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Allometric trophic network (ATN) models offer high flexibility and scalability while minimizing the number of parameters and have been successfully applied to investigate complex food web dynamics and their influence on food web diversity and stability. However, the realism of ATN model energetics has never been assessed in detail, despite their critical influence on dynamic biomass and production patterns. Here, we compare the energetics of the currently established original ATN model, considering only biomass-dependent basal respiration, to an extended ATN model version, considering both basal and assimilation-dependent activity respiration. The latter is crucial in particular for unicellular and invertebrate organisms which dominate the metabolism of pelagic and soil food webs. Based on metabolic scaling laws, we show that the extended ATN version reflects the energy transfer through a chain of four trophic levels of unicellular and invertebrate organisms more realistically than the original ATN version. Depending on the strength of top-down control, the original ATN model yields trophic transfer efficiencies up to 71% at either the third or the fourth trophic level, which considerably exceeds any realistic values. In contrast, the extended ATN version yields realistic trophic transfer efficiencies 30% at all trophic levels, in accordance with both physiological considerations and empirical evidence from pelagic systems. Our results imply that accounting for activity respiration is essential for consistently implementing the metabolic theory of ecology in ATN models and for improving their quantitative predictions, which makes them more powerful tools for investigating the dynamics of complex natural communities.
Parasites, such as bacterial viruses (phages), can have large effects on host populations both at the ecological and evolutionary levels. In the case of cyanobacteria, phages can reduce primary production and infected hosts release intracellular nutrients influencing planktonic food web structure, community dynamics, and biogeochemical cycles. Cyanophages may be of great importance in aquatic food webs during large cyanobacterial blooms unless the host population becomes resistant to phage infection. The consequences on plankton community dynamics of the evolution of phage resistance in bloom forming cyanobacterial populations are still poorly studied. Here, we examined the effect of different frequencies of a phage-resistant genotype within a filamentous nitrogen-fixing Nodularia spumigena population on an experimental plankton community. Three Nodularia populations with different initial frequencies (0%, 5%, and 50%) of phage-resistant genotypes were inoculated in separate treatments with the phage 2AV2, the green alga Chlorella vulgaris, and the rotifer Brachionus plicatilis, which formed the experimental plankton community subjected to either nitrogen-limited or nitrogen-rich conditions. We found that the frequency of the phage-resistant Nodularia genotype determined experimental community dynamics. Cyanobacterial populations with a high frequency (50%) of the phage-resistant genotype dominated the cultures despite the presence of phages, retaining most of the intracellular nitrogen in the plankton community. In contrast, populations with low frequencies (0% and 5%) of the phage-resistant genotype were lysed and reduced to extinction by the phage, transferring the intracellular nitrogen held by Nodularia to Chlorella and rotifers, and allowing Chlorella to dominate the communities and rotifers to survive. This study shows that even though phages represent minuscule biomass, they can have key effects on community composition and eco-evolutionary feedbacks in plankton communities.
Estimating parameters from multiple time series of population dynamics using bayesian inference
(2019)
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.
The size structure of autotroph communities - the relative abundance of small vs. large individuals - shapes the functioning of ecosystems. Whether common mechanisms underpin the size structure of unicellular and multicellular autotrophs is, however, unknown. Using a global data compilation, we show that individual body masses in tree and phytoplankton communities follow power-law distributions and that the average exponents of these individual size distributions (ISD) differ. Phytoplankton communities are characterized by an average ISD exponent consistent with three-quarter-power scaling of metabolism with body mass and equivalence in energy use among mass classes. Tree communities deviate from this pattern in a manner consistent with equivalence in energy use among diameter size classes. Our findings suggest that whilst universal metabolic constraints ultimately underlie the emergent size structure of autotroph communities, divergent aspects of body size (volumetric vs. linear dimensions) shape the ecological outcome of metabolic scaling in forest vs. pelagic ecosystems.
