Global patterns of tropical forest fragmentation.

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.

General statistical scaling laws for stability in ecological systems.

Ecological stability refers to a family of concepts used to describe how systems of interacting species vary through time and respond to disturbances. Because observed ecological stability depends on sampling scales and environmental context, it is notoriously difficult to compare measurements across sites and systems. Here, we apply stochastic dynamical systems theory to derive general statistical scaling relationships across time, space, and ecological level of organisation for three fundamental stability aspects: resilience, resistance, and invariance. These relationships can be calibrated using random or representative samples measured at individual scales, and projected to predict average stability at other scales across a wide range of contexts. Moreover deviations between observed vs. extrapolated scaling relationships can reveal information about unobserved heterogeneity across time, space, or species. We anticipate that these methods will be useful for cross-study synthesis of stability data, extrapolating measurements to unobserved scales, and identifying underlying causes and consequences of heterogeneity.

Lianas in silico, ecological insights from a model of structural parasitism.

Tropical forests are a critical component of the Earth system, storing half of the global forest carbon stocks and accounting for a third of terrestrial photosynthesis. Lianas are structural parasites that can substantially reduce the carbon sequestration capacity of these forests. Simulations of this peculiar growth form have only recently started and a single vegetation model included lianas so far. In this work we present a new liana implementation within the individual based model Formind. Initial tests indicate high structural realism both horizontal and vertical. In particular, we benchmarked the model against empirical observations of size distribution, mean liana cluster size and vertical leaf distribution for the Paracou site in French Guiana. Our model predicted a reduction of above-ground biomass between 10% for mature stands to 45% for secondary plots upon inclusion of lianas in the simulations. The reduced biomass was the result of a lower productivity due to a combination of lower tree photosynthesis and high liana respiration. We evaluated structural metrics (LAI, basal area, mean tree-height) and carbon fluxes (GPP, respiration) by comparing simulations with and without lianas. At the equilibrium, liana productivity was 1.9t C ha - 1 y - 1 , or 23% of the total GPP and the forest carbon stocks were between 5% and 11% lower in simulations with lianas. We also highlight the main strengths and limitations of this new approach and propose new field measurements to further the understanding of liana ecology in a modelling framework.

The structure of tropical forests and sphere packings.

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.

What drives the spatial distribution and dynamics of local species richness in tropical forest?

Understanding the structure and dynamics of highly diverse tropical forests is challenging. Here we investigate the factors that drive the spatio-temporal variation of local tree numbers and species richness in a tropical forest (including 1250 plots of 20 × 20 m2). To this end, we use a series of dynamic models that are built around the local spatial variation of mortality and recruitment rates, and ask which combination of processes can explain the observed spatial and temporal variation in tree and species numbers. We find that processes not included in classical neutral theory are needed to explain these fundamental patterns of the observed local forest dynamics. We identified a large spatio-temporal variability in the local number of recruits as the main missing mechanism, whereas variability of mortality rates contributed to a lesser extent. We also found that local tree numbers stabilize at typical values which can be explained by a simple analytical model. Our study emphasized the importance of spatio-temporal variability in recruitment beyond demographic stochasticity for explaining the local heterogeneity of tropical forests.

Do abundance distributions and species aggregation correctly predict macroecological biodiversity patterns in tropical forests?

AIM: It has been recently suggested that different 'unified theories of biodiversity and biogeography' can be characterized by three common 'minimal sufficient rules': (1) species abundance distributions follow a hollow curve, (2) species show intraspecific aggregation, and (3) species are independently placed with respect to other species. Here, we translate these qualitative rules into a quantitative framework and assess if these minimal rules are indeed sufficient to predict multiple macroecological biodiversity patterns simultaneously. LOCATION: Tropical forest plots in Barro Colorado Island (BCI), Panama, and in Sinharaja, Sri Lanka. METHODS: We assess the predictive power of the three rules using dynamic and spatial simulation models in combination with census data from the two forest plots. We use two different versions of the model: (1) a neutral model and (2) an extended model that allowed for species differences in dispersal distances. In a first step we derive model parameterizations that correctly represent the three minimal rules (i.e. the model quantitatively matches the observed species abundance distribution and the distribution of intraspecific aggregation). In a second step we applied the parameterized models to predict four additional spatial biodiversity patterns. RESULTS: Species-specific dispersal was needed to quantitatively fulfil the three minimal rules. The model with species-specific dispersal correctly predicted the species-area relationship, but failed to predict the distance decay, the relationship between species abundances and aggregations, and the distribution of a spatial co-occurrence index of all abundant species pairs. These results were consistent over the two forest plots. MAIN CONCLUSIONS: The three 'minimal sufficient' rules only provide an incomplete approximation of the stochastic spatial geometry of biodiversity in tropical forests. The assumption of independent interspecific placements is most likely violated in many forests due to shared or distinct habitat preferences. Furthermore, our results highlight missing knowledge about the relationship between species abundances and their aggregation.

