Contents

Distance Based Redundancy AnalysisEdit

Distance Based Redundancy Analysis

Distance Based Redundancy Analysis (db-RDA) is a constrained ordination technique used to explore how environmental or experimental factors shape multivariate community data. Unlike classic redundancy analysis (RDA) that operates on raw species data under Euclidean assumptions, db-RDA accommodates a variety of distance measures between samples, allowing ecologists to model patterns in data that are count-based, presence-absence, or otherwise non-normally distributed. In practice, db-RDA builds on the idea of reducing complex multivariate relationships to a few interpretable axes that are expressly tied to measured predictors, making it easier to quantify and test the influence of environmental gradients on community composition. It is widely implemented in ecologically focused statistical workflows, notably within the R ecosystem as part of the Vegan (R package) suite and related tools, where the core function is dbrda and the broader framework can be explored with capscale for constrained ordination on distance matrices. For background on the core ideas, see Redundancy Analysis and Principal Coordinates Analysis.

In many applications, the distance between samples is computed using ecologically meaningful dissimilarities such as Bray-Curtis dissimilarity or Jaccard distance, which better reflect community turnover than straight Euclidean distance on raw counts. After the distance matrix is formed, db-RDA proceeds in two conceptual steps: (1) a principal coordinates analysis (PCoA) is performed on the distance matrix to embed the samples in a Euclidean space that best preserves the pairwise distances; (2) a redundancy analysis is conducted on the resulting coordinates with environmental variables as predictors. The result is a set of constrained axes that summarize how much of the variation in community composition can be explained by the measured factors, along with significance tests based on permutations.

Methodology

  • Core idea: relate multivariate response data (e.g., species composition) to a set of explanatory variables through a distance-based representation of samples.
  • Distance step: compute a distance (dissimilarity) matrix among samples using measures such as Bray-Curtis dissimilarity, Jaccard distance, or other suitable metrics. The choice of distance matters and can influence interpretation, particularly when the data include many zeros or uneven sampling.
  • Dimension reduction: apply a principal coordinates analysis (PCoA) to the distance matrix to obtain a Euclidean representation of samples via principal coordinates. See Principal Coordinates Analysis.
  • Constrained ordination: perform a redundancy analysis (RDA) on the principal coordinates with the environmental or experimental variables as predictors. This yields constrained axes that quantify the portion of variation in the community data that is explainable by the predictors.
  • Output and interpretation: the analysis provides the proportion of variation explained by predictors, partial relationships when conditioning on covariates, and ordination plots that display samples and species or variables in relation to environmental gradients. The approach is compatible with permutation-based significance testing to assess whether observed associations are unlikely under a null model.
  • Implementation notes: in practice, researchers often use dbrda within the Vegan (R package) library, and may employ capscale for more general constrained ordination on distance matrices.

For methodological details and alternatives, see references to RDA and Canonical Correspondence Analysis as contrasting approaches to multivariate community data.

Relationship to other multivariate methods

  • RDA vs db-RDA: Classical redundancy analysis operates best when data meet linear, Euclidean assumptions and are transformed appropriately. When those assumptions fail, db-RDA provides a flexible alternative by working with a distance matrix rather than raw data. See Redundancy Analysis.
  • CCA and NMDS: Canonical correspondence analysis (Canonical Correspondence Analysis) is often preferred when species respond unimodally along gradients, while non-metric multidimensional scaling (NMDS) focuses on preserving rank order of dissimilarities without imposing a linear relationship to predictors. db-RDA sits between these approaches, offering a constrained representation tied to predictors while using a distance-based foundation. See Canonical Correspondence Analysis and Non-metric multidimensional scaling.
  • Permutational tests and variation partitioning: db-RDA commonly pairs with permutation tests to assess significance and with variation partitioning to separate environmental, spatial, and other components of variation. See PERMANOVA and Variation partitioning for related concepts.

Assumptions and limitations

  • Distance choice and interpretation: the analyst must select a distance measure that reflects the ecological relationships of interest. Different distances can emphasize different aspects of community structure, and non-Euclidean distances can yield negative eigenvalues in the initial PCoA step, complicating interpretation. See Distance and Bray-Curtis dissimilarity.
  • Linear associations on transformed space: db-RDA searches for linear relationships in the principal coordinates space, which may not correspond to linear relationships in the original data space. This can limit interpretability if the underlying ecological processes are nonlinear.
  • Sensitivity to rare species and zeros: the presence of many rare species or zero-inflated data can influence both the distance matrix and the resulting ordination. Preprocessing choices (e.g., rarefaction, transformation) can have substantial effects. See discussions on data preparation in ecological multivariate methods.
  • Statistical power and permutation tests: permutation-based significance depends on exchangeability of samples; care is needed when spatial or temporal structure violates independence. See references on permutation testing in multivariate ecology.
  • Multicollinearity and model specification: as with other constrained ordination methods, highly collinear predictors or overfitting can distort interpretation of constrained axes. Appropriate model selection and cross-validation help mitigate these issues.

Practical considerations and workflow

  • Define the ecological question and choose distance accordingly (e.g., Bray-Curtis for abundance data, Jaccard for presence-absence).
  • Compute the distance matrix among samples, then perform PCoA to obtain a Euclidean representation.
  • Specify a set of environmental or experimental predictors, possibly including covariates to partial out confounding effects.
  • Run the constrained ordination to obtain the explained variation and assess significance with permutation tests.
  • Inspect biplots or triplots to interpret how predictors relate to community composition; consider supplementary analyses (e.g., variation partitioning) to disentangle different sources of variation.
  • Validate robustness by trying alternative distances, transformations, or predictor sets.

Applications and examples

  • Community ecology: relating plant or animal assemblages to soil properties, climate gradients, disturbance regimes, or management practices.
  • Microbial ecology: linking microbiome composition to pH, moisture, nutrient availability, or host-related factors, especially when count data and sparse matrices are involved.
  • Environmental impact assessments: evaluating how pollution gradients or land-use changes shape community structure across sites.
  • Landscape ecology: integrating spatial and environmental predictors to understand patterns of biodiversity across scales.

Controversies and debates

  • When to prefer db-RDA vs alternative modeling: proponents highlight the method’s flexibility with non-normal data and its ability to incorporate multiple predictors in a single multivariate framework. Critics argue that, in some cases, simpler generalized linear models, mixed models, or distance-based regression approaches may offer more transparent interpretation or better accommodate complex error structures. See general discussions of multivariate ecological modeling for context.
  • Interpretation of constrained axes: because db-RDA relies on a transformation of distances and a subsequent linear model on coordinates, the ecological meaning of axes can be less straightforward than in direct species-by-environment models. Researchers emphasize careful interpretation and, when possible, use of supplementary analyses to corroborate findings.
  • Dependence on distance choice: the ecological conclusions can hinge on which distance is used. Sensitivity analyses with multiple distance metrics are common, and some practitioners advocate reporting results across several distances to demonstrate robustness.
  • Role in policy and management: as with many ecological modeling tools, results from db-RDA are one piece of evidence among others informing management decisions. Critics caution against overreliance on any single multivariate ordination method for policy-critical conclusions and urge corroboration with independent lines of evidence.

See also