Ecological analyses typically involve many interacting variables. Ecologists often specify lagged interactions in community dynamics (i.e. vector‐autoregressive models) or simultaneous interactions (e.g. structural equation models), but there is less familiarity with dynamic structural equation models (DSEM) that can include any simultaneous or lagged effect in multivariate time‐series analysis.
We propose a novel approach to parameter estimation for DSEM, which involves constructing a Gaussian Markov random field (GMRF) representing simultaneous and lagged path coefficients, and then fitting this as a generalized linear mixed model to missing and/or non‐normal data. We provide a new R‐packagedsem, which extends the ‘arrow interface’ from path analysis to represent user‐specified lags when constructing the GMRF. We also outline how the resulting nonseparable precision matrix can generalize existing separable models, for example, for time‐series and species interactions in a vector‐autoregressive model.
We first demonstratedsemby simulating a two‐species vector‐autoregressive model based on wolf–moose interactions on Isle Royale. We show that DSEM has improved precision when data are missing relative to a conventional dynamic linear model. We then demonstrate DSEM via two contrasting case studies. The first identifies a trophic cascade where decreased sunflower starfish has increased urchin and decreased kelp densities, while sea otters have a simultaneous positive effect on kelp in the California Current from 1999 to 2018. The second estimates how declining sea ice has decreased cold‐water habitats, driving a decreased density for fall copepod predation and inhibiting early‐life survival for Alaska pollock from 1963 to 2023.
We conclude that DSEM can be fitted efficiently as a GLMM involving missing data, while allowing users to specify both simultaneous and lagged effects in a time‐series structural model. DSEM then allows conceptual models (developed with stakeholder input or from ecological expertise) to be fitted to incomplete time series and provides a simple interface for granular control over the number of estimated time‐series parameters. Finally, computational methods are sufficiently simple that DSEM can be embedded as component within larger (e.g. integrated population) models. We therefore recommend greater exploration and performance testing for DSEM relative to familiar time‐series forecasting methods.
Strauss, Alexander T.; Henning, Jeremiah A.; Porath‐Krause, Anita; Asmus, Ashley L.; Shaw, Allison K.; Borer, Elizabeth T.; Seabloom, Eric W.; Biere, ed., Arjen(
, Functional Ecology)
Abstract
The spread of many diseases depends on the demography and dispersal of arthropod vectors. Classic epidemiological theory typically ignores vector dynamics and instead makes the simplifying assumption of frequency‐dependent transmission. Yet, vector ecology may be critical for understanding the spread of disease over space and time and how disease dynamics respond to environmental change.
Here, we ask how environmental change shapes vector demography and dispersal, and how these traits of vectors govern the spatiotemporal spread of disease.
We developed disease models parameterised by traits of vectors and fit them to experimental epidemics. The experiment featured a viral pathogen (CYDV‐RPV) vectored by aphidsRhopalosiphum padiamong populations of grass hostsAvena sativaunder two rates of environmental resource supply (i.e. fertilisation of the host). We compared anon‐spatialmodel that ignores vector movement, alagged dispersalmodel that emphasises the delay between vector reproduction and dispersal, and atravelling wavemodel that generates waves of infections across space and time.
Resource supply altered both vector demography and dispersal. Thelagged dispersalmodel fit best, indicating that vectors first reproduced locally and then dispersed globally among hosts in the experiment. Elevated resources decreased vector population growth rates, nearly doubled their carrying capacity per host, increased dispersal rates when vectors carried the virus, and homogenised disease risk across space.
Together, the models and experiment show how environmental eutrophication can shape spatial disease dynamics—for example, homogenising disease risk across space—by altering the demography and behaviour of vectors.
A freePlain Language Summarycan be found within the Supporting Information of this article.
Estimation of an unstructured covariance matrix is difficult because of the challenges posed by parameter space dimensionality and the positive‐definiteness constraint that estimates should satisfy. We consider a general nonparametric covariance estimation framework for longitudinal data using the Cholesky decomposition of a positive‐definite matrix. The covariance matrix of time‐ordered measurements is diagonalized by a lower triangular matrix with unconstrained entries that are statistically interpretable as parameters for a varying coefficient autoregressive model. Using this dual interpretation of the Cholesky decomposition and allowing for irregular sampling time points, we treat covariance estimation as bivariate smoothing and cast it in a regularization framework for desired forms of simplicity in covariance models. Viewing stationarity as a form of simplicity or parsimony in covariance, we model the varying coefficient function with components depending on time lag and its orthogonal direction separately and penalize the components that capture the nonstationarity in the fitted function. We demonstrate construction of a covariance estimator using the smoothing spline framework. Simulation studies establish the advantage of our approach over alternative estimators proposed in the longitudinal data setting. We analyze a longitudinal dataset to illustrate application of the methodology and compare our estimates to those resulting from alternative models.
