An official website of the United States government
Abstract Missing values are ubiquitous in ecological time series. Methods like linear interpolation,k‐nearest neighbour (kNN) imputation or regression‐based imputation are commonly used to repair these gaps, but may be unsuitable when the data are infrequently sampled or have nonlinear dynamics.We introduce multiview cross‐mapping (MVCM), a novel method based in empirical dynamic modelling (EDM) that exploits shared information between dynamically coupled time series. Rather than using points nearby in time, MVCM uses similar system states on an attractor to estimate the value of a missing data point. MVCM works best where other dynamically coupled variables have been observed, but it can also predict into short gaps where all variables are missing (data void).Using model data from a coupled five‐species system, and observational data from a long‐term plankton survey in Lake Zurich, Switzerland, we show that MVCM is robust and performs significantly better than linear methods (linear interpolation, linear regression‐based imputation) and kNN imputation.Crucially, this approach differs from methods based on a purely statistical paradigm because it assumes that the time series are generated by underlying deterministic rules. This dynamical framework allows us to exploit information shared between time series from a mechanistically coupled system, making complexity an asset for the analysis of imperfect observational data.
more »
« less
Random errors are neither: On the interpretation of correlated data
Abstract Many statistical models currently used in ecology and evolution account for covariances among random errors. Here, I address five points: (i) correlated random errors unite many types of statistical models, including spatial, phylogenetic and time‐series models; (ii) random errors are neither unpredictable nor mistakes; (iii) diagnostics for correlated random errors are not useful, but simulations are; (iv) model predictions can be made with random errors; and (v) can random errors be causal?These five points are illustrated by applying statistical models to analyse simulated spatial, phylogenetic and time‐series data. These three simulation studies are paired with three types of predictions that can be made using information from covariances among random errors: predictions for goodness‐of‐fit, interpolation, and forecasting.In the simulation studies, models incorporating covariances among random errors improve inference about the relationship between dependent and independent variables. They also imply the existence of unmeasured variables that generate the covariances among random errors. Understanding the covariances among random errors gives information about possible processes underlying the data.Random errors are caused by something. Therefore, to extract full information from data, covariances among random errors should not just be included in statistical models; they should also be studied in their own right. Data are hard won, and appropriate statistical analyses can make the most of them.
more »
« less
- Award ID(s):
- 2134446
- PAR ID:
- 10489669
- Publisher / Repository:
- John Wiley and Sons
- Date Published:
- Journal Name:
- Methods in Ecology and Evolution
- Volume:
- 13
- Issue:
- 10
- ISSN:
- 2041-210X
- Page Range / eLocation ID:
- 2092 to 2105
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Matrix population models are frequently built and used by ecologists to analyse demography and elucidate the processes driving population growth or decline. Life Table Response Experiments (LTREs) are comparative analyses that decompose the realized difference or variance in population growth rate () into contributions from the differences or variances in the vital rates (i.e. the matrix elements). Since their introduction, LTREs have been based on approximations and have not included biologically relevant interaction terms.We used the functional analysis of variance framework to derive an exact LTRE method, which calculates the exact response of to the difference or variance in a given vital rate, for all interactions among vital rates—including higher‐order interactions neglected by the classical methods. We used the publicly available COMADRE and COMPADRE databases to perform a meta‐analysis comparing the results of exact and classical LTRE methods. We analysed 186 and 1487 LTREs for animal and plant matrix population models, respectively.We found that the classical methods often had small errors, but that very high errors were possible. Overall error was related to the difference or variance in the matrices being analysed, consistent with the Taylor series basis of the classical method. Neglected interaction terms accounted for most of the errors in fixed design LTRE, highlighting the importance of two‐way interaction terms. For random design LTRE, errors in the contribution terms present in both classical and exact methods were comparable to errors due to neglected interaction terms. In most examples we analysed, evaluating exact contributions up to three‐way interaction terms was sufficient for interpreting 90% or more of the difference or variance in .Relative error, previously used to evaluate the accuracy of classical LTREs, is not a reliable metric of how closely the classical and exact methods agree. Error compensation between estimated contribution terms and neglected contribution terms can lead to low relative error despite faulty biological interpretation. Trade‐offs or negative covariances among matrix elements can lead to high relative error despite accurate biological interpretation. Exact LTRE provides reliable and accurate biological interpretation, and the R packageexactLTREmakes the exact method accessible to ecologists.more » « less
