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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Stochasticity is a core component of ecology, as it underlies key processes that structure and create variability in nature. Despite its fundamental importance in ecological systems, the concept is often treated as synonymous with unpredictability in community ecology, and studies tend to focus on single forms of stochasticity rather than taking a more holistic view. This has led to multiple narratives for how stochasticity mediates community dynamics. Here, we present a framework that describes how different forms of stochasticity (notably demographic and environmental stochasticity) combine to provide underlying and predictable structure in diverse communities. This framework builds on the deep ecological understanding of stochastic processes acting at individual and population levels and in modules of a few interacting species. We support our framework with a mathematical model that we use to synthesize key literature, demonstrating that stochasticity is more than simple uncertainty. Rather, stochasticity has profound and predictable effects on community dynamics that are critical for understanding how diversity is maintained. We propose next steps that ecologists might use to explore the role of stochasticity for structuring communities in theoretical and empirical systems, and thereby enhance our understanding of community dynamics.

Precise descriptions of forest productivity, biomass, and structure are essential for understanding ecosystem responses to climatic and anthropogenic changes. However, relations between these components are complex, in particular for tropical forests.We developed an approach to simulate carbon dynamics in the Amazon rainforest including around 410 billion individual trees within 7.8 million km 2 . We integrated canopy height observations from space-borne LIDAR in order to quantify spatial variations in forest state and structure reflecting small-scale to large-scale natural and anthropogenic disturbances.Under current conditions, we identified the Amazon rainforest as a carbon sink, gaining 0.56 GtC per year. This carbon sink is driven by an estimated mean gross primary productivity (GPP) of 25.1 tC ha −1 a −1 , and a mean woody aboveground net primary productivity (wANPP) of 4.2 tC ha −1 a −1 . We found that successional states play an important role for the relations between productivity and biomass. Forests in early to intermediate successional states are the most productive, and woody above-ground carbon use efficiencies are non-linear. Simulated values can be compared to observed carbon fluxes at various spatial resolutions (>40 m). Notably, we found that our GPP corresponds to the values derived from MODIS. For NPP, spatial differences can be observed due to the consideration of forest successional states in our approach.We conclude that forest structure has a substantial impact on productivity and biomass. It is an essential factor that should be taken into account when estimating current carbon budgets or analyzing climate change scenarios for the Amazon rainforest.

Large areas of tropical forests have been lost through deforestation, resulting in fragmented forest landscapes. However, the dynamics of forest fragmentation are still unknown, especially the critical forest edge areas, which are sources of carbon emissions due to increased tree mortality. We analyzed the changes in forest fragmentation for the entire tropics using high-resolution forest cover maps. We found that forest edge area increased from 27 to 31% of the total forest area in just 10 years, with the largest increase in Africa. The number of forest fragments increased by 20 million with consequences for connectivity of tropical landscapes. Simulations suggest that ongoing deforestation will further accelerate forest fragmentation. By 2100, 50% of tropical forest area will be at the forest edge, causing additional carbon emissions of up to 500 million MT carbon per year. Thus, efforts to limit fragmentation in the world's tropical forests are important for climate change mitigation.