The Allometry of Prey Preferences

The distribution of weak and strong non-linear feeding interactions (i.e., functional responses) across the links of complex food webs is critically important for their stability. While empirical advances have unravelled constraints on single-prey functional responses, their validity in the context of complex food webs where most predators have multiple prey remain uncertain. In this study, we present conceptual evidence for the invalidity of strictly density-dependent consumption as the null model in multi-prey experiments. Instead, we employ two-prey functional responses parameterised with allometric scaling relationships of the functional response parameters that were derived from a previous single-prey functional response study as novel null models. Our experiments included predators of different sizes from two taxonomical groups (wolf spiders and ground beetles) simultaneously preying on one small and one large prey species. We define compliance with the null model predictions (based on two independent single-prey functional responses) as passive preferences or passive switching, and deviations from the null model as active preferences or active switching. Our results indicate active and passive preferences for the larger prey by predators that are at least twice the size of the larger prey. Moreover, our approach revealed that active preferences increased significantly with the predator-prey body-mass ratio. Together with prior allometric scaling relationships of functional response parameters, this preference allometry may allow estimating the distribution of functional response parameters across the myriads of interactions in natural ecosystems

Predator traits determine food-web architecture across ecosystems

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 because 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 analysed 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

Allometry, temperature, and the stability of food webs

Understanding the mechanisms driving stability in natural ecosystems is of crucial importance, especially in the current context of global change. A classic paradigm in ecology was that complex food webs (the “who eats whom” of natural ecosystems) should be unstable. This paradigm, however, was based on simple mathematical models. Throughout the last decades, scientists proposed solutions to the contradictions between the predictions of simple models and the observation of the complexity of nature. However, the fundamental mechanisms driving these stabilizing effects are still rather unexplored. Especially, exploring and predicting the reaction of natural ecosystems to changes of the environment is a pressing issue of our time. Forecasting models predicted global warming up to 8°C until 2100, also nutrient enrichment is caused by anthropogenic land use. This causes changes in species composition and may lead to species extinctions. A fundamental unit of natural ecosystems is the interaction between species. The most obvious interaction is the feeding interaction between a predator and its prey. This interaction is mainly influenced by the metabolism and the feeding rate of the predator, as well as by the population density of the prey. Combining a mechanistic understanding of these interactions and traditional population models led to ground-breaking insights into the mechanisms stabilizing food-webs. For example, a non-random distribution of feeding interactions in a food web increases its resistance against destabilizing effects. This might be caused by strong constraints introduced by the distributions of body masses across the species in a food web. Additionally, relatively weak interactions are known to have a positive effect on stability, if they occur in a specific way within small food-web motifs (e.g., a weak interaction from a top predator to the basal species and a strong interaction to its main prey, the intermediate predator). Also, models suggested that the stability of natural populations may change, if the feeding capacity and the metabolism (or the death rate) of a predator are not equally influenced by the environmental temperature. However, empirical support for this is still scarce. In this thesis, I explored the impact of body masses and environmental temperature on feeding interactions (Chapters 3.1., 3.2.& 4.1.). Additionally, I explored the influence of these constraints on population and food-web stability by using mathematical models (Chapters 3.3., 3.4., 4.1. & 4.2.). The body-mass dependence of metabolism generally followed the 3/4 power laws as predicted by the Metabolic Theory of Ecology (Chapter 3.1.). However, the strength of the feeding rates follows a hump-shaped curve with the body mass ratio of the predator to its prey (Chapters 3.1.& 3.2.). This leads to the phenomenon that a predator would not be able to fulfil its metabolic demands if only insufficient small prey would be available (Chapter 3.2.). Moreover, with increasing temperature, the metabolism increases more than the ability of the predator to consume food (Chapter 4.1.). These findings have fundamental implications for food web stability. Predators only are able to exist within a given range of body mass ratios to their prey. Approximately 97% of all tri-trophic food chains existing in natural food webs fall within this range (Chapter 3.3.). Additionally, at high body-mass ratios an additional interaction from the top predator to the basal species (omnivory) leads to a higher stability when incorporating the results from chapters 3.1. & 3.2. into the population models. Together with the distribution of the interactions as given in natural food webs (Chapter 3.3.), omnivory motifs are stabilised within the whole range of natural body-mass ratios (Chapter 3.4.). The different temperature dependencies found for metabolism and feeding in chapter 5.1 led to more stable population cycles but may also lead to extinction events caused by starvation of the predators. In addition, warming affects the food web structure, increasing or decreasing these starvation effects, as found in chapter 4.1. Also, enrichment effects on population stability and food-web persistence can be overcome by incorporating naturally plausible feeding interactions (Chapter 5.1.). Overall, incorporating naturally relevant feeding interactions from laboratory studies into population and food-web models provides important insights into the functioning of populations and their stability in the context of food webs and their response to global change

Source R-file including nll functions

This r-file contains the negative likelihood functions plus some underlying functions needed to perform the code in the file “main_fr_manual.r”. Please see the supplemental "manual" published along with the main paper in MEE for further and in-depth instructions

Main R-file including main code

This r-file contains the main statistical procedures to estimate functional responses following the manual of our paper. Please see the supplemental "manual" published along with the main paper in MEE for further and in-depth instructions

Source R-file including speedy odeintr code

This r-file contains the negative likelihood functions plus some underlying functions needed to perform functional response fitting using the faster differential equation solver “odeintr” compared to the one used in “source_fr_manual.r”. Please see the supplemental "manual" published along with the main paper in MEE for further and in-depth instructions

Data from: Fitting functional responses: direct parameter estimation by simulating differential equations

1. 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

Animal diversity and ecosystem functioning in dynamic food webs

International audienceSpecies diversity is changing globally and locally, but the complexity of ecological communities hampers a general understanding of the consequences of animal species loss on ecosystem functioning. High animal diversity increases complementarity of herbivores but also increases feeding rates within the consumer guild. Depending on the balance of these counteracting mechanisms, species-rich animal communities may put plants under top-down control or may release them from grazing pressure. Using a dynamic food-web model with body-mass constraints, we simulate ecosystem functions of 20,000 communities of varying animal diversity. We show that diverse animal communities accumulate more biomass and are more exploitative on plants, despite their higher rates of intra-guild predation. However, they do not reduce plant biomass because the communities are composed of larger, and thus energetically more efficient, plant and animal species. This plasticity of community body-size structure reconciles the debate on the consequences of animal species loss for primary productivity

Data from Fussmann et al. (2017) for main publication and manual supplement

Functional response data provided by Katarina Fussmann and colleagues (https://doi.org/10.1101/101675). “N0” is the initial prey density; “Nend” is the remaining prey density after the experiment; “Ndead” is the number of dead prey individuals after the experiment; "T" is the time in minutes, "P" is the number of predators in the experiment (0 == control). These data appear both in the main publication (D8) and are needed to perform examples in the supplemental "manual" published in MEE. Please also refer to the original publication (https://doi.org/10.1101/101675) if you use these data