Remote sensing enables the quantification of tropical deforestation with high spatial resolution. This in-depth mapping has led to substantial advances in the analysis of continent-wide fragmentation of tropical forests. 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 distributions have been observed in many natural phenomena such as wildfires, landslides and earthquakes. The principles of percolation theory 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 theory, 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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The Overview, Design concepts and Details (ODD) protocol for describing Individual-and Agent-Based Models (ABMs) is now widely accepted and used to document such models in journal articles. As a standardized document for providing a consistent, logical and readable account of the structure and dynamics of ABMs, some research groups also find it useful as a workflow for model design. Even so, there are still limitations to ODD that obstruct its more widespread adoption. Such limitations are discussed and addressed in this paper: the limited availability of guidance on how to use ODD; the length of ODD documents; limitations of ODD for highly complex models; lack of su icient details of many ODDs to enable reimplementation without access to the model code; and the lack of provision for sections in the document structure covering model design rationale, the model's underlying narrative, and the means by which the model's fitness for purpose is evaluated. We document the steps we have taken to provide better guidance on: structuring complex ODDs and an ODD summary for inclusion in a journal article (with full details in supplementary material; Table ); using ODD to JASSS, ( ) , http://jasss.soc.surrey.ac.uk/ / / .html Doi: . /jasss.point readers to relevant sections of the model code; update the document structure to include sections on model rationale and evaluation. We also further advocate the need for standard descriptions of simulation experiments and argue that ODD can in principle be used for any type of simulation model. Thereby ODD would provide a lingua franca for simulation modelling.