Moving beyond abundance distributions: neutral theory and spatial patterns in a tropical forest.

Assessing the relative importance of different processes that determine the spatial distribution of species and the dynamics in highly diverse plant communities remains a challenging question in ecology. Previous modelling approaches often focused on single aggregated forest diversity patterns that convey limited information on the underlying dynamic processes. Here, we use recent advances in inference for stochastic simulation models to evaluate the ability of a spatially explicit and spatially continuous neutral model to quantitatively predict six spatial and non-spatial patterns observed at the 50 ha tropical forest plot on Barro Colorado Island, Panama. The patterns capture different aspects of forest dynamics and biodiversity structure, such as annual mortality rate, species richness, species abundance distribution, beta-diversity and the species-area relationship (SAR). The model correctly predicted each pattern independently and up to five patterns simultaneously. However, the model was unable to match the SAR and beta-diversity simultaneously. Our study moves previous theory towards a dynamic spatial theory of biodiversity and demonstrates the value of spatial data to identify ecological processes. This opens up new avenues to evaluate the consequences of additional process for community assembly and dynamics.

Neighborhood diversity of large trees shows independent species patterns in a mixed dipterocarp forest in Sri Lanka.

Interactions among neighboring individuals influence plant performance and should create spatial patterns in local community structure. In order to assess the role of large trees in generating spatial patterns in local species richness, we used the individual species-area relationship (ISAR) to evaluate the species richness of trees of different size classes (and dead trees) in circular neighborhoods with varying radius around large trees of different focal species. To reveal signals of species interactions, we compared the ISAR function of the individuals of focal species with that of randomly selected nearby locations. We expected that large trees should strongly affect the community structure of smaller trees in their neighborhood, but that these effects should fade away with increasing size class. Unexpectedly, we found that only few focal species showed signals of species interactions with trees of the different size classes and that this was less likely for less abundant focal species. However, the few and relatively weak departures from independence were consistent with expectations of the effect of competition for space and the dispersal syndrome on spatial patterns. A noisy signal of competition for space found for large trees built up gradually with increasing life stage; it was not yet present for large saplings but detectable for intermediates. Additionally, focal species with animal-dispersed seeds showed higher species richness in their neighborhood than those with gravity- and gyration-dispersed seeds. Our analysis across the entire ontogeny from recruits to large trees supports the hypothesis that stochastic effects dilute deterministic species interactions in highly diverse communities. Stochastic dilution is a consequence of the stochastic geometry of biodiversity in species-rich communities where the identities of the nearest neighbors of a given plant are largely unpredictable. While the outcome of local species interactions is governed for each plant by deterministic fitness and niche differences, the large variability of competitors causes also a large variability in the outcomes of interactions and does not allow for strong directed responses at the species level. Collectively, our results highlight the critical effect of the stochastic geometry of biodiversity in structuring local spatial patterns of tropical forest diversity.

A new approach to derive productivity of tropical forests using radar remote sensing measurements.

