Tree BuildingTree Building

What is a tree ? Cladograms Trees Scenario

How to build a tree ? Observations First Principles Assumptions Methods

WhatWhat is a tree ? is a tree ?

Cladograms and Trees Both are graphs in

mathematical terms:• A graph is a collection of nodes (vertices) and lines / branches (edges) connecting the nodes.

• A cladogram/tree for our purposes is allowed at most one edge between any two vertices.

Cladogram Cladogram & Trees - 1& Trees - 1

The degree of a node is the number of branches that contain that node.

A node of degree 1 is called a leaf (or terminal node)

All nodes that are not leaves are called internal.

CladogramsCladograms& Trees - 2& Trees - 2

A tree is elementary if no node has degree 2 (‘net-work’ in cladistic jargon).

A root is a distinguished node with degree 2, locating the ‘start’ of the tree.

CladogramsCladograms& Trees - 3& Trees - 3

An unrooted tree is binary if every node has degree 1 or 3.

A rooted tree is binary if it has a root of degree 2 and every other node has degree 1 or 3.

CladogramsCladograms& Trees - 4& Trees - 4

Leaf

Root

NodeBranch

CA B Label

?

Labeled rooted binary tree

Cladograms Cladograms & Trees - 5& Trees - 5

What’s the difference? Cladogram

Cladogenesis:

branching events as indicated by character state changes

Tree+ Anagenesis:

amount and duration of change + inference of ancestor-descendant relationships

A Cladogram is a:A Cladogram is a:

Statement about the distribution of (shared) character states.

Branching diagram depicting nested sets of synapomorphies resulting in a summary statement of sister-group relations among taxa.

Nested sets of Nested sets of SynapomorphiesSynapomorphies

Detection of relationships by distribution of character-states in species X, Y, and Z.

abcde

aBCde

aBCdeaBCdEabcdE

BCSyn-

apomorphy

E

convergencead

Sym-plesiomorphy

XZ Y

Relationship, and Kind of Relationship, and Kind of GroupsGroups

Relationship criterion: Recency of common ancestry

“A species X is more closely related to another species Y than it is to another species Z if, and only if, it has at least one stem species in common with species Y that is not a stem species of Z”

(Hennig, 1966, p.74) X and Y are sistergroups.

A Phylogenetic Tree is A Phylogenetic Tree is a:a:

Branching diagram where: the nodes represent real or

hypothetical ancestors, the branching represents

speciation, and the branches represent

descent with modification.

CladogramsCladograms & Trees - 6 & Trees - 6

Cladogram = set of trees Every picture tells a story

A B C

= ?

Cladogram = Cladogram = Set of TreesSet of Trees

C

B

A

B

C

A

A B C

= ?

?

A

C

B

?

A

B C

?

A

B C

B A

C

?

B

AC

?

The Cladistic Party The Cladistic Party Line ...Line ...

“There is simply no possible way to distinguish ancestors from extinct lineages.”

“… if something is in fact an ancestor, there are no data that can refute the hypothesis that it is an extinct lineage and not an ancestor.”

(Mark Siddal, 09/01/96, sci.bio.systematics).

… … and its Counterpartand its Counterpart

“…’A is the ancestor of B’ is a perfectly valid hypothesis, and one that is easily falsified. All it would take to falsify it is to find an autapomorphy in A that is not found in B.”

(Ron DeBry, 18/01/96, sci.bio.systematics)

HowHow to build a to build a cladogramcladogram

Observations•Character-state distri-butions over taxa (data matrix), or derivation thereof (distance matrix)

First principles Assumptions

•ProcessModel

•DataType and Quality

First PrinciplesFirst Principles

Evolution (descent with modification) occurs.

Evolution results predominantly in a hierarchical scheme of relationships among the entities involved.

...?

Assumptions - 1Assumptions - 1

“ The fact that parsimony methods are known to fail in reconstructing phylogeny when there are unequal rates of evolution, and fail in a systematic way (e.g., put long branches together when they really should each go with one of the short branches) suggest […] that certain conditions of the process of evolution have to be met in order for the method to be useful […]. If a method is only useful when certain conditions of the evolutionary process are met, I would think that these conditions might as well be thought of as assumptions.”

(Andrew J. Roger, 08/01/96, sci.bio.systematics)

ProcessProcess

“I have a pretty good idea of how evolution works, thus I can check how my data fit these ideas.”

“Given the phylogeny, what is the probability to find the data as I did ?”

Model = Statistical Framework Maximum likelihood

Assumptions - 2Assumptions - 2

“The philosophical part that deserves more explanation is how you get from whatever general principles you invoke (‘parsimony’) to the specific numerical method used.”

“Compatibility methods represent discarding a character because it has some sign of conflict with others. If there are two kinds of characters, really horribly noisy and pretty clean, that is a sensible thing to do. If there are instead two kinds, pretty clean and a little noisy, it is not. So I do not see how the principle of parsimony decides in advance which of these situations we are facing.”

(Joe Felsenstein, 14/12/95, sci.bio.systematics)

DataData

“My data will tell me what the optimal set of branching events is and from there I will try to grasp what actually could have happened.” Parsimony Group / Component

Compatibility Character Compatibility

ObservationsObservations

Molecular data DNA sequences:

• nuclear, mitochondrial, ribosomal DNA-DNA hybridization Restriction-site and -fragment Allelic isozymes

Morphological data Anatomical data Chemical data

Principles - 1

Black Boxes ?Black Boxes ?

Observations

Methods

Assumptions

PhylogeneticTrees

Cladogram(s)

Assumptions

Optimality