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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Deforestation in the tropics is not only responsible for direct carbon emissions but also extends the forest edge wherein trees suffer increased mortality. Here we combine high-resolution (30 m) satellite maps of forest cover with estimates of the edge effect and show that 19% of the remaining area of tropical forests lies within 100 m of a forest edge. The tropics house around 50 million forest fragments and the length of the world's tropical forest edges sums to nearly 50 million km. Edge effects in tropical forests have caused an additional 10.3 Gt (2.1–14.4 Gt) of carbon emissions, which translates into 0.34 Gt per year and represents 31% of the currently estimated annual carbon releases due to tropical deforestation. Fragmentation substantially augments carbon emissions from tropical forests and must be taken into account when analysing the role of vegetation in the global carbon cycle.

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.

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Individual-based models (IBMs) of complex systems emerged in the 1960s and early 1970s, across diverse disciplines from astronomy to zoology. Ecological IBMs arose with seemingly independent origins out of the tradition of understanding the ecosystems dynamics of ecosystems from a 'bottom-up' accounting of the interactions of the parts. Individual trees are principal among the parts of forests. Because these models are computationally demanding, they have prospered as the power of digital computers has increased exponentially over the decades following the 1970s.This review will focus on a class of forest IBMs called gap models. Gap models simulate the changes in forests by simulating the birth, growth and death of each individual tree on a small plot of land. The summation of these plots comprise a forest (or set of sample plots on a forested landscape or region). Other, more aggregated forest IBMs have been used in global applications including cohort-based models, ecosystem demography models, etc. Gap models have been used to provide the parameters for these bulk models. Currently, gap models have grown from local-scale to continental-scale and even global-scale applications to assess the potential consequences of climate change on natural forests. Modifications to the models have enabled simulation of disturbances including fire, insect outbreak and harvest.Our objective in this review is to provide the reader with an overview of the history, motivation and applications, including theoretical applications, of these models. In a time of concern over global changes, gap models are essential tools to understand forest responses to climate change, modified disturbance regimes and other change agents. Development of forest surveys to provide the starting points for simulations and better estimates of the behavior of the diversity of tree species in response to the environment are continuing needs for improvement for these and other IBMs.

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Current technological advances mean that we are on the verge of a fusion of ecological modeling and remote sensing that should improve our prediction of ecological responses to global change for forests over continental scales. The need for such a capability could not be greater: the planet is warming (IPCC 2014) and past changes in climate have resulted in extinctions, major shifts in species distributions, and ecosystems with novel species combinations (Shugart and Woodward 2011). Predicting the consequences of warming involves extrapolation, which is always a tricky scientific proposition. The changes that human actions are causing thus highlight the need for better model prediction capabilities.Two technological innovations have the potential to bring about improved prediction of forest-ecosystem dynamics at large scales: first, innovations in airborne and satellite remote-sensing instruments are providing increased potential for large-scale measurement of forest structure, notably forest height and biomass; second, increased computing power is permitting continentalscale implementation of forest individual-based models (IBMs), which simulate the dynamic changes originating from interactions between individual trees ( Figure 1) over very large areas. Shugart and Woodward (2011) provided several examples of individual tests of model predictions against independent data for different forest IBMs. At the continental scale, however, independent data are still needed that can test IBM predictions; these data could be produced by new remote-sensing technology. If successful at these large scales, such tests will assess the accuracy of large-area predictions; if not, they can be used to improve the models. This predict-and-test cycle is the hypothetico-deductive paradigm -the scientific method often used by high-school physics teachers -applied to forest dynamics over large regions and under novel conditions. Critical to this evaluation is the statistical independence of the test data from the calibration data. Successful tests against spatially extensive data would provide confidence in direct scaling up of forest IBMs.n New infrastructure and technology: an opportunity for a new level of model-data synthesisThe scaled-up cousins of traditional ecosystem process models -both land-surface models (LSMs), which are components of the general circulation models that are Global environmental change necessitates increased predictive capacity; for forests, recent advances in technology provide the response to this challenge. "Next-generation" remote-sensing instruments can measure forest biogeochemistry and structural change, and individual-based models can predict the fates of vast numbers of simulated trees, all growing and competing according to their ecological attributes in altered environments across large areas. Application of these models at continental scales is now feasible using current computing power. The results obtained from individual-based models are testable against remotely sensed data, and so can be u...