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Satellite data and modelling reveal that tropical forest fragments have similar size distributions across continents, and that forest fragmentation is close to a critical point, beyond which fragment numbers will strongly increase. Forest fragmentation patterns Agriculture, logging and urban growth have caused unprecedented losses of tropical forest in the past few decades. Franziska Taubert and colleagues examine patterns of tropical forest fragmentation using high-resolution satellite data. They identify 130 million forest fragments across three continental regions, which each have size frequency distributions that are similar, being described by power laws with almost identical exponents. The principles of percolation theory provide one explanation for the observed patterns, and suggest that forest fragmentation is close to a critical threshold, beyond which fragmentation can be expected to accelerate strongly. Numerical modelling supports this hypothesis, suggesting that additional forest loss will strongly increase the total number of forest fragments over the next 50 years. However, the simulations also suggest that reforestation and reductions in deforestation can mitigate this projected increase in fragmentation. Remote sensing enables the quantification of tropical deforestation with high spatial resolution 1 , 2 . This in-depth mapping has led to substantial advances in the analysis of continent-wide fragmentation of tropical forests 1 , 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 distributions 5 , 6 , 7 have been observed in many natural phenomena 8 , 9 such as wildfires, landslides and earthquakes. The principles of percolation theory 7 , 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 theory 10 , 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.

Grasslands contribute to global biogeochemical cycles and can host a high number of plant species. Both-species dynamics and biogeochemical fluxes-are influenced by abiotic and biotic environmental factors, management and natural disturbances. In order to understand and project grassland dynamics under global change, vegetation models which explicitly capture all relevant processes and drivers are required. However, the parameterization of such models is often challenging. Here, we report on testing an individual- and process-based model for simulating the dynamics and structure of a grassland experiment in temperate Europe. We parameterized the model for three species and confront simulated grassland dynamics with empirical observations of their monocultures and one two-species mixture. The model reproduces general trends of vegetation patterns (vegetation cover and height, aboveground biomass and leaf area index) for the monocultures and two-species community. For example, the model simulates well an average annual grassland cover of 70% in the species mixture (observed cover of 77%), but also shows mismatches with specific observation values (e.g. for aboveground biomass). By a sensitivity analysis of the applied inverse model parameterization method, we demonstrate that multiple vegetation attributes are important for a successful parameterization while leaf area index revealed to be of highest relevance. Results of our study pinpoint to the need of improved grassland measurements (esp. of temporally higher resolution) in close combination with advanced modelling approaches.

Remote sensing is an important tool to monitor forests to rapidly detect changes due to global change and other threats. Here, we present a novel methodology to infer the tree size distribution from light detection and ranging (lidar) measurements. Our approach is based on a theoretical leaf–tree matrix derived from allometric relations of trees. Using the leaf–tree matrix, we compute the tree size distribution that fit to the observed leaf area density profile via lidar. To validate our approach, we analyzed the stem diameter distribution of a tropical forest in Panama and compared lidar-derived data with data from forest inventories at different spatial scales (0.04 ha to 50 ha). Our estimates had a high accuracy at scales above 1 ha (1 ha: root mean square error (RMSE) 67.6 trees ha−1/normalized RMSE 18.8%/R² 0.76; 50 ha: 22.8 trees ha−1/6.2%/0.89). Estimates for smaller scales (1-ha to 0.04-ha) were reliably for forests with low height, dense canopy or low tree height heterogeneity. Estimates for the basal area were accurate at the 1-ha scale (RMSE 4.7 tree ha−1, bias 0.8 m² ha−1) but less accurate at smaller scales. Our methodology, further tested at additional sites, provides a useful approach to determine the tree size distribution of forests by integrating information on tree allometries.

Modelling and applying multivariate distributions is an important topic in ecology. In particular in plant ecology, the multidimensional nature of plant traits comes with challenges such as wide ranges in observations as well as correlations between several characteristics. In other disciplines (e.g., finances and economics), copulas have been proven as a valuable tool for modelling multivariate distributions. However, applications in ecology are still rarely used. Here, we present a copula-based methodology of fitting multivariate distributions to ecological data. We used product copula models to fit multidimensional plant traits, on example of observations from the global trait database TRY. The fitting procedure is split into two parts: fitting the marginal distributions and fitting the copula. We found that product copulas are well suited to model ecological data as they have the advantage of being asymmetric (similar to the observed data). Challenges in the fitting were mainly addressed to limited amount of data. In view of growing global databases, we conclude that copula modelling provides a great potential for ecological modelling.

