CALCULATION OF MORPHOLOGIC DEBT WITH POLYMORPHIC TAXA

In most instances, StrataPhy uses the same algorithms for calculating morphologic debt as MacClade (see Maddison and Maddison 2000). However, StrataPhy and MacClade differ in the way each calculates morphologic debt when polymorphic taxa are present, and particularly when they are fixed as ancestors. This issue applies only to terminal taxa with more than one observed state (e.g., states 0 and 1), and not to taxa that possess a single uncertain state (e.g., state 0 or 1, but not state 2). Differences in calculated debt arise under two specific conditions: 1) two sister-taxa are both polymorphic, or 2) a polymorphic taxon is fixed as an ancestor. If there are no instances of polymorphic sister-taxa or polymorphic taxa assigned to be ancestors, the calculation of morphologic debt in StrataPhy will be identical to that in MacClade. Here, we describe, in general terms, the novel algorithms used in StrataPhy to calculate morphologic debt when polymorphic taxa are present.

One main difference between the algorithms in the two programs is that StrataPhy allows polymorphism to be heritable (i.e., from a common ancestor), but minimizes its occurrence otherwise. For example, if two sister-taxa – which may be either terminal taxa or internal nodes – are both polymorphic (e.g., possess both states 0 and 1), then their ancestor is reconstructed to be polymorphic for those states as well (Figure 3.1). MacClade assumes that only one of their states (e.g., 0 or 1) is present in the ancestor (Figure 3.2). This causes the other state to evolve once in each descendant, for a total of two units of morphologic debt (Figure 3.2). In StrataPhy, the ancestor is reconstructed to be polymorphic for both states, yielding only a single step – the evolution of state 1 in the lineage prior to the most recent common ancestor of the two polymorphic descendants, if the ancestor of that lineages was not polymorphic (Figure 3.1).

As previously mentioned, StrataPhy minimizes the occurrence of polymorphism – if one of the descendants is not polymorphic, then the reconstructed ancestor is assumed to possess only one state, as well (Figure 3.3). A single unit of debt is added for all of the polymorphic taxon's states that do not match its sister-taxon. This matches the behavior of MacClade (Figure 3.4). In the event that two polymorphic descendants do not completely overlap in their states (Figure 3.5), the ancestor is reconstructed to possess all states common to both descendants; the ancestor is therefore polymorphic. If only one state overlaps between the two polymorphic descendants' state sets (Figure 3.7), then the ancestor is reconstructed with that single state and is not polymorphic. In these two instances, the debt incurred is simply the number of unshared states from each taxon. If both descendants are polymorphic, but there are no shared states (Figure 3.8), StrataPhy assumes that at only one of the states observed in the descendants is present in the ancestor, which is therefore not polymorphic. Accordingly, the debt is the number of states observed in the two descendants, minus one for the undetermined ancestral state.

As in MacClade, when a polymorphic taxon is fixed as an ancestor, the states observed in that taxon are assigned to the corresponding node, unless the taxon's state is uncertain or unknown. However, MacClade underestimates the morphologic debt in these circumstances – a property that is well documented in the MacClade manual (Maddison and Maddison 2000, p. 332), and is accompanied by a warning in the MacClade program. When a polymorphic taxon is fixed and its direct descendant (formerly, its sister-taxon) is not polymorphic (Figure 4.1), or if a non-polymorphic taxon is fixed, but its direct descendant is polymorphic (Figure 4.2), a unit of debt is added for each state not shared between the two taxa.