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Population and community ecology traditionally has a very strong theoretical foundation with well-known dynamical models, such as the logistic and its variations, and many modification of the classical Lotka-Volterra predator-prey and interspecific competition models. More and more, these classical models are being confronted with data via fitting to empirical time series for purposes of projections or for estimating model parameters of interest. However, using statistical models to fit theoretical models to data is far from trivial, especially for time series data where subsequent measurements are not independent. This raises the question of whether statistical inferences using pure observation error models, such as simple (non-)linear regressions, are biased, and whether more elaborate process error models or state-space models have to be used to address this complexity.In order to help empiricists, especially researchers working with experimental laboratory populations in micro- and mesocosms, make informed decisions about the statistical formalism to use, we here compare different error structures one could use when fitting classical deterministic ODE models to empirical data. We consider a large range of biological scenarios and theoretical models, from single species to community dynamics and trophic interactions. In order to compare the performance of different error structure models, we use both realistically simulated data and empirical data from microcosms in a Bayesian framework.We find that many model parameters can be estimated precisely with an appropriate choice of error structure using pure observation error or state-space models, if observation errors are not too high. However, Allee effect models are typically hard to identify and state-space models should be preferred when model complexity increases.Our work shows that, at least in the context of low environmental stochasticity and high quality observations, deterministic models can be used to describe stochastic population dynamics that include process variability and observation error. We discuss when more complex state-space model formulations may be required for obtaining accurate parameter estimates. Finally, we provide a comprehensive tutorial for fitting these models in R.Open researchCode for stochastic individual-based simulations is available fromhttps://doi.org/10.5281/zenodo.5500442. A tutorial for fitting ODE models to time series data in R is presented in the Supplementary Information and is also available onlinehttps://github.com/benjamin-rosenbaum/fittingdeterministic population models. Data (Fronhofer et al., 2020) will be provided via GitHub and Zenodo.

Understanding the formation of feeding links provides insights into processes underlying food webs. Generally, predators feed on prey within a certain body-size range, but a systematic quantification of such feeding niches is lacking. We developed a size-constrained feeding-niche (SCFN) model and parameterized it with information on both realized and non-realized feeding links in 72 aquatic and 65 terrestrial food webs. Our analyses revealed profound differences in feeding niches between aquatic and terrestrial predators and variation along a temperature gradient. Specifically, the predator-prey body-size ratio and the range in prey sizes increase with the size of aquatic predators, whereas they are nearly constant across gradients in terrestrial predator size. Overall, our SCFN model well reproduces the feeding relationships and predation architecture across 137 natural food webs (including 3878 species and 136,839 realized links). Our results illuminate the organisation of natural food webs and enables novel trait-based and environment-explicit modelling approaches.

Environmental temperature and body size are two prominent drivers of predation. Despite the ample evidence of their independent effects, the combined impact of temperature and predator-prey body size ratio on the strength and stability of trophic interactions is not fully understood. We experimentally tested how water temperature alters the functional response and population stability of dragonfly nymphs (Cordulegaster boltonii) feeding on freshwater amphipods (Gammarus pulex) across a gradient of their body size ratios. Attack coefficients were highest for small predators feeding on small prey at low temperatures, but shifted toward the largest predators feeding on larger prey in warmer environments. Handling time appeared to decrease with increasing predator and prey body size in the cold environment, but increase at higher temperatures. These findings indicate interactive effects of temperature and body size on functional responses. There was also a negative effect of warming on the stability of predator and prey populations, but this was counteracted by a larger predator-prey body size ratio at higher temperatures. Here, a greater Hill exponent reduced feeding at low prey densities when predators were much larger than their prey, enhancing the persistence of both predator and prey populations in the warmer environment. These experimental findings provide new mechanistic insights into the destabilizing effect of warming on trophic interactions and the key role of predator-prey body size ratios in mitigating these effects.

Despite intensive research on species dissimilarity patterns across communities (i.e. β-diversity), we still know little about their implications for variation in food-web structures. Our analyses of 50 lake and 48 forest soil communities show that, while species dissimilarity depends on environmental and spatial gradients, these effects are only weakly propagated to the networks. Moreover, our results show that species and food-web dissimilarities are consistently correlated, but that much of the variation in food-web structure across spatial, environmental, and species gradients remains unexplained. Novel food-web assembly models demonstrate the importance of biotic filtering during community assembly by (1) the availability of resources and (2) limiting similarity in species' interactions to avoid strong niche overlap and thus competitive exclusion. This reveals a strong signature of biotic filtering processes during local community assembly, which constrains the variability in structural food-web patterns across local communities despite substantial turnover in species composition.

