Statistical approaches to R-values and the pollen- vegetation relationship

R-values are ratios of pollen to vegetational percentages for different taxa. They may be used as correction factors for Late Quaternary pollen spectra-subject to certain caveats. The use of R-values implies a particular mathematical model, which is discussed in depth. Various problems are shown to arise; three computer-based statistical approaches are described in an attempt to overcome these problems. The first uses cluster and principal component analyses to group modern sites according to "R-spectra" and to detect departures from the model. The other two approaches obtain maximum likelihood estimates of (a) R-values and (b) representation coefficients and "background" coefficients in a model that attempts to allow for long-distance transport. Each approach is illustrated by application to Livingstone's surface pollen and forest-inventory data from southeast Canada. It is shown how long-distance Quercus (oak) pollen inflates R-values for oak at sites where oak trees are scarce. Livingstone's average R-values for oak was much too high since it was heavily biased by these sites. Maximum likelihood estimation gave a more realistic overall figure. Background oak pollen values estimated via the third approach are close to total oak pollen percentage at many sites, i.e. the method ascribes much of the incoming oak pollen to non-local sources. It is concluded that the three approaches together will make it possible to avoid the worst statistical problems associated with R-values, although vegetational heterogeneity and differential pollen transport will continue to limit achievable precision in the reconstruction of vegetation.