Circumventing structural uncertainty: A Bayesian perspective on nonlinear forecasting for ecology (original) (raw)
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Leveraging spatial information to forecast nonlinear ecological dynamics
Methods in Ecology and Evolution, 2020
Methods in Ecology and Evolution This article has been accepted for publication and undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process, which may lead to differences between this version and the Version of Record.
Model-free forecasting outperforms the correct mechanistic model for simulated and experimental data
Proceedings of the National Academy of Sciences, 2013
Accurate predictions of species abundance remain one of the most vexing challenges in ecology. This observation is perhaps unsurprising, because population dynamics are often strongly forced and highly nonlinear. Recently, however, numerous statistical techniques have been proposed for fitting highly parameterized mechanistic models to complex time series, potentially providing the machinery necessary for generating useful predictions. Alternatively, there is a wide variety of comparatively simple model-free forecasting methods that could be used to predict abundance. Here we pose a rather conservative challenge and ask whether a correctly specified mechanistic model, fit with commonly used statistical techniques, can provide better forecasts than simple model-free methods for ecological systems with noisy nonlinear dynamics. Using four different control models and seven experimental time series of flour beetles, we found that Markov chain Monte Carlo procedures for fitting mechanistic models often converged on best-fit parameterizations far different from the known parameters. As a result, the correctly specified models provided inaccurate forecasts and incorrect inferences. In contrast, a model-free method based on state-space reconstruction gave the most accurate short-term forecasts, even while using only a single time series from the multivariate system. Considering the recent push for ecosystem-based management and the increasing call for ecological predictions, our results suggest that a flexible model-free approach may be the most promising way forward. U nderstanding fluctuations in species abundance is a longstanding goal of ecology and is particularly important for the conservation of severely depleted populations (1, 2). Dramatic changes in species abundance are common (3) and large declines can have disastrous impacts on ecosystem users (4). Accurate forecasts could allow for improved conservation efforts and increased fishery yields, however, ecological surprises are common (5), and accurate predictions remain a major challenge (6).
Modeling and Prediction of Time-Varying Environmental Data Using Advanced Bayesian Methods
The problem of state/parameter estimation represents a key issue in crop models which are nonlinear, non-Gaussian and include a large number of parameters. The prediction errors are often important due to uncertainties in the equations, the input variables, and the parameters. The measurements needed to run the model (input data), to perform calibration and validation are sometimes not numerous or known with some uncertainty. In these cases, estimating the state variables and/or parameters from easily obtained measurements can be extremely useful. In this work, we address the problem of modeling and prediction of leaf area index and soil moisture (LSM) using state estimation. The performances of various conventional and state-of-the-art state estimation techniques are compared when they are utilized to achieve this objective. These techniques include the extended Kalman filter (EKF), unscented Kalman filter (UKF), particle filter (PF), and the more recently developed technique variational Bayesian filter (VF). The objective of this work is to extend the state and parameter estimation techniques (i.e., EKF, UKF, PF and VF) to better handle nonlinear and non-Gaussian processes without a priori state information, by utilizing a time-varying assumption of statistical parameters. In this case, the state vector to be estimated k z at any instant k is assumed to follow a Gaussian model, where the expectation k µ and the covariance matrix k λ are both random. The randomness of the expectation and the covariance of the state/parameter vector are assumed here to further capture the uncertainty of the state distribution. One practical choice of these distributions can be a Gaussian distribution for the expectation and a multidimensional Wishart distribution for the covariance matrix. The assumption of random mean and random covariance of the state leads to a probability distribution covering a wide range of tail behaviors, which allows discrete jumps in the state variables, k z The results of the comparative studies show that the PF provides a higher accuracy than the EKF, which is due to the limited ability of the EKF to handle highly nonlinear processes. The results also show that the PF provides a significant improvement over the UKF. This is because the covariance is propagated through linearization of the underlying non-linear model, when the state transition and observation models are highly non-linear. The results also indicate that the VF provides a significant improvement over the PF because, unlike the PF which depends on the choice of sampling distribution used to estimate the posterior distribution, the VF yields an optimum choice of the sampling distribution, which also accounts for the observed data. The original data were issued from experiments carried out on a silty soil in Belgium, with a wheat crop, during two consecutive years, the seasons 2008-09 and 2009-10.
2019
Gaussian processes are certainly not a new tool in the field of science. However, alongside the quick increasing of computer power during the last decades, Gaussian processes have proved to be a successful and flexible statistical tool for data analysis. Its practical interpretation as a nonparametric procedure to represent prior beliefs about the underlying data generating mechanism has gained attention among a variety of research fields ranging from ecology, inverse problems and deep learning in artificial intelligence. The core of this thesis deals with multivariate Gaussian process model as an alternative method to classical methods of regression analysis in Statistics. I develop hierarchical models, where the vector of predictor functions (in the sense of generalized linear models) is assumed to follow a multivariate Gaussian process. Statistical inference over the vector of predictor functions is approached by means of the Bayesian paradigm with analytical approximations. I de...
