Understanding how flow-related disturbance regimes influence species interactions is critical for conserving threatened species in freshwater ecosystems, where both the alteration of these regimes and the invasion of non-native species pose major threats. Using 30 years of sampling data from a well-studied river system in Aotearoa New Zealand, we applied empirically– parameterized Lotka–Volterra competition models across a gradient of flood disturbance regimes to assess the potential for coexistence between threatened native galaxiids and invasive trout. Our models suggest trout dominate under low disturbance regimes, leading to galaxiid extinction. Coexistence peaks at intermediate disturbance regimes, though native fish densities are highly suppressed. Only at high disturbance regimes do native fish prevail, but priority effects are likely. Thus, restoration and conservation efforts focused solely on high disturbance habitats without accompanying biological interventions may not ensure native fish persistence. Further, prioritizing such habitats at the expense of others risks misdirecting resources towards sub-optimal conditions, particularly under climate change. ### Competing Interest Statement The authors have declared no competing interest. Ministry of Business, Innovation and Employment, https://ror.org/02jtq1b51, Fish Futures: preparing for novel freshwater ecosystems; CAWX2101

In the last few years, the dynamical characterization of the power output of a wind turbine by means of a Langevin equation has been well established. For this approach, temporally highly resolved measurements of wind speed and power output are used to obtain the drift and diffusion coefficients of the energy conversion process. These coefficients fully determine a Langevin stochastic differential equation with Gaussian white noise. The drift term specifies the deterministic behavior of the system whereas the diffusion term describes the stochastic behavior of the system. A precise estimation of these coefficients is essential to understand the dynamics of the power conversion process of the wind turbine. We show that the dynamics of the power output of a wind turbine have a hidden dependency on turbine's different operational states. Here, we use an approach based on clustering Pearson correlation matrices for different observables on a moving time window to identify different operational states. We have identified five operational states in total, for example the state of rated power. Those different operational states distinguish non-stationary behavior in the mutual dependencies and represent different turbine control settings. As a next step, we condition our Langevin analysis on these different states to reveal distinctly different behaviors of the power conversion process for each operational state. Moreover, in our new representation hysteresis effects which have typically appeared in the Langevin dynamics of wind turbines seem to be resolved. We assign these typically observed hysteresis effects clearly to the change of the wind energy system between our estimated different operational states. In this contribution, we discuss further consequences for the meaning of hysteric switching and detection of malbehaviors in wind turbines.

This study introduces an innovative local statistical moment approach for estimating Kramers-Moyal coefficients, effectively bridging the gap between nonparametric and parametric methodologies. These coefficients play a crucial role in characterizing stochastic processes. Our proposed approach provides a versatile framework for localized coefficient estimation, combining the flexibility of nonparametric methods with the interpretability of global parametric approaches. We showcase the efficacy of our approach through use cases involving both stationary and non-stationary time series analysis. Additionally, we demonstrate its applicability to real-world complex systems, specifically in the energy conversion process analysis of a wind turbine.

Stochastic differential equations (SDEs) are commonly used to model various systems. Data-driven methods have been widely used to estimate the drift and diffusion terms of a Langevin equation. Among the most commonly used estimation methods is the Nadaraya–Watson estimator, which is a non-parametric data-driven approach. In this study, we propose a method to improve the estimation of the drift coefficient of a stochastic process using optimal local bandwidths that minimize the error of the approximation of the first conditional moments of a univariate system. This approach is compared to a global bandwidth estimation and an estimation based on a fixed number of nearest neighbors. The proposed method has the potential to reduce the error of the drift estimation, thereby improving the accuracy of the model.

Time series often exhibit a combination of long-range drift and short-term stochastic fluctuations. Traditional methods for analyzing such series involve fitting regression models to capture the drift component and using the residuals to estimate the random component. We demonstrate, however, that estimating the drift in a real-time (time-resolved) manner poses significant challenges. We find, surprisingly, that contrary to conventional expectations, estimation of the drift is less accurate than evaluating short-term fluctuations in data with a given number of data points. Two factors contribute to this unexpected complexity: measurement noise, and the slower convergence rate of the drift estimation. As a result, real-time estimation of stochastic fluctuations can be more accurate. We introduce the term stochasticity, as the square of the estimated short-term fluctuations within a time window of length dt, which can be estimated in real-time (time-resolved) for given non-stationary time series and those exhibiting unique trajectories. To demonstrate the practical applications of the concept of real-time stochasticity, we calculate it for synthetic time series generated by both linear and nonlinear dynamical equations, which generate stationary and non-stationary trajectories for which we have access to the ground truth. We have also analyzed various real-world datasets: global temperature anomalies in 12 distinct geographical regions, keystroke time series from Parkinson's disease patients, fluctuations in gold prices, atmospheric CO2 concentration, wind velocity data, and earthquake occurrences. Our method exclusively provides the time dependency, rather than both state and time dependencies, of the stochasticity.

