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Biodiversity monitoring is undergoing a revolution, with fauna observation data being increasingly gathered continuously over extended periods, through sensors like camera traps and acoustic recorders, or via opportunistic observations. These data are often analysed with discrete‐time ecological models, requiring the transformation of continuously collected data into arbitrarily chosen, non‐independent discrete‐time intervals. To overcome this issue, ecologists are increasingly turning to the existing continuous‐time models in the literature. Closer to the real detection process, they are lesser known than discrete‐time models, not always easily accessible and can be more complex. Focusing on occupancy models, a type of species distribution models, we asked ourselves: Should we dedicate time and effort to learning and using these continuous‐time models, or can we go on using discrete‐time models?We conducted a comparative simulation study using data generated within a continuous‐time framework. We assessed the performance of five static occupancy models with varying detection processes: discrete detection/non‐detection process, discrete count process, continuous‐time Poisson process and two types of modulated Poisson processes. Our goal was to assess their abilities to estimate occupancy probability with continuously collected data. We applied all models to empirical lynx data as an illustrative example.In scenarios with easily detectable animals, we found that all models accurately estimated occupancy. All models reached their limits with highly elusive animals. Variation in discretisation intervals had minimal impact on the discrete models' capacity to estimate occupancy accurately.Our study underscores that opting for continuous‐time models with an increased number of parameters, aiming to get closer to the sensor detection process, may not offer substantial advantages over simpler models when the sole aim is to accurately estimate occupancy. Model choice can thus be driven by practical considerations such as data availability or implementation time. However, occupancy models can encompass goals beyond estimating occupancy probability. Continuous‐time models, particularly those considering temporal variations in detection, can offer valuable insights into specific species behaviour and broader ecological inquiries. We hope that our findings offer valuable guidance for researchers and practitioners working with continuously collected data in wildlife monitoring and modelling.

In populations across many taxa, a large fraction of sexually mature individuals do not breed but are attempting to enter the breeding population. Such individuals, often referred to as \"floaters,\" can play critical roles in the dynamics and stability of these populations and buffer them through periods of high adult mortality. Floaters are difficult to study, however, so we lack data needed to understand their roles in the population ecology and conservation status of many species. Here, we analyzed satellite telemetry data with a newly developed mechanistic space use model based on an Ornstein–Uhlenbeck process to help overcome the paucity of data in studying the differential habitat selection and space use of floater and territorial golden eagles Aquila chrysaetos. Our sample consisted of 49 individuals tracked over complete breeding seasons across 4 years, totaling 104 eagle breeding seasons. Modeling these data mechanistically was required to disentangle key differences in movement and particularly to separate aspects of movement driven by resource selection from those driven by use of a central place. We found that floaters generally had more expansive space use patterns and larger home ranges, as well as evidence that they partition space with territorial individuals seemingly on fine scales through differential habitat and resource selection. Floater and territorial eagle home ranges overlapped markedly, suggesting that floaters use the interstices between territories. Furthermore, floater and territorial eagles differed in how they selected for uplift variables, key components of soaring birds' energy landscape, with territorial eagles apparently better able to find and use thermal uplift. We also found relatively low individual heterogeneity in resource selection, especially among territorial individuals, suggesting a narrow realized niche for breeding individuals, which varied from the level of among-individual variation present during migration. This work furthers our understanding of floaters' potential roles in the population ecology of territorial species and suggests that conserving landscapes occupied by territorial eagles also protects floaters.

Resource selection functions (RSFs) are among the most commonly used statistical tools in both basic and applied animal ecology. They are typically parameterized using animal tracking data, and advances in animal tracking technology have led to increasing levels of autocorrelation between locations in such data sets. Because RSFs assume that data are independent and identically distributed, such autocorrelation can cause misleadingly narrow confidence intervals and biased parameter estimates. Data thinning, generalized estimating equations and step selection functions (SSFs) have been suggested as techniques for mitigating the statistical problems posed by autocorrelation, but these approaches have notable limitations that include statistical inefficiency, unclear or arbitrary targets for adequate levels of statistical independence, constraints in input data and (in the case of SSFs) scale-dependent inference. To remedy these problems, we introduce a method for likelihood weighting of animal locations to mitigate the negative consequences of autocorrelation on RSFs. In this study, we demonstrate that this method weights each observed location in an animal's movement track according to its level of non-independence, expanding confidence intervals and reducing bias that can arise when there are missing data in the movement track. Ecologists and conservation biologists can use this method to improve the quality of inferences derived from RSFs. We also provide a complete, annotated analytical workflow to help new users apply our method to their own animal tracking data using the ctmm R package.

We develop general model-free adjustment procedures for the calculation of unbiased volatility loss functions based on practically feasible realized volatility benchmarks. The procedures, which exploit recent nonparametric asymptotic distributional results, are both easy-to-implement and highly accurate in empirically realistic situations. We also illustrate that properly accounting for the measurement errors in the volatility forecast evaluations reported in the existing literature can result in markedly higher estimates for the true degree of return volatility predictability.