In ecological communities, especially the pelagic zones of aquatic ecosystems, certain bodysize ranges are often over-represented compared to others. Community size spectra, the distributions of community biomass over the logarithmic body-mass axis, tend to exhibit regularly spaced local maxima, called "domes", separated by steep troughs. Contrasting established theory, we explain these dome patterns as manifestations of top-down trophic cascades along aquatic food chains. Compiling high quality size-spectrum data and comparing these with a size-spectrum model introduced in this study, we test this theory and develop a detailed picture of the mechanisms by which bottom-up and top-down effects interact to generate dome patterns. Results imply that strong top-down trophic cascades are common in freshwater communities, much more than hitherto demonstrated, and may arise in nutrient rich marine systems as well. Transferring insights from the general theory of nonlinear pattern formation to domes patterns, we provide new interpretations of past lake-manipulation experiments.
Biodiversity decline causes a loss of functional diversity, which threatens ecosystems through a dangerous feedback loop: This loss may hamper ecosystems’ ability to buffer environmental changes, leading to further biodiversity losses. In this context, the increasing frequency of human-induced excessive loading of nutrients causes major problems in aquatic systems. Previous studies investigating how functional diversity influences the response of food webs to disturbances have mainly considered systems with at most two functionally diverse trophic levels. We investigated the effects of functional diversity on the robustness, that is, resistance, resilience, and elasticity, using a tritrophic—and thus more realistic—plankton food web model. We compared a non-adaptive food chain with no diversity within the individual trophic levels to a more diverse food web with three adaptive trophic levels. The species fitness differences were balanced through trade-offs between defense/growth rate for prey and selectivity/half-saturation constant for predators. We showed that the resistance, resilience, and elasticity of tritrophic food webs decreased with larger perturbation sizes and depended on the state of the system when the perturbation occurred. Importantly, we found that a more diverse food web was generally more resistant and resilient but its elasticity was context-dependent. Particularly, functional diversity reduced the probability of a regime shift toward a non-desirable alternative state. The basal-intermediate interaction consistently determined the robustness against a nutrient pulse despite the complex influence of the shape and type of the dynamical attractors. This relationship was strongly influenced by the diversity present and the third trophic level. Overall, using a food web model of realistic complexity, this study confirms the destructive potential of the positive feedback loop between biodiversity loss and robustness, by uncovering mechanisms leading to a decrease in resistance, resilience, and potentially elasticity as functional diversity declines.
The shape of trait distributions may inform about the selective forces that structure ecological communities. Here, we present a new moment-based approach to classify the shape of observed biomass-weighted trait distributions into normal, peaked, skewed, or bimodal that facilitates spatio-temporal and cross-system comparisons. Our observed phytoplankton trait distributions exhibited substantial variance and were mostly skewed or bimodal rather than normal. Additionally, mean, variance, skewness und kurtosis were strongly correlated. This is in conflict with trait-based aggregate models that often assume normally distributed trait values and small variances. Given these discrepancies between our data and general model assumptions we used the observed trait distributions to test how well different aggregate models with first- or second-order approximations and different types of moment closure predict the biomass, mean trait, and trait variance dynamics using weakly or moderately nonlinear fitness functions. For weakly non-linear fitness functions aggregate models with a second-order approximation and a data-based moment closure that relied on the observed correlations between skewness and mean, and kurtosis and variance predicted biomass and often also mean trait changes fairly well and better than models with first-order approximations or a normal-based moment closure. In contrast, none of the models reflected the changes of the trait variances reliably. Aggregate model performance was often also poor for moderately nonlinear fitness functions. This questions a general applicability of the normal-based approach, in particular for predicting variance dynamics determining the speed of trait changes and maintenance of biodiversity. We evaluate in detail how and why better approximations can be obtained.
