Residual Ordination Analysis: A Method for Exploring Vegetation‐Environment Relationships

A technique of analysis is proposed for investigating relationships between a set of vegetation data and environmental variables from the same survey sample sites. The vegetation data are first condensed and transformed by detrended correspondence analysis, an ordination technique. From this point residual ordination analysis proceeds on the assumption that all relationships are linear. Canonical—correlation analysis is used to examine the relationships between the transformed vegetation variables (stand scores on ordination axes) and additive combinations of environmental variables. That combination which most parsimoniously explains the variance (redundancy) on the ordination axes is taken as the basic set of predictor variables. On the assumption that these environmental variables show mutual covariation, they are split into a single natural group (e.g., soil variables) and a remainder. Using linear regression techniques, the unique variation in the predictors of the remainder subset is derived. Through a similar sequence of operations the unique variation of this reminder subset is partialled out of the vegetation ordination and a residual ordination derived. Relationships between this residual ordination and the single natural group of the predictor set are investigated through canonical correlation and visual assessment of scatter plots. The process is repeated for other natural groups of environmental variables in the basic predictor set. The technique is illustrated with a small set of jack pine understory survey data. Residual ordination analysis indicates that forest fire frequency, soil type, and tree canopy composition all play a role in determining understory composition. The assumptions of the method are discussed, and residual ordination analysis is identified as an exploratory, rather than a confirmatory, technique in ecology.