Benjamin Rosenbaum

Beyond the fast-slow continuum: demographic dimensions structuring a tropical tree community

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 (≥xa01xa0cm 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.

fluxweb: a R package to easily estimate energy fluxes in food webs

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://bit.ly/2OC0uKF). 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 throughflow 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.

The intrinsic predictability of ecological time series and its potential to guide forecasting

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 v. 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 dataset 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. Glossary Active information: The amount of information that is available to forecasting models (redundant information minus lost information; Fig. 1). Forecasting error (FE): A measure of the discrepancy between a model’s forecasts and the observed dynamics of a system. Common measures of forecast error are root mean squared error and mean absolute error. Entropy: Measures the average amount of information in the outcome of a stochastic process. Information: Any entity that provides answers and resolves uncertainty about a process. When information is calculated using logarithms to the base two (i.e. information in bits), it is the minimum number of yes/no questions required, on average, to determine the identity of the symbol (Jost 2006). The information in an observation consists of information inherited from the past (redundant information), and of new information. Intrinsic predictability: the maximum achievable predictability of a system (Beckage et al. 2011). Lost information: The part of the redundant information lost due to measurement or sampling error, or transformations of the data (Fig. 1). New information, Shannon entropy rate: The Shannon entropy rate quantifies the average amount of information per observation in a time series that is unrelated to the past, i.e., the new information (Fig. 1). Nonlinearity: When the deterministic processes governing system dynamics depend on the state of the system. Permutation entropy (PE): permutation entropy is a measure of the complexity of a time series (Bandt & Pompe, 2002) that is negatively correlated with a system’s predictability (Garland et al. 2015). Permutation entropy quantifies the combined new and lost information. PE is scaled to range between a minimum of 0 and a maximum of 1. Realized predictability: the achieved predictability of a system from a given forecasting model. Redundant information: The information inherited from the past, and thus the maximum amount of information available for use in forecasting (Fig. 1). Symbols, words, permutations: symbols are simply the smallest unit in a formal language such as the letters in the English alphabet i.e., {“A”, “B”,…, “Z”}. In information theory the alphabet is more abstract, such as elements in the set {“up”, “down”} or {“1”, “2”, “3”}. Words, of length m refer to concatenations of the symbols (e.g., up-down-down) in a set. Permutations are the possible orderings of symbols in a set. In this manuscript, the words are the permutations that arise from the numerical ordering of m data points in a time series. Weighted permutation entropy (WPE): a modification of permutation entropy (Fadlallah et al., 2013) that distinguishes between small-scale, noise-driven variation and large-scale, system-driven variation by considering the magnitudes of changes in addition to the rank-order patterns of PE.

The geometry of habitat fragmentation: effects of distribution patterns on short-term species persistence

Land-use changes cause habitat loss and fragmentation and are thus important drivers of anthropogenic biodiversity change. However, there is an ongoing debate about how fragmentation per se affects biodiversity in a given amount of habitat. We illustrate why it is important to distinguish two different aspects of fragmentation to resolve this debate: (i) geometric fragmentation effects, which exclusively arise from the spatial distributions of species and habitat fragments, and (ii) demographic fragmentation effects due to reduced fragment size, increased isolation, or edge effects. While most empirical studies are primarily interested in quantifying demographic fragmentation effects, geometric effects are typically invoked only as post-hoc explanations of biodiversity responses to fragmentation per se. Here, we present an approach to quantify geometric fragmentation effects on species persistence probability. We illustrate this approach using spatial simulations where we systematically varied the initial abundances and distribution patterns (i.e. random, aggregated, and regular) of species as well as habitat amount and fragmentation per se. As expected, we found no geometric fragmentation effects when species were randomly distributed. However, when species were aggregated, we found positive effects of fragmentation per se on persistence probability for a large range of scenarios. For regular species distributions, we found weakly negative geometric effects. These findings are independent of the ecological mechanisms which generate non-random species distributions. Our study helps to reconcile seemingly contradictory results of previous fragmentation studies. Since intraspecific aggregation is a ubiquitous pattern in nature, our findings imply widespread positive geometric fragmentation effects. This expectation is supported by many studies that find positive effects of fragmentation per se on species occurrences and diversity after controlling for habitat amount. We outline how to disentangle geometric and demographic effects of fragmentation, which is critical for predicting the response of biodiversity to landscape change.

Estimating parameters from multiple time series of population dynamics using Bayesian inference

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.

Bridging Scales: Allometric Random Walks Link Movement and Biodiversity Research

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.