Compositional measurements from species assemblages define a high dimensional dataspace in which the data can form complex structures, termed manifolds. Comparing assemblages in this dataspace is difficult because the data is often sparse relative to its dimensionality and the complex structure of the manifold introduces bias and error in measurements of distance. Here, we apply diffusion maps, a manifold learning method, to find and characterize manifolds in high‐dimensional compositional data. We show that diffusion maps embed the data in reduced dimensions in which the Euclidean distance between data points approximates the distance between them along the manifold. This is especially useful when species turnover is high, as it provides a way to measure meaningful distances between assemblages even when they harbor disjoint sets of species. We anticipate diffusion maps will therefore be particularly useful for characterizing community change over large spatial and temporal scales.

Modern wind turbines gather a wealth of data with Supervisory Control And Data Acquisition (SCADA) systems. We study the short-term mutual dependencies of a variety of observables by evaluating Pearson correlation matrices on a moving time window. Using clustering on these matrices, we identify multiple stable operational states, which characterize the non-stationarity of mutual dependencies at a single turbine. They represent different turbine operational settings. Moreover, we combine the clustering analysis with a construction of a stochastic process to study the switching dynamics of those states in more detail. Calculating the distances between correlation matrices we obtain a time series that describes the behavior of the complex system in a collective way. Assuming this time series to be governed by a Langevin equation, we estimate the deterministic (drift) and stochastic (diffusion) components of the dynamics to understand the underlying non-stationarity. After adapting our method to specific features of our data, we are able to study the dynamics of operational states and their transitions as well as to resolve hysteresis effects.

We report the observation of a nontrivial emergent state in a chain of nonidentical, heterogeneously coupled oscillators where a set of weakly coupled oscillators becomes phase synchronized while the strongly coupled ones remain drifting. This intriguing "weak-winner" synchronization phenomenon can be explained by the interplay between nonisochronicity and the natural frequency of the oscillator, as coupling strength is varied. Furthermore, we present sufficient conditions under which the weak-winner phase synchronization can occur for limit cycles as well as chaotic oscillators. Employing a model system from ecology as well as a paradigmatic model from physics, we demonstrate that this phenomenon is a generic feature for a large class of coupled oscillator systems. The realization of this peculiar, yet quite generic weak-winner dynamics can have far-reaching consequences in a wide range of scientific disciplines that deal with the phenomenon of phase synchronization, including synchronization of networks. Our results also highlight the role of nonisochronicity (shear) as a fundamental feature of an oscillator in shaping emergent dynamical patterns in complex networks.

The temporal dynamics of dissolved organic matter (DOM) are inherently linked with the functioning of aquatic ecosystems. Because DOM represents a complex mixture of millions of different compounds, the statistical analysis of DOM dynamics poses a huge challenge. Here, we present a statistical approach based on hierarchical clustering of time series that groups DOM compounds with synchronous dynamics. We applied this approach to time series of Fourier‐transform ion cyclotron resonance mass spectrometry data of DOM sampled over a period of 26 months near Helgoland, an island in the Southern North Sea. We identified three DOM clusters, which represented a total of 1392 different molecular formulae and showed distinct chemical properties and noticeably compound matches within the PubChem database. Correlations of the three DOM clusters with abundance data of prokaryote and phytoplankton species and with environmental parameters provided consistent indications on the potential origin of the clustered compounds. The first cluster integrated terrestrial DOM originating from riverine discharge reaching Helgoland waters. The second cluster was attributed to DOM related to phytoplankton and microbial activity, whereas the third cluster was interpreted as representing the marine refractory DOM background. Accordingly, while further partitioning divided each of the first two clusters into five sub‐clusters with distinct temporal dynamics and molecular characteristics, the third cluster persisted as a stable feature. Applying a purely mathematical approach, we thus confirmed the differential dynamics of individual DOM compounds and compound groups and showed that temporal dynamics of dissolved molecules are linked to their origin and transformation history.