This article is categorized under:
Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data
Statistical and Graphical Methods of Data Analysis > Nonparametric Methods
Algorithms and Computational Methods > Maximum Likelihood Methods
Huxley, Jared D.; White, Caitlin T.; Humphries, Hope C.; Weber, Soren E.; Spasojevic, Marko J.(
, Journal of Ecology)
Abstract
A central goal at the interface of ecology and conservation is understanding how the relationship between biodiversity and ecosystem function (B–EF) will shift with changing climate. Despite recent theoretical advances, studies which examine temporal variation in the functional traits and mechanisms (mass ratio effects and niche complementarity effects) that underpin the B–EF relationship are lacking.
Here, we use 13 years of data on plant species composition, plant traits, local‐scale abiotic variables, above‐ground net primary productivity (ANPP), and climate from the alpine tundra of Colorado (USA) to investigate temporal dynamics in the B–EF relationship. To assess how changing climatic conditions may alter the B–EF relationship, we built structural equation models (SEMs) for 11 traits across 13 years and evaluated the power of different trait SEMs to predict ANPP, as well as the relative contributions of mass ratio effects (community‐weighted mean trait values; CWM), niche complementarity effects (functional dispersion; FDis) and local abiotic variables. Additionally, we coupled linear mixed effects models with Multimodel inference methods to assess how inclusion of trait–climate interactions might improve our ability to predict ANPP through time.
In every year, at least one SEM exhibited good fit, explaining between 19.6% and 57.2% of the variation in ANPP. However, the identity of the trait which best explained ANPP changed depending on winter precipitation, with leaf area, plant height and foliar nitrogen isotope content (δ15N) SEMs performing best in high, middle and low precipitation years, respectively. Regardless of trait identity, CWMs exerted a stronger influence on ANPP than FDis and total biotic effects were always greater than total abiotic effects. Multimodel inference reinforced the results of SEM analysis, with the inclusion of climate–trait interactions marginally improving our ability to predict ANPP through time.
Synthesis. Our results suggest that temporal variation in climatic conditions influences which traits, mechanisms and abiotic variables were most responsible for driving the B–EF relationship. Importantly, our findings suggest that future research should consider temporal variability in the B–EF relationship, particularly how the predictive power of individual functional traits and abiotic variables may fluctuate as conditions shift due to climate change.
Thorson, James T.; Maureaud, Aurore A.; Frelat, Romain; Mérigot, Bastien; Bigman, Jennifer S.; Friedman, Sarah T.; Palomares, Maria Lourdes D.; Pinsky, Malin L.; Price, Samantha A.; Wainwright, Peter(
, Methods in Ecology and Evolution)
Abstract
Traits underlie organismal responses to their environment and are essential to predict community responses to environmental conditions under global change. Species differ in life‐history traits, morphometrics, diet type, reproductive characteristics and habitat utilization.
Trait associations are widely analysed using phylogenetic comparative methods (PCM) to account for correlations among related species. Similarly, traits are measured for some but not all species, and missing continuous traits (e.g. growth rate) can be imputed using ‘phylogenetic trait imputation’ (PTI), based on evolutionary relatedness and trait covariance. However, PTI has not been available for categorical traits, and estimating covariance among traits without ecological constraints risks inferring implausible evolutionary mechanisms.
Here, we extend previous PCM and PTI methods by (1) specifying covariance among traits as a structural equation model (SEM), and (2) incorporating associations among both continuous and categorical traits. Fitting a SEM replaces the covariance among traits with a set of linear path coefficients specifying potential evolutionary mechanisms. Estimated parameters then represent regression slopes (i.e. the average change in trait Y given an exogenous change in trait X) that can be used to calculate both direct effects (X impacts Y) and indirect effects (X impacts Z and Z impacts Y).
We demonstrate phylogenetic structural‐equation mixed‐trait imputation using 33 variables representing life history, reproductive, morphological, and behavioural traits for all >32,000 described fishes worldwide. SEM coefficients suggest that one degree Celsius increase in habitat is associated with an average 3.5% increase in natural mortality (including a 1.4% indirect impact that acts via temperature effects on the growth coefficient), and an average 3.0% decrease in fecundity (via indirect impacts on maximum age and length). Cross‐validation indicates that the model explains 54%–89% of variance for withheld measurements of continuous traits and has an area under the receiver‐operator‐characteristics curve of 0.86–0.99 for categorical traits.
