Abstract
The most common type of multivariate data collected in ecology is also one of the most challenging types to analyse—when some abundance-related measure (e.g. counts, presence–absence, biomass) is simultaneously collected for all taxa or species encountered in a sample, as in Exercises 14.1–14.3. The rest of the book will focus on the analysis of these multivariate abundances.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
He also defined γ-diversity, the richness of species in a region, but this is of less interest to us here.
- 2.
Although the methods in CANOCO have some connections to Poisson regression.
References
Anderson, M. J. (2001). A new method for non-parametric multivariate analysis of variance. Austral Ecology, 26, 32–46.
Anderson, M. J., Gorley, R. N., & Clarke, K. R. (2008). PERMANOVA+ for PRIMER: Guide to Software and Statistical Methods. Plymouth: PRIMER-E.
Bates, D., & Maechler, M. (2015). MatrixModels: Modelling with sparse and dense matrices. R package version 0.4-1.
Bray, J. R., & Curtis, J. T. (1957). An ordination of the upland forest communities of southern Wisconsin. Ecological Monographs, 27, 325–349.
Clarke, K. R. (1993). Non-parametric multivariate analyses of changes in community structure. Australian Journal of Ecology, 18, 117–143.
Dray, S., Dufour, A.-B., et al. (2007). The ade4 package: Implementing the duality diagram for ecologists. Journal of Statistical Software, 22, 1–20.
Greenslade, P. (1964). Pitfall trapping as a method for studying populations of carabidae (coleoptera). The Journal of Animal Ecology, 33, 301–310.
Hardin, J. W., & Hilbe, J. M. (2002). Generalized estimating equations. Boca Raton: Chapman & Hall.
Liang, K. Y., & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13–22.
Oksanen, J., Blanchet, F. G., Friendly, M., Kindt, R., Legendre, P., McGlinn, D., Minchin, P. R., O’Hara, R. B., Simpson, G. L., Solymos, P., Stevens, M. H. H., Szoecs, E., & Wagner, H. (2017). vegan: Community ecology package. R package version 2.4-3.
Ovaskainen, O., & Soininen, J. (2011). Making more out of sparse data: Hierarchical modeling of species communities. Ecology, 92, 289–295.
Popovic, G. C., Warton, D. I., Thomson, F. J., Hui, F. K. C., & Moles, A. T. (2019). Untangling direct species associations from indirect mediator species effects with graphical models. Methods in Ecology and Evolution, 10, 1571–1583.
Rao, C. R. (1973). Linear statistical inference and its applications (2nd ed.). New York: Wiley.
ter Braak, C. J. F., & Smilauer, P. (1998). CANOCO reference manual and user’s guide to CANOCO for Windows: Software for canonical community ordination (version 4). New York: Microcomputer Power.
Walker, S. C., & Jackson, D. A. (2011). Random-effects ordination: Describing and predicting multivariate correlations and co-occurrences. Ecological Monographs, 81, 635–663.
Wang, Y., Naumann, U., Wright, S. T., & Warton, D. I. (2012). mvabund—an R package for model-based analysis of multivariate abundance data. Methods in Ecology and Evolution, 3, 471–474.
Warton, D. I. (2008). Penalized normal likelihood and ridge regularization of correlation and covariance matrices. Journal of the American Statistical Association, 103, 340–349.
Warton, D. I. (2011). Regularized sandwich estimators for analysis of high dimensional data using generalized estimating equations. Biometrics, 67, 116–123.
Warton, D. I. (2018). Why you cannot transform your way out of trouble for small counts. Biometrics, 74, 362–368
Warton, D. I., & Hui, F. K. C. (2017). The central role of mean-variance relationships in the analysis of multivariate abundance data: A response to Roberts (2017). Methods in Ecology and Evolution, 8, 1408–1414.
Warton, D. I., Wright, S. T., & Wang, Y. (2012b). Distance-based multivariate analyses confound location and dispersion effects. Methods in Ecology and Evolution, 3, 89–101.
Whittaker, R. H. (1972). Evolution and measurement of species diversity. Taxon, 21, 213–251.
Yee, T. (2006). Constrained additive ordination. Ecology, 87, 203–213.
Zeger, S. L., & Liang, K. Y. (1986). Longitudinal data analysis for discrete and continuous outcomes. Biometrics, 42, 121–130.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2022 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Warton, D.I. (2022). Multivariate Abundances—Inference About Environmental Associations. In: Eco-Stats: Data Analysis in Ecology. Methods in Statistical Ecology. Springer, Cham. https://doi.org/10.1007/978-3-030-88443-7_14
Download citation
DOI: https://doi.org/10.1007/978-3-030-88443-7_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-88442-0
Online ISBN: 978-3-030-88443-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)