Network analysis is an important tool to analyze the structure of complex systems such as tropical forests. Here, we infer spatial proximity networks in tropical forests by using network science. First, we focus on tree neighborhoods to derive spatial tree networks from forest inventory data. In a second step, we construct species networks to describe the potential for interactions between species. We find remarkably similar tree and species networks among tropical forests in Panama, Sri Lanka and Taiwan. Across these sites only 32 to 51% of all possible connections between species pairs were realized in the species networks. The species networks show the common small-world property and constant node degree distributions not yet described and explained by network science. Our application of network analysis to forest ecology provides a new approach in biodiversity research to quantify spatial neighborhood structures for better understanding interactions between tree species. Our analyses show that details of tree positions and sizes have no important influence on the detected network structures. This suggests existence of simple principles underlying the complex interactions in tropical forests.

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 km2. 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.

The search for simple principles underlying the complex architecture of ecological communities such as forests still challenges ecological theorists. We use tree diameter distributions—fundamental for deriving other forest attributes—to describe the structure of tropical forests. Here we argue that tree diameter distributions of natural tropical forests can be explained by stochastic packing of tree crowns representing a forest crown packing system: a method usually used in physics or chemistry. We demonstrate that tree diameter distributions emerge accurately from a surprisingly simple set of principles that include site-specific tree allometries, random placement of trees, competition for space, and mortality. The simple static model also successfully predicted the canopy structure, revealing that most trees in our two studied forests grow up to 30–50 m in height and that the highest packing density of about 60% is reached between the 25- and 40-m height layer. Our approach is an important step toward identifying a minimal set of processes responsible for generating the spatial structure of tropical forests.

The relation between species diversity and ecosystem functioning is one of the most frequently discussed topics in ecology. Experiments often revealed an increase of productivity in species‐rich ecosystems. But large variations in these relationships, both on a local scale and in comparisons of sites along environmental gradients, still challenge our understanding of the role of species (with specific traits) and their interactions in ecosystems. In this study, we explored the role of species traits for ecosystem functioning. We used an individual‐based mechanistic grassland model which captures intra‐ and interspecific competition between plants for light and soil resources. We explored how the dynamics and productivity of grasslands are influenced by species traits and analyzed in a simulation study two species, which differ only in one particular trait. Our focus was on traits that determine how species can cope with resource limitations, for which we identified their relative importance for (1) individual plant growth, (2) monoculture dynamics, and (3) species mixture dynamics. We observed diverse relationships between species traits and different vegetation attributes for the different ecosystem levels. Most traits showed positive but saturating trends of increasing trait values but the variability in these relations increased in monocultures with intraspecific plant interactions and even more pronounced in mixtures with interspecific interactions. Using a process‐based grassland model, we were able to simulate overyielding even though it was not correlated with trait values or trait differences between both species. Correlations were also not found in terms of stability of vegetation dynamics. In contrast, for some traits already small differences supported the dominance of a species in the mixture in which species dynamics generally followed trade‐offs. The here presented simulation study demonstrates the use of process‐based models for analyzing trait‐productivity relationships in grasslands. Such models can complement previous approaches in empirical and theoretical biodiversity research and can help to move closer to understanding the mechanisms governing grassland dynamics.

European grassland management has often favoured high production through frequent mowing and heavy fertilisation over biodiversity conservation, which is typically supported by less intensive management. Besides management, climate change and extremes are increasingly affecting grassland productivity and biodiversity, requiring timely adaptation of management practices. Here, we describe the development of a prototype Digital Twin (pDT) of grassland biodiversity dynamics intended to support researchers, farmers or regulatory decision-makers in monitoring the current state of selected grassland sites and projecting their future state under various management and climate scenarios.

Patterns that resemble strongly skewed size distributions are frequently observed in ecology. A typical example represents tree size distributions of stem diameters. Empirical tests of ecological theories predicting their parameters have been conducted, but the results are difficult to interpret because the statistical methods that are applied to fit such decaying size distributions vary. In addition, binning of field data as well as measurement errors might potentially bias parameter estimates. Here, we compare three different methods for parameter estimation--the common maximum likelihood estimation (MLE) and two modified types of MLE correcting for binning of observations or random measurement errors. We test whether three typical frequency distributions, namely the power-law, negative exponential and Weibull distribution can be precisely identified, and how parameter estimates are biased when observations are additionally either binned or contain measurement error. We show that uncorrected MLE already loses the ability to discern functional form and parameters at relatively small levels of uncertainties. The modified MLE methods that consider such uncertainties (either binning or measurement error) are comparatively much more robust. We conclude that it is important to reduce binning of observations, if possible, and to quantify observation accuracy in empirical studies for fitting strongly skewed size distributions. In general, modified MLE methods that correct binning or measurement errors can be applied to ensure reliable results.