D(N, INT(M)) = 2 D(N, INT(L)) = 2.5 D (N, INT(Y)) = 3

N is found to differ least from INT(M), so it is added to that interval via a hypothetical intermediate, X, whose character states are the median of M, N, and Y. The network is now complete (© Figure 5.3).

Farris (1970) concluded that it was unnecessary to have an ancestor from which to begin the construction of the tree. He observed that the choice of

ancestor of a given group of taxa changed the topology of the tree. Since the "simple" algorithm did not impose directionality to the evolution of the group, he reasoned that the choice of ancestor is not crucial. Since parsimony assumes the least about the way evolution works, then choosing one taxon as an ancestor would be assumption about the status of that taxon. He thus argued that a rootless network would reduce the dependency of the form of the tree on the ancestor. For the creation of networks, he used a method for creating networks that minimized the length ofthe intervals between taxa (symbolized by nodes), using the shortest network connections method ofPrim (1957; Sokaland Sneath 1963). Farris differentiated his use of this method from previous phenetic applications by its use of shared, derived characters, and also by the evolutionary implications of the method. This new Wagner algorithm differed from that of the "simple Wagner algorithm'' as follows:

1. Find the pair of OTU's that differs the most (using equation 1 from above).

2. Compute the advancement index of each taxon from the interval formed between the two initial taxa.

3. Take the taxa with the largest advancement index and add it to the interval via an HTU.

4. Find the next unplaced OTU with the largest "advancement index,'' find the interval from which it differs least.

This produces a network, rather than a tree, and does not assume that any of the taxa are ancestral. Farris suggested that the network could be converted into a phylogenetic tree by rooting it at one of the taxa within the tree, or an interval within the network. Completing the process of constructing phylogenies using this method requires that the characters be optimized onto the tree.

The earliest programs implementing the Wagner algorithm did not necessarily find the most parsimonious tree for large data sets. The program needed to run multiple times and have a method ofcomparison in order to determine whether it has indeed found the shortest tree, or if there were multiple equally parsimonious trees. In a large matrix, examining every possible tree could require an enormous amount of computer time, and thus it became necessary to develop heuristic methods to try to find the shortest tree. Today's parsimony programs, such as those in PAUP, Hennig 86, and NONA, use a variety of heuristic algorithms to rerun the data to attempt to ensure that the most parsimonious tree or trees are found. For small numbers of taxa and characters, the Branch and Bound algorithm (Hendy and Penny 1982), which guarantees finding the shortest tree, or the Exhaustive Search option, which enumerates all possible trees, can be employed.

As phylogeneticists began to analyze increasingly larger and more complicated data sets, shortcomings in the original computer programs became evident. In the decade following Farris' (1970) contribution, a number of algorithms were developed, such as Fitch parsimony (Fitch 1971) and Dollo parsimony (Farris 1977), which were incorporated into the existing programs as alternatives to Wagner parsimony. These differed primarily in their assumptions and restrictions regarding character evolution and are discussed in more detail by Wiley et al. (1991).

The first iteration of the Wagner algorithm did not take into account multistate characters, and therefore technically it was not possible to have unordered states, since polarized binary characters are automatically ordered. Initially, before more variations were developed for the algorithm, it was suggested that all multiple character states be divided into multiple binary characters [e.g., a single multistate transformation series of an imaginary character (absent (0), short (1), long (2)) would be divided into two separate characters (absent (0), present (1)) and (short (0), long (1)]. Current algorithms allow for multistate transformation series and allow characters to be run either polarized or unpolarized, and either ordered or unordered, at the discretion of the user. Again, the advantage of phylogenetic methodology is that these decisions are transparent (if they are reported) and repeatable; with the same data set, anyone can rerun an analysis using the same settings to check the reliability of the analysis, or change the settings to see if the results are different.

Whatever algorithm you use to build a tree, in most cases some characters will not be decisive at every node (Farris 1970). It is therefore important for the purpose of studying character evolution to be able to optimize characters on a tree. There are two types of optimization, ACCTRAN (Farris 1970; Wiley et al. 1991) and DELTRAN (Swofford and Maddison 1987; Wiley et al. 1991). The ACCTRAN setting accelerates the transformation of a character on a tree, pushing the evolution toward the root. This is equivalent to preferring parallelisms to reversals, if the choice does not affect the tree length. DELTRAN delays the transformation of a character on a tree, essentially choosing reversals over parallelisms when they are equally parsimonious (Wiley et al. 1991). When there are no equally parsimonious alternatives, both ACCTRAN and DELTRAN will provide the same result (© Figures 5.4 and 5.5).

