-organized critical forest-fire model. Phys. Rev. Lett. 69, 1629–1632 (1992)
Ziff, R. M. Test of scaling exponents for percolation-cluster perimeters. Phys. Rev. Lett. 56, 545–548 (1986)
Solé, R. V. & Bascompte, J. Self-Organization in Complex Ecosystems Vol. 42 (Princeton Univ. Press, 2006)
Turner, M. G., Gardner, R. H. & O’Neill, R. V. Landscape Ecology in Theory and Practice (Springer, 2001)
Gardner, R. H., Milne, B. T., Turner, M. G. & O’Neill, R. V. Neutral models for the analysis of broadscale landscape pattern. Landsc. Ecol. 1, 19–28 (1987)
Bascompte, J. & Solé, R. V. Habitat fragmentation and extinction thresholds in spatially explicit models. J. Anim. Ecol. 65, 465–473 (1996)
Meyfroidt, P. & Lambin, E. F. Global forest transition: prospects for an end to deforestation. Annu. Rev. Environ. Resour. 36, 343–371 (2011)
Rudel, T. K. et al. Forest transitions: towards a global understanding of land use change. Glob. Environ. Change 15, 23–31 (2005)
Debinski, D. M. & Holt, R. D. A survey and overview of habitat fragmentation experiments. Conserv. Biol. 14, 342–355 (2000)
Andrén, H. Effects of habitat fragmentation on birds and mammals in landscapes with different proportions of suitable habitat: a review. Oikos 71, 355–366 (1994)
Brinck, K. et al. High resolution analysis of tropical forest fragmentation and its impact on the global carbon cycle. Nat. Commun. 8, 14855 (2017)
Barnosky, A. D. et al. Approaching a state shift in Earth’s biosphere. Nature 486, 52–58 (2012)
R Core Team. R: A Language and Environment for Statistical Computing ; https://www.R-project.org/ (R Foundation for Statistical Computing, 2015)
South, A. rworldmap: A new R package for mapping global data. R J. 3, 35–43 (2011)
Ostberg, S., Schaphoff, S., Lucht, W. & Gerten, D. Three centuries of dual pressure from land use and climate change on the biosphere. Environ. Res. Lett. 10, 044011 (2015)
CDO 2015: Climate Data Operators. The Max Planck Institute for Meteorology, http://www.mpimet.mpg.de/cdo (2017)
Virkar, Y. & Clauset, A. Power-law distributions in binned empirical data. Ann. Appl. Stat. 8, 89–119 (2014)
Sugihara, G. & May, R. M. Applications of fractals in ecology. Trends Ecol. Evol. 5, 79–86 (1990)
Bisoi, A. K. & Mishra, J. On calculation of fractal dimension of images. Pattern Recognit. Lett. 22, 631–637 (2001)
The project has been supported by the Helmholtz Alliance Remote Sensing and Earth System Dynamics. A.H. and T.W. were supported by the European Research Council Advanced Grant 233066. We thank A. Hein and A. Bogdanowski for assistance, A. Hartmann for discussion, M. Dantas de Paula for data handling, and S. Paulick and F. Bohn for technical support.
The authors declare no competing financial interests.
Reviewer Information Nature thanks B. Barzel, B. DeVries, R. Ewers and P. Marquet for their contribution to the peer review of this work.
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Extended data figures and tables
Extended Data Figure 1 Continental-scale fragment perimeter distribution of tropical and subtropical forest.
a–c, Observed fragment perimeter distributions (orange dots; fragment perimeters >1,000 m) for the Americas (a, n = 55.5 million fragments), Africa (b, n = 44.8 million fragments) and Asia–Australia (c, n = 30.5 million fragments); solid black lines show the fitted power laws with exponent κ. Forest fragments were estimated from Hansen’s forest cover map2 (see Methods for details).
a, A landscape occupied by 90% randomly and independently distributed forest cells (green, p = 0.9) is dominated by one large cluster. b, For values of p larger than the percolation threshold (p = 0.6 > 0.59) there exists a continuous path from two opposite-side borders (yellow path within the spanning cluster). c, Below the percolation threshold (here, p = 0.55 < 0.59) larger clusters emerge but no spanning cluster can be detected. d, A landscape occupied by 20% forest shows small unconnected clusters. Landscape size is 20 × 20 cells.
a, Spatial patterns of fragments for different snapshots in time, and b, fragment size distributions (green bars indicate values from the FRAG model, solid black line indicates observation from remote sensing; fragment sizes ≥ 0.1 ha). The critical phase at which the spanning fragment disappears is indicated as ‘critical’. For each phase, a map of a selected subarea of 900 ha is shown (from the FRAG model, cleared sites are white and colours indicate fragment size; see Methods for details). See also Supplementary Video 1.
