Characters. Characters

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Gregory Richardson
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1 Characters Character = set of evidence (character states) about the relationships among a set of taxa. A character comprises a homologous set of states. Characters are variables, and character states are instantiations of variables. Character states represent evolutionary transformations of one another. Characters (1) Simple variables: scored by direct observation. (a) Nominal (b) Ordinal (c) Mensural Discrete (counts) Continuous (interval and ratio) (2) Derived (composite) variables (a) Ratios (b) Factors and functions (e.g., warps) 1

2 Simple variables Nominal variables: named states, no implied transitional sequence. Properties, attributes (e.g. color). Categories (e.g., DNA/RNA bases, amino acids). Ordinal variables: states ordered or ranked. Values arbitrary and relative. Sequenced by magnitude or other criterion. Differences between consecutive states not important. E.g., transition series: Morphology: bump on bone absent, small, elongated, bifed. Simple variables Mensural variables: measured. States expressed in a numerically ordered fashion, on an interval scale Differences between units are constant. (1) Discrete variables (discontinuous, cardinal, meristic): Non-arbitrary integer values, usually non-negative or positive. For example: Number of petals/flower. Number of dorsal fin rays. Number of abdominal setae

3 Simple variables Mensural variables: measured. (2) Continuous variables: Lengths, densities, colors, frequencies. E.g., humerus length, pelt color, allele frequency. Distance between two morphometric landmarks Can theoretically assume an infinite number of values. Actual continuous values are estimated as discrete states by a measurement procedure or device. E.g., calipers, densitometer. Each has some degree of resolution or precision. Measurements are expressed by an interval of indistinguishable values. Issues with discrete characters (1) Ordering: Character-state graphs (transformation series) and corresponding transition (step) matrices. Evidence: ontogeny, morphoclines in adults. Represent evolutionary constraints (longer trees). Phylogenetic information always lost when states treated as unordered. Swofford and Maddison

4 Issues with discrete characters (2) Polarity: identification of ancestral vs derived states. Terminology: Plesiomorphy ancestral state. Apomorphy derived state. Two basic choices for inferring polarity: (a) Specify on a character-by-character basis, based on: Outgroup criterion: state outside study group is plesiomorphic. Ontogenetic criterion: developmentally earlier is plesiomorphic. Paleontologic criterion: stratigraphically earlier is plesiomorphic. (b) Use outgroup assumption to root tree: Assess polarities from distribution of character states on tree. Issues with discrete characters (3) Polymorphism: Variation in character states within taxa (e.g., species). Independent of ontogenetic and sexual variation. Common problem in phylogenetic studies. Evolving characters must vary within taxa at some point in history. Several methods: Subdivide taxon into homogeneous groups. Code character state as missing Code character state as missing. Code polymorphism as intermediate state between two fixed states. Most common: reject polymorphic character. (Wiens 2000) 4

Issues with discrete characters Change in 3 rd -codon position may be differentially weighted relative to change in 1 st or 2

5 Issues with discrete characters (4) Character weighting: characterizing cost of the transformation from one state to another. Higher weight designates more likely or significant change from one state to another. E.g., Transitions may be weighted less than transversions, in proportion to observed frequency. Issues with discrete characters Change in 3 rd -codon position may be differentially weighted relative to change in 1 st or 2 nd position, due to degeneracy of genetic code. Up-weight or down-weight? 5

6 Issues with discrete characters Iterative re-weighting (Farris) and dynamic weighting (Goloboff, etc.): Find shortest tree by parsimony. Re-weight characters inversely proportional to the number of character-state changes on the tree (homoplasy). Find shortest tree with weights imposed. Repeat until solution stabilizes. Problem: circularity.» Iterates toward best solution, but best in what sense? Issues with discrete characters (5) Kinds of inference methods: Distance: based on pairwise measures of similarity. Usually give unique tree. Parsimony : based on finding topology having minimum tree length. Tree length measured as total number of characterstates changes across tree. Usually gives sets of equally parsimonious trees. Maximum likelihood and Bayesian: Based on particular models of character-state change. Usually give unique tree. 6

7 Tree length A B C D a 1 b 0 a 1 b 0 a 0 b 1 a 0 b 0 b 1 a 1 a 0 b 0 Tree length = 2 Discrete vs. continuous Characters have two evolutionary options : Remain constant from ancestor to descendant. Change between ancestor and descendant. Issues with discrete vs. continuous characters: Change in state between nodes on tree: Discrete character states might change or not. Synapomorphies can be identified qualitatively. Character-state changes can be counted. Total tree length can be defined in term of number of character-state changes. Continuous character states are likely to always change between tree nodes. Cladistic premise (based on parsimony): continuous characters are inappropriate for phylogenetic analysis. 7

8 Two approaches: Issues with continuous characters (1) Convert continuous characters to discrete characters. Gap-coding (Archie 1985). Range-coding (Pimentel and Riggins 1987). Homogeneous subsets (Mishler and De Luna 1991). (2) Use continuous characters directly: Taxa summarized by means or medians. Distance methods: pairwise similarity. Maximum likelihood lih or Bayesian methods. Brownian motion model (random walk). Tree length A B C D A B C D a 1 b 0 a 1 b 0 a 0 b 1 a 0 b b 1 a a 0 b 0 Tree length = Tree length = 2.0 (Requires explicit reconstruction of ancestral states) 8

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