Recent developments in complex systems analysis have led to new techniques for detecting causal relationships using relatively short time series, on the order of 30 sequential observations. Although many ecological observation series are even shorter, perhaps fewer than ten sequential observations, these shorter time series are often highly replicated in space (i.e., plot replication). Here, we combine the existing techniques of convergent cross mapping (CCM) and dewdrop regression to build a novel test of causal relations that leverages spatial replication, which we call multispatial CCM. Using examples from simulated and real-world ecological data, we test the ability of multispatial CCM to detect causal relationships between processes. We find that multispatial CCM successfully detects causal relationships with as few as five sequential observations, even in the presence of process noise and observation error. Our results suggest that this technique may constitute a useful test for causality in systems where experiments are difficult to perform and long time series are not available. This new technique is available in the multispatialCCM package for the R programming language.

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Much uncertainty remains about traits linked with successful invasion – the establishment and spread of non‐resident species into existing communities. Using a 20‐year experiment, where 50 non‐resident (but mostly native) grassland plant species were sown into savannah plots, we ask how traits linked with invasion depend on invasion stage (establishment, spread), indicator of invasion success (occupancy, relative abundance), time, environmental conditions, propagule rain, and traits of invaders and invaded communities. Trait data for 164 taxa showed that invader occupancy was primarily associated with traits of invaders, traits of recipient communities, and invader‐community interactions. Invader abundance was more strongly associated with community traits (e.g. proportion legume) and trait differences between invaders and the most similar resident species. Annuals and invaders with high‐specific leaf area were only successful early in stand development, whereas invaders with conservative carbon capture strategies persisted long‐term. Our results indicate that invasion is context‐dependent and long‐term experiments are required to comprehensively understand invasions.

for helpful comments and advice and to Louis Mitchell for editorial assistance. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.

Declines in global biodiversity have inspired a generation of studies that seek to characterize relationships between biodiversity and ecosystem functioning. The metrics for complementarity and selection effects derived by Loreau and Hector in 2001 remain some of the most influential and widely used statistics for studying these relationships. These metrics quantify the degree to which the effect of biodiversity on a given ecosystem function depends on only a few species that perform well in monoculture and in mixture (the selection effect) or if the effect of biodiversity on a given ecosystem function is independent of monoculture performance (the complementarity effect). This distinction may be useful in determining the consequences of the loss of rare versus common or dominant species in natural systems. However, because these metrics require observations of all species in a community in monoculture, applications in natural systems have been limited.Here, we derive a statistical augmentation of the original partition, which can be applied to incomplete random samples of species drawn from a larger pool. This augmentation controls for the bias introduced by using only a subsample of species in monocultures rather than having monocultures of all species.Using simulated and empirical examples, we demonstrate the robustness of these metrics, and provide source code for calculating them. We find that these augmentations provide a reliable estimate of complementarity and selection effects as long as approximately 50% of the species present in mixture are present in monoculture and these species represent a random subset of the mixture.We foresee two primary applications for this method: (a) estimating complementarity and selection effects for experimentally assembled communities where monoculture data are lacking for some species, and (b) extrapolating results from biodiversity experiments to diverse natural systems.

A hopeful vision of the future is a world in which both people and nature thrive, but there is little evidence to support the feasibility of such a vision. We used a global, spatially explicit, systems modeling approach to explore the possibility of meeting the demands of increased populations and economic growth in 2050 while simultaneously advancing multiple conservation goals. Our results demonstrate that if, instead of “business as usual” practices, the world changes how and where food and energy are produced, this could help to meet projected increases in food (54%) and energy (56%) demand while achieving habitat protection (>50% of natural habitat remains unconverted in most biomes globally; 17% area of each ecoregion protected in each country), reducing atmospheric greenhouse‐gas emissions consistent with the Paris Climate Agreement (≤1.6°C warming by 2100), ending overfishing, and reducing water stress and particulate air pollution. Achieving this hopeful vision for people and nature is attainable with existing technology and consumption patterns. However, success will require major shifts in production methods and an ability to overcome substantial economic, social, and political challenges.

“Old fields” are ecosystems that have been previously managed and subsequently abandoned, usually from agricultural use. These systems are classic testing grounds for hypotheses about community assembly. However, old field succession can be difficult to predict: seemingly similar fields often diverge in terms of species composition and environmental conditions. Here, we test the relative roles of contingency and stochasticity in driving vegetative successional dynamics. We draw on three decades of surveys in 24 old fields at the Cedar Creek Ecosystem Science Reserve (Minnesota, USA), and focus on five drivers that are known to shape local plant communities: soil fertility, fire, climate, competition, and demography. These drivers can contribute to contingency when they act consistently across fields and years (e.g., soil nitrogen accumulation, experimental fire regimes, or average climate), or to stochasticity when their effects are variable (e.g., annual variations in weather, or colonization and mortality events). We proceed in two steps. First, we fit regressions estimating abundance, colonization, and mortality for eight major functional groups in relation to these five drivers. We then use these regressions to parameterize a series of metacommunity simulation models, and test whether observed levels of stochasticity and variation in the drivers are sufficient to explain successional divergence. All drivers were significantly associated with plant species abundances, colonization, and mortality. Contingent factors strongly altered predicted successional trajectories. However, replicate simulations with similar conditions followed similar successional trajectories, suggesting that stochastic processes did not lead to divergence. This robustness of successional dynamics may be explained by compensatory trade‐offs. For example, species that were abundant late in succession typically suffered from low colonization rates and high mortality rates early in succession. Synthesis. Average successional dynamics among old fields at Cedar Creek follow largely consistent trends. Though dynamics of individual fields vary, much of this variation can be explained by contingent factors. Stochastic processes appear not to be sufficiently strong to create divergent successional trajectories among fields with similar sets of drivers. Our results therefore suggest that divergence among successional trajectories in chronosequences may be the result of predictable contingent factors, rather than unpredictable stochastic fluctuations.

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.