Animals require a certain amount of habitat to persist and thrive, and habitat loss is one of the most critical drivers of global biodiversity decline. While habitat requirements have been predicted by relationships between species traits and home-range size, little is known about constraints imposed by environmental conditions and human impacts on a global scale. Our meta-analysis of 395 vertebrate species shows that global climate gradients in temperature and precipitation exert indirect effects via primary productivity, generally reducing space requirements. Human pressure, however, reduces realised space use due to ensuing limitations in available habitat, particularly for large carnivores. We show that human pressure drives extinction risk by increasing the mismatch between space requirements and availability. We use large-scale climate gradients to predict current species extinction risk across global regions, which also offers an important tool for predicting future extinction risk due to ongoing space loss and climate change.

1. Models of natural processes necessarily sacrifice some realism for the sake of tractability. Detailed, parameter‐rich models often provide accurate estimates of system behaviour but can be data‐hungry and difficult to operationalize. Moreover, complexity increases the danger of ‘over‐fitting’, which leads to poor performance when models are applied to novel conditions. This challenge is typically described in terms of a trade‐off between bias and variance (i.e. low accuracy vs. low precision). 2. In studies of ecological communities, this trade‐off often leads to an argument about the level of detail needed to describe interactions among species. Here, we used data from a grassland biodiversity experiment containing nine locally abundant plant species (the Jena ‘dominance experiment’) to parameterize models representing six increasingly complex hypotheses about interactions. For each model, we calculated goodness‐of‐fit across different subsets of the data based on sown species richness levels, and tested how performance changed depending on whether or not the same data were used to parameterize and test the model (i.e. within vs. out‐of‐sample), and whether the range of diversity treatments being predicted fell inside or outside of the range used for parameterization. 3. As expected, goodness‐of‐fit improved as a function of model complexity for all within‐sample tests. In contrast, the best out‐of‐sample performance generally resulted from models of intermediate complexity (i.e. with only two interaction coefficients per species—an intraspecific effect and a single pooled interspecific effect), especially for predictions that fell outside the range of diversity treatments used for parameterization. In accordance with other studies, our results also demonstrate that commonly used selection methods based on AIC of models fitted to the full dataset correspond more closely to within‐sample than out‐of‐sample performance. 4. Synthesis. Our results demonstrate that models which include only general intra and interspecific interaction coefficients can be sufficient for estimating species‐level abundances across a wide range of contexts and may provide better out‐of‐sample performance than do more complex models. These findings serve as a reminder that simpler models may often provide a better trade‐off between bias and variance in ecological systems, particularly when applying models beyond the conditions used to parameterize them. This paper arose as part of the ‘BEF-Coexist’ workshop, organized by Y.F., C.R., and W.S.H., with funding from the German Research Foundation (RO2397/8). A.T.C. was supported by a ‘catalyst’ postdoctoral fellowship from sDiv. S.S. was supported by the Spanish Government under a Ramón y Cajal contract (RYC-2016- 20604). Funding and support for the Jena Experiment were provided by the German Research Foundation (FOR456/1451), Friedrich Schiller University of Jena, and Max Planck Society.

1. The inference of pairwise competitive outcomes (PCO) and multispecies competitive ranks and intransitivity from empirical data is essential to evaluate how competition shapes plant communities. Three categories of methods, differing in theoretical background and data requirements, have been used: (a) theoretically sound coexistence theory‐based methods, (b) index‐based methods, and (c) ‘process‐from‐pattern’ methods. However, how they are related is largely unknown. 2. In this study, we explored the relations between the three categories by explicitly comparing three representatives of them: (a) relative fitness difference (RFD), (b) relative yield (RY), and (c) a reverse‐engineering approach (RE). Specifically, we first conducted theoretical analyses with Lotka–Volterra competition models to explore their theoretical linkages. Second, we used data from a long‐term field experiment and a short‐term greenhouse experiment with eight herbaceous perennials to validate the theoretical findings. 3. The theoretical analyses showed that RY or RE applied with equilibrium data indicated equivalent, or very similar, PCO respectively to RFD, but these relations became weaker or absent with data further from equilibrium. In line with this, both RY and RE converged with RFD in indicating PCO over time in the field experiment as the communities became closer to equilibrium. Moreover, the greenhouse PCO (far from equilibrium) were only similar to the field PCO of earlier rather than later years. Intransitivity was more challenging to infer because it could be reshuffled by even a small competitive shift among similar competitors. For example, the field intransitivity inferred by three methods differed greatly: no intransitivity was detected with RFD; intransitivity detected with RY and RE was poorly correlated, changed substantially over time (even after equilibrium) and failed to explain coexistence. 4. Our findings greatly help the comparison and generalization of studies using different methods. For future studies, if equilibrium data are available, one can infer PCO and multispecies competitive ranks with RY or RE. If not, one should apply RFD with density gradient or time‐series data. Equilibria could be evaluated with T tests or standard deviations. To reliably infer intransitivity, one needs high quality data for a given method to first accurately infer PCO, especially among similar competitors. This study has been supported by the German Science Foundation (RO2397/8) in the framework of the Jena Experiment (FOR 456/1451). Y.H.F. was also supported by the Fundamental Research Funds for the Central Universities (lzujbky-2019-32). S.S. was supported by the Spanish Government under a Ramón y Cajal contract (RYC-2016-20604).

