Briefly, Zander's pluralistic systematics is based on the incompleteness of each of the theories: A method that cannot falsify a hypothesis is as unscientific as a hypothesis that cannot be falsified. Cladistics generates only trees of shared ancestry, not serial ancestry. Taxa evolving seriatim cannot be dealt with by analyzing shared ancestry with cladistic methods. Hypotheses such as adaptive radiation from a single ancestral taxon cannot be falsified with cladistics. Cladistics offers a way to cluster by trait transformations but no evolutionary tree can be entirely dichotomous. Phylogenetics posits shared ancestral taxa as causal agents for dichotomies yet there is no evidence for the existence of such taxa. Molecular systematics uses DNA sequence data for tracking evolutionary changes, thus paraphyly and sometimes phylogenetic polyphyly signal ancestor-descendant transformations at the taxon level, but otherwise molecular phylogenetics makes no provision for extinct paraphyly. Additional transformational analysis is needed to infer serial descent.
The Besseyan cactus or commagram is the best evolutionary tree for showing both shared and serial ancestry. First, a cladogram or natural key is generated. Generalized ancestral taxa are identified and specialized descendant taxa are noted as coming off the lineage with a line of one color representing the progenitor through time. A Besseyan cactus or commagram is then devised that represents both shared and serial ancestry. Progenitor taxa may have one or more descendant taxa. Support measures in terms of Bayes factors may be given, following Zander's method of transformational analysis using decibans.
Cladistic analysis groups taxa by shared traits but incorporates a dichotomous branching model borrowed from phenetics. It is essentially a simplified dichotomous natural key, although reversals are tolerated. The problem, of course, is that evolution is not necessarily dichotomous. An ancestral taxon generating two or more descendants requires a longer, less parsimonious tree. A cladogram node summarizes all traits distal to it, not of any one taxon, and continuity in a cladogram is from node to node, not taxon to taxon. This is not a model of evolution, but is a variant of hierarchical cluster analysis (trait changes and non-ultrametric branches. This is why a tree based solely on shared traits is not called an evolutionary tree but merely a cladistic tree. This tree reflects to a large extent evolutionary relationships through trait transformations but ignores relationships made by species-level transformation of extant taxa.