Terminology of Phylogenetic Trees Dan Graur
Evolutionary relationships are usually illustrated by means of a phylogenetic tree (dendogram). • The “tree metaphor” cannot always be used.
Ernst Heinrich Haeckel 1834-1919
Jean-Baptiste [Pierre Antoine de Monet, Chevalier de] Lamarck. 1809
Charles Darwin July 1837 July 2007
Charles Darwin November 1859
Graduate Student Assignments Instead of a stream of emails that will yield unsatisfactory results, kindly set up appointments and let’s talk.
In mathematics, a graph is an abstract representation of a set of objects called nodes (or vertices), some of which are connected to one another by links called branches (or edges). A path in a graph is a sequence of branches that connect any two nodes.
Graphs = Trees + Non-Tree Graphs (or Networks) In a tree (b), any two nodes are connected by a single path. In a network (a), there may be multiple pathways connecting two nodes.
The evolutionary relationships among a group of organisms are illustrated by means of phylogenetic trees (or dendrograms).
Internal External or Peripheral Branch
The branching pattern of a tree is called its topology. Three different styles of trees, one topology.
Terminal node = Operational taxonomic unit (OTU) Internal node = Hypothetical taxonomic unit (HTU) Peripheral ( or terminal) branch = relationship between OTU and HTU Internal branch = relationship between two HTUs
Bifurcating and multifurcating trees A node is bifurcating (or binary or dichotomous) if it has only two immediate descendant lineages, but multifurcating (or polytomous) if it has three or more than two immediate descendant lineages. In a strictly bifurcating tree, each internal node is incident to exactly three branches, two derived and one ancestral.
A bifurcation is always interpreted as a speciation event Two possible interpretations for a multifurcation (polytomy) in a tree: 1. The polytomy represents the true sequence of events (hard polytomy), whereby an ancestral taxon gave rise to three or more descendant taxa simultaneously. 2. The polytomy represents a lack of resolution. The exact order of two or more bifurcations cannot be determined unambiguously with the available data (soft polytomy).
Rooted and unrooted trees In a rooted tree there exists a particular node, called the root, from which a unique path leads to any other node. The direction of each path corresponds to evolutionary time, and the root is the common ancestor of all the taxonomic units under study.
In an unrooted tree with four external nodes, the internal branch is referred to as the central branch.
How many unrooted topologies are here? a b d d 1 2 b a e e c c a c e e 3 4 a b d d b c
In an unrooted phylogenetic tree you cannot immediately assess evolutionary relationships. • In a rooted phylogenetic tree, evolutionary relationships are evident.
Phoronida (horseshoe worms) Brachiopoda (lampshells) Arthropoda (arthropods) Vertebrata (vertebrates) Which of the following taxa are evolutionarily the closest to Rick Perry? (a) Phoronida, (b) Brachiopoda, (c) Arthropoda, (d) all three taxa are equidistant from Perry, or (e) two taxa are closer to Perry than the third taxon.
Bacterium 1 Cladogramsshow branching order - branch lengths are meaningless Bacterium 2 Bacterium 3 Eukaryote 1 Eukaryote 2 Eukaryote 3 Eukaryote 4 Phylogramsshow branch order and branch lengths Bacterium 1 Bacterium 2 Bacterium 3 Eukaryote 1 Eukaryote 2 Eukaryote 3 Eukaryote 4 Cladograms & Phylograms(collectively Dendograms)
Unscaled phylogram Scaled phylogram The branch length is number of changes (e.g., nucleotide substitutions) that have occurred along a branch. The total number of changes in a particular tree is called the tree length.
Tree balance Tree balance is a measure of the degree of symmetry of a rooted phylogenetic tree. It serves as an indication of the pattern of speciation events in the group of taxa under study. Balanced tree Unbalanced or Pectinate (comb-like) tree
Tree balance In an unbalanced tree, only one descendant of a node continues to speciate after a splitting event. In a balanced tree, all descendants of a node participate equally in cladogenesis. Balanced tree Unbalanced or Pectinate (comb-like) tree
Tree balance Tree balance is an important indicator of the ease of phylogenetic reconstruction. Because, by definition, unbalanced trees contain long branches, they are more difficult to reconstruct phylogenetically than balanced trees. In fact, unbalanced and balanced tree are sometimes referred to as “good” and “bad” trees, respectively (Sackin 1972). Balanced tree Unbalanced or Pectinate (comb-like) tree
The Newick format In computer programs, trees are represented in a linear form by a string of nested parentheses, enclosing taxon names (and possibly also branch lengths and bootstrap values), and separated by commas. This type of representation is called the Newick format. The originator of this format in mathematics was Arthur Cayley (1821–1895).
The Newick format The Newick format for phylogenetic trees was adopted on June 26, 1986 at an informal meeting at Newick's Lobster House in Dover, New Hampshire. The Newick format currently serves as the de facto standard for representing phylogenetic tree and is employed by almost all phylogenetic software tools. Unfortunately, it has never been described in a formal publication; the first time it is mentioned in a publication is in 1992.
The Newick format In the Newick format, the pattern of the parentheses indicates the topology of the tree by having each pair of parentheses enclose all members of a monophyletic group. A phylogenetic tree in the Newick format always ends in a semicolon (;). ;
The Newick format One can use the Newick format to write down rooted trees, unrooted trees, multifurcations, branch lengths, and bootstrap values.
3 OTUs 1 unrooted tree = 3 rooted trees
4 OTUs 3 unrooted trees = 15 rooted trees
The number of possible bifurcating rooted trees (NR) for n 2OTUs The number of possible bifurcating unrooted trees (NU) for n 3OTUs
¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾ Number of OTUs Number of possible rooted tree ¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾ 2 1 3 3 4 15 5 105 6 954 7 10,395 8 135,135 9 2,027,025 10 34,459,425 15 213,458,046,676,875 20 8,200,794,532,637,891,559,375 ¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾¾
Evolution is an historical process. Only one historical narrative is true. From 8,200,794,532,637,891,559,375 possibilities, 1 possibility is true and 8,200,794,532,637,891,559,374 are false. Truth is one, falsehoods are many.
How do we know which of the 8,200,794,532,637,891,559,375 trees is true?
True and inferred trees The sequence of speciation events that has led to the formation of a group of OTUs is historically unique. A tree representing the true evolutionary history is called the true tree. A tree that is obtained by using a certain set of data and a certain method of tree reconstruction is called an inferred tree. An inferred tree may or may not be the true tree.
ancestor descendant 1 descendant 2 Cladogenesis = the splitting of an evolutionary lineage into two genetically independent lineages.
Anagenesis = changes occurring along an evolutionary lineage. descendant
In molecular phylogenetics, we assume that species are only created by cladogenesis.
Species Trees & Gene Trees
At every locus, if we trace back the history of any two alleles from any two populations, we will eventually reach a common ancestral allele from which both contemporary alleles have been derived.
The routes of inheritance represent the passage of genes from parents to offspring, and the branching pattern depicts a gene tree.