Parsimony and explanatory power

Parsimony can be related to explanatory power, either by noting that each additional requirement for a separate origin of a feature reduces the number of observed similarities that can be explained as inheritance from a common ancestor; or else by applying Popper’s formula for explanatory power together with the fact that parsimony yields maximum likelihood trees under No Common Mechanism (NCM). Despite deceptive claims made by some likelihoodists, most maximum likelihood methods cannot be justified in this way because they rely on unrealistic background assumptions. These facts have been disputed on the various grounds that ad hoc hypotheses of homoplasy are explanatory, that they are not explanatory, that character states are ontological individuals, that character data do not comprise evidence, that unrealistic theories can be used as background knowledge, that NCM is unrealistic, and that likelihoods cannot be used to evaluate explanatory power. None of these objections is even remotely well founded, and indeed most of them do not even seem to have been meant seriously, having instead been put forward merely to obstruct the development of phylogenetic methods. © The Willi Hennig Society 2008.     

Parsimony via consensus

The parsimony score of a character on a tree equals the number of state changes required to fit that character onto the tree. We show that for unordered, reversible characters this score equals the number of tree rearrangements required to fit the tree onto the character. We discuss implications of this connection for the debate over the use of consensus trees or total evidence and show how it provides a link between incongruence of characters and recombination.     

Rooting with Multiple Outgroups: Consensus Versus Parsimony

Using outgroup(s) is the most frequent method to root trees. Rooting through unconstrained simultaneous analysis of several outgroups is a favoured option because it serves as a test of the supposed monophyly of the ingroup. When contradiction occurs among the characters of the outgroups, the branching pattern of basal nodes of the rooted tree is dependent on the order of the outgroups listed in the data matrix, that is, on the prime outgroup (even in the case of exhaustive search). Different equally parsimonious rooted trees (=cladograms) can be obtained by permutation of prime outgroups. An alternative to a common implicit practice (select one outgroup to orientate the tree) is that the accepted cladogram is the strict consensus of the different equally parsimonious rooted trees. The consensus tree is less parsimonious but is not hampered with extra assumption such as the choice of one outgroup (or more) among the initial number of outgroup terminals. It also does not show sister-group relations that are ambiguously resolved or not resolved at all.     

The Parsimony Ratchet, a New Method for Rapid Parsimony Analysis

The Parsimony Ratchet ¹ 1 This method, the Parsimony Ratchet, was originally presented at the Numerical Cladistics Symposium at the American Museum of Natural History, New York, in May 1998 (see Horovitz, 1999) and at the Meeting of the Willi Hennig Society (Hennig XVII) in September 1998 in São Paulo, Brazil.
is presented as a new method for analysis of large data sets. The method can be easily implemented with existing phylogenetic software by generating batch command files. Such an approach has been implemented in the programs DADA (Nixon, 1998) and Winclada (Nixon, 1999). The Parsimony Ratchet has also been implemented in the most recent versions of NONA (Goloboff, 1998). These implementations of the ratchet use the following steps: (1) Generate a starting tree (e.g., a “Wagner” tree followed by some level of branch swapping or not). (2) Randomly select a subset of characters, each of which is given additional weight (e.g., add 1 to the weight of each selected character). (3) Perform branch swapping (e.g., “branch-breaking” or TBR) on the current tree using the reweighted matrix, keeping only one (or few) tree. (4) Set all weights for the characters to the “original” weights (typically, equal weights). (5) Perform branch swapping (e.g., branch-breaking or TBR) on the current tree (from step 3) holding one (or few) tree. (6) Return to step 2. Steps 2–6 are considered to be one iteration, and typically, 50–200 or more iterations are performed. The number of characters to be sampled for reweighting in step 2 is determined by the user; I have found that between 5 and 25% of the characters provide good results in most cases. The performance of the ratchet for large data sets is outstanding, and the results of analyses of the 500 taxon seed plant rbcL data set (Chase et al., 1993) are presented here. A separate analysis of a three-gene data set for 567 taxa will be presented elsewhere (Soltis et al., in preparation) demonstrating the same extraordinary power. With the 500-taxon data set, shortest trees are typically found within 22 h (four runs of 200 iterations) on a 200-MHz Pentium Pro. These analyses indicate efficiency increases of 20×–80× over “traditional methods” such as varying taxon order randomly and holding few trees, followed by more complete analyses of the best trees found, and thousands of times faster than nonstrategic searches with PAUP. Because the ratchet samples many tree islands with fewer trees from each island, it provides much more accurate estimates of the “true” consensus than collecting many trees from few islands. With the ratchet, Goloboff's NONA, and existing computer hardware, data sets that were previously intractable or required months or years of analysis with PAUP* can now be adequately analyzed in a few hours or days.     