Deriving gross & net primary productivity (GPP & NPP) and carbon turnover time of forests from remote sensing remains challenging. This study presents a novel approach to estimate forest productivity by combining radar remote sensing measurements, machine learning and an individual-based forest model. In this study, we analyse the role of different spatial resolutions on predictions in the context of the Radar BIOMASS mission (by ESA). In our analysis, we use the forest gap model FORMIND in combination with a boosted regression tree (BRT) to explore how spatial biomass distributions can be used to predict GPP, NPP and carbon turnover time (τ) at different resolutions. We simulate different spatial biomass resolutions (4 ha, 1 ha and 0.04 ha) in combination with different vertical resolutions (20, 10 and 2 m). Additionally, we analysed the robustness of this approach and applied it to disturbed and mature forests. Disturbed forests have a strong influence on the predictions which leads to high correlations (R2 > 0.8) at the spatial scale of 4 ha and 1 ha. Increased vertical resolution leads generally to better predictions for productivity (GPP & NPP). Increasing spatial resolution leads to better predictions for mature forests and lower correlations for disturbed forests. Our results emphasize the value of the forthcoming BIOMASS satellite mission and highlight the potential of deriving estimates for forest productivity from information on forest structure. If applied to more and larger areas, the approach might ultimately contribute to a better understanding of forest ecosystems.

Testing the independent species' arrangement assertion made by theories of stochastic geometry of biodiversity.

The assertion that the spatial location of different species is independent of each other is fundamental in major ecological theories such as neutral theory that describes a stochastic geometry of biodiversity. However, this assertion has rarely been tested. Here we use techniques of spatial point pattern analysis to conduct a comprehensive test of the independence assertion by analysing data from three large forest plots with different species richness: a species-rich tropical forest at Barro Colorado Island (Panama), a tropical forest in Sinharaja (Sri Lanka), and a temperate forest in Changbaishan (China). We hypothesize that stochastic dilution effects owing to increasing species richness overpower signals of species associations, thereby yielding approximate species independence. Indeed, the proportion of species pairs showing: (i) no significant interspecific association increased with species richness, (ii) segregation decreased with species richness, and (iii) small-scale interspecific interaction decreased with species richness. This suggests that independence may indeed be a good approximation in the limit of very species-rich communities. Our findings are a step towards a better understanding of factors governing species-rich communities and we propose a hypothesis to explain why species placement in species-rich communities approximates independence.

Statistical inference for stochastic simulation models--theory and application.

Statistical models are the traditional choice to test scientific theories when observations, processes or boundary conditions are subject to stochasticity. Many important systems in ecology and biology, however, are difficult to capture with statistical models. Stochastic simulation models offer an alternative, but they were hitherto associated with a major disadvantage: their likelihood functions can usually not be calculated explicitly, and thus it is difficult to couple them to well-established statistical theory such as maximum likelihood and Bayesian statistics. A number of new methods, among them Approximate Bayesian Computing and Pattern-Oriented Modelling, bypass this limitation. These methods share three main principles: aggregation of simulated and observed data via summary statistics, likelihood approximation based on the summary statistics, and efficient sampling. We discuss principles as well as advantages and caveats of these methods, and demonstrate their potential for integrating stochastic simulation models into a unified framework for statistical modelling.

Accelerated forest fragmentation leads to critical increase in tropical forest edge area.

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.

Tackling unresolved questions in forest ecology: The past and future role of simulation models.

Understanding the processes that shape forest functioning, structure, and diversity remains challenging, although data on forest systems are being collected at a rapid pace and across scales. Forest models have a long history in bridging data with ecological knowledge and can simulate forest dynamics over spatio-temporal scales unreachable by most empirical investigations.We describe the development that different forest modelling communities have followed to underpin the leverage that simulation models offer for advancing our understanding of forest ecosystems.Using three widely applied but contrasting approaches - species distribution models, individual-based forest models, and dynamic global vegetation models - as examples, we show how scientific and technical advances have led models to transgress their initial objectives and limitations. We provide an overview of recent model applications on current important ecological topics and pinpoint ten key questions that could, and should, be tackled with forest models in the next decade.Synthesis. This overview shows that forest models, due to their complementarity and mutual enrichment, represent an invaluable toolkit to address a wide range of fundamental and applied ecological questions, hence fostering a deeper understanding of forest dynamics in the context of global change.

Consequences of spatial patterns for coexistence in species-rich plant communities.