5.3.2 Development of outgroup comparison

As noted above, Wagner algorithm generates a minimum-length network (sometimes called an ''unrooted tree''). In order to convert a Wagner network into a phylogenetic tree, the network must be rooted in some manner. Increasingly, published studies convert the network into a tree by rooting it with an arbitrarily chosen single taxon not included in the group being analyzed (called the ingroup). This protocol should not be mistaken for the method of outgroup comparisons that emerged in phylogenetics during the 1970s. The distinction is slight, but significant, and must be understood in light of Hennig's perspective on the issue of ancestors.

Hennig objected strongly to the notion that phylogeny reconstruction could be achieved by reconstructing a series of archetypal ancestors, from which particular descendant species could be derived. His position was that each species was a unique mosaic of plesiomorphic and apomorphic traits. Archetypes, defined as ancestral species exhibiting only plesiomorphic traits, thus did not exist; therefore, no single taxon could be used to determine the plesiomorphic and apomorphic traits for any analysis. Or, using current jargon, rooting a network with a single outgroup taxon is sufficiently robust in the Hennigian system only if that taxon is the archetype ancestor of the ingroup, something the Hennigian system disavows.

As can be seen from the discussion above, the early development of the Wagner algorithm was not informed directly by Hennigian reasoning. Rather, it relied on the groundplan-divergence method, based on a priori recognition of an archetypal ancestor. When Farris (1970) abandoned the a priori reliance on an ancestor, the Wagner algorithm reverted to a method for producing an unrooted network. Lundberg (1972) made a significant contribution to linking the results of Wagner analyses with Henngian analyses by differentiating ancestors from outgroups.

He developed a method to determine an ancestor from within a network from the data within that same network. He opined that the structure of a network makes certain character states more likely to be ancestral, helping to determine which interval should form the root of the tree of a parsimony-optimized network. The transition of emphasis from searching for ancestors to identifying outgroups was critical in linking Wagner with Hennig.

The idea that similarity in traits even among distantly related species was due to homology (i.e., plesiomorphy) rather than independent evolution (homopla-sy) was established before the development of Hennigian systematics

► ... it would in most cases be extremely rash to attribute to convergence a close and general similarity of structure in the modified descendants of widely distinct forms. The shape of a crystal is determined solely by the molecular forces and it is not surprising that dissimilar substances should sometimes assume the same form; but with organic beings we should bear in mind that the form of each depends on an infinitude of complex relations, namely on the variations that have arisen, these being due to causes far too intricate to be followed out,-on the nature of the variations that have been preserved or selected, and this depends on the surrounding physical conditions, and in a still higher degree on the surrounding organisms with which each being has come into competition,-and lastly, on inheritance (in itself a fluctuating element) from innumerable progenitors, all of which had their forms determined through equally complex relations. It is incredible that the descendants of two organisms, which had originally differed in a marked manner, should ever afterwards converge so closely as to lead to a near approach to identity throughout their whole organisation. If this had occurred, we should meet with the same form, independent of genetic connection, recurring in widely separated geological formations; and the balance of evidence is opposed to any such admission. Darwin (1872 pp 127-128)

Despite the fact that the connection between outgroups and the Auxiliary Principle had been around for a long time, there was no codification until the late 1970s. Engelmann and Wiley (1977) were the first to provide a rationale for outgroup comparisons. They pointed out that the reference to species outside the ingroup permits a researcher to distinguish traits that truly conflict with phylog-eny (homoplasies) from those that only appear to conflict (plesiomorphies). This in turn creates the possibility that phylogenetic analysis could become testable, at least with respect to Darwinian concepts. Watrous and Wheeler (1981) expanded on this idea, suggesting a number of rules to determine ancestral states for each independent character on the basis of comparisons with an outgroup taxon. The first algorithm to determine ingroup relationships with reference to multiple outgroups was presented by Maddison et al. (1984), who showed that the most robust outgroup comparisons relied on two or more paraphyletic outgroups. This algorithm is incorporated in the program PAUP to root networks when out-groups are specified.

Closely related to the issue of using outgroups to reconstruct ancestral character states are the terms and meanings of "global'' and "local'' parsimony, which were first applied by Maddison et al. (1984). They proposed a two-step procedure that measures parsimony locally among the outgroups to determine ancestral states and given that these ancestral states then measures locally within the ingroup. This results in one or multiple ingroup cladograms that are most parsimonious globally, i.e., most parsimonious in the context of related groups.

We previously addressed the connection between the Auxiliary Principle and epistemological parsimony. Linking the Auxiliary Principle to outgroup comparisons thus provides a connection, through the Auxiliary Principle, between out-group comparisons and parsimony. It is the use of outgroups to root the shortest network that makes the Wagner algorithm Hennigian, accounting for high degrees of consistency between Wagner algorithm, groundplan-divergence method, and Hennig argumentation of the same data (Churchill et al. 1984).

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