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Principal Coordinates Analysis (PCoA)
Principal Coordinates Analysis is an eigenanalysis technique similar to PCA, except that one extracts eigenvectors from a distance matrix among sample units (rows), rather than from a correlation or covariance matrix. In PCoA one can use any square symmetrical distance matrix, including semi-metrics such as Sorensen distance, as well as metric distance measures such as Euclidean distance.
Because the hilltops are based on a contoured response surface, you can better understand the basis for hilltop plots by reading about contour overlays. The chief difference in use between the hilltops and the contour plots is that contour plots can be shown for only one variable at a time, while one can graph many hilltops on the same ordination. This comes at a loss of information in that most of the contour plot is discarded when converting to a hilltop, but has the advantage of representing multiple nonlinear relationships at once..
Principal Components Analysis (PCA)
Principal Components Analysis is the basic eigenanalysis technique. It maximizes the variance explained by each successive axis. Although it has severe faults with many community data sets, it is probably the best technique to use when a data set approximates multivariate normality. PCA is usually a poor method for community data, but it is the best method for many other kinds of multivariate data. Broken-stick eigenvalues are provided to help you evaluate statistical significance.
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