Parsimony, likelihood, and simplicity

The latest charge against parsimony in phylogenetic inference is that it involves estimating too many parameters. The charge is derived from the fact that, when each character is allowed a branch length vector of its own (instead of the homogeneous branch lengths assumed in current likelihood models), the results for likelihood and parsimony are identical. Parsimony, however, can also be derived from simpler models, involving fewer parameters. Therefore, parsimony provides (as many authors had argued before) the simplest explanation of the data, or the most realistic, depending on one's views. If (as argued by likelihoodists) phylogenetic inference is to use the simplest model that provides sufficient explanation of the data, the starting point of phylogenetic analyses should be parsimony, not maximum likelihood. If the addition of new parameters (which increase the likelihood) to a parsimony estimation is seen as desirable, this may lead to a preference for results based on current likelihood models. If the addition of parameters is continued, however, the results will eventually come back to the same place where they had started, since allowing each character a branch length of its own also produces parsimony. Parsimony can be justified by very different types of models—either very complex or very simple. This suggests that parsimony does have a unique place among methods of phylogenetic estimation.     

Non-hereditary Maximum Parsimony trees

In this paper, we investigate a conjecture by Arndt von Haeseler concerning the Maximum Parsimony method for phylogenetic estimation, which was published by the Newton Institute in Cambridge on a list of open phylogenetic problems in 2007. This conjecture deals with the question whether Maximum Parsimony trees are hereditary. The conjecture suggests that a Maximum Parsimony tree for a particular (DNA) alignment necessarily has subtrees of all possible sizes which are most parsimonious for the corresponding subalignments. We answer the conjecture affirmatively for binary alignments on 5 taxa but also show how to construct examples for which Maximum Parsimony trees are not hereditary. Apart from showing that a most parsimonious tree cannot generally be reduced to a most parsimonious tree on fewer taxa, we also show that compatible most parsimonious quartets do not have to provide a most parsimonious supertree. Last, we show that our results can be generalized to Maximum Likelihood for certain nucleotide substitution models.     

Tree Searches Under Sankoff Parsimony

Algorithms to speed up tree searches under Sankoff parsimony are described. For T terminal taxa, an exact algorithm allows calculating length during searches T to 2T times faster than a complete down-pass optimization. An approximate but accurate method is from 3T to 8T times faster than a down-pass. Other algorithms that provide additional increases of speed for simple symmetrical transformation costs are described.     

Approximate Maximum Parsimony and Ancestral Maximum Likelihood

We explore the maximum parsimony (MP) and ancestral maximum likelihood (AML) criteria in phylogenetic tree reconstruction. Both problems are NP-hard, so we seek approximate solutions. We formulate the two problems as Steiner tree problems under appropriate distances. The gist of our approach is the succinct characterization of Steiner trees for a small number of leaves for the two distances. This enables the use of known Steiner tree approximation algorithms. The approach leads to a 16/9 approximation ratio for AML and asymptotically to a 1.55 approximation ratio for MP.     

Parsimony, simplicity and what actually happened

The role of a parsimony principle is unclear in most methods which have been claimed to be valid for the reconstruction of tionary kinship. There appear to be two reasons for this: first, the role of parsimony is generally uncertain in scientific method; second, the majority of methods proposed transform data and order them, but are not appropriate to the reconstruction of phyto Commitment to a probabilistic model of tionary processes seems to be the essential component which may enable us justifiably to estimate phylo An example is provided which emphasizes the importance of knowledge about the nature of the process before undertaking estimation of the pattern of kinship.     

Problems with Parsimony in Sequences of Biased Base Composition

Parsimony is commonly used to infer the direction of substitution and mutation. However, it is known that parsimony is biased when the base composition of the DNA sequence is skewed. Here I quantify this effect for several simple cases. The analysis demonstrates that parsimony can be misleading even when levels of sequence divergence are as low as 10%; parsimony incorrectly infers an excess of common to rare changes. Caution must therefore be excercised in the use of parsimony. Received: 13 November 1997 / Accepted: 18 June 1998     

Maximum Parsimony on Phylogenetic networks

Background

Phylogenetic networks are generalizations of phylogenetic trees, that are used to model evolutionary events in various contexts. Several different methods and criteria have been introduced for reconstructing phylogenetic trees. Maximum Parsimony is a character-based approach that infers a phylogenetic tree by minimizing the total number of evolutionary steps required to explain a given set of data assigned on the leaves. Exact solutions for optimizing parsimony scores on phylogenetic trees have been introduced in the past.