Hydrological Processes, 2008
Forecasting of hydrologic time series, with the quantification of uncertainty, is an important tool for adaptive water resources management. Nonstationarity, caused by climate forcing and other factors, such as change in physical properties of catchment (urbanization, vegetation change, etc.), makes the forecasting task too difficult to model by traditional Box-Jenkins approaches. In this paper, the potential of the Bayesian dynamic modelling approach is investigated through an application to forecast a nonstationary hydroclimatic time series using relevant climate index information. The target is the time series of the volume of Devil's Lake, located in North Dakota, USA, for which it was proved difficult to forecast and quantify the associated uncertainty by traditional methods. Two different Bayesian dynamic modelling approaches are discussed, namely, a constant model and a dynamic regression model (DRM). The constant model uses the information of past observed values of the same time series, whereas the DRM utilizes the information from a causal time series as an exogenous input. Noting that the North Atlantic Oscillation (NAO) index appears to co-vary with the time series of Devil's Lake annual volume, its use as an exogenous predictor is explored in the case study. The results of both the Bayesian dynamic models are compared with those from the traditional Box-Jenkins time series modelling approach. Although, in this particular case study, it is observed that the DRM performs marginally better than traditional models, the major strength of Bayesian dynamic models lies in the quantification of prediction uncertainty, which is of great value in hydrology, particularly under the recent climate change scenario.
Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling
Proceedings of the National Academy of Sciences of the United States of America, 2015
It is well known that current equilibrium-based models fall short as predictive descriptions of natural ecosystems, and particularly of fisheries systems that exhibit nonlinear dynamics. For example, model parameters assumed to be fixed constants may actually vary in time, models may fit well to existing data but lack out-of-sample predictive skill, and key driving variables may be misidentified due to transient (mirage) correlations that are common in nonlinear systems. With these frailties, it is somewhat surprising that static equilibrium models continue to be widely used. Here, we examine empirical dynamic modeling (EDM) as an alternative to imposed model equations and that accommodates both nonequilibrium dynamics and nonlinearity. Using time series from nine stocks of sockeye salmon (Oncorhynchus nerka) from the Fraser River system in British Columbia, Canada, we perform, for the the first time to our knowledge, real-data comparison of contemporary fisheries models with equiva...
Ecological forecasting and data assimilation in a data-rich era
2011
Several forces are converging to transform ecological research and increase its emphasis on quantitative forecasting. These forces include (1) dramatically increased volumes of data from observational and experimental networks, (2) increases in computational power, (3) advances in ecological models and related statistical and optimization methodologies, and most importantly, (4) societal needs to develop better strategies for natural resource management in a world of ongoing global change. Traditionally, ecological forecasting has been based on process-oriented models, informed by data in largely ad hoc ways. Although most ecological models incorporate some representation of mechanistic processes, today's models are generally not adequate to quantify real-world dynamics and provide reliable forecasts with accompanying estimates of uncertainty. A key tool to improve ecological forecasting and estimates of uncertainty is data assimilation (DA), which uses data to inform initial conditions and model parameters, thereby constraining a model during simulation to yield results that approximate reality as closely as possible. This paper discusses the meaning and history of DA in ecological research and highlights its role in refining inference and generating forecasts. DA can advance ecological forecasting by (1) improving estimates of model parameters and state variables, (2) facilitating selection of alternative model structures, and (3) quantifying uncertainties arising from observations, models, and their interactions. However, DA may not improve forecasts when ecological processes are not well understood or never observed. Overall, we suggest that DA is a key technique for converting raw data into ecologically meaningful products, which is especially important in this era of dramatically increased availability of data from observational and experimental networks.
An introduction to state-space modeling of ecological time series
arXiv: Methodology, 2020
State-space models (SSMs) are an important modeling framework for analyzing ecological time series. These hierarchical models are commonly used to model population dynamics and animal movement, and are now increasingly being used to model other ecological processes. SSMs are popular because they are flexible and they model the natural variation in ecological processes separately from observation error. Their flexibility allows ecologists to model continuous, count, binary, and categorical data with linear or nonlinear processes that evolve in discrete or continuous time. Modeling the two sources of stochasticity separately allows researchers to differentiate between biological stochasticity (e.g., in birth processes) and imprecision in the sampling methodology, and generally provides better estimates of the ecological quantities of interest than if only one source of stochasticity is directly modeled. Since the introduction of SSMs, a broad range of fitting procedures have been prop...
The Ecological Forecast Horizon, and examples of its uses and determinants
2015
Forecasts of ecological dynamics in changing environments are increasingly important, and are available for a plethora of variables, such as species abundance and distribution, community structure and ecosystem processes. There is, however, a general absence of knowledge about how far into the future, or other dimensions (space, temperature, phylogenetic distance), useful ecological forecasts can be made, and about how features of ecological systems relate to these distances. The ecological forecast horizon is the dimensional distance for which useful forecasts can be made. Five case studies illustrate the influence of various sources of uncertainty (e.g. parameter uncertainty, environmental variation, demographic stochasticity and evolution), level of ecological organisation (e.g. population or community), and organismal properties (e.g. body size or number of trophic links) on temporal, spatial and phylogenetic forecast horizons. Insights from these case studies demonstrate that the ecological forecast horizon is a flexible and powerful tool for researching and communicating ecological predictability. It also has potential for motivating and guiding agenda setting for ecological forecasting research and development.
Symposium 23. Toward Ecological Forecasting
Bulletin of the Ecological Society of America, 2008
Seven presentations were delivered at the symposium. The key message that emerged was that, as more and more data become available from the measurement networks, it is urgent to develop techniques and expertise in the ecological community to integrate data and models together to enhance our capability for ecological forecasting.