@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} } @article{KathBoitGuilletal.2018, author = {Kath, Nadja J. and Boit, Alice and Guill, Christian and Gaedke, Ursula}, title = {Accounting for activity respiration results in realistic trophic transfer efficiencies in allometric trophic network (ATN) models}, series = {Theoretical ecology}, volume = {11}, journal = {Theoretical ecology}, number = {4}, publisher = {Springer}, address = {Heidelberg}, issn = {1874-1738}, doi = {10.1007/s12080-018-0378-z}, pages = {453 -- 463}, year = {2018}, abstract = {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.}, 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{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{MehnerLischkeScharnweberetal.2018, author = {Mehner, Thomas and Lischke, Betty and Scharnweber, Inga Kristin and Attermeyer, Katrin and Brothers, Soren and Gaedke, Ursula and Hilt, Sabine and Brucet, Sandra}, title = {Empirical correspondence between trophic transfer efficiency in freshwater food webs and the slope of their size spectra}, series = {Ecology : a publication of the Ecological Society of America}, volume = {99}, journal = {Ecology : a publication of the Ecological Society of America}, number = {6}, publisher = {Wiley}, address = {Hoboken}, issn = {0012-9658}, doi = {10.1002/ecy.2347}, pages = {1463 -- 1472}, year = {2018}, abstract = {The density of organisms declines with size, because larger organisms need more energy than smaller ones and energetic losses occur when larger organisms feed on smaller ones. A potential expression of density-size distributions are Normalized Biomass Size Spectra (NBSS), which plot the logarithm of biomass independent of taxonomy within bins of logarithmic organismal size, divided by the bin width. Theoretically, the NBSS slope of multi-trophic communities is exactly - 1.0 if the trophic transfer efficiency (TTE, ratio of production rates between adjacent trophic levels) is 10\% and the predator-prey mass ratio (PPMR) is fixed at 10(4). Here we provide evidence from four multi-trophic lake food webs that empirically estimated TTEs correspond to empirically estimated slopes of the respective community NBSS. Each of the NBSS considered pelagic and benthic organisms spanning size ranges from bacteria to fish, all sampled over three seasons in 1 yr. The four NBSS slopes were significantly steeper than -1.0 (range -1.14 to -1.19, with 95\% CIs excluding -1). The corresponding average TTEs were substantially lower than 10\% in each of the four food webs (range 1.0\% to 3.6\%, mean 1.85\%). The overall slope merging all biomass-size data pairs from the four systems (-1.17) was almost identical to the slope predicted from the arithmetic mean TTE of the four food webs (-1.18) assuming a constant PPMR of 10(4). Accordingly, our empirical data confirm the theoretically predicted quantitative relationship between TTE and the slope of the biomass-size distribution. Furthermore, we show that benthic and pelagic organisms can be merged into a community NBSS, but future studies have yet to explore potential differences in habitat-specific TTEs and PPMRs. We suggest that community NBSS may provide valuable information on the structure of food webs and their energetic pathways, and can result in improved accuracy of TTE-estimates.}, language = {en} } @article{vanVelzenThieserBerendonketal.2018, author = {van Velzen, Ellen and Thieser, Tamara and Berendonk, Thomas U. and Weitere, Markus and Gaedke, Ursula}, title = {Inducible defense destabilizes predator-prey dynamics}, series = {Oikos}, volume = {127}, journal = {Oikos}, number = {11}, publisher = {Wiley}, address = {Hoboken}, issn = {0030-1299}, doi = {10.1111/oik.04868}, pages = {1551 -- 1562}, year = {2018}, abstract = {Phenotypic plasticity in prey can have a dramatic impact on predator-prey dynamics, e.g. by inducible defense against temporally varying levels of predation. Previous work has overwhelmingly shown that this effect is stabilizing: inducible defenses dampen the amplitudes of population oscillations or eliminate them altogether. However, such studies have neglected scenarios where being protected against one predator increases vulnerability to another (incompatible defense). Here we develop a model for such a scenario, using two distinct prey phenotypes and two predator species. Each prey phenotype is defended against one of the predators, and vulnerable to the other. In strong contrast with previous studies on the dynamic effects of plasticity involving a single predator, we find that increasing the level of plasticity consistently destabilizes the system, as measured by the amplitude of oscillations and the coefficients of variation of both total prey and total predator biomasses. We explain this unexpected and seemingly counterintuitive result by showing that plasticity causes synchronization between the two prey phenotypes (and, through this, between the predators), thus increasing the temporal variability in biomass dynamics. These results challenge the common view that plasticity should always have a stabilizing effect on biomass dynamics: adding a single predator-prey interaction to an established model structure gives rise to a system where different mechanisms may be at play, leading to dramatically different outcomes.}, language = {en} } @article{MittlerBlasiusGaedkeetal.2018, author = {Mittler, Udo and Blasius, Bernd and Gaedke, Ursula and Ryabov, Alexey B.}, title = {Length-volume relationship of lake phytoplankton}, series = {Limnology and Oceanography: Methods}, volume = {17}, journal = {Limnology and Oceanography: Methods}, number = {1}, publisher = {Wiley}, address = {Hoboken}, issn = {1541-5856}, doi = {10.1002/lom3.10296}, pages = {58 -- 68}, year = {2018}, abstract = {The shapes of phytoplankton units (unicellular organisms and colonies) are extremely diverse, and no unique relationship exists between their volume, V, and longest linear dimension, L. However, an approximate scaling between these parameters can be found because the shape variations within each size class are constrained by cell physiology, grazing pressure, and optimality of resource acquisition. To determine this scaling and to test for its seasonal and interannual variation under changing environmental conditions, we performed weighted regression analysis of time-dependent length-volume relations of the phytoplankton community in large deep Lake Constance from 1979 to 1999. We show that despite a large variability in species composition, the V(L) relationship can be approximated as a power law, V similar to L-alpha, with a scaling exponent alpha = 3 for small cells (L < 25 mu m) and alpha = 1.7 if the fitting is performed over the entire length range, including individual cells and colonies. The best description is provided by a transitional power function describing a regime change from a scaling exponent of 3 for small cells to an exponent of 0.4 in the range of large phytoplankton. Testing different weighted fitting approaches we show that remarkably the best prediction of the total community biovolume from measurements of L and cell density is obtained when the regression is weighted with the squares of species abundances. Our approach should also be applicable to other systems and allows converting phytoplankton length distributions (e.g., obtained with automatic monitoring such as flow cytometry) into distributions of biovolume and biovolume-related phytoplankton traits.