The Stochastic Nature of Functional Responses.

Functional responses are non-linear functions commonly used to describe the variation in the rate of consumption of resources by a consumer. They have been widely used in both theoretical and empirical studies, but a comprehensive understanding of their parameters at different levels of description remains elusive. Here, by depicting consumers and resources as stochastic systems of interacting particles, we present a minimal set of reactions for consumer resource dynamics. We rigorously derived the corresponding system of ODEs, from which we obtained via asymptotic expansions classical 2D consumer-resource dynamics, characterized by different functional responses. We also derived functional responses by focusing on the subset of reactions describing only the feeding process. This involves fixing the total number of consumers and resources, which we call chemostatic conditions. By comparing these two ways of deriving functional responses, we showed that classical functional response parameters in effective 2D consumer-resource dynamics differ from the same parameters obtained by measuring (or deriving) functional responses for typical feeding experiments under chemostatic conditions, which points to potential errors in interpreting empirical data. We finally discuss possible generalizations of our models to systems with multiple consumers and more complex population structures, including spatial dynamics. Our stochastic approach builds on fundamental ecological processes and has natural connections to basic ecological theory.

Network motifs involving both competition and facilitation predict biodiversity in alpine plant communities.

Biological diversity depends on multiple, cooccurring ecological interactions. However, most studies focus on one interaction type at a time, leaving community ecologists unsure of how positive and negative associations among species combine to influence biodiversity patterns. Using surveys of plant populations in alpine communities worldwide, we explore patterns of positive and negative associations among triads of species (modules) and their relationship to local biodiversity. Three modules, each incorporating both positive and negative associations, were overrepresented, thus acting as "network motifs." Furthermore, the overrepresentation of these network motifs is positively linked to species diversity globally. A theoretical model illustrates that these network motifs, based on competition between facilitated species or facilitation between inferior competitors, increase local persistence. Our findings suggest that the interplay of competition and facilitation is crucial for maintaining biodiversity.

Biodiversity increases and decreases ecosystem stability.

Losses and gains in species diversity affect ecological stability1-7 and the sustainability of ecosystem functions and services8-13. Experiments and models have revealed positive, negative and no effects of diversity on individual components of stability, such as temporal variability, resistance and resilience2,3,6,11,12,14. How these stability components covary remains poorly understood15. Similarly, the effects of diversity on overall ecosystem stability16, which is conceptually akin to ecosystem multifunctionality17,18, remain unknown. Here we studied communities of aquatic ciliates to understand how temporal variability, resistance and overall ecosystem stability responded to diversity (that is, species richness) in a large experiment involving 690 micro-ecosystems sampled 19 times over 40 days, resulting in 12,939 samplings. Species richness increased temporal stability but decreased resistance to warming. Thus, two stability components covaried negatively along the diversity gradient. Previous biodiversity manipulation studies rarely reported such negative covariation despite general predictions of the negative effects of diversity on individual stability components3. Integrating our findings with the ecosystem multifunctionality concept revealed hump- and U-shaped effects of diversity on overall ecosystem stability. That is, biodiversity can increase overall ecosystem stability when biodiversity is low, and decrease it when biodiversity is high, or the opposite with a U-shaped relationship. The effects of diversity on ecosystem multifunctionality would also be hump- or U-shaped if diversity had positive effects on some functions and negative effects on others. Linking the ecosystem multifunctionality concept and ecosystem stability can transform the perceived effects of diversity on ecological stability and may help to translate this science into policy-relevant information.

The effects of demographic stochasticity and parameter uncertainty on predicting the establishment of introduced species.

