Chaos in a long-term experiment with a plankton community
TL;DR: The first experimental demonstration of chaos in a long-term experiment with a complex food web, isolated from the Baltic Sea, demonstrates that species interactions in food webs can generate chaos, and 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.
Abstract: 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.
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TL;DR: Organizing the material of community ecology according to this framework can clarify the essential similarities and differences among the many conceptual and theoretical approaches to the discipline, and allow for the articulation of a very general theory of community dynamics.
Abstract: Community ecology is often perceived as a mess, given the seemingly vast number of processes that can underlie the many patterns of interest, and the apparent uniqueness of each study system. However, at the most general level, patterns in the composition and diversity of speciesthe subject matter of community ecologyare influenced by only four classes of process: selection, drift, speciation, and dispersal. Selection represents deterministic fitness differences among species, drift represents stochastic changes in species abundance, speciation creates new species, and dispersal is the movement of organisms across space. All theoretical and conceptual models in community ecology can be understood with respect to their emphasis on these four processes. Empirical evidence exists for all of these processes and many of their interactions, with a predominance of studies on selection. Organizing the material of community ecology according to this framework can clarify the essential similarities and dif...
1,792 citations
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...Density-dependent species interactions can also lead to complex, chaotic dynamics with species persistence in aquatic laboratory food webs (Benincà et al. 2008)....
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TL;DR: There is need not only to continue to focus on the impacts of climate change on the actors in ecological networks but also and more intensively tofocus on the linkages between them, and to acknowledge that biotic interactions and feedback processes lead to highly complex, nonlinear and sometimes abrupt responses.
Abstract: There is ample evidence for ecological responses to recent climate change. Most studies to date have concentrated on the effects of climate change on individuals and species, with particular emphasis on the effects on phenology and physiology of organisms as well as changes in the distribution and range shifts of species. However, responses by individual species to climate change are not isolated; they are connected through interactions with others at the same or adjacent trophic levels. Also from this more complex perspective, recent case studies have emphasized evidence on the effects of climate change on biotic interactions and ecosystem services. This review highlights the ‘knowns’ but also ‘unknowns’ resulting from recent climate impact studies and reveals limitations of (linear) extrapolations from recent climate-induced responses of species to expected trends and magnitudes of future climate change. Hence, there is need not only to continue to focus on the impacts of climate change on the actors in ecological networks but also and more intensively to focus on the linkages between them, and to acknowledge that biotic interactions and feedback processes lead to highly complex, nonlinear and sometimes abrupt responses.
1,112 citations
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...…(Gassmann et al. 2000, 2005) that range from sensitivities towards initial conditions (e.g. Körner et al. 2008) to limited predictability (e.g. Benincà et al. 2008; Sarewitz 2010), and pose obvious limitations to simple and linear extrapolations of recent responses to longer time scales,…...
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TL;DR: In this article, the authors present a standardized assessment of 25 532 rates of phenological change for 726 UK terrestrial, freshwater and marine taxa and trophic levels and show that the majority of spring and summer events have advanced, and more rapidly than previously documented.
Abstract: Recent changes in the seasonal timing (phenology) of familiar biological events have been one of the most conspicuous signs of climate change. However, the lack of a standardized approach to analysing change has hampered assessment of consistency in such changes among different taxa and trophic levels and across freshwater, terrestrial and marine environments. We present a standardized assessment of 25 532 rates of phenological change for 726 UK terrestrial, freshwater and marine taxa. The majority of spring and summer events have advanced, and more rapidly than previously documented. Such consistency is indicative of shared large scale drivers. Furthermore, average rates of change have accelerated in a way that is consistent with observed warming trends. Less coherent patterns in some groups of organisms point to the agency of more local scale processes and multiple drivers. For the first time we show a broad scale signal of differential phenological change among trophic levels; across environments advances in timing were slowest for secondary consumers, thus heightening the potential risk of temporal mismatch in key trophic interactions. If current patterns and rates of phenological change are indicative of future trends, future climate warming may exacerbate trophic mismatching, further disrupting the functioning, persistence and resilience of many ecosystems and having a major impact on ecosystem services.
761 citations
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..., 2008) and interspecific interactions that have potentially unpredictable outcomes (Benincà et al., 2008)....
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...…growth is directly affected by temperature, bloom timings reflect population dynamics that are also influenced by light and nutrient availability, grazing and sedimentation (Thackeray et al., 2008) and interspecific interactions that have potentially unpredictable outcomes (Benincà et al., 2008)....
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TL;DR: This article showed that the percentage of the total phytoplankton biovolume attributable to cyanobacteria increases steeply with temperature, indicating a synergistic effect of nutrients and climate.