Understanding how changes in biodiversity will impact the stability and functioning of ecosystems is a central challenge in ecology. Food‐web approaches have been advocated to link community composition with ecosystem functioning by describing the fluxes of energy among species or trophic groups. However, estimating such fluxes remains problematic because current methods become unmanageable as network complexity increases. We developed a generalisation of previous indirect estimation methods assuming a steady state system [1, 2, 3]: the model estimates energy fluxes in a top‐down manner assuming system equilibrium; each node's losses (consumption and physiological) balances its consumptive gains. Jointly, we provide theoretical and practical guidelines to use the fluxweb R package (available on CRAN at https://cran.r-project.org/web/packages/fluxweb/index.html We also present how the framework can merge with the allometric theory of ecology [4] to calculate fluxes based on easily obtainable organism‐level data (i.e. body masses and species groups ‐eg, plants animals), opening its use to food webs of all complexities. Physiological losses (metabolic losses or losses due to death other than from predation within the food web) may be directly measured or estimated using allometric relationships based on the metabolic theory of ecology, and losses and gains due to predation are a function of ecological efficiencies that describe the proportion of energy that is used for biomass production. The primary output is a matrix of fluxes among the nodes of the food web. These fluxes can be used to describe the role of a species, a function of interest (e.g. predation; total fluxes to predators), multiple functions, or total energy flux (system throughow or multitrophic functioning). Additionally, the package includes functions to calculate network stability based on the Jacobian matrix, providing insight into how resilient the network is to small perturbations at steady state. Overall, fluxweb provides a flexible set of functions that greatly increase the feasibility of implementing food‐web energetic approaches to more complex systems. As such, the package facilitates novel opportunities for mechanistically linking quantitative food webs and ecosystem functioning in real and dynamic natural landscapes.

Life-history theory posits that trade-offs between demographic rates constrain the range of viable life-history strategies. For coexisting tropical tree species, the best established demographic trade-off is the growth-survival trade-off. However, we know surprisingly little about co-variation of growth and survival with measures of reproduction. We analysed demographic rates from seed to adult of 282 co-occurring tropical tree and shrub species, including measures of reproduction and accounting for ontogeny. Besides the well-established fast-slow continuum, we identified a second major dimension of demographic variation: a trade-off between recruitment and seedling performance vs. growth and survival of larger individuals (≥ 1 cm dbh) corresponding to a 'stature-recruitment' axis. The two demographic dimensions were almost perfectly aligned with two independent trait dimensions (shade tolerance and size). Our results complement recent analyses of plant life-history variation at the global scale and reveal that demographic trade-offs along multiple axes act to structure local communities.

International audience; Predator-prey interactions in natural ecosystems generate complex food webs that have a simple universal body-size architecture where predators are systematically larger than their prey. Food-web theory shows that the highest predator-prey body-mass ratios found in natural food webs may be especially important as they create weak interactions with slow dynamics that stabilize communities against perturbations and maintain ecosystem functioning. Identifying these vital interactions in real communities typically requires arduous identification of interactions in complex food webs. Here, we overcome this obstacle by developing predator-trait models to predict average body-mass ratios based on a database comprising 290 food webs from freshwater, marine and terrestrial ecosystems across all continents. We analyzed how species traits constrain body-size architecture by changing the slope of the predator-prey body-mass scaling. Across ecosystems, we found high body-mass ratios for predator groups with specific trait combinations including (1) small vertebrates and (2) large swimming or flying predators. Including the metabolic and movement types of predators increased the accuracy of predicting which species are engaged in high body-mass ratio interactions. We demonstrate that species traits explain striking patterns in the body-size architecture of natural food webs that underpin the stability and functioning of ecosystems, paving the way for community-level management of the most complex natural ecosystems.