Dynamics of deforestation rate (percentage per year related to landscape size), forest cover (%), number of fragments and mean fragment size (in ha) in America projected until 2050 using the FRAG model. a, Scenario S1 assumes constant deforestation without reforestation. b, Scenario S2 considers added reforestation. c, Scenario S3 assumes that deforestation decreases yearly. d, Scenario S4 considers a stronger yearly reduction in deforestation, leading to a turning point with net reforestation. See Methods for details. e, Comparison of observed (Table 1) and projected fragment numbers (rounded) and mean fragment size.
a, Spatial patterns of fragments for different snapshots in time, and b, fragment size distributions (green bars indicate values from the FRAG-B model, dborder = 0.995; solid black line denotes observation from remote sensing; fragment sizes ≥ 0.1 ha). The critical phase at which the spanning fragment disappears is indicated as ‘critical’. For each phase, a map of a selected subarea of 900 ha is shown (from the FRAG-B model, cleared sites are white and colours indicate fragment size; see Methods for details). See also Supplementary Video 2.
a, Critical points and b, fitted power-law exponents of fragment sizes for different probabilities (dborder) of deforestation restricted to the border of forest fragments (FRAG-B model for landscape size of Cmax = 106 cells). Each point in b represents one power-law fit based on n = 29,788 (dborder = 0) to n = 1,278 (dborder = 1.0) fragments (see Methods for detailed values). Calculated R2 values of fits are approximately 1 for the entire range of dborder probabilities (see Methods).
a, For different landscape sizes, with Cmax based on the FRAG model. b, Comparison between random (FRAG model) and border deforestation (FRAG-B model, dborder = 0.5 and dborder = 0.9). In b, the landscape size was Cmax = 1010 cells. In both a and b we show only results for fits with correlation coefficients R2 of ≥0.9. The grey horizontal line shows the exponent predicted by percolation theory.
Extended Data Figure 8 Dynamics of fragment numbers comparing implicit and explicit modelling of reforestation.
a, We assume a gross deforestation rate of d = 0.51% per year and a reforestation rate of r = 0.14% per year for the Americas1 (with random and independent selection of sites for deforestation and reforestation, blue dots). This model version is equivalent to the original FRAG model assuming a net deforestation rate of dnet = 0.37% per year (green line). b, The same scenario (green line as in a), but now explicit reforestation occurs exclusively at the border of forest fragments (blue dots).
Dynamics of forest fragment numbers (normalized by landscape size Cmax) in America using a, the FRAG model and b, the FRAG-B model (dborder = 0.5) for different landscape sizes. The pattern is independent of landscape size.
Extended Data Figure 10 Dynamics of the number of forest fragments, without (FRAG model) and with (FRAG-P model) consideration of protected forest areas.
Simulations with the FRAG-P model account for 10% (fprotected = 0.1, orange) and 50% (fprotected = 0.5, blue) of the landscape area to be protected while the remaining forest area is prone to deforestation (FRAG model). Forest areas affected by deforestation in both models were simulated using a deforestation rate of d = 0.51% per year in the Americas1.
Fragment size distributions (green bars: FRAG, line: observation from remote sensing) and the spatial patterns of fragments on a map of a selected sub-area of 900 ha is shown (FRAG, cleared sites are white and colours indicate fragment size, see Methods for details). For graphical purposes only, fragments < 10 ha are also shown. (MPG 4739 kb)
Fragment size distributions (green bars: FRAG-B with dborder = 0.995, line: observation from remote sensing) and the spatial patterns of fragments on a map of a selected sub-area of 900 ha is shown (FRAG-B, cleared sites are white and colours indicate fragment size, see Methods for details). For graphical purposes only, fragments < 10 ha are also shown. (MPG 2238 kb)
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Taubert, F., Fischer, R., Groeneveld, J. et al. Global patterns of tropical forest fragmentation. Nature 554, 519–522 (2018). https://doi.org/10.1038/nature25508
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