We use imputed traits to classify all fishes into life‐history types, and confirm a phylogenetic signal in three dominant life‐history strategies in fishes. PTI using phylogenetic SEMs ensures that estimated parameters are interpretable as regression slopes, such that the inferred evolutionary relationships can be compared with long‐term evolutionary and rearing experiments.
Yang, Qiuling; Coutino, Mario; Leus, Geert; Giannakis, Georgios B.(
, EURASIP Journal on Advances in Signal Processing)
Abstract
Graph-based learning and estimation are fundamental problems in various applications involving power, social, and brain networks, to name a few. While learning pair-wise interactions in network data is a well-studied problem, discovering higher-order interactions among subsets of nodes is still not yet fully explored. To this end, encompassing and leveraging (non)linear structural equation models as well as vector autoregressions, this paper proposes autoregressive graph Volterra models (AGVMs) that can capture not only the connectivity between nodes but also higher-order interactions presented in the networked data. The proposed overarching model inherits the identifiability and expressibility of the Volterra series. Furthermore, two tailored algorithms based on the proposed AGVM are put forth for topology identification and link prediction in distribution grids and social networks, respectively. Real-data experiments on different real-world collaboration networks highlight the impact of higher-order interactions in our approach, yielding discernible differences relative to existing methods.
Thorson, James T., Andrews, III, Alexander G., Essington, Timothy E., and Large, Scott I. Dynamic structural equation models synthesize ecosystem dynamics constrained by ecological mechanisms. Methods in Ecology and Evolution 15.4 Web. doi:10.1111/2041-210X.14289.
Thorson, James T., Andrews, III, Alexander G., Essington, Timothy E., & Large, Scott I. Dynamic structural equation models synthesize ecosystem dynamics constrained by ecological mechanisms. Methods in Ecology and Evolution, 15 (4). https://doi.org/10.1111/2041-210X.14289
Thorson, James T., Andrews, III, Alexander G., Essington, Timothy E., and Large, Scott I.
"Dynamic structural equation models synthesize ecosystem dynamics constrained by ecological mechanisms". Methods in Ecology and Evolution 15 (4). Country unknown/Code not available: Wiley-Blackwell. https://doi.org/10.1111/2041-210X.14289.https://par.nsf.gov/biblio/10490701.
@article{osti_10490701,
place = {Country unknown/Code not available},
title = {Dynamic structural equation models synthesize ecosystem dynamics constrained by ecological mechanisms},
url = {https://par.nsf.gov/biblio/10490701},
DOI = {10.1111/2041-210X.14289},
abstractNote = {Abstract Ecological analyses typically involve many interacting variables. Ecologists often specify lagged interactions in community dynamics (i.e. vector‐autoregressive models) or simultaneous interactions (e.g. structural equation models), but there is less familiarity with dynamic structural equation models (DSEM) that can include any simultaneous or lagged effect in multivariate time‐series analysis.We propose a novel approach to parameter estimation for DSEM, which involves constructing a Gaussian Markov random field (GMRF) representing simultaneous and lagged path coefficients, and then fitting this as a generalized linear mixed model to missing and/or non‐normal data. We provide a new R‐packagedsem, which extends the ‘arrow interface’ from path analysis to represent user‐specified lags when constructing the GMRF. We also outline how the resulting nonseparable precision matrix can generalize existing separable models, for example, for time‐series and species interactions in a vector‐autoregressive model.We first demonstratedsemby simulating a two‐species vector‐autoregressive model based on wolf–moose interactions on Isle Royale. We show that DSEM has improved precision when data are missing relative to a conventional dynamic linear model. We then demonstrate DSEM via two contrasting case studies. The first identifies a trophic cascade where decreased sunflower starfish has increased urchin and decreased kelp densities, while sea otters have a simultaneous positive effect on kelp in the California Current from 1999 to 2018. The second estimates how declining sea ice has decreased cold‐water habitats, driving a decreased density for fall copepod predation and inhibiting early‐life survival for Alaska pollock from 1963 to 2023.We conclude that DSEM can be fitted efficiently as a GLMM involving missing data, while allowing users to specify both simultaneous and lagged effects in a time‐series structural model. DSEM then allows conceptual models (developed with stakeholder input or from ecological expertise) to be fitted to incomplete time series and provides a simple interface for granular control over the number of estimated time‐series parameters. Finally, computational methods are sufficiently simple that DSEM can be embedded as component within larger (e.g. integrated population) models. We therefore recommend greater exploration and performance testing for DSEM relative to familiar time‐series forecasting methods.},
journal = {Methods in Ecology and Evolution},
volume = {15},
number = {4},
publisher = {Wiley-Blackwell},
author = {Thorson, James T. and Andrews, III, Alexander G. and Essington, Timothy E. and Large, Scott I.},
}
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