@article{KlauschiesCoutinhoGaedke2018,
  author    = {Klauschies, Toni and Coutinho, Renato Mendes and Gaedke, Ursula},
  title     = {A beta distribution-based moment closure enhances the reliability of trait-based aggregate models for natural populations and communities},
  series = {Ecological modelling : international journal on ecological modelling and engineering and systems ecolog},
  volume    = {381},
  journal   = {Ecological modelling : international journal on ecological modelling and engineering and systems ecolog},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0304-3800},
  doi       = {10.1016/j.ecolmodel.2018.02.001},
  pages     = {46 -- 77},
  year      = {2018},
  abstract  = {Ecological communities are complex adaptive systems that exhibit remarkable feedbacks between their biomass and trait dynamics. Trait-based aggregate models cope with this complexity by focusing on the temporal development of the community's aggregate properties such as its total biomass, mean trait and trait variance. They are based on particular assumptions about the shape of the underlying trait distribution, which is commonly assumed to be normal. However, ecologically important traits are usually restricted to a finite range, and empirical trait distributions are often skewed or multimodal. As a result, normal distribution-based aggregate models may fail to adequately represent the biomass and trait dynamics of natural communities. We resolve this mismatch by developing a new moment closure approach assuming the trait values to be beta-distributed. We show that the beta distribution captures important shape properties of both observed and simulated trait distributions, which cannot be captured by a Gaussian. We further demonstrate that a beta distribution-based moment closure can strongly enhance the reliability of trait-based aggregate models. We compare the biomass, mean trait and variance dynamics of a full trait distribution (FD) model to the ones of beta (BA) and normal (NA) distribution-based aggregate models, under different selection regimes. This way, we demonstrate under which general conditions (stabilizing, fluctuating or disruptive selection) different aggregate models are reliable tools. All three models predicted very similar biomass and trait dynamics under stabilizing selection yielding unimodal trait distributions with small standing trait variation. We also obtained an almost perfect match between the results of the FD and BA models under fluctuating selection, promoting skewed trait distributions and ongoing oscillations in the biomass and trait dynamics. In contrast, the NA model showed unrealistic trait dynamics and exhibited different alternative stable states, and thus a high sensitivity to initial conditions under fluctuating selection. Under disruptive selection, both aggregate models failed to reproduce the results of the FD model with the mean trait values remaining within their ecologically feasible ranges in the BA model but not in the NA model. Overall, a beta distribution-based moment closure strongly improved the realism of trait-based aggregate models.},
  language  = {en}
}
@misc{MooijTrolleJeppesenetal.2010,
  author    = {Mooij, Wolf M. and Trolle, Dennis and Jeppesen, Erik and Arhonditsis, George B. and Belolipetsky, Pavel V. and Chitamwebwa, Deonatus B. R. and Degermendzhy, Andrey G. and DeAngelis, Donald L. and Domis, Lisette Nicole de Senerpont and Downing, Andrea S. and Elliott, J. Alex and Fragoso Jr., Carlos Ruberto and Gaedke, Ursula and Genova, Svetlana N. and Gulati, Ramesh D. and H{\aa}kanson, Lars and Hamilton, David P. and Hipsey, Matthew R. and 't Hoen, Jochem and H{\"u}lsmann, Stephan and Los, F. Hans and Makler-Pick, Vardit and Petzoldt, Thomas and Prokopkin, Igor G. and Rinke, Karsten and Schep, Sebastiaan A. and Tominaga, Koji and Van Dam, Anne A. and Van Nes, Egbert H. and Wells, Scott A. and Janse, Jan H.},
  title     = {Challenges and opportunities for integrating lake ecosystem modelling approaches},
  series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {1326},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-42983},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-429839},
  pages     = {35},
  year      = {2010},
  abstract  = {A large number and wide variety of lake ecosystem models have been developed and published during the past four decades. We identify two challenges for making further progress in this field. One such challenge is to avoid developing more models largely following the concept of others ('reinventing the wheel'). The other challenge is to avoid focusing on only one type of model, while ignoring new and diverse approaches that have become available ('having tunnel vision'). In this paper, we aim at improving the awareness of existing models and knowledge of concurrent approaches in lake ecosystem modelling, without covering all possible model tools and avenues. First, we present a broad variety of modelling approaches. To illustrate these approaches, we give brief descriptions of rather arbitrarily selected sets of specific models. We deal with static models (steady state and regression models), complex dynamic models (CAEDYM, CE-QUAL-W2, Delft 3D-ECO, LakeMab, LakeWeb, MyLake, PCLake, PROTECH, SALMO), structurally dynamic models and minimal dynamic models. We also discuss