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The extent to which populations in nature are regulated by density-dependent processes is unresolved. While experiments increasingly find evidence of strong density dependence, unmanipulated population time series yield much more ambiguous evidence of regulation, especially when accounting for effects of observation error. Here, we reexamine the evidence for density dependence in time series of population sizes in nature, by conducting an aggregate analysis of the populations in the Global Population Dynamics Database (GPDD). First, following the conventional approach, we fit a density-dependent and a density-independent variant of the Gompertz state-space model to each time series. Then, we conduct an aggregate analysis of the entire database by considering two random-effects density-dependent models that leverage information across data sets. When individual time series are tested independently, we find very little evidence for density dependence. However, in the aggregate, we find very strong evidence for density dependence, even though, paradoxically, estimated strengths of density dependence for individual time series tend to be weaker than when each individual time series is analyzed independently. Furthermore, a hierarchical model that accounts for taxonomic variation in the strength of density dependence reveals that density dependence is consistently stronger in insects and fish than in birds and mammals. Our findings resolve apparent inconsistencies between observational and experimental studies of density dependence by revealing that the observational record does indeed contain strong support for the hypothesis that density dependence is widespread in nature.

Near-term ecological forecasts provide resource managers advance notice of changes in ecosystem services, such as fisheries stocks, timber yields, or water quality. Importantly, ecological forecasts can identify where there is uncertainty in the forecasting system, which is necessary to improve forecast skill and guide interpretation of forecast results. Uncertainty partitioning identifies the relative contributions to total forecast variance introduced by different sources, including specification of the model structure, errors in driver data, and estimation of current states (initial conditions). Uncertainty partitioning could be particularly useful in improving forecasts of highly variable cyanobacterial densities, which are difficult to predict and present a persistent challenge for lake managers. As cyanobacteria can produce toxic and unsightly surface scums, advance warning when cyanobacterial densities are increasing could help managers mitigate water quality issues. Here, we fit 13 Bayesian state-space models to evaluate different hypotheses about cyanobacterial densities in a low nutrient lake that experiences sporadic surface scums of the toxin-producing cyanobacterium, Gloeotrichia echinulata. We used data from several summers of weekly cyanobacteria samples to identify dominant sources of uncertainty for near-term (1- to 4-week) forecasts of G. echinulata densities. Water temperature was an important predictor of cyanobacterial densities during model fitting and at the 4-week forecast horizon. However, no physical covariates improved model performance over a simple model including the previous week's densities in 1-week-ahead forecasts. Even the best fit models exhibited large variance in forecasted cyanobacterial densities and did not capture rare peak occurrences, indicating that significant explanatory variables when fitting models to historical data are not always effective for forecasting. Uncertainty partitioning revealed that model process specification and initial conditions dominated forecast uncertainty. These findings indicate that long-term studies of different cyanobacterial life stages and movement in the water column as well as measurements of drivers relevant to different life stages could improve model process representation of cyanobacteria abundance. In addition, improved observation protocols could better define initial conditions and reduce spatial misalignment of environmental data and cyanobacteria observations. Our results emphasize the importance of ecological forecasting principles and uncertainty partitioning to refine and understand predictive capacity across ecosystems.

1. Collisions of large soaring raptors with wind turbines and other infrastructures represent a growing conservation concern. We describe a way to leverage knowledge about raptor soaring behaviour to forecast the probability that raptors fly in the rotor-swept zone. Soaring raptors are theoretically expected to select energy sources (uplift) optimally, making their flight height dependent on uplift conditions. This approach can be used to forecast collision hazard when planning or operating wind farms. Empirical investigations of the factors influencing flight height have, however, so far been hindered by observation error. 2. We propose a two-pronged approach. First, we fitted state-space models to z-axis GPS tracking data to filter heavy-tailed observation error and estimate the relationship between vertical movement parameters and weather variables describing the energy landscape (thermal and orographic uplift potential). Second, we fitted a mechanistic model of flight height above ground based on aerodynamics and resource selection theories. The approach was replicated for five GPS-tracked Andean condors Vultur gryphus, eight griffon vultures Gyps fulvus, and six golden eagles Aquila chrysaetos. 3. In all individuals, movement parameters correlated with thermal uplift potential in the expected direction. In all species, collision hazard was lowest for high thermal uplift potential values. Species specificities in the presence of a peak in collision hazard for medium values of thermal uplift potential could be explained by differences in wing loading and aspect ratio. 4. Synthesis and applications. Our fitted models convert weather data (thermal uplift potential) into a prediction of collision hazard (probability to fly in the rotor-swept zone), making it possible to prioritize different wind development projects with respect to the relative hazard they would pose to raptors. However, our model should be combined with post-construction monitoring to document, and eventually account for turbine avoidance behaviours in collision rate predictions.

1. Invasive mammalian predators commonly coexist with invasive mammalian herbivore prey. Managers often advocate controlling invasive prey in the belief that this will also reduce invasive predator abundance. Such an outcome would have desirable ecological and financial benefits, but there have been few tests of this hypothesis. 2. We used large-scale and long-term monitoring data to test the prediction that invasive red fox Vulpes vulpes populations decline following control of invasive European rabbit Oryctolagus cuniculus populations in Australia. Both species severely impact natural and agricultural ecosystems, and significant resources are expended to reduce these impacts. We fitted a hierarchical state-space model to spotlight counts of both species conducted at 21 transects between 1998 and 2015. The effects of rainfall, control activities (warren ripping and surface harbour removal), and density dependence on the population growth rates of both species were also evaluated. 3. Control activities at 18 transects substantially reduced average rabbit abundances. Rabbit populations showed little response to rainfall, but exhibited negative density dependence and higher rates of increase during the autumn-spring interval. 4. There was no numerical response of foxes to changes in rabbit abundance. Rather, fox populations increased rapidly after high rainfall and exhibited negative density dependence. The equilibrium abundance of foxes varied with rainfall and season, but was always <0.2 foxes per spotlight km. 5. Synthesis and applications. We conclude that controlling rabbits to low abundances does not substantially reduce fox abundances in south eastern Australia. Rather, efforts to reduce fox abundance should directly target fox populations. Managers of invasive predator-invasive prey systems should not assume that controlling prey will, by itself, reduce predator abundances. Quantifying the numerical response is critical for understanding the likely response of predators to changes in prey abundance.

