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Weekly reading: Missing values, inapplicable states and polymorphic taxa

The third and likely penultimate session in our “explore cladistic coding” series. A brief primer below; more during our discussions and practices.

Missing values, inapplicable states and polymorphic taxa are used in phylogenetic analyses whenever information is either unavailable (= not yet observed), when hypotheses of homology are categorically not possible (due to “nested” homologies; see the no/red-/blue-tail problem), or when character states are variable within a terminal taxon.

Missing values and inapplicable states are treated by phylogenetic programs as if the taxon had all character states. Thus, a question mark (“?” = missing value) or a dash (“–” = inapplicable state) placed in the matrix are computationally the same as {0, 1} for a binary character, or {0, 1, 2} for a three-state character, and so on. Given that a missing value or an inapplicable state “match” with any other scored state, they never add steps to the tree. In other words, if a taxon is scored as missing or inapplicable for any particular character, then that character has no effect on the placement of the taxon in the tree. Thus, if all characters are missing and/or inapplicable for a particular terminal (= taxon), then no character has any effect on its placement on the tree, and all topologically imaginable placements are equally parsimonious.

Polymorphic taxa have variable character states for one or more characters. These can include all states, in which case they labeled complete polymorphisms, or only a subset of all possible states, in which case they are named subset polymorphisms. Obviously, complete polymorphisms are computationally equivalent to a missing value or an inapplicable state, since the computer algorithm will treat the taxon as having all possible states for the corresponding character. However, a subset polymorphism can add steps to the tree, since it only “matches” a subset of all available states, thus excluding some scenarios which may result in shorter trees.

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