Parsimony (continued) Character weighting In the worked example given in the last reading, all changes were counted equally. Changes at any character and between any pair of character states were all given equal weight in determining the score of a given tree. This criterion for selecting a tree is therefore called equally-weighted parsimony. It is also sometimes called Fitch parsimony because it resembles a model proposed by Walter Fitch in the 1970’s. It is a misleading to call it “unweighted parsimony” because all characters are assigned some weight, albeit an equal one. If we have reason to believe that some characters are less likely to show homoplasy and, thus, provide more reliable information about phylogeny, then we can modify the parsimony criterion to differentially count those characters. Such weighting can alter the rank order of tree length and can result in a change in the identity of the most-parsimonious tree. For example, suppose we had assigned a weight of five to character four in the example given on page X, whereas other characters retained a weight of one. This would mean that any change of character four would be counted as equivalent to five changes of the other characters. The score of a tree is no longer simply the number of changes needed to explain the data but a sum of the cost of each character’s evolution, where cost is the product of the character’s length (number of steps) and its weight. The table shows the length and cost for each of the three trees. It can be seen that the scores of all trees have gone up relative to the flat-weighted case. However, whereas the scores of trees 2 and 3 have increased by eight (because two changes of character 4 have to be invoked) the score of tree 1 has only increased by four. As a result, tree 1 is now the most parsimonious. 1 2 3 4 5 6 7 8 O 0 0 1 0 1 1 0 0 A 0 1 1 0 1 0 1 0 B 1 1 1 1 0 0 1 1 C 0 0 0 1 1 1 0 0 Total cost Weight 1 1 1 5 1 1 1 1 Cost of tree 1 1 2 1 5 1 2 2 1 15 Cost of tree 2 1 2 1 10 1 2 2 1 20 Cost of tree 3 1 1 1 10 1 1 1 1 16 This result shows us that differential weighting of parsimony informative characters can alter the outcome of parsimony analysis. So what weighting scheme is correct? Equally weighting all characters is often seen as a safe starting point for analysis in cases where we lack any clear insights into the different characters’ propensity for homoplasy. But Most-parsimonious treewhen we have reason to suppose that some characters are evolving more slowly than others, equal weighting is not appropriate. Because parsimony is most effective when rates of evolution are low (see Justification for Parsimony, above), traits evolving more slowly provide more reliable evidence. To assign all characters equal weight even when some provide worse evidence than others is tantamount to giving these weak characters more weight than they deserve. Different kinds of characters are often expected to evolve at different rates. Molecular data often include both slowly evolving regions (e.g., conserved domains, coding regions) and more rapidly evolving regions (e.g., introns, third codon position) (see chapter x on molecular evolution). Likewise, indels and other structural molecular mutations (especially large ones) are usually thought to evolve more slowly than substitutions (Chap. 7). And, while it can be more difficult to determine, there may be certain morphological characters that evolve more slowly than others. In such cases, assigning different weight to different characters is an appropriate practice. You may be worried that the choice of a weight seems arbitrary. Even when you have good reasons to favor something other than equal weighting, how do we choose the appropriate weights. Why use 2:1 not 1.1:1, 5:1, or 100:1? You have good reason for such a concern because there is no well-grounded theory to tell you what cost is most appropriate. The underlying problem, which will be discussed in subsequent chapters, is that parsimony is not based on a formal model of how characters evolve. Nonetheless, parsimony is still useful because it is easy to explore a range of different weighting schemes to see whether the conclusions are sensitive to a range of different assumptions. Using parsimony you can build a convincing cases for one tree over another by showing that your conclusions are statistically sound and robust to a range of weights. Before leaving character weighting it is worth mentioning, successive weighting, a method that is occasionally used in publications. The logic of this method goes as follows. Characters that are more homoplastic should be down-weighted. We don’t know how much homoplasy a character has experienced until we have a tree in hand. So why not search for the most-parsimonious trees using flat-weighting, down-weight characters based on the amount of homoplasy on those trees, search for trees under these revised weights, and reiterate the procedure until the trees stops changing? While this procedure sounds reasonable, it is circular because it tends to reinforce findings from the original, flat-weighted analysis. As a result it ends up by lending an unwarranted level of support for a tree that is identical or very close to the tree found with flat-weights. My advice is to treat as suspect strong conclusions that rest on the use of successive weighting. Character-state weighting Upweighting a character entails an elevated cost of all changes among states of that character. However, sometimes we have reason to believe that the rate of evolution between certain pairs of states are higher or lower than the rate of change between other character states for the same character. In cases you can apply character state weighting.In order to understand character state weighting it will be helpful to introduce the idea of a step matrix, which shows the cost of transitions between each possible pair of states. Here is a step matrix that corresponds to flat-weighted parsimony for DNA sequence data. As you can see all possible changes of state count the same, and in this case have a cost of one. With DNA sequence data it is common to take account of the fact that transitions (purine-to-purine) are more frequent mutations than transversions (purine-to-pyrimidine, or vice verse). This means that transversions occur less frequently and should be less prone to homoplasy. The step-matrix shown assigns