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Mono-, para- and polyphyletic taxa can be understood based on the shape of the tree (as done above), as well as based on their character states.A clade is characterized by one or more apomorphies: derived character states present in the first member of the taxon, inherited by its descendants (unless secondarily lost), and not inherited by any other taxa.Such is the nature of empirical science, and for this reason, most cladists refer to their cladograms as hypotheses of relationship.Cladograms that are supported by a large number and variety of different kinds of characters are viewed as more robust than those based on more limited evidence.Phenetics was championed at this time by the numerical taxonomists Peter Sneath and Robert Sokal and the evolutionary taxonomist Ernst Mayr.Originally conceived, if only in essence, by Willi Hennig in a book published in 1950, cladistics did not flourish until its translation into English in 1966 (Lewin 1997).

Phenetics did not try to reconstruct phylogenetic trees; rather, it tried to build dendrograms from similarity data; its algorithms required less computer power than phylogenetic ones.

Since the cladograms provide competing accounts of real events, at most one of them is correct.

Cladogram of the primates, showing a monophyletic taxon (a clade: the simians or Anthropoidea, in yellow), a paraphyletic taxon (the prosimians, in blue, including the red patch), and a polyphyletic taxon (the nocturnal primates – the lorises and the tarsiers – in red) The cladogram to the right represents the current universally accepted hypothesis that all primates, including strepsirrhines like the lemurs and lorises, had a common ancestor all of whose descendants were primates, and so form a clade; the name Primates is therefore recognized for this clade.

Only scientific investigation can show which is more likely to be correct.

Until recently, for example, cladograms like the following have generally been accepted as accurate representations of the ancestral relations among turtles, lizards, crocodilians, and birds: If this is accurate, then the last common ancestor of turtles and birds lived later than the last common ancestor of lizards and birds.

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