Invasive species are a serious threat to biodiversity worldwide and predicting whether an introduced species will first establish and then become invasive can be useful to preserve ecosystem services. Establishment is influenced by multiple factors, such as the interactions between the introduced individuals and the resident community, and demographic and environmental stochasticity. Field observations are often incomplete or biased. This, together with an imperfect knowledge of the ecological traits of the introduced species, makes the prediction of establishment challenging. Methods that consider the combined effects of these factors on our ability to predict the establishment of an introduced species are currently lacking. We develop an inference framework to assess the combined effects of demographic stochasticity and parameter uncertainty on our ability to predict the probability of establishment following the introduction of a small number of individuals. We find that even moderate levels of demographic stochasticity influence both the probability of establishment, and, crucially, our ability to correctly predict that probability. We also find that estimation of the demographic parameters of an introduced species is fundamental to obtain precise estimates of the interaction parameters. For typical values of demographic stochasticity, the drop in our ability to predict an establishment can be 30% when having priors on the demographic parameters compared to having their accurate values. The results from our study illustrate how demographic stochasticity may bias the prediction of the probability of establishment. Our method can be applied to estimate probability of establishment of introduced species in field scenarios, where time series data and prior information on the demographic traits of the introduced species are available.

The ecological forecast horizon, and examples of its uses and determinants.

Forecasts of ecological dynamics in changing environments are increasingly important, and are available for a plethora of variables, such as species abundance and distribution, community structure and ecosystem processes. There is, however, a general absence of knowledge about how far into the future, or other dimensions (space, temperature, phylogenetic distance), useful ecological forecasts can be made, and about how features of ecological systems relate to these distances. The ecological forecast horizon is the dimensional distance for which useful forecasts can be made. Five case studies illustrate the influence of various sources of uncertainty (e.g. parameter uncertainty, environmental variation, demographic stochasticity and evolution), level of ecological organisation (e.g. population or community), and organismal properties (e.g. body size or number of trophic links) on temporal, spatial and phylogenetic forecast horizons. Insights from these case studies demonstrate that the ecological forecast horizon is a flexible and powerful tool for researching and communicating ecological predictability. It also has potential for motivating and guiding agenda setting for ecological forecasting research and development.

Inferring the temperature dependence of population parameters: the effects of experimental design and inference algorithm.

Understanding and quantifying the temperature dependence of population parameters, such as intrinsic growth rate and carrying capacity, is critical for predicting the ecological responses to environmental change. Many studies provide empirical estimates of such temperature dependencies, but a thorough investigation of the methods used to infer them has not been performed yet. We created artificial population time series using a stochastic logistic model parameterized with the Arrhenius equation, so that activation energy drives the temperature dependence of population parameters. We simulated different experimental designs and used different inference methods, varying the likelihood functions and other aspects of the parameter estimation methods. Finally, we applied the best performing inference methods to real data for the species Paramecium caudatum. The relative error of the estimates of activation energy varied between 5% and 30%. The fraction of habitat sampled played the most important role in determining the relative error; sampling at least 1% of the habitat kept it below 50%. We found that methods that simultaneously use all time series data (direct methods) and methods that estimate population parameters separately for each temperature (indirect methods) are complementary. Indirect methods provide a clearer insight into the shape of the functional form describing the temperature dependence of population parameters; direct methods enable a more accurate estimation of the parameters of such functional forms. Using both methods, we found that growth rate and carrying capacity of Paramecium caudatum scale with temperature according to different activation energies. Our study shows how careful choice of experimental design and inference methods can increase the accuracy of the inferred relationships between temperature and population parameters. The comparison of estimation methods provided here can increase the accuracy of model predictions, with important implications in understanding and predicting the effects of temperature on the dynamics of populations.

Predation effects on mean time to extinction under demographic stochasticity.

Methods for predicting the probability and timing of a species' extinction are typically based on single species population dynamics. Assessments of extinction risk often lack effects of interspecific interactions. We study a birth and death process in which the death rate includes an effect of predation. Predation is included via a general nonlinear expression for the functional response of predation to prey density. We investigate the effects of the foraging parameters (e.g. attack rate and handling time) on the mean time to extinction. Mean time to extinction varies by orders of magnitude when we alter the foraging parameters, even when we exclude the effects of these parameters on the equilibrium population size. Conclusions are robust to assumptions about initial conditions and variable predator abundance. These findings clearly show that accounting for the nature of interspecific interactions is likely to be critically important when estimating extinction risk.