Diverse communities can adjust their trait composition to altered environmental conditions, which may strongly influence their dynamics. Previous studies of trait-based models mainly considered only one or two trophic levels, whereas most natural system are at least tritrophic. Therefore, we investigated how the addition of trait variation to each trophic level influences population and community dynamics in a tritrophic model. Examining the phase relationships between species of adjacent trophic levels informs about the strength of top-down or bottom-up control in non-steadystate situations. Phase relationships within a trophic level highlight compensatory dynamical patterns between functionally different species, which are responsible for dampening the community temporal variability. Furthermore, even without trait variation, our tritrophic model always exhibits regions with two alternative states with either weak or strong nutrient exploitation, and correspondingly low or high biomass production at the top level. However, adding trait variation increased the basin of attraction of the high-production state, and decreased the likelihood of a critical transition from the high- to the lowproduction state with no apparent early warning signals. Hence, our study shows that trait variation enhances resource use efficiency, production, stability, and resilience of entire food webs.
Biological invasions are a major threat to natural biodiversity; hence, understanding the mechanisms underlying invasibility (i.e., the susceptibility of a community to invasions by new species) is crucial. Invasibility of a resident community may be affected by a complex but hitherto hardly understood interplay of (1) productivity of the habitat, (2) diversity, (3) herbivory, and (4) the characteristics of both invasive and resident species. Using experimental phytoplankton microcosms, we investigated the effect of nutrient supply and species diversity on the invasibility of resident communities for two functionally different invaders in the presence or absence of an herbivore. With increasing nutrient supply, increased herbivore abundance indicated enhanced phytoplankton biomass production, and the invasion success of both invaders showed a unimodal pattern. At low nutrient supply (i.e., low influence of herbivory), the invasibility depended mainly on the competitive abilities of the invaders, whereas at high nutrient supply, the susceptibility to herbivory dominated. This resulted in different optimum nutrient levels for invasion success of the two species due to their individual functional traits. To test the effect of diversity on invasibility, a species richness gradient was generated by random selection from a resident species pool at an intermediate nutrient level. Invasibility was not affected by species richness; instead, it was driven by the functional traits of the resident and/or invasive species mediated by herbivore density. Overall, herbivory was the driving factor for invasibility of phytoplankton communities, which implies that other factors affecting the intensity of herbivory (e.g., productivity or edibility of primary producers) indirectly influence invasions.
It is well known that functional diversity strongly affects ecosystem functioning. However, even in rather simple model communities consisting of only two or, at best, three trophic levels, the relationship between multitrophic functional diversity and ecosystem functioning appears difficult to generalize, because of its high contextuality. In this study, we considered several differently structured tritrophic food webs, in which the amount of functional diversity was varied independently on each trophic level. To achieve generalizable results, largely independent of parametrization, we examined the outcomes of 128,000 parameter combinations sampled from ecologically plausible intervals, with each tested for 200 randomly sampled initial conditions. Analysis of our data was done by training a random forest model. This method enables the identification of complex patterns in the data through partial dependence graphs, and the comparison of the relative influence of model parameters, including the degree of diversity, on food-web properties. We found that bottom-up and top-down effects cascade simultaneously throughout the food web, intimately linking the effects of functional diversity of any trophic level to the amount of diversity of other trophic levels, which may explain the difficulty in unifying results from previous studies. Strikingly, only with high diversity throughout the whole food web, different interactions synergize to ensure efficient exploitation of the available nutrients and efficient biomass transfer to higher trophic levels, ultimately leading to a high biomass and production on the top level. The temporal variation of biomass showed a more complex pattern with increasing multitrophic diversity: while the system initially became less variable, eventually the temporal variation rose again because of the increasingly complex dynamical patterns. Importantly, top predator diversity and food-web parameters affecting the top trophic level were of highest importance to determine the biomass and temporal variability of any trophic level. Overall, our study reveals that the mechanisms by which diversity influences ecosystem functioning are affected by every part of the food web, hampering the extrapolation of insights from simple monotrophic or bitrophic systems to complex natural food webs.