Mathematical models predict that species interactions such as competition and predation can generate chaos. However, experimental demonstrations of chaos in ecology are scarce, and have been limited to simple laboratory systems with a short duration and artificial species combinations. Here, we present the first experimental demonstration of chaos in a long-term experiment with a complex food web. Our food web was isolated from the Baltic Sea, and consisted of bacteria, several phytoplankton species, herbivorous and predatory zooplankton species, and detritivores. The food web was cultured in a laboratory mesocosm, and sampled twice a week for more than 2,300 days. Despite constant external conditions, the species abundances showed striking fluctuations over several orders of magnitude. These fluctuations displayed a variety of different periodicities, which could be attributed to different species interactions in the food web. The population dynamics were characterized by positive Lyapunov exponents of similar magnitude for each species. Predictability was limited to a time horizon of 15-30 days, only slightly longer than the local weather forecast. Hence, our results demonstrate that species interactions in food webs can generate chaos. This implies that stability is not required for the persistence of complex food webs, and that the long-term prediction of species abundances can be fundamentally impossible.

Nitrogen (N) and phosphorus (P) limit primary production in many aquatic ecosystems, with major implications for ecological interactions in plankton communities. Yet it remains unclear how evolution may affect the N∶P stoichiometry of phytoplankton-zooplankton interactions. Here, we address this issue by analyzing an eco-evolutionary model of phytoplankton-zooplankton interactions with explicit nitrogen and phosphorus dynamics. In our model, investment of phytoplankton in nitrogen versus phosphorus uptake is an evolving trait, and zooplankton display selectivity for phytoplankton with N∶P ratios matching their nutritional requirements. We use this model to explore implications of the contrasting N∶P requirements of copepods versus cladocerans. The model predicts that selective zooplankton strongly affect the N∶P ratio of phytoplankton, resulting in deviations from their optimum N∶P ratio. Specifically, selective grazing by nitrogen-demanding copepods favors dominance of phytoplankton with low N∶P ratios, whereas phosphorus-demanding cladocerans favor dominance of phytoplankton with high N∶P ratios. Interestingly, selective grazing by nutritionally balanced zooplankton leads to the occurrence of alternative stable states, where phytoplankton may evolve either low, optimum, or high N∶P ratios, depending on the initial conditions. These results offer a new perspective on commonly observed differences in N∶P stoichiometry between plankton of freshwater and those of marine ecosystems and indicate that selective grazing by zooplankton can have a major impact on the stoichiometric composition of phytoplankton.

Phytoplankton are among the smallest primary producers on Earth, yet they display a wide range of cell sizes. Typically, small phytoplankton species are stronger nutrient competitors than large phytoplankton species, but they are also more easily grazed. In contrast, evolution of large phytoplankton is often explained as a physical defense against grazing. Conceptually, this explanation is problematic, however, because zooplankton can coevolve larger size to counter this size-dependent escape from grazing. Here, we hypothesize that there is another advantage for the evolution of large phytoplankton size not so readily overcome: larger phytoplankton often provide lower nutritional quality for zooplankton. We investigate this hypothesis by analyzing an eco-evolutionary model that combines the ecological stoichiometry of phytoplanktonzooplankton interactions with coevolution of phytoplankton and zooplankton size. In our model, evolution of cell size modifies the nutrient uptake kinetics of phytoplankton according to known allometric relationships, which in turn affect the nutritional quality of phytoplankton. With this size-based mechanism, the model predicts that low grazing pressure or nonselective grazing by zooplankton favors evolution of small phytoplankton cells of high nutritional quality. In contrast, selective grazing for nutritious food favors evolution of large phytoplankton of low nutritional quality, which are preyed on by medium-to large-sized zooplankton. This size-dependent change in food quality may explain the commonly observed shift from dominance by small picophytoplankton in oligotrophic waters with low grazing pressure to large phytoplankton species in nutrient-rich waters with high grazing pressure.

Evolution of nutrient uptake reveals a trade-off in the ecological stoichiometry of plantherbivore interactions Mayer Branco, P.M.; Stomp, M.; Egas, C.J.M.; Huisman, J. Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. abstract: Nutrient limitation determines the primary production and species composition of many ecosystems. Here we apply an adaptive dynamics approach to investigate evolution of the ecological stoichiometry of primary producers and its implications for plantherbivore interactions. The model predicts a trade-off between the competitive ability and grazing susceptibility of primary producers, driven by changes in their nutrient uptake rates. High nutrient uptake rates enhance the competitiveness of primary producers but also increase their nutritional quality for herbivores. This trade-off enables coexistence of nutrient exploiters and grazing avoiders. If herbivores are not selective, evolution favors runaway selection toward high nutrient uptake rates of the primary producers. However, if herbivores select nutritious food, the model predicts an evolutionarily stable strategy with lower nutrient uptake rates. When the model is parameterized for phytoplankton and zooplankton, the evolutionary dynamics result in plant-herbivore oscillations at ecological timescales, especially in environments with high nutrient availability and low selectivity of the herbivores. High herbivore selectivity stabilizes the community dynamics. These model predictions show that evolution permits nonequilibrium dynamics in plant-herbivore communities and shed new light on the evolutionary forces that shape the ecological stoichiometry of primary producers.

The fastest-growing renewable source of energy is solar photovoltaic (PV) energy, which is likely to become the largest electricity source in the world by 2050. In order to be a viable alternative energy source, PV systems should maximise their efficiency and operate flawlessly. However, in practice, many PV systems do not operate at their full capacity due to several types of anomalies. We propose tailored algorithms for the detection of different PV system anomalies, including suboptimal orientation, daytime and sunrise/sunset shading, brief and sustained daytime zero-production, and low maximum production. Furthermore, we establish simple metrics to assess the severity of suboptimal orientation and daytime shading. The proposed detection algorithms were applied to a set of time-series of electricity production in Portugal, which are based on two periods with distinct weather conditions. Under favourable weather conditions, the algorithms successfully detected most of the time-series labelled with either daytime or sunrise/sunset shading, and with either sustained or brief daytime zero-production. There was a relatively low percentage of false positives, such that most of the anomaly detections were correct. As expected, the algorithms tend to be more robust under favourable rather than under adverse weather conditions. The proposed algorithms may prove to be useful not only to research specialists, but also to energy utilities and owners of small- and medium-sized PV systems, who may thereby effortlessly monitor their operation and performance.

We would like to make a small correction to our article "Eco-Evolutionary Dynamics of Ecological Stoichiometry in Plankton Communities" (American Naturalist 192:E1-E20). Specifically, the search rate, a, of cladoceran zooplankton listed in table 1 should read a p 0:0024 L ind 21 d 21 (instead of a p 0:072 L ind 21 d 21), and the source from which this value was obtained should be replaced by DeMott (1982). All of our model simulations were based on the above corrected value. Hence, this correction does not influence the results of our article. We thank Junkun Ren (Peking University, China) for noticing this mistake.

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