The principle of parsimony (Latin parcere, to spare) is also known as the principle of simplicity. The principle is often connected to the English philosopher and Franciscan monk William of Ockham (ca. 1285-1349), who advocated the use of the principle so forcefully that it is also known as "Ockham's razor'': Pluralitas non est ponenda sine neccesitate (plurality should not be posited without necessity) and non sunt multiplicanda entia praeter necessitatem (entities should not be multiplied unnecessarily). In this sense, the principle represents an epistemologi-cal tool or rule of thumb, which obliges us to favor theories or hypotheses that make the fewest unwarranted, or ad hoc, assumptions about the data from which they are derived. This does not necessarily imply that nature itself is parsimonious. Aristotle (350 bce) articulated an ontological basis for the principle of parsimony, the postulate that "nature operates in the shortest way possible''
and "the more limited, if adequate, is always preferable" (Charlesworth 1956). This sense of the principle postulates that nature is itself parsimonious in some manner. Phylogeneticists have used the term "parsimony" in both senses, resulting in much confusion and, from our perspective, unnecessary conflict.
The most important concept introduced by Hennig (1950, 1966) was the stipulation that we should assume homology in the absence of contradictory evidence. Although now known as Hennig's Auxiliary Principle, this concept lies at the foundation of evolutionary theory, "[pjerhaps the correct way of viewing the whole subject, would be, to look at the inheritance of every character whatever as the rule, and noninheritance as the anomaly'' (Darwin 1859 p 13), and "Mr. Waterhouse has remarked that, when a member belonging to one group of animals exhibits an affinity to a quite distinct group, this affinity in most cases is general and not special'' (Darwin 1872 p 409). Hennig's argumentation method is clearly intended to maximize hypotheses of homology and minimize hypothesis of homoplasy, which invokes the principle of parsimony by avoiding the assumption of unnecessary ad hoc hypotheses of parallelism. In the Hennigian system, if evolution were parsimonious, all traits would be logically consistent with the true phylogeny—there would be no conflicting relationships suggested by any set of traits, that is, there would be no homoplasy. The Auxiliary Principle implies that there will be conflicts in the data, which should be resolved in favor of the hypothesis postulating the fewest number of assumptions of multiple origins (homoplasy) over single origins (homology). Contemporary Hennigians assert that both the Auxiliary Principle and the use of parsimony are logical requirements of any attempt to reconstruct phylogeny; if one were to assert that all similarities were due to homoplasy, there would be no evidence of common descent, and thus no evidence of evolution. Therefore, if one is going to study evolution, one must use a method that is capable of finding evidence of evolution. Likewise, if one is going to invoke the Auxiliary Principle, one must invoke it for all traits, thereby choosing the phylogenetic hypothesis that minimizes the total number of violations of the Auxiliary Principle for a given set of data. In this manner, the Auxiliary Principle is an epistemological tool practically synonymous with the principle of parsimony (Farris 1983; Wiley et al. 1991). Wiley (1981) suggested four main assumption of phylogenetics: (1) evolution occurs and has occurred, documented by the characters of different species; (2) each species is a historically unique mosaic of plesiomorphic, synapomorphic, and autapo-morphic traits; (3) before the analysis we do not have knowledge about which characters are homologous and homoplasious; and (4) we do not know beforehand what the phylogenetic relationships are, nor do we know the relative or absolute rates of divergence. The presumption of homology embodied in Hennig's Auxiliary Principle is not an a priori assumption in the sense of a formal model, because the method is designed in part to recognize all mistakenly presumed homologies as homoplasies.
Edwards and Cavalli-Sforza (1963, 1964) reconstructed a tree of extant human populations based on frequencies of blood-group alleles, using an approach they developed and called the "Method of Minimum Evolution.'' Their studies originally aimed to present a maximum likelihood method for phylogeny reconstruction, but their algorithm for a likelihood approach did not work. Edwards (1996 p 83) later emphasized that "[t]he idea of the method of minimum evolution arose solely from a desire to approximate the maximum likelihood solution,'' that is, from a maximum likelihood model based on the assumption that evolution has been parsimonious. Felsenstein (2004 p 127) characterized the method of minimum evolution as a parsimony method, while at the same time not seeing a direct connection between Hennig's Auxiliary Principle and the principle of parsimony, e.g., "[i]t is not obvious how to get from this 'auxiliary principle' to the parsimony criterion'' (Felsenstein 2004 p 138). This reveals that for Felsenstein and like-minded phylogeneticists, parsimony is an ontological issue, whereas Hennigians see it as an epistemological issue.
There are two critical distinctions between these positions. The ontological perspective on parsimony requires first that evolution be parsimonious in some manner, usually as defined by certain assumptions and parameters of a model; and second, that the resulting phylogenetic hypothesis be accepted as true so long as the model is accepted as true. Practitioners are thus preoccupied with the accuracy of their results, and believe it is possible to develop means by which their preferred hypotheses can be verified with respect to the true phylogeny. The Hennigian or epistemological use of parsimony does not imply that the evolutionary process itself is parsimonious. In fact, it suggests that evolution has been so complex that we should always expect to find conflicts in the data, which will require the use of a logical decision-making principle to resolve. An important corollary of this perspective is that there need be no necessary connection between the most parsimonious hypothesis and truth. Practitioners are thus preoccupied with the empirical robustness of their results. The expectation is that if the most parsimonious hypothesis is not true, the accumulation of additional data will force phylogeneticists to abandon it in favor of a new most parsimonious hypothesis; they do not believe that their hypotheses can be verified, but do believe that they can use new data to falsify all or parts of previous hypotheses. Phylogeny reconstruction is thus an open-ended process involving a potentially endless search for information. If, at some point in the future, the accumulation of data has led to a situation in which the phylogenetic hypothesis for a given group is no longer changing with the addition of new data, Hennigians may express the belief that the hypothesis has approached the truth as closely as possible, but in principle it is never appropriate for a Hennigian to claim to have the true phylogeny. Hennigians do feel justified in claiming that they have the most robust hypothesis possible for any set of data.
Today numerous quantitative methods for reconstructing phylogenetic trees are applied to multiple kinds of characters. These methods can be divided into two main types, commonly called parsimony (invoking epistemological parsimony) and likelihood (invoking ontological parsimony) approaches.
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