Aim Biodiversity dynamics comprise evolutionary and ecological changes on multiple temporal scales from millions of years to decades, but they are often interpreted within a single time frame. Planktonic foraminifera communities offer a unique opportunity for analysing the dynamics of marine biodiversity over different temporal scales. Our study aims to provide a baseline for assessments of biodiversity patterns over multiple time-scales, which is urgently needed to interpret biodiversity responses to increasing anthropogenic pressure. Location Global (26 sites). Time period Five time-scales: multi-million-year (0-7 Myr), million-year (0-0.5 Myr), multi-millennial (0-15 thousand years), millennial (0-1,100 years) and decadal (0-32 years). Major taxa studied Planktonic foraminifera. Methods We analysed community composition of planktonic foraminifera at five time-scales, combining measures of standing diversity (richness and effective number of species, ENS) with measures of temporal community turnover (presence-absence-based, dominance-based). Observed biodiversity patterns were compared with the outcome of a neutral model to separate the effects of sampling resolution (the highest in the shortest time series) from biological responses. Results Richness and ENS decreased from multi-million-year to millennial time-scales, but higher standing diversity was observed on the decadal scale. As predicted by the neutral model, turnover in species identity and dominance was strongest at the multi-million-year time-scale and decreased towards the millennial scale. However, contrary to the model predictions, modern time series show rapid decadal variation in the dominance structure of foraminifera communities, which is of comparable magnitude as over much longer time periods. Community turnover was significantly correlated with global temperature change, but not on the shortest time-scale. Main conclusions Biodiversity patterns can be to some degree predicted from the scaling effects related to different durations of time series, but changes in the dominance structure observed over the last few decades reach higher magnitude, probably forced by anthropogenic effects, than those observed over much longer durations.

Fourier-transform ion cyclotron resonance mass spectrometry (FT-ICR-MS) is one of the state-of-the-art methods to analyze complex natural organic mixtures. The precision of detected masses is crucial for molecular formula attribution. Random errors can be reduced by averaging multiple measurements of the same mass, but because of limited availability of ultrahigh-resolution mass spectrometers, most studies cannot afford analyzing each sample multiple times. Here we show that random errors can be eliminated also by averaging mass spectral data from independent environmental samples. By averaging the spectra of 30 samples analyzed on our 15 T instrument we reach a mass precision comparable to a single spectrum of a 21 T instrument. We also show that it is possible to accurately and reproducibly determine isotope ratios with FT-ICR-MS. Intensity ratios of isotopologues were improved to a degree that measured deviations were within the range of natural isotope fractionation effects. In analogy to δ13C in environmental studies, we propose Δ13C as an analytical measure for isotope ratio deviances instead of widely employed C deviances. In conclusion, here we present a simple tool, extensible to Orbitrap-based mass spectrometers, for postdetection data processing that significantly improves mass accuracy and the precision of intensity ratios of isotopologues at no extra cost.

To understand ecosystem responses to anthropogenic global change, a prevailing framework is the definition of threshold levels of pressure, above which response magnitudes and their variances increase disproportionately. However, we lack systematic quantitative evidence as to whether empirical data allow definition of such thresholds. Here, we summarize 36 meta-analyses measuring more than 4,600 global change impacts on natural communities. We find that threshold transgressions were rarely detectable, either within or across meta-analyses. Instead, ecological responses were characterized mostly by progressively increasing magnitude and variance when pressure increased. Sensitivity analyses with modelled data revealed that minor variances in the response are sufficient to preclude the detection of thresholds from data, even if they are present. The simulations reinforced our contention that global change biology needs to abandon the general expectation that system properties allow defining thresholds as a way to manage nature under global change. Rather, highly variable responses, even under weak pressures, suggest that 'safe-operating spaces' are unlikely to be quantifiable.

Untargeted molecular analyses of complex mixtures are relevant for many fields of research, including geochemistry, pharmacology, and medicine. Ultrahigh-resolution mass spectrometry is one of the most powerful tools in this context. The availability of open scripts and online tools for specific data processing steps such as noise removal or molecular formula assignment is growing, but an integrative tool where all crucial steps are reproducibly evaluated and documented is lacking. We developed a novel, server-based tool (ICBM-OCEAN, Institute for Chemistry and Biology of the Marine Environment, Oldenburg-complex molecular mixtures, evaluation & analysis) that integrates published and novel approaches for standardized processing of ultrahigh-resolution mass spectrometry data of complex molecular mixtures. Different from published approaches, we offer diagnostic and validation tools for all relevant steps. Among other features, we included objective and reproducible reduction of noise and systematic errors, spectra recalibration and alignment, and identification of likeliest molecular formulas. With 15 chemical elements, the tool offers high flexibility in formula attribution. Alignment of mass spectra among different samples prior to molecular formula assignment improves mass error and facilitates molecular formula confirmation with the help of isotopologues. The online tool and the detailed instruction manual are freely accessible at www.icbm.de/icbm-ocean.