Empirical time series of interacting entities, e.g. species abundances, are highly useful to study ecological mechanisms. Mathematical models are valuable tools to further elucidate those mechanisms and underlying processes. However, obtaining an agreement between model predictions and experimental observations remains a demanding task. As models always abstract from reality one parameter often summarizes several properties. Parameter measurements are performed in additional experiments independent of the ones delivering the time series. Transferring these parameter values to different settings may result in incorrect parametrizations. On top of that, the properties of organisms and thus the respective parameter values may vary considerably. These issues limit the use of a priori model parametrizations.In this study, we present a method suited for a direct estimation of model parameters and their variability from experimental time series data. We combine numerical simulations of a continuous-time dynamical population model with Bayesian inference, using a hierarchical framework that allows for variability of individual parameters. The method is applied to a comprehensive set of time series from a laboratory predator-prey system that features both steady states and cyclic population dynamics.Our model predictions are able to reproduce both steady states and cyclic dynamics of the data. Additionally to the direct estimates of the parameter values, the Bayesian approach also provides their uncertainties. We found that fitting cyclic population dynamics, which contain more information on the process rates than steady states, yields more precise parameter estimates. We detected significant variability among parameters of different time series and identified the variation in the maximum growth rate of the prey as a source for the transition from steady states to cyclic dynamics.By lending more flexibility to the model, our approach facilitates parametrizations and shows more easily which patterns in time series can be explained also by simple models. Applying Bayesian inference and dynamical population models in conjunction may help to quantify the profound variability in organismal properties in nature.

Successfully predicting the future states of systems that are complex, stochastic, and potentially chaotic is a major challenge. Model forecasting error (FE) is the usual measure of success; however model predictions provide no insights into the potential for improvement. In short, the realized predictability of a specific model is uninformative about whether the system is inherently predictable or whether the chosen model is a poor match for the system and our observations thereof. Ideally, model proficiency would be judged with respect to the systems’ intrinsic predictability, the highest achievable predictability given the degree to which system dynamics are the result of deterministic vs. stochastic processes. Intrinsic predictability may be quantified with permutation entropy (PE), a model‐free, information‐theoretic measure of the complexity of a time series. By means of simulations, we show that a correlation exists between estimated PE and FE and show how stochasticity, process error, and chaotic dynamics affect the relationship. This relationship is verified for a data set of 461 empirical ecological time series. We show how deviations from the expected PE–FE relationship are related to covariates of data quality and the nonlinearity of ecological dynamics. These results demonstrate a theoretically grounded basis for a model‐free evaluation of a system's intrinsic predictability. Identifying the gap between the intrinsic and realized predictability of time series will enable researchers to understand whether forecasting proficiency is limited by the quality and quantity of their data or the ability of the chosen forecasting model to explain the data. Intrinsic predictability also provides a model‐free baseline of forecasting proficiency against which modeling efforts can be evaluated., Ecological Monographs, 89 (2), ISSN:0012-9615, ISSN:1557-7015, ISSN:1741-7015

Integrating mechanistic models of movement and behavior into large-scale movement ecology and biodiversity research is one of the major challenges in current ecological science. This is mainly due to a large gap between the spatial scales at which these research lines act. Here, we propose to apply trait-based movement models to bridge this gap and generalize movement trajectories across species and ecosystems. We show how to use species traits (e.g., body mass) to generate allometric random walks and illustrate in two worked examples how this facilitates general predictions of species-interaction traits, meta-community structures, and biodiversity patterns. Thereby, allometric random walks foster a closer integration of movement ecology and biodiversity research by scaling up from small-scale mechanistic measurements to a predictive understanding of movement and biodiversity patterns in different landscapes.

The feeding functional response is one of the most widespread mathematical frameworks in Ecology, Marine Biology, Freshwater Biology, Microbiology and related scientific fields describing the resource-dependent uptake of a consumer. Since the exact knowledge of its parameters is crucial in order to predict, for example, the efficiency of biocontrol agents, population dynamics, food web structure and subsequently biodiversity, a trustful parameter estimation is of utmost importance for scientists using this framework. Classical approaches for estimating functional response parameters lack flexibility and can often only serve as approximation for a correct parameter estimation. Moreover, they do not allow to incorporate side effects such as resource growth or background mortality. Both call for a new method to be established solving these problems. Here, we combined ordinary differential equation models (ODE models), that were numerically solved using computer simulations, with an iterative maximum likelihood fitting approach. We compared our method to classical approaches of fitting functional responses, using data both with and without additional resource growth and mortality. We found that for classical functional response models, like the often used type II and type III functional response, the established fitting methods are reliable. However, using more complex and flexible functional responses, our new established method outperforms the traditional methods. Additionally, only our method allows to analyze experiments correctly when resources experience growth or background mortality. Our method will enable researchers from different scientific fields that are measuring functional responses to estimate parameters correctly. These estimates will enable community ecologists to parameterize their models more precisely, allowing for a deeper understanding of complex ecological systems, and will increase the quality of ecological prediction models.