Analyzing spatial ecological data using linear regression and wavelet analysis

Carl, Gudrun; Kühn, Ingolf

doi:10.1007/s00477-007-0117-2

Cited by 41 publications

(39 citation statements)

References 24 publications

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“…Linear models are primary tools in the context of 509 environmental problems. There are many contributions 510 (Carl and Kühn 2008;Mouriño and Barão 2009;Paschal-511 idou et al 2009). Linear models are simple and have good 512 statistical properties; they are very robust statistical meth-513 ods and this feature makes them a very attractive frame-514 work to describe the quality variables under study.…”

Section: 1 Linear Modelsmentioning

confidence: 99%

Clustering and forecasting of dissolved oxygen concentration on a river basin

Costa

Gonçalves

2010

Stoch Environ Res Risk Assess

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6 Ó Springer-Verlag 20107 Abstract The aim of this contribution is to combine 8 statistical methodologies to geographically classify homo-9 geneous groups of water quality monitoring sites based on 10 similarities in the temporal dynamics of the dissolved 11 oxygen (DO) concentration, in order to obtain accurate 12 forecasts of this quality variable. Our methodology intends 13 to classify the water quality monitoring sites into spatial 14 homogeneous groups, based on the DO concentration, 15 which has been selected and considered relevant to char-16 acterize the water quality. We apply clustering techniques 17 based on Kullback Information, measures that are obtained 18 in the state space modelling process. For each homoge-19 neous group of water quality monitoring sites we model the 20 DO concentration using linear and state space models, 21 which incorporate tendency and seasonality components in 22 different ways. Both approaches are compared by the mean 23 squared error (MSE) of forecasts. 24 25 Keywords Hydrological basin Á Water quality Á 26 Clustering Á State space model Á Linear model Á 27 Kalman filter 28

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Section: 1 Linear Modelsmentioning

confidence: 99%

Clustering and forecasting of dissolved oxygen concentration on a river basin

Costa

Gonçalves

2010

Stoch Environ Res Risk Assess

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“…Furthermore, the wavelet coefficients at a given scale represent variation in the variable at that scale which are orthogonal to variation at other scales (Daubechies ). Consequently, the analysis of the wavelet coefficients is likely to be more robust in direct assessment of scale‐specific relationships with controls for confounding background noise and autocorrelation (Carl and Kühn ). From these perspectives, the wavelet‐based method is promising and can be used in a wide range of ecological applications such as presence–absence analysis of species distribution (Carl and Kühn ) or resource selection analysis of use‐availability data (Manly et al ).…”

Section: Discussionmentioning

confidence: 99%

A wavelet‐based approach to evaluate the roles of structural and functional landscape heterogeneity in animal space use at multiple scales

Wang

Fortin

et al. 2014

Ecography

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The functional relationship between habitat utilization and landscape spatial heterogeneity is fundamental to understanding the spatial nature of animal distribution across scales. Although structural and functional properties of landscape spatial heterogeneity can have different consequences for animal species, few studies have explicitly considered both forms of heterogeneity, partly due to the lack of general methods for direct assessment of scale‐specific associations between variables. We present a wavelet‐based approach to evaluate the roles of structural and functional landscape spatial heterogeneity in animal space use at multiple spatial scales. As a case study, we examined scale‐specific space use patterns of American black bears Ursus americanus in response to structural and functional spatial heterogeneity as well as spatial patterns of vegetation age‐classes in a Canadian boreal forest. We found strong differences in the effects of structural and functional spatial heterogeneity and the scales at which they are associated with the patterns of habitat use by black bears. Functional heterogeneity alone affected space use at 800 and 1600‐m scales, but had significant effects when interacting with structural heterogeneity at 400, 800, and 1600‐m scales. Compared with male bears, female black bears were most sensitive to patterns of forage abundance at intermediate scales, or more specifically, in young and regenerating forests that provide abundant soft mast in boreal forests. Our study highlights the importance of accounting for scale‐dependent properties of (structural and functional) spatial heterogeneity in assessing the ecological effects of landscape components and the effectiveness of the wavelet transform technique in identifying such scale‐specific relationships.

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“…Yet, the GAM‐based methods (GAMMiid, GAMM), even though they removed SAC from residuals, still exhibited inflated type I errors on grids. Beale et al (2010) also mentioned a badly performing method with no residual SAC (the Wavelet Revised Method (WRM) developed by Carl and Kuhn (2008)). Without fail, for spatial count regression methods, the presence of significant residual SAC is associated with reduced performance.…”

Section: Discussionmentioning

confidence: 99%

Comparison of regression methods for spatially‐autocorrelated count data on regularly‐ and irregularly‐spaced locations

Saas¹,

Gosselin²

2014

Ecography

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It has long been known that insufficient consideration of spatial autocorrelation leads to unreliable hypothesis‐tests and inaccurate parameter estimates. Yet, ecologists are confronted with a confusing array of methods to account for spatial autocorrelation. Although Beale et al. (2010) provided guidance for continuous data on regular grids, researchers still need advice for other types of data in more flexible spatial contexts. In this paper, we extend Beale et al. (2010)‘s work to count data on both regularly‐ and irregularly‐spaced plots, the latter being commonly encountered in ecological studies. Through a simulation‐based approach, we assessed the accuracy and the type I errors of two frequentist and two Bayesian ready‐to‐use methods in the family of generalized mixed models, with distance‐based or neighbourhood‐based correlated random effects. In addition, we tested whether the methods are robust to spatial non‐stationarity, and over‐ and under‐dispersion – both typical features of species distribution count data which violate standard regression assumptions. In the simplest of our simulated datasets, the two frequentist methods gave inflated type I errors, while the two Bayesian methods provided satisfying results. When facing real‐world complexities, the distance‐based Bayesian method (MCMC with Langevin–Hastings updates) performed best of all. We hope that, in the light of our results, ecological researchers will feel more comfortable including spatial autocorrelation in their analyses of count data.

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Analyzing spatial ecological data using linear regression and wavelet analysis

Cited by 41 publications

References 24 publications

Clustering and forecasting of dissolved oxygen concentration on a river basin

Clustering and forecasting of dissolved oxygen concentration on a river basin

A wavelet‐based approach to evaluate the roles of structural and functional landscape heterogeneity in animal space use at multiple scales

Comparison of regression methods for spatially‐autocorrelated count data on regularly‐ and irregularly‐spaced locations

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