Abstract: Dominance by cyanobacteria hampers human use of lakes and reservoirs worldwide. Previous studies indicate that excessive nutrient loading and warmer conditions promote dominance by cyanobacteria, but evidence from global scale field data has so far been scarce. Our analysis, based on a study of 143 lakes along a latitudinal transect ranging from subarctic Europe to southern South America, shows that although warmer climates do not result in higher overall phytoplankton biomass, the percentage of the total phytoplankton biovolume attributable to cyanobacteria increases steeply with temperature. Our results also reveal that the percent cyanobacteria is greater in lakes with high rates of light absorption. This points to a positive feedback because restriction of light availability is often a consequence of high phytoplankton biovolume, which in turn may be driven by nutrient loading. Our results indicate a synergistic effect of nutrients and climate. The implications are that in a future warmer climate, nutrient concentrations may have to be reduced substantially from present values in many lakes if cyanobacterial dominance is to be controlled.
674 citations
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...These may also be explained by the inherent chaotic behavior of phytoplankton communities, complicating the predictability of phytoplankton community composition (Beninca et al., 2008) and hence the proportion of cyanobacteria within the community....
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...These may also be explained by the inherent chaotic behavior of phytoplankton communi- ties, complicating the predictability of phytoplankton community composition (Beninca et al., 2008) and hence the proportion of cyanobacteria within the com- munity....
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References
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TL;DR: In this paper, a different approach to problems of multiple significance testing is presented, which calls for controlling the expected proportion of falsely rejected hypotheses -the false discovery rate, which is equivalent to the FWER when all hypotheses are true but is smaller otherwise.
Abstract: SUMMARY The common approach to the multiplicity problem calls for controlling the familywise error rate (FWER). This approach, though, has faults, and we point out a few. A different approach to problems of multiple significance testing is presented. It calls for controlling the expected proportion of falsely rejected hypotheses -the false discovery rate. This error rate is equivalent to the FWER when all hypotheses are true but is smaller otherwise. Therefore, in problems where the control of the false discovery rate rather than that of the FWER is desired, there is potential for a gain in power. A simple sequential Bonferronitype procedure is proved to control the false discovery rate for independent test statistics, and a simulation study shows that the gain in power is substantial. The use of the new procedure and the appropriateness of the criterion are illustrated with examples.
83,420 citations
TL;DR: In this article, a step-by-step guide to wavelet analysis is given, with examples taken from time series of the El Nino-Southern Oscillation (ENSO).
Abstract: A practical step-by-step guide to wavelet analysis is given, with examples taken from time series of the El Nino–Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finite-length time series, and the relationship between wavelet scale and Fourier frequency. New statistical significance tests for wavelet power spectra are developed by deriving theoretical wavelet spectra for white and red noise processes and using these to establish significance levels and confidence intervals. It is shown that smoothing in time or scale can be used to increase the confidence of the wavelet spectrum. Empirical formulas are given for the effect of smoothing on significance levels and confidence intervals. Extensions to wavelet analysis such as filtering, the power Hovmoller, cross-wavelet spectra, and coherence are described. The statistical significance tests are used to give a quantitative measure of change...
12,803 citations
IBM1
TL;DR: In this article, the use of the fast Fourier transform in power spectrum analysis is described, and the method involves sectioning the record and averaging modified periodograms of the sections.
Abstract: The use of the fast Fourier transform in power spectrum analysis is described. Principal advantages of this method are a reduction in the number of computations and in required core storage, and convenient application in nonstationarity tests. The method involves sectioning the record and averaging modified periodograms of the sections.
9,705 citations
"Chaos in a long-term experiment wit..." refers methods in this paper
...We smoothed the power spectrum using the modified Welch periodogram (Welch 1967)....
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Book•
30 May 2017
TL;DR: In this article, a simple linear model is proposed to describe the geometry of linear models, and a general linear model specification in R is presented. But the theory of linear model theory is not discussed.
Abstract: LINEAR MODELS A simple linear model Linear models in general The theory of linear models The geometry of linear modelling Practical linear models Practical modelling with factors General linear model specification in R Further linear modelling theory Exercises GENERALIZED LINEAR MODELS The theory of GLMs Geometry of GLMs GLMs with R Likelihood Exercises INTRODUCING GAMS Introduction Univariate smooth functions Additive models Generalized additive models Summary Exercises SOME GAM THEORY Smoothing bases Setting up GAMs as penalized GLMs Justifying P-IRLS Degrees of freedom and residual variance estimation Smoothing Parameter Estimation Criteria Numerical GCV/UBRE: performance iteration Numerical GCV/UBRE optimization by outer iteration Distributional results Confidence interval performance Further GAM theory Other approaches to GAMs Exercises GAMs IN PRACTICE: mgcv Cherry trees again Brain imaging example Air pollution in Chicago example Mackerel egg survey example Portuguese larks example Other packages Exercises MIXED MODELS and GAMMs Mixed models for balanced data Linear mixed models in general Linear mixed models in R Generalized linear mixed models GLMMs with R Generalized additive mixed models GAMMs with R Exercises APPENDICES A Some matrix algebra B Solutions to exercises Bibliography Index
8,393 citations