Quantifying spatiotemporally explicit interactions within animal populations facilitates the understanding of social structure and its relationship with ecological processes. Data from animal tracking technologies (Global Positioning Systems [“GPS”]) can circumvent longstanding challenges in the estimation of spatiotemporally explicit interactions, but the discrete nature and coarse temporal resolution of data mean that ephemeral interactions that occur between consecutive GPS locations go undetected. Here, we developed a method to quantify individual and spatial patterns of interaction using continuous‐time movement models (CTMMs) fit to GPS tracking data. We first applied CTMMs to infer the full movement trajectories at an arbitrarily fine temporal scale before estimating interactions, thus allowing inference of interactions occurring between observed GPS locations. Our framework then infers indirect interactions—individuals occurring at the same location, but at different times—while allowing the identification of indirect interactions to vary with ecological context based on CTMM outputs. We assessed the performance of our new method using simulations and illustrated its implementation by deriving disease‐relevant interaction networks for two behaviorally differentiated species, wild pigs (Sus scrofa) that can host African Swine Fever and mule deer (Odocoileus hemionus) that can host chronic wasting disease. Simulations showed that interactions derived from observed GPS data can be substantially underestimated when temporal resolution of movement data exceeds 30‐min intervals. Empirical application suggested that underestimation occurred in both interaction rates and their spatial distributions. CTMM‐Interaction method, which can introduce uncertainties, recovered majority of true interactions. Our method leverages advances in movement ecology to quantify fine‐scale spatiotemporal interactions between individuals from lower temporal resolution GPS data. It can be leveraged to infer dynamic social networks, transmission potential in disease systems, consumer–resource interactions, information sharing, and beyond. The method also sets the stage for future predictive models linking observed spatiotemporal interaction patterns to environmental drivers. This study developed a method to estimate absolute animal interactions in space and time using continuous‐time movement models (CTMM) fit to GPS tracking data, which set up the foundation for understanding various ecological processes

Worldwide, the recent SARS-CoV-2 virus has infected more than 670 million people and killed nearly 67.0 million. In Africa, the number of confirmed COVID-19 cases was approximately 12.7 million as of January 11, 2023, that is about 2% of the infections around the world. Many theories and modeling techniques have been used to explain this lower-than-expected number of reported COVID-19 cases in Africa relative to the high disease burden in most developed countries. We noted that most epidemiological mathematical models are formulated in continuous-time interval, and taking Cameroon in Sub-Saharan Africa, and New York State in the USA as case studies, in this paper we developed parameterized hybrid discrete-time-continuous-time models of COVID-19 in Cameroon and New York State. We used these hybrid models to study the lower-than-expected COVID-19 infections in developing countries. We then used error analysis to show that a time scale for a data-driven mathematical model should match that of the actual data reporting.

This study presents the first attempt of direct continuous-time model identification using instrumental variable method for Hammerstein–Wiener systems from sampled data. Under the assumption of monotonic function for the Wiener part, the whole non-linear model is first estimated as an augmented multiple-input single-output linear model, from which the model parameters are then extracted by singular value decomposition. A refined instrumental variable method is proposed to consistently identify this non-linear system acting in a coloured noisy environment. Monte Carlo simulation analysis is presented to illustrate the effectiveness of the proposed method.

This paper analyzes the case of a principal who wants to provide an agent with proper incentives to explore a hypothesis that can be either true or false. The agent can shirk, thus never proving the hypothesis, or he can avail himself of a known technology to produce fake successes. This latter option either makes the provision of incentives for honesty impossible or does not distort its costs at all. In the latter case, the principal will optimally commit to rewarding later successes even though he only cares about the first one. Indeed, after an honest success, the agent is more optimistic about his ability to generate further successes. This, in turn, provides incentives for the agent to be honest before a first success.

Continuous-time Markov models are commonly used to analyze longitudinal transitions between multiple disease states in panel data, where participants' disease states are only observed at multiple time points, and the exact state paths between observations are unknown. However, when covariate effects are incorporated and allowed to vary for different transitions, the number of potential parameters to estimate can become large even when the number of covariates is moderate, and traditional maximum likelihood estimation and subset model selection procedures can easily become unstable due to overfitting. We propose a novel regularized continuous-time Markov model with the elastic net penalty, which is capable of simultaneous variable selection and estimation for large number of parameters. We derive an efficient coordinate descent algorithm to solve the penalized optimization problem, which is fully automatic and data driven. We further consider an extension where one of the states is death, and time of death is exactly known but the state path leading to death is unknown. The proposed method is extensively evaluated in a simulation study, and demonstrated in an application to real-world data on airflow limitation state transitions.

In this study, the authors present an overview of closed-loop subspace identification methods found in the recent literature. Since a significant number of algorithms has appeared over the last decade, the authors highlight some of the key algorithms that can be shown to have a common origin in autoregressive modelling. Many of the algorithms found in the literature are variants on the algorithms that are discussed here. In this study, the aim is to give a clear overview of some of the more successful methods presented throughout the last decade. Furthermore, the authors retrace these methods to a common origin and show how they differ. The methods are compared both on the basis of simulation examples and real data. Although the main focus in the literature has been on the identification of discrete-time models, identification of continuous-time models is also of practical interest. Hence, the authors also provide an overview of the continuous-time formulation of the identification framework.