Results

In this paper, we define the parsimony score on networks as the sum of the substitution costs along all the edges of the network; and show that certain well-known algorithms that calculate the optimum parsimony score on trees, such as Sankoff and Fitch algorithms extend naturally for networks, barring conflicting assignments at the reticulate vertices. We provide heuristics for finding the optimum parsimony scores on networks. Our algorithms can be applied for any cost matrix that may contain unequal substitution costs of transforming between different characters along different edges of the network. We analyzed this for experimental data on 10 leaves or fewer with at most 2 reticulations and found that for almost all networks, the bounds returned by the heuristics matched with the exhaustively determined optimum parsimony scores.

Conclusion

The parsimony score we define here does not directly reflect the cost of the best tree in the network that displays the evolution of the character. However, when searching for the most parsimonious network that describes a collection of characters, it becomes necessary to add additional cost considerations to prefer simpler structures, such as trees over networks. The parsimony score on a network that we describe here takes into account the substitution costs along the additional edges incident on each reticulate vertex, in addition to the substitution costs along the other edges which are common to all the branching patterns introduced by the reticulate vertices. Thus the score contains an in-built cost for the number of reticulate vertices in the network, and would provide a criterion that is comparable among all networks. Although the problem of finding the parsimony score on the network is believed to be computationally hard to solve, heuristics such as the ones described here would be beneficial in our efforts to find a most parsimonious network.     

Parsimony,Exhaustivity and Balanced Detection in Neocortex

The layout of sensory brain areas is thought to subtend perception. The principles shaping these architectures and their role in information processing are still poorly understood. We investigate mathematically and computationally the representation of orientation and spatial frequency in cat primary visual cortex. We prove that two natural principles, local exhaustivity and parsimony of representation, would constrain the orientation and spatial frequency maps to display a very specific pinwheel-dipole singularity. This is particularly interesting since recent experimental evidences show a dipolar structures of the spatial frequency map co-localized with pinwheels in cat. These structures have important properties on information processing capabilities. In particular, we show using a computational model of visual information processing that this architecture allows a trade-off in the local detection of orientation and spatial frequency, but this property occurs for spatial frequency selectivity sharper than reported in the literature. We validated this sharpening on high-resolution optical imaging experimental data. These results shed new light on the principles at play in the emergence of functional architecture of cortical maps, as well as their potential role in processing information.     

A Note on Opportunism and Parsimony in Data Collection

ABSTRACT Out of precaution, opportunism, and a general tendency towards thoroughness, researchers studying wildlife often collect multiple, sometimes highly correlated measurements or samples. Although such redundancy has its benefits in terms of quality control, increased resolution, and unforeseen future utility, it also comes at a cost if animal welfare (e.g., duration of handling) or time and resource limitation are a concern. Using principle components analysis and bootstrapping, we analyzed sets of morphometric measurements collected on 171 brown bears in Sweden during a long-term monitoring study (1984–2006). We show that of 11 measurements, 7 were so similar in terms of their predictive power for an overall size index that each individual measurement provided little additional information. We argue that when multiple research objectives or data collection goals compete for a limited amount of time or resources, it is advisable to critically evaluate the amount of additional information contributed by extra measurements. We recommend that wildlife researchers look critically at the data they collect not just in terms of quality but also in terms of need.     

Brooks Parsimony Analysis: a valiant failure

A recent comparison of two methods for examining correlated host and parasite phylogenies, namely TreeMap 1.0 and Brooks Parsimony Analysis concluded that the latter method performed better and is to be preferred. Reevaluation of the examples contrived for that study demonstrates that the two methods were only compared on one kind of problem (widespread parasite) for which there is an easy fix for TreeMap 1.0. Other kinds of problems like host‐switching among sister taxa or host‐switching over great distances across a host tree befuddle BPA even as they are readily resolved parsimoniously by TreeMap 1.0. These difficulties, compounded with inaccurate counting of ad hoc hypotheses required by its solutions render BPA unsuitable for comparison of host and parasite phylogenies.     

On the Three-Taxon Approach to Parsimony Analysis

The following three basic defects for which three-taxon analysis has been rejected as a method for biological systematics are reviewed: (1) character evolution is a priori assumed to be irreversible; (2) basic statements that are not logically independent are treated as if they are; (3) three-taxon statements that are considered as independent support for a given tree may be mutually exclusive on that tree. It is argued that these criticisms only relate to the particular way the three-taxon approach was originally implemented. Four-taxon analysis, an alternative implementation that circumvents these problems, is derived. Four-taxon analysis is identical to standard parsimony analysis except for an unnatural restriction on the maximum amount of homoplasy that may be concentrated in a single character state. This restriction follows directly from the basic tenet of the three-taxon approach, that character state distributions should be decomposed into basic statements that are, in themselves, still informative with respect to relationships. A reconsideration of what constitutes an elementary relevant statement in systematics leads to a reformulation of standard parsimony as two-taxon analysis and to a rejection of four-taxon analysis as a method for biological systematics.