Linkage trees – rationale

Another technique for linking sample patterns based on assemblage data to a suite of environmental (or other) explanatory variables was also discussed in Clarke KR et al 2008 J Exp Mar Biol Ecol 366: 56-69 (see the last topic in Chapter 11, CiMC). The well-established statistical procedure of Classification And Regression Trees (CART) was further developed in an ecological context by De’ath G 2002, Ecology 83: 1105-1117, termed Multivariate Regression Trees (MRT). PRIMER implements a modification of this, in a form which is consistent with the non-metric philosophy underlying the rest of the package. The connection with regression is minimal (and confusing) so the more descriptive term linkage trees is used by PRIMER for its variation of the procedure. Its real affinity is with Cluster analysis (Section 6, under heading Binary divisive clustering), and it is therefore accessed in PRIMER v7 by running Analyse>Cluster>LINKTREE. In fact, it is a form of constrained binary divisive clustering in which the successive divisions of the full set of biotic samples, seen in the unconstrained divisive clustering of Analyse>Cluster>UNCTREE (Section 6), are limited to those splits of each group (into two new sub-groups) which have an explanation in terms of larger or smaller values of a specific explanatory (typically abiotic) variable – consistently so on either side of that divide. In other words, all constraints are a threshold inequality on a single abiotic variable and this set of inequalities form the possible ‘explanation’ for the biotic structure.

We have already seen two techniques for linking assemblage patterns to abiotic variables: bubble plots (Section 8) and the above BEST procedure. BEST has the advantage of looking at the abiotic variables in combination, trying to identify a subset which is sufficient to ‘explain’ all the biotic structure capable of explanation, and the matching procedure takes place in the full high-d space, i.e. on the respective resemblance matrices. But on its own, this falls short of a full interpretation because it does not demonstrate which variables take high or low values for which samples. Bubble plots give the latter but are only satisfactory where the low-d biotic nMDS has acceptable stress as an approximation to the full biotic pattern. Linkage trees can fill this gap: they can take the subset of abiotic variables identified by BEST, and use them to describe how the assemblage samples are optimally split into groups (in the high-d space), and interpret this, e.g. Group 1 communities have Salinity<23ppt but Group 2 are from >26ppt (with no samples between these salinity thresholds). Group 1 and 2 samples are then each divided into two by a different threshold on the same abiotic variable, or more likely by a different abiotic variable. The result is divisive clustering of the biotic samples, and an environmental interpretation, e.g. for the lagoon diatoms, the cluster of sites 13,14, 15 below has (Salinity<23), (54<PO4<82) and (In-N<965), the only sites to meet those conditions.