Over the past 50 years, many different quantitative approaches have been developed to infer systematic relationships, and these have led to three distinct schools of systematics: phenetics, cladistics, and quantitative evolutionary systematics (= explicit phyletics). Phenetics emphasized
quantitative assessment of overall similarity and taught the distinction between character and character state. Cladistics stressed reconstruction of phylogeny by use of synapomorphies and emphasized holophyly in classification. Quantitative evolutionary systematics built upon cladistic analysis
and stressed incorporation of quantitative measures of divergence within lineages. In parallel with these conceptual and algorithmic developments have come technological advances that have allowed deep access to genetic data, beginning with allozymes, then DNA restriction site data, nuclear
and organellar DNA sequences and fragment patterns, and now large-scale genomics. The challenge in recent years has not been for new philosophical reflections on how best to interpret evolutionary history, but rather on methods to make sense of the torrents of new genetic data that apply at
all levels of the taxonomic hierarchy. The search for patterns in these new data has led to use of whatever methods seem best suited for the job at hand. Phylogenetic reconstructions are now routinely done with formerly phenetic algorithms, and cladistic methods are sometimes used at the populational
level. More sophisticated approaches have also been developed, such as likelihood and Bayesian statistics, and these are applicable at many different hierarchical levels. Awareness of lateral gene transfer, pervasive polyploidy, and ancient hybridizations, has led to new methods to allow better
understanding of complex reticulate relationships. It is no longer productive, therefore, to worry about ideological aspects of schools of systematics but rather to focus on which algorithms and statistics are best suited to answer specific questions. For formal classification, however, areas
of conflict still remain. The challenge is to determine which combination of quantitative methods will result in the most information-rich and predictive hierarchical system, realizing that special-purpose classifications will continue to be used in certain instances.
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