a group of approaches that could all be classified as individual based: super-individual models (Piscator, Charisma), physiologically structured models, stage-structured models and traitbased models. We briefly mention genetic algorithms, neural networks, Kalman filters and fuzzy logic. Thereafter, we zoom in, as an in-depth example, on the multi-decadal development and application of the lake ecosystem model PCLake and related models (PCLake Metamodel, Lake Shira Model, IPH-TRIM3D-PCLake). In the discussion, we argue that while the historical development of each approach and model is understandable given its 'leading principle', there are many opportunities for combining approaches. We take the point of view that a single 'right' approach does not exist and should not be strived for. Instead, multiple modelling approaches, applied concurrently to a given problem, can help develop an integrative view on the functioning of lake ecosystems. We end with a set of specific recommendations that may be of help in the further development of lake ecosystem models.},
  language  = {en}
}
@article{MooijTrolleJeppesenetal.2010,
  author    = {Mooij, Wolf M. and Trolle, Dennis and Jeppesen, Erik and Arhonditsis, George B. and Belolipetsky, Pavel V. and Chitamwebwa, Deonatus B. R. and Degermendzhy, Andrey G. and DeAngelis, Donald L. and Domis, Lisette Nicole de Senerpont and Downing, Andrea S. and Elliott, J. Alex and Fragoso Jr, Carlos Ruberto and Gaedke, Ursula and Genova, Svetlana N. and Gulati, Ramesh D. and H{\aa}kanson, Lars and Hamilton, David P. and Hipsey, Matthew R. and 't Hoen, Jochem and H{\"u}lsmann, Stephan and Los, F. Hans and Makler-Pick, Vardit and Petzoldt, Thomas and Prokopkin, Igor G. and Rinke, Karsten and Schep, Sebastiaan A. and Tominaga, Koji and Van Dam, Anne A. and Van Nes, Egbert H. and Wells, Scott A. and Janse, Jan H.},
  title     = {Challenges and opportunities for integrating lake ecosystem modelling approaches},
  series = {Aquatic ecology},
  volume    = {44},
  journal   = {Aquatic ecology},
  publisher = {Springer Science + Business Media B.V.},
  address   = {Dordrecht},
  issn      = {1573-5125},
  doi       = {10.1007/s10452-010-9339-3},
  pages     = {633 -- 667},
  year      = {2010},
  abstract  = {A large number and wide variety of lake ecosystem models have been developed and published during the past four decades. We identify two challenges for making further progress in this field. One such challenge is to avoid developing more models largely following the concept of others ('reinventing the wheel'). The other challenge is to avoid focusing on only one type of model, while ignoring new and diverse approaches that have become available ('having tunnel vision'). In this paper, we aim at improving the awareness of existing models and knowledge of concurrent approaches in lake ecosystem modelling, without covering all possible model tools and avenues. First, we present a broad variety of modelling approaches. To illustrate these approaches, we give brief descriptions of rather arbitrarily selected sets of specific models. We deal with static models (steady state and regression models), complex dynamic models (CAEDYM, CE-QUAL-W2, Delft 3D-ECO, LakeMab, LakeWeb, MyLake, PCLake, PROTECH, SALMO), structurally dynamic models and minimal dynamic models. We also discuss a group of approaches that could all be classified as individual based: super-individual models (Piscator, Charisma), physiologically structured models, stage-structured models and traitbased models. We briefly mention genetic algorithms, neural networks, Kalman filters and fuzzy logic. Thereafter, we zoom in, as an in-depth example, on the multi-decadal development and application of the lake ecosystem model PCLake and related models (PCLake Metamodel, Lake Shira Model, IPH-TRIM3D-PCLake). In the discussion, we argue that while the historical development of each approach and model is understandable given its 'leading principle', there are many opportunities for combining approaches. We take the point of view that a single 'right' approach does not exist and should not be strived for. Instead, multiple modelling approaches, applied concurrently to a given problem, can help develop an integrative view on the functioning of lake ecosystems. We end with a set of specific recommendations that may be of help in the further development of lake ecosystem models.},
  language  = {en}
}
@article{EhrlichGaedke2020,
  author    = {Ehrlich, Elias and Gaedke, Ursula},
  title     = {Coupled changes in traits and biomasses cascading through a tritrophic plankton food web},
  series = {Limnology and oceanography},
  volume    = {65},
  journal   = {Limnology and oceanography},
  number    = {10},
  publisher = {Wiley},
  address   = {Hoboken},
  issn      = {0024-3590},
  doi       = {10.1002/lno.11466},
  pages     = {2502 -- 2514},
  year      = {2020},