}, language = {en} } @article{EhrlichGaedke2018, author = {Ehrlich, Elias and Gaedke, Ursula}, title = {Not attackable or not crackable}, series = {Ecology and evolution}, volume = {8}, journal = {Ecology and evolution}, number = {13}, publisher = {Wiley}, address = {Hoboken}, issn = {2045-7758}, doi = {10.1002/ece3.4145}, pages = {6625 -- 6637}, year = {2018}, abstract = {It is well-known that prey species often face trade-offs between defense against predation and competitiveness, enabling predator-mediated coexistence. However, we lack an understanding of how the large variety of different defense traits with different competition costs affects coexistence and population dynamics. Our study focusses on two general defense mechanisms, that is, pre-attack (e.g., camouflage) and post-attack defenses (e.g., weaponry) that act at different phases of the predator—prey interaction. We consider a food web model with one predator, two prey types and one resource. One prey type is undefended, while the other one is pre- or post-attack defended paying costs either by a higher half-saturation constant for resource uptake or a lower maximum growth rate. We show that post-attack defenses promote prey coexistence and stabilize the population dynamics more strongly than pre-attack defenses by interfering with the predator's functional response: Because the predator spends time handling "noncrackable" prey, the undefended prey is indirectly facilitated. A high half-saturation constant as defense costs promotes coexistence more and stabilizes the dynamics less than a low maximum growth rate. The former imposes high costs at low resource concentrations but allows for temporally high growth rates at predator-induced resource peaks preventing the extinction of the defended prey. We evaluate the effects of the different defense mechanisms and costs on coexistence under different enrichment levels in order to vary the importance of bottom-up and top-down control of the prey community.}, language = {en} } @article{EhrlichGaedke2018, author = {Ehrlich, Elias and Gaedke, Ursula}, title = {Not attackable or not crackable}, series = {Ecology and Evolution}, volume = {8}, journal = {Ecology and Evolution}, number = {13}, publisher = {Wiley}, issn = {2045-7758}, doi = {10.1002/ece3.4145}, pages = {6625 -- 6637}, year = {2018}, abstract = {It is well-known that prey species often face trade-offs between defense against predation and competitiveness, enabling predator-mediated coexistence. However, we lack an understanding of how the large variety of different defense traits with different competition costs affects coexistence and population dynamics. Our study focusses on two general defense mechanisms, that is, pre-attack (e.g., camouflage)and post-attack defenses (e.g., weaponry) that act at different phases of the predator—prey interaction. We consider a food web model with one predator, two prey types and one resource. One prey type is undefended, while the other one is pre-or post-attack defended paying costs either by a higher half-saturation constant for resource uptake or a lower maximum growth rate. We show that post-attack defenses promote prey coexistence and stabilize the population dynamics more strongly than pre-attack defenses by interfering with the predator's functional response: Because the predator spends time handling "noncrackable" prey, the undefended prey is indirectly facilitated. A high half-saturation constant as defense costs promotes coexistence more and stabilizes the dynamics less than a low maximum growth rate. The former imposes high costs at low resource concentrations but allows for temporally high growth rates at predator-induced resource peaks preventing the extinction of the defended prey. We evaluate the effects of the different defense mechanisms and costs on coexistence under different enrichment levels in order to vary the importance of bottom-up and top-down control of the prey community.}, language = {en} } @misc{EhrlichGaedke2018, author = {Ehrlich, Elias and Gaedke, Ursula}, title = {Not attackable or not crackable}, series = {Ecology and Evolution}, journal = {Ecology and Evolution}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-417391}, pages = {12}, year = {2018}, abstract = {It is well-known that prey species often face trade-offs between defense against predation and competitiveness, enabling predator-mediated coexistence. However, we lack an understanding of how the large variety of different defense traits with different competition costs affects coexistence and population dynamics. Our study focusses on two general defense mechanisms, that is, pre-attack (e.g., camouflage) and post-attack defenses (e.g., weaponry) that act at different phases of the predator—prey interaction. We consider a food web model with one predator, two prey types and one resource. One prey type is undefended, while the other one is pre-or post-attack defended paying costs either by a higher half-saturation constant for resource uptake or a lower maximum growth rate. We show that post-attack defenses promote prey coexistence and stabilize the population dynamics more strongly than pre-attack defenses by interfering with the predator's functional response: Because the predator spends time handling "noncrackable" prey, the undefended prey is indirectly facilitated. A high half-saturation constant as defense costs promotes coexistence more and stabilizes the dynamics less than a low maximum growth rate. The former imposes high costs at low resource concentrations but allows for temporally high growth rates at predator-induced resource peaks preventing the extinction of the defended prey. We evaluate the effects of the different defense mechanisms and costs on coexistence under different enrichment levels in order to vary the importance of bottom-up and top-down control of the prey community.}, language = {en} }