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Ordination analysis

Introduction

The following is conceptual schema, created by combination of Lepš & Šmilauer (2003) and Legendre & Legendre (2012), combining all analyses together:

Raw data-based Transformation-
-based
Distance-based
Linear Unimodal
Unconstrained PCA CA & DCA tb-PCA PCoA, NMDS
Constrained RDA CCA tb-RDA db-RDA

Depending on what data are used as input, we can recognize several types of ordination analyses:

  • Raw-data-based methods, which are based on analysis of raw sample-species matrices with abundance or presence/absence data; examples are PCA, CA or DCA. Within these methods, two categories are traditionally recognized, differing by an assumption of species response along the environmental gradient:
  • linear – species response linearly along environmental gradient, which could be true for rather homogeneous ecological data, where ecological gradients are not too long;
  • unimodal – species response unimodally along gradient, having its optima at certain gradient position; this model is more close to the reality of ecological data and is more suitable for heterogeneous datasets (structured by a strong or long ecological gradient, with high species turnover and many zeroes in the species matrix).
  • Transformation-based methods (tb-PCA and tb-RDA) represent analysis using raw species-site data, pre-transformed using e.g. Hellinger transformation (which, combined with Euclidean distance implicit for PCA/RDA, creates Hellinger distance). Legendre & Gallagher (2001) consider this to be suitable option how to analyse heterogeneous data (otherwise suitable for unimodal methods) using linear ordinations1).
  • Distance-based methods, which use matrix of distances between samples, measured by compositional similarity/dissimilarity measures, and projecting these distances into two or more dimensional ordination diagrams; examples are NMDS and PCoA.

Further, we can recognize two types of ordination methods, depending on how they deal with the matrix of environmental variables (if there is any):

  • Unconstrained ordination (indirect gradient analysis, ordination axes are not constrained by environmental factors) aims to uncover the main gradients (directions of changes) in species composition data; optionally, these gradients can be interpreted by known (estimated, measured) environmental factors (if these are available). Environmental variables do not enter the ordination algorithm, but they are used post hoc, after the analysis. Unconstrained ordination is primarily descriptive method, used to uncover and describe the pattern in multivariate data. It generates hypotheses, but cannot test them.
  • Constrained ordination (direct gradient analysis, ordination axes are constrained by environmental factors) relates the species composition directly to the environmental variables and extracts the variance in species composition which is directly related to the environment. Environmental variables directly enter the algorithm. The method is able to test the hypotheses about the relationship between environmental factors on species composition. Regarding environmental factors, it offers several interesting treatments: selection of important environmental variables by excluding those which are not relevant for species composition (forward selection), a test of significance of the variance explained by environmental factors (Monte Carlo permutation test) and partitioning of the variance explained by different groups of environmental variables (variance partitioning).

Distance-based RDA (db-RDA) is combination of PCoA, applied on raw data using selected distance measure, and RDA applied on eigenvectors resulting from PCoA. It offers an alternative to RDA (and tb-RDA) with freedom to choose distance measure suitable for investigated data.

To decide whether to apply linear or unimodal ordination method on your data, you can use the rule of thumb introduced by Lepš & Šmilauer (2003): first, calculate DCA (detrended by segments) on your data, and check the length of the first DCA axis. If the length is > 4, data are heterogeneous and you should go for unimodal methods, if the length is < 3, data are homogeneous and you can use linear methods (in the grey zone between 3 and 4 both methods are OK). Or, if your data are heterogeneous, but you still want to use linear constrained ordination (RDA), you can calculate PCA/RDA using Hellinger's transformation of species data (as recommended e.g. by Borcard et al. 2011).

Further reading

1)
There is, however, also opposing opinion, presented by Minchin & Rennie at the ESA conference in 2010.
en/ordination.txt · Last modified: 2017/02/22 15:56 by David Zelený