page_title: Ancestral reconstruction
section_title: Maximum parsimony
hierarchical_section_title: Ancestral reconstruction / Methods and algorithms / Maximum parsimony
caption_attribution_description: English: Graphical illustration of ancestral reconstruction by maximum parsimony.
context_page_description: Ancestral reconstruction is the extrapolation back in time from measured characteristics of individuals to their common ancestors. It is an important application of phylogenetics, the reconstruction and study of the evolutionary relationships among individuals, populations or species to their ancestors. In the context of evolutionary biology, ancestral reconstruction can be used to recover different kinds of ancestral character states of organisms that lived millions of years ago. These states include the genetic sequence, the amino acid sequence of a protein, the composition of a genome, a measurable characteristic of an organism, and the geographic range of an ancestral population or species. This is desirable because it allows us to examine parts of phylogenetic trees corresponding to the distant past, clarifying the evolutionary history of the species in the tree. Since modern genetic sequences are essentially a variation of ancient ones, access to ancient sequences may identify other variations and organisms which could have arisen from those sequences.
context_section_description: Parsimony, known colloquially as "Occam's razor", refers to the principle of selecting the simplest of competing hypotheses. In the context of ancestral reconstruction, parsimony endeavours to find the distribution of ancestral states within a given tree which minimizes the total number of character state changes that would be necessary to explain the states observed at the tips of the tree. This method of maximum parsimony is one of the earliest formalized algorithms for reconstructing ancestral states, as well as one of the simplest.
  Maximum parsimony can be implemented by one of several algorithms. One of the earliest examples is Fitch's method, which assigns ancestral character states by parsimony via two traversals of a rooted binary tree. The first stage is a post-order traversal that proceeds from the tips toward the root of a tree by visiting descendant (child) nodes before their parents. Initially, we are determining the set of possible character states Sᵢ for the i-th ancestor based on the observed character states of its descendants. Each assignment is the set intersection of the character states of the ancestor's descendants; if the intersection is the empty set, then it is the set union. In the latter case, it is implied that a character state change has occurred between the ancestor and one of its two immediate descendants. Each such event counts towards the algorithm's cost function, which may be used to discriminate among alternative trees on the basis of maximum parsimony. Next, a pre-order traversal of the tree is performed, proceeding from the root towards the tips. Character states are then assigned to each descendant based on which character states it shares with its parent. Since the root has no parent node, one may be required to select a character state arbitrarily, specifically when more than one possible state has been reconstructed at the root.
  For example, consider a phylogeny recovered for a genus of plants containing 6 species A - F, where each plant is pollinated by either a "bee", "hummingbird" or "wind". One obvious question is what the pollinators at deeper nodes were in the phylogeny of this genus of plants. Under maximum parsimony, an ancestral state reconstruction for this clade reveals that "hummingbird" is the most parsimonious ancestral state for the lower clade (plants D, E, F), that the ancestral states for the nodes in the top clade (plants A, B, C) are equivocal and that both "hummingbird" or "bee" pollinators are equally plausible for the pollination state at the root of the phylogeny. Supposing we have strong evidence from the fossil record that the root state is "hummingbird". Resolution of the root to "hummingbird" would yield the pattern of ancestral state reconstruction depicted by the symbols at the nodes with the state requiring the fewest changes circled.
  Parsimony methods are intuitively appealing and highly efficient, such that they are still used in some cases to seed maximum likelihood optimization algorithms with an initial phylogeny. However, the underlying assumption that evolution attained a certain end result as fast as possible is inaccurate. Natural selection and evolution do not work towards a goal, they simply select for or against randomly occurring genetic changes. Parsimony methods impose six general assumptions: that the phylogenetic tree you are using is correct, that you have all of the relevant data, in which no mistakes were made in coding, that all branches of the phylogenetic tree are equally likely to change, that the rate of evolution is slow, and that the chance of losing or gaining a characteristic is the same. In reality, assumptions are often violated, leading to several issues:
  Variation in rates of evolution. Fitch's method assumes that changes between all character states are equally likely to occur; thus, any change incurs the same cost for a given tree. This assumption is often unrealistic and can limit the accuracy of such methods. For example, transitions tend to occur more often than transversions in the evolution of nucleic acids. 
caption: Phylogeny of a hypothetical genus of plants with pollination states of either "bees", "hummingbirds" or "wind" denoted by pictures at the tips. Pollination state nodes in the phylogenetic tree inferred under maximum parsimony are coloured on the branches leading into them (yellow represents "bee" pollination, red representing "hummingbird" pollination, and black representing "wind" pollination, dual coloured branches are equally parsimonious for the two states coloured). Assignment of "hummingbird" as the root state (because of prior knowledge from the fossil record) leads to the pattern of ancestral states represented by symbols at the nodes of the phylogeny, the state requiring the fewest changes to give rise to the pattern observed at the tips is circled at each node.
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