Cross-scale contradictions in ecological relationships
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Not accounting for spatial heterogeneity in ecological analyses can cause modeled relationships to vary across spatial scales, specifically different levels of spatial resolution. These varying results hinder both the utility of data collected at one spatial scale for analyses at others and the determination of underlying processes.
To briefly review existing methods for analyzing data collected at multiple scales, highlight the effects of spatial heterogeneity on the utility of these methods, and to illustrate a practical statistical method to account for the sources of spatial heterogeneity when they are unknown.
Using simulated examples, we show how not accounting for the drivers of spatial heterogeneity in statistical models can cause contradictory findings regarding relationship direction across spatial scales. We then show how mixed effects models can remedy this multiscaling issue.
Ignoring sources of spatial heterogeneity in statistical models with coarse spatial scales produced contradictory results to the true underlying relationship. Treating drivers of spatial heterogeneity as random effects in a mixed effects model, however, allowed us to uncover this true relationship.
Mixed effects models is advantageous as it is not always necessary to know the influential explanatory variables that cause spatial heterogeneity and no additional data are required. Furthermore, this approach is well documented, can be applied to data having various distribution types, and is easily executable using multiple statistical packages.
KeywordsEcological fallacy MAUP Missing variables Multiscale Mixed effects models Spatial transmutation
- Araújo MB, Rozenfeld A (2014) The geographic scaling of biotic interactions. Ecography (Cop) 37:406–415Google Scholar
- Bates D, Maechler M, Bolker B, Walker S (2014) lme4: linear mixed-effects models using Eigen and S4Google Scholar
- Cleland DT, Avers PE, McNab WH, Jensen ME, Bailey RG, King T, Russell WE (1997) National Hierarchical Framework of Ecological Units. In: Boyce M, Haney A (eds) Ecosyst manag appl sustain for wildl resour. Yale University Press, New Haven, pp 181–200Google Scholar
- Cleland DT, Freeouf JA, Keys JE, Nowacki GJ, Carpenter CA, McNab WH (2007) Ecological subregions: sections and subsections for the conterminous United States. General Technical. Report WO-76. U.S. Department of Agriculture, Forest Service, Washington, D.C. Map, presentation scale 1:3,500,000; Albers equal area projection; coloredGoogle Scholar
- Cressie NA (1993) Statistics for spatial data, revised. Wiley, New YorkGoogle Scholar
- Faraway J (2006) Extending the linear model with r: generalized linear, mixed effects and nonparametric regression models. Chapman & Hall/CRC Taylor & Francis Group, Boca RatonGoogle Scholar
- Fotheringham A (1989) Scale-independent spatial analysis. In: Goodchild M, Gopal S (eds) Accuracy spat databases. Taylor and Francis, London, pp 221–228Google Scholar
- Heffernan JB, Soranno PA, Angilletta MJ, Buckley LB, Gruner DS, Keitt TH, Kellner JR, Kominoski JS, Rocha AV, Xiao J, Harms TK, Goring SJ, Koenig LE, McDowell WH, Powell H, Richardson AD, Stow C, Vargas R, Weathers KC (2014) Macrosystems ecology: Understanding ecological patterns and processes at continental scales. Front Ecol Environ 12:5–14CrossRefGoogle Scholar
- Iannone BI, Potter KM, Dixon Hamil K, Huang W, Zhang H, Guo Q, Oswalt CM, Woodall CW, Fei S. Understanding biotic resistance to invasions across forests of the Eastern USA. Landscape Ecol current is. (this issue)Google Scholar
- Laird NM, Ware JH (1982) Random-effects models for longitudinal data. Biometr Int Biometr Soc 38:963–974Google Scholar
- McGill BJ (2010) Matters of scale. Science (80-) 328:575–576Google Scholar
- Openshaw S (1983) The modifiable areal unit problem. Geo Books, Norwick, NorfolkGoogle Scholar
- Pinheiro J, Bates D, DebRoy S, Sarkar D, R Core Team (2013) nlme: linear and nonlinear mixed effects models, R package version 3, p 57Google Scholar
- Powell KI, Chase JM, Knight TM (2013) Invasive plants have scale-dependent species-area relationships. Science 339(80):317–319Google Scholar
- R Core Team (2014) R: A language and environment for statistical computing. R Foundation for Statistical Computing, ViennaGoogle Scholar
- Renne IJ, Tracy BF, Rejmánek M (2003) The rich get richer: responses. Front Ecol Environ 1:122–123Google Scholar
- Soranno PA, Cheruvelil KS, Bissell EG, Bremigan MT, Downing JA, Fergus CE, Filstrup CT, Henry EN, Lottig NR, Stanley EH, Stow CA, Tan P, Wagner T, Webster KE (2014) Cross-scale interactions: quantifying multi-scaled cause-effect relationships in macrosystems. Front Ecol Environ 12:65–73CrossRefGoogle Scholar
- Taylor BW, Irwin RE (2004) Linking economic activities to the distribution of exotic plants. Proc Natl Acad Sci U S A 51:17725–17730Google Scholar
- Wu J, Gao W, Tueller P (1997) Effects of changing spatial scale on the results of statistical analysis with landscape data: a case study. Geogr Inf Sci 3:30–41Google Scholar
- Zhang H, El-Shaarawi A (2010) On spatial skew-Gaussian processes and applications. Environmetrics 21:33–47Google Scholar