Digital twins: dynamic model-data fusion for ecology.

Digital twins (DTs) are an emerging phenomenon in the public and private sectors as a new tool to monitor and understand systems and processes. DTs have the potential to change the status quo in ecology as part of its digital transformation. However, it is important to avoid misguided developments by managing expectations about DTs. We stress that DTs are not just big models of everything, containing big data and machine learning. Rather, the strength of DTs is in combining data, models, and domain knowledge, and their continuous alignment with the real world. We suggest that researchers and stakeholders exercise caution in DT development, keeping in mind that many of the strengths and challenges of computational modelling in ecology also apply to DTs.

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.

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.

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.

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.

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.

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.

Monodominance in tropical forests: modelling reveals emerging clusters and phase transitions.

Tropical forests are highly diverse ecosystems, but within such forests there can be large patches dominated by a single tree species. The myriad presumed mechanisms that lead to the emergence of such monodominant areas is currently the subject of intensive research. We used the most generic of these mechanisms, large seed mass and low dispersal ability of the monodominant species, in a spatially explicit model. The model represents seven identical species with long-distance dispersal of small seeds, competing with one potentially monodominant species with short-distance dispersal of large seeds. Monodominant patches emerged and persisted only for a narrow range of species traits; these results have the characteristic features of phase transitions. Additional mechanisms may explain monodominance in different ecological contexts, but our results suggest that percolation-like phenomena and phase transitions might be pervasive in this type of system.

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.

On the challenge of fitting tree size distributions in ecology.

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.