Connectivity between physiological networks is an issue of particular importance for understanding the complex interaction brain-heart. In the present study, this interaction was analyzed in polysomnography recordings of 28 patients diagnosed with obstructive sleep apnea (OSA) and compared with a group of 10 control subjects. Electroencephalography and electrocardiography signals from these polysomnography time series were characterized employing Granger causality computation to measure the directed connectivity among five brain waves and three spectral subbands of heart rate variability. Polysomnography data from OSA patients were recorded before and during a first session of continuous positive air pressure (CPAP) therapy in a split-night study. Results showed that CPAP therapy allowed the recovery of inner brain connectivities, mainly in subsystems involving the theta wave. In addition, differences between control and OSA patients were established in connections that involve lower frequency ranges of heart rate variability. This information can be potentially useful in the initial diagnosis of OSA, and determine the role of cardiac activity in sleep dynamics based on the use of three subbands of heart rate variability.

This work deals with an analysis of Granger Causality computation based on artificial neural networks, including a nonlinear relation between the involved variables. Information about the training parameters are exhibited in order to visualize how the conditions of the chosen model to obtain the connectivity information depend on the architecture of network. Three chaotic maps with a bivariate case built from two time series were employed to see the effect of training parameters of the models. Nonlinear autoregressive and nonlinear autoregressive with exogenous inputs were used to forecast the time series, and then, obtain the causality information based on differences of errors between both approximations. Results show that the causality computation is sensible to neural network parameters previously untreated in a detailed mode.

The availability of growth data in N. norvegicus is important for management purposes due to a lack of aging criteria and the commercial importance of fisheries in this species. Growth varies as a function of stock density, hence comparisons of growth rates between stocks at known density is particularly valuable. Growth is also related to starting size in males, making raw data on size-specific growth rates more valuable. Internally injected passive tags allowed us to track the growth of male and female individuals over one or two years. The spatial position of tagged recaptures was recorded to measure site fidelity of tagged releases. A total of 3300 pots were fished and their spatial positions were recorded to enable Catch Per Unit Effort calculations. Similarly, spatially geo-referenced v-notching and notched recovery enables spatially gridded densities to be calculated. Finally, acoustic mapping was carried out both on and off the fishing ground and was ground-truthed with sedimentology from grabs at 22 stations. These data are useful for fisheries and macroecological studies.

Stock enhancement activities provide an opportunity to examine density-dependent suppression of population biomass which is a fundamental issue for resource management and design of no-take-zones. We document 'catch-and-wait' fisheries enhancement where all but the largest lobsters are thrown back, recapturing them later after they have grown to a larger size. The residency, rate of return, and potential negative density-dependent effects of this activity are described using a combination of tagging and v-notching and by relating spatial growth patterns to population density defined with Catch Per Unit Effort. The results successfully demonstrated the concept of catch-and-wait practices. However, a density-dependent suppression of growth (in body size) was observed in male lobsters. This demonstrates a mechanism to explain differences in lobster sizes previously observed across EU fishing grounds with different stock densities. This negative effect of density could also affect individual biomass production in marine reserve or no-take zones.

In a coupled system, predictive information flows from the causing to the caused variable. The amount of transferred predictive information can be quantified through the use of transfer entropy or, for Gaussian variables, equivalently via Granger causality. It is natural to expect and has been repeatedly observed that a tight coupling does not permit to reconstruct a causal connection between causing and caused variables. Here, we show that for a model of interacting social groups, carried from the master equation to the Fokker–Planck level, a residual predictive information flow can remain for a pair of uni-directionally coupled variables even in the limit of infinite coupling strength. We trace this phenomenon back to the question of how the synchronizing force and the noise strength scale with the coupling strength. A simplified model description allows us to derive analytic expressions that fully elucidate the interplay between deterministic and stochastic model parts.

Being globally and locally prevalent, beach litter has been monitored at 29 sites along the German North Sea coastline. This study offers an exploratory analysis of data from 1991 to 2016. Schleswig-Holstein exhibited lower mean litter pollution levels than Lower Saxony, possibly because the locations in Lower Saxony are situated along the main coastal current, whereas the North Frisian Islands act as a barrier for the mainland sites in Schleswig-Holstein. Locations close to the Elbe estuary had significantly larger amounts of debris, likely receiving litter from marine and riverine sources. No clear overall pattern in litter abundance or composition could be detected. Significant quantitative similarities between debris types were inconsistent. The effect of wind, tides, and exposure appeared to be marginal. Recurring data inconsistencies, gaps, and outliers were partly attributed to human error. This could be reduced through hypothesis-driven monitoring with a simpler litter classification and continuous data checking.