Ecology cannot yet fully explain why so many tree species coexist in natural communities such as tropical forests. A major difficulty is linking individual-level processes to community dynamics. We propose a combination of tree spatial data, spatial statistics and dynamical theory to reveal the relationship between spatial patterns and population-level interaction coefficients and their consequences for multispecies dynamics and coexistence. Here we show that the emerging population-level interaction coefficients have, for a broad range of circumstances, a simpler structure than their individual-level counterparts, which allows for an analytical treatment of equilibrium and stability conditions. Mechanisms such as animal seed dispersal, which result in clustering of recruits that is decoupled from parent locations, lead to a rare-species advantage and coexistence of otherwise neutral competitors. Linking spatial statistics with theories of community dynamics offers new avenues for explaining species coexistence and calls for rethinking community ecology through a spatial lens.

How individual species structure diversity in tropical forests.

A persistent challenge in ecology is to explain the high diversity of tree species in tropical forests. Although the role of species characteristics in maintaining tree diversity in tropical forests has been the subject of theory and debate for decades, spatial patterns in local diversity have not been analyzed from the viewpoint of individual species. To measure scale-dependent local diversity structures around individual species, we propose individual species-area relationships (ISAR), a spatial statistic that marries common species-area relationships with Ripley's K to measure the expected alpha diversity in circular neighborhoods with variable radius around an arbitrary individual of a target species. We use ISAR to investigate if and at which spatial scales individual species increase in tropical forests' local diversity (accumulators), decrease local diversity (repellers), or behave neutrally. Our analyses of data from Barro Colorado Island (Panama) and Sinharaja (Sri Lanka) reveal that individual species leave identifiable signatures on spatial diversity, but only on small spatial scales. Most species showed neutral behavior outside neighborhoods of 20 m. At short scales (<20 m), we observed, depending on the forest type, two strongly different roles of species: diversity repellers dominated at Barro Colorado Island and accumulators at Sinharaja. Nevertheless, we find that the two tropical forests lacked any key species structuring species diversity at larger scales, suggesting that "balanced" species-species interactions may be a characteristic of these species-rich forests. We anticipate our analysis method will be a starting point for more powerful investigations of spatial structures in diversity to promote a better understanding of biodiversity in tropical forests.

Confronting an individual-based simulation model with empirical community patterns of grasslands.

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.

Network science applied to forest megaplots: tropical tree species coexist in small-world networks.

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.

Integrating the underlying structure of stochasticity into community ecology.

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.

Recruitment in tropical tree species: revealing complex spatial patterns.

Seed dispersal should leave a signature on the spatial distribution of recruits that can be quantified using sophisticated techniques of spatial pattern analysis. Here we study spatial patterns of five frugivore-dispersed tropical tree species at the Barro Colorado Island forest, Panama, to describe detailed properties of the spatial patterns of recruits and to investigate whether these patterns were produced by temporally consistent mechanisms. Our spatial point pattern analyses detected the existence of surprising spatial structures, such as double-cluster and superposition patterns, and they allowed for a detailed quantification of their properties. The spatial recruitment patterns were composed of two independent components comprising a random component and a component showing a complex spatial pattern with two critical scales of clustering. The analysis allowed an estimation of the relative contribution of scatter dispersal versus clump dispersal in effective seed dispersal for our study species. Additionally, the cluster characteristics were temporally consistent over 25 years and correlated with several species traits. We are just beginning to discover the richness of spatial patterns found at tropical forests, and we are confident that a combination of advanced point pattern analysis with field data will allow for significant advances in establishing the link between spatial patterns and processes.

An Approach to Study Species Persistence in Unconstrained Random Networks.

The connection between structure and stability of ecological networks has been widely studied in the last fifty years. A challenge that scientists continue to face is that in-depth mathematical model analysis is often difficult, unless the considered systems are specifically constrained. This makes it challenging to generalize results. Therefore, methods are needed that relax the required restrictions. Here, we introduce a novel heuristic approach that provides persistence estimates for random systems without limiting the admissible parameter range and system behaviour. We apply our approach to study persistence of species in random generalized Lotka-Volterra systems and present simulation results, which confirm the accuracy of our predictions. Our results suggest that persistence is mainly driven by the linkage density, whereby additional links can both favour and hinder persistence. In particular, we observed "persistence bistability", a rarely studied feature of random networks, leading to a dependency of persistence on initial species densities. Networks with this property exhibit tipping points, in which species loss can lead to a cascade of extinctions. The methods developed in this paper may facilitate the study of more general models and thereby provide a step forward towards a unifying framework of network architecture and stability.