Fitting functional responses: Direct parameter estimation by simulating differential equations

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 to predict, for example, the efficiency of biocontrol agents, population dynamics, food web structure and subsequently biodiversity, a trustworthy parameter estimation method is highly important for scientists using this framework. Classical approaches for estimating functional response parameters lack flexibility and often only provide approximations of the correct parameters. 2 Here, we combined ordinary differential equation (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. 3. We found that for classical functional response models, such as the frequently used type II and type III functional responses, the established fitting methods are reliable. However, by using more complex and flexible functional responses,our new method outperforms the traditional methods. Additionally, our method allows the incorporation of side effects such as resource growth and background mortality. 4. Our method will enable researchers from different scientific fields who are measuring functional responses to calculate more accurate parameter estimates. These estimates will enable community ecologists to parameterize their models more precisely, thus allowing a deeper understanding of complex ecological systems, and will increase the quality of ecological prediction models.

Coupling relations underlying the production of speech articulator movements and their invariance to speech rate

Since the seminal works of Bernstein (The coordination and regulation of movements. Pergamon Press, Oxford, 1967) several authors have supported the idea that, to produce a goal-oriented movement in general, and a movement of the organs responsible for the production of speech sounds in particular, individuals activate a set of coupling relations that coordinate the behavior of the elements of the motor system involved in the production of the target movement or sound. In order to characterize the configurations of the coupling relations underlying speech production articulator movements, we introduce an original method based on recurrence analysis. The method is validated through the analysis of simulated dynamical systems adapted to reproduce the features of speech gesture kinematics and it is applied to the analysis of speech articulator movements recorded in five German speakers during the production of labial and coronal plosive and fricative consonants at variable speech rates. We were able to show that the underlying coupling relations change systematically between labial and coronal consonants, but are not affected by speech rate, despite the presence of qualitative changes observed in the trajectory of the jaw at fast speech rate.

Interactive effects of shifting body size and feeding adaptation drive interaction strengths of protist predators under warming

Global change is heating up ecosystems fuelling biodiversity loss and species extinctions. High-trophic-level predators are especially prone to extinction due to an energetic mismatch between increasing feeding rates and metabolism with warming. Different adaptation mechanisms such as decreasing body size to reduce energy requirements (morphological response) as well as direct effects of adaptation to feeding parameters (physiological response) have been proposed to overcome this problem. Here, we use protist-bacteria microcosm experiments to show how those adaptations may have the potential to buffer the impact of warming on predator-prey interactions. After adapting the ciliate predator Tetrahymena pyriformis to three different temperatures (15°C, 20°C and 25°C) for approximately 20 generations we conducted functional response experiments on bacterial prey along an experimental temperature gradient (15°C, 20°C and 25°C). We found an increase of maximum feeding rates and half-saturation densities with rising experimental temperatures. Adaptation temperature had on average slightly negative effects on maximum feeding rates, but maximum feeding rates increased more strongly with rising experimental temperature in warm adapted predators than in cold adapted predators. There was no effect of adaptation temperature on half-saturation densities characterising foraging efficiency. Besides the mixed response in functional response parameters, predators also adapted by decreasing body size. As smaller predators need less energy to fulfil their energetic demands, maximum feeding rates relative to the energetic demands increased slightly with increased adaptation temperature. Accordingly, predators adapted to 25°C showed the highest feeding rates at 25°C experimental temperature, while predators adapted to 15°C showed the highest maximum feeding rate at 15°C. Therefore, adaptation to different temperatures potentially avoids an energetic mismatch with warming. Especially a shift in body size with warming additionally to an adaptation of physiological parameters potentially helps to maintain a positive energy balance and prevent predator extinction with rising temperatures.

Warming alters energetic structure and function but not resilience of soil food webs

Climate warming is predicted to alter the structure, stability, and functioning of food webs1–5. Yet, despite the importance of soil food webs for energy and nutrient turnover in terrestrial ecosystems, the effects of warming on these food webs—particularly in combination with other global change drivers—are largely unknown. Here, we present results from two complementary field experiments that test the interactive effects of warming with forest canopy disturbance and drought on energy flux in boreal–temperate ecotonal forest soil food webs. The first experiment applied a simultaneous above- and belowground warming treatment (ambient, +1.7u2009°C, +3.4u2009°C) to closed-canopy and recently clear-cut forest, simulating common forest disturbance6. The second experiment crossed warming with a summer drought treatment (−40% rainfall) in the clear-cut habitats. We show that warming reduces energy flux to microbes, while forest canopy disturbance and drought facilitates warming-induced increases in energy flux to higher trophic levels and exacerbates the reduction in energy flux to microbes, respectively. Contrary to expectations, we find no change in whole-network resilience to perturbations, but significant losses in ecosystem functioning. Warming thus interacts with forest disturbance and drought, shaping the energetic structure of soil food webs and threatening the provisioning of multiple ecosystem functions in boreal–temperate ecotonal forests.Warming interacts with forest disturbance and drought to shape the energetic structure of soil food webs; these changes can undermine the provision of multiple ecosystem functions in transitional boreal–temperate forests.