We present a novel formulation of a mark–recapture–resight model that allows estimation of population size, stopover duration, and arrival and departure schedules at migration areas. Estimation is based on encounter histories of uniquely marked individuals and relative counts of marked and unmarked animals. We use a Bayesian analysis of a state–space formulation of the Jolly–Seber mark–recapture model, integrated with a binomial model for counts of unmarked animals, to derive estimates of population size and arrival and departure probabilities. We also provide a novel estimator for stopover duration that is derived from the latent state variable representing the interim between arrival and departure in the state–space model. We conduct a simulation study of field sampling protocols to understand the impact of superpopulation size, proportion marked, and number of animals sampled on bias and precision of estimates. Simulation results indicate that relative bias of estimates of the proportion of the population with marks was low for all sampling scenarios and never exceeded 2%. Our approach does not require enumeration of all unmarked animals detected or direct knowledge of the number of marked animals in the population at the time of the study. This provides flexibility and potential application in a variety of sampling situations (e.g., migratory birds, breeding seabirds, sea turtles, fish, pinnipeds, etc.). Application of the methods is demonstrated with data from a study of migratory sandpipers.

1. Altitude measurements from wildlife tracking devices, combined with elevation data, are commonly used to estimate the flight altitude of volant animals. However, these data often include measurement error. Understanding this error may improve estimation of flight altitude and benefit applied ecology. 2. There are a number of different approaches that have been used to address this measurement error. These include filtering based on GPS data, filtering based on behaviour of the study species, and use of state-space models to correct measurement error. The effectiveness of these approaches is highly variable. 3. Recent studies have based inference of flight altitude on misunderstandings about avian natural history and technical or analytical tools. In this Commentary, we discuss these misunderstandings and suggest alternative strategies both to resolve some of these issues and to improve estimation of flight altitude. These strategies also can be applied to other measures derived from telemetry data. 4. Synthesis and applications. Our Commentary is intended to clarify and improve upon some of the assumptions made when estimating flight altitude and, more broadly, when using GPS telemetry data. We also suggest best practices for identifying flight behaviour, addressing GPS error, and using flight altitudes to estimate collision risk with anthropogenic structures. Addressing the issues we describe would help improve estimates of flight altitude and advance understanding of the treatment of error in wildlife telemetry studies.

In this article, we aim to improve the prediction from experts’ aggregation by using the underlying properties of the models that provide the experts involved in the aggregation procedure. We restrict ourselves to the case where experts perform their predictions by fitting state-space models to the data using Kalman recursions. Using exponential weights, we construct different Kalman recursions Aggregated Online (KAO) algorithms that compete with the best expert or the best convex combination of experts in a more or less adaptive way. When the experts are Kalman recursions, we improve the existing results on experts’ aggregation literature, taking advantage of the second-order properties of the Kalman recursions. We apply our approach to Kalman recursions and extend it to the general adversarial expert setting by state-space modeling the experts’ errors. We apply these new algorithms to a real-data set of electricity consumption and show how they can improve forecast performances compared to other exponentially weighted average procedures.

Particle filters have been widely used for online filtering problems in state-space models (SSMs). The current available proposal distributions depend either only on the state dynamics, or only on the observation, or on both sources of information but are not available for general SSMs. In this article, we develop a new particle filtering algorithm, called the augmented particle filter (APF), for online filtering problems in SSMs. The APF combines two sets of particles from the observation equation and the state equation, and the state space is augmented to facilitate the weight computation. Theoretical justification of the APF is provided, and the connection between the APF and the optimal particle filter (OPF) in some special SSMs is investigated. The APF shares similar properties as the OPF, but the APF can be applied to a much wider range of models than the OPF. Simulation studies show that the APF performs similarly to or better than the OPF when the OPF is available, and the APF can perform better than other filtering algorithms in the literature when the OPF is not available.

We propose a methodology for decomposing time series data into multiple components, including constrained components and remaining components containing cyclical variation. Our approach employs a moving linear model and utilizes state space representation, allowing for estimation of the components using the Kalman filter. The key parameter in our model is the width of the time interval, which can be estimated using the maximum likelihood method. Notably, our approach only requires a local linear model for the constrained component, while a strict model is not necessary for the remaining component. By applying our approach iteratively, we can decompose a time series into multiple components. Furthermore, we introduce a procedure to transform the decomposed components into uncorrelated components using principal component analysis. The proposed methodology demonstrates its applicability in analyzing business cycles. To illustrate its performance, we apply it to analyze two sets of monthly time series data from Japan.

Probably because of their interpretability and transparent nature, synthetic controls have become widely applied in empirical research in economics and the social sciences. This article aims to provide practical guidance to researchers employing synthetic control methods. The article starts with an overview and an introduction to synthetic control estimation. The main sections discuss the advantages of the synthetic control framework as a research design, and describe the settings where synthetic controls provide reliable estimates and those where they may fail. The article closes with a discussion of recent extensions, related methods, and avenues for future research.