-
Abstract Predictions of biodiversity trajectories under climate change are crucial in order to act effectively in maintaining the diversity of species. In many ecological applications, future predictions are made under various global warming scenarios, as described by a range of different climate models. We propose a clustering methodology to synthesize and interpret the outputs of these various predictions.We propose an interpretable and flexible two‐step methodology to measure the similarity between predicted species range maps and to cluster the future scenario predictions utilizing a spectral clustering technique. We implement and provide code for this method.We find that clustering based on predicted species range maps is mainly driven by the amount of warming rather than climate model or future scenario. We contrast this with clustering based only on predicted climate variables, which is driven primarily by climate models, that is, scenarios of the same climate model are clustered together, even when the amount of warming input to the models is varied.The differences between species‐based and climate‐based clusterings illustrate that it is crucial to incorporate ecological information to understand the relevant differences between climate models. Our findings can be used to better synthesize forecasts of biodiversity change under the wide spectrum of results that emerge when considering potential future scenarios.more » « less
-
Abstract Change‐point detection studies the problem of detecting the changes in the underlying distribution of the data stream as soon as possible after the change happens. Modern large‐scale, high‐dimensional, and complex streaming data call for computationally (memory) efficient sequential change‐point detection algorithms that are also statistically powerful. This gives rise to a computation versus statistical power trade‐off, an aspect less emphasized in the past in classic literature. This tutorial takes this new perspective and reviews several sequential change‐point detection procedures, ranging from classic sequential change‐point detection algorithms to more recent non‐parametric procedures that consider computation, memory efficiency, and model robustness in the algorithm design. Our survey also contains classic performance analysis, which provides useful techniques for analyzing new procedures. This article is categorized under:Statistical Models > Time Series ModelsAlgorithms and Computational Methods > AlgorithmsData: Types and Structure > Time Series, Stochastic Processes, and Functional Datamore » « less
-
ABSTRACT Freshwater mussels (Bivalvia: Unionida) are among the most imperilled freshwater taxa. Yet, there is a lack of basic life history information for mussels, including data on their growth and longevity. These data help inform conservation efforts, as they can indicate whether species or populations may be vulnerable to decline and inform which species may be best adapted to certain habitats. We aimed to quantify growth and longevity in five mussel species from four river systems in the southeastern United States and test whether growth was related to stream flow. We also interpreted our findings in the context of life history theory.To model mussel growth and longevity, we cut radial thick sections from the shells of mussels and used high‐resolution photography to image the shells. We identified annual growth rings (annuli) and used von Bertalanffy growth models to estimate growth rate (K) and maximum age (Amax) across 13 mussel populations. We then used biochronological methods to remove age‐related variation in annual growth in each shell. We tested whether annual growth was correlated with stream flow using discharge‐based statistics.We found substantial variation inKandAmaxamong species and among populations of the same species.Kwas negatively related toAmax. We did not find consistent correlations between annual growth and stream flow.Our estimates ofKandAmaxalign with previous studies on closely related species and populations. They also match the eco‐evolutionary prediction that growth rate and longevity are negatively related. Life history theory predicts that short‐lived species with higher growth rates should be better adapted to environments with cyclical disturbance regimes, whereas longer‐lived species with low growth rates should be better adapted to stable environments. The lack of correlation between annual growth and stream flow suggests that mussel growth may be limited by other factors in our study system.While some species seem to have relatively narrow ranges for growth and longevity, other species show wide variation among populations. This highlights the need for species‐ and population‐specific conservation efforts. Fundamental life history information can be integrated with other species traits to predict how freshwater taxa may respond to ecological threats.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1111/2041-210X.13971