  abstract  = {Trait-based approaches have broadened our understanding of how the composition of ecological communities responds to environmental drivers. This research has mainly focussed on abiotic factors and competition determining the community trait distribution, while effects of trophic interactions on trait dynamics, if considered at all, have been studied for two trophic levels at maximum. However, natural food webs are typically at least tritrophic. This enables indirect interactions of traits and biomasses among multiple trophic levels leading to underexplored effects on food web dynamics. Here, we demonstrate the occurrence of mutual trait adjustment among three trophic levels in a natural plankton food web (Lake Constance) and in a corresponding mathematical model. We found highly recurrent seasonal biomass and trait dynamics, where herbivorous zooplankton increased its size, and thus its ability to counter phytoplankton defense, before phytoplankton defense actually increased. This is contrary to predictions from bitrophic systems where counter-defense of the consumer is a reaction to prey defense. In contrast, counter-defense of carnivores by size adjustment followed the defense of herbivores as expected. By combining observations and model simulations, we show how the reversed trait dynamics at the two lower trophic levels result from a "trophic biomass-trait cascade" driven by the carnivores. Trait adjustment between two trophic levels can therefore be altered by biomass or trait changes of adjacent trophic levels. Hence, analyses of only pairwise trait adjustment can be misleading in natural food webs, while multitrophic trait-based approaches capture indirect biomass-trait interactions among multiple trophic levels.},
  language  = {en}
}
@misc{RaatzvanVelzenGaedke2018,
  author    = {Raatz, Michael and van Velzen, Ellen and Gaedke, Ursula},
  title     = {Co-adaptation impacts the robustness of predator-prey dynamics against perturbations},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {809},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-44248},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-442489},
  pages     = {16},
  year      = {2018},
  abstract  = {Global change threatens the maintenance of ecosystem functions that are shaped by the persistence and dynamics of populations. It has been shown that the persistence of species increases if they possess larger trait adaptability. Here, we investigate whether trait adaptability also affects the robustness of population dynamics of interacting species and thereby shapes the reliability of ecosystem functions that are driven by these dynamics. We model co-adaptation in a predator-prey system as changes to predator offense and prey defense due to evolution or phenotypic plasticity. We investigate how trait adaptation affects the robustness of population dynamics against press perturbations to environmental parameters and against pulse perturbations targeting species abundances and their trait values. Robustness of population dynamics is characterized by resilience, elasticity, and resistance. In addition to employing established measures for resilience and elasticity against pulse perturbations (extinction probability and return time), we propose the warping distance as a new measure for resistance against press perturbations, which compares the shapes and amplitudes of pre- and post-perturbation population dynamics. As expected, we find that the robustness of population dynamics depends on the speed of adaptation, but in nontrivial ways. Elasticity increases with speed of adaptation as the system returns more rapidly to the pre-perturbation state. Resilience, in turn, is enhanced by intermediate speeds of adaptation, as here trait adaptation dampens biomass oscillations. The resistance of population dynamics strongly depends on the target of the press perturbation, preventing a simple relationship with the adaptation speed. In general, we find that low robustness often coincides with high amplitudes of population dynamics. Hence, amplitudes may indicate the robustness against perturbations also in other natural systems with similar dynamics. Our findings show that besides counteracting extinctions, trait adaptation indeed strongly affects the robustness of population dynamics against press and pulse perturbations.},
  language  = {en}
}
@article{RaatzvanVelzenGaedke2019,
  author    = {Raatz, Michael and van Velzen, Ellen and Gaedke, Ursula},
  title     = {Co-adaptation impacts the robustness of predator-prey dynamics against perturbations},
  series = {Ecology and Evolution},
  volume    = {9},
  journal   = {Ecology and Evolution},
  number    = {7},
  publisher = {John Wiley \& Sons},
  address   = {Hoboken, NJ},
  issn      = {2045-7758},
  doi       = {10.1002/ece3.5006},
  pages     = {3823 -- 3836},
  year      = {2019},
  abstract  = {Global change threatens the maintenance of ecosystem functions that are shaped by the persistence and dynamics of populations. It has been shown that the persistence of species increases if they possess larger trait adaptability. Here, we investigate whether trait adaptability also affects the robustness of population dynamics of interacting species and thereby shapes the reliability of ecosystem functions that are driven by these dynamics. We model co-adaptation in a predator-prey system as changes to predator offense and prey defense due to evolution or phenotypic plasticity. We investigate how trait adaptation affects the robustness of population dynamics against press perturbations to environmental parameters and against pulse perturbations targeting species abundances and their trait values. Robustness of population dynamics is characterized by resilience, elasticity, and resistance. In addition to employing established measures for resilience and elasticity against pulse perturbations (extinction probability and return time), we propose the warping distance as a new measure for resistance against press perturbations, which compares the shapes and amplitudes of pre- and post-perturbation population dynamics. As expected, we find that the robustness of population dynamics depends on the speed of adaptation, but in nontrivial ways. Elasticity increases with speed of adaptation as the system returns more rapidly to the pre-perturbation state. Resilience, in turn, is enhanced by intermediate speeds of adaptation, as here trait adaptation dampens biomass oscillations. The resistance of population dynamics strongly depends on the target of the press perturbation, preventing a simple relationship with the adaptation speed. In general, we find that low robustness often coincides with high amplitudes of population dynamics. Hence, amplitudes may indicate the robustness against perturbations also in other natural systems with similar dynamics. Our findings show that besides counteracting extinctions, trait adaptation indeed strongly affects the robustness of population dynamics against press and pulse perturbations.},
  language  = {en}
}
@article{SpijkermanBehrendFachetal.2018,
  author    = {Spijkerman, Elly and Behrend, Hella and Fach, Bettina and Gaedke, Ursula},
  title     = {Decreased phosphorus incorporation explains the negative effect of high iron concentrations in the green microalga Chlamydomonas acidophila},
  series = {The science of the total environment : an international journal for scientific research into the environment and its relationship with man},
  volume    = {626},
  journal   = {The science of the total environment : an international journal for scientific research into the environment and its relationship with man},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0048-9697},
  doi       = {10.1016/j.scitotenv.2018.01.188},
  pages     = {1342 -- 1349},
  year      = {2018},
  abstract  = {The green microalga Chlamydomonas acidophila is an important primary producer in very acidic lakes (pH 2.0-3.5), characterized by high concentrations of ferric iron (up to 1 g total Fe L-1) and low rates of primary production. It was previously suggested that these high iron concentrations result in high iron accumulation and inhibit photosynthesis in C. acidophila. To test this, the alga was grown in sterilized lake water and in medium with varying total iron concentrations under limiting and sufficient inorganic phosphorus (Pi) supply, because Pi is an important growth limiting nutrient in acidic waters. Photosynthesis and growth of C. acidophila as measured over 5 days were largely unaffected by high total iron concentrations and only decreased if free ionic Fe3+ concentrations exceeded 100 mg Fe3+ L-1. Although C. acidophila was relatively rich in iron (up to 5 mmol Fe: mol C), we found no evidence of iron toxicity. In contrast, a concentration of 260 mg total Fe L-1 (i.e. 15 mg free ionic Fe3+ L-1), which is common in many acidic lakes, reduced Pi-incorporation by 50\% and will result in Pi-limited photosynthesis. The resulting Pi-limitation present at high iron and Pi concentrations was illustrated by elevated maximum Pi-uptake rates. No direct toxic effects of high iron were found, but unfavourable chemical Pi-speciation reduced growth of the acidophile alga.},
  language  = {en}
}
@article{RossbergGaedkeKratina2019,
  author    = {Rossberg, Axel G. and Gaedke, Ursula and Kratina, Pavel},
  title     = {Dome patterns in pelagic size spectra reveal strong trophic cascades},
  series = {Nature Communications},
  volume    = {10},
  journal   = {Nature Communications},
  publisher = {Nature Publ. Group},
  address   = {London},
  issn      = {2041-1723},
  doi       = {10.1038/s41467-019-12289-0},
  pages     = {11},
  year      = {2019},
  abstract  = {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.},
  language  = {en}
}
@article{RosenbaumRaatzWeithoffetal.2019,
  author    = {Rosenbaum, Benjamin and Raatz, Michael and Weithoff, Guntram and Fussmann, Gregor F. and Gaedke, Ursula},
  title     = {Estimating parameters from multiple time series of population dynamics using bayesian inference},
  series = {Frontiers in ecology and evolution},
  volume    = {6},
  journal   = {Frontiers in ecology and evolution},
  publisher = {Frontiers Research Foundation},
  address   = {Lausanne},
  issn      = {2296-701X},
  doi       = {10.3389/fevo.2018.00234},
  pages     = {14},
  year      = {2019},
  abstract  = {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.},
  language  = {en}
}
@article{ColomaGaedkeSivonenetal.2019,
  author    = {Coloma, Sebastian and Gaedke, Ursula and Sivonen, Kaarina and Hiltunen, Teppo},
  title     = {Frequency of virus-resistant hosts determines experimental community dynamics},
  series = {Ecology : a publication of the Ecological Society of America},
  volume    = {100},
  journal   = {Ecology : a publication of the Ecological Society of America},
  number    = {1},
  publisher = {Wiley},
  address   = {Hoboken},
  issn      = {0012-9658},
  doi       = {10.1002/ecy.2554},
  pages     = {10},
  year      = {2019},
  abstract  = {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.},
  language  = {en}
}