. Class 9: Phylogenetic Trees

The Tree of Life D’après Ernst Haeckel, 1891

Evolution u Many theories of evolution u Basic idea: l speciation events lead to creation of different species l Speciation caused by physical separation into groups where different genetic variants become dominant u Any two species share a (possibly distant) common ancestor

Phylogenies u A phylogeny is a tree that describes the sequence of speciation events that lead to the forming of a set of current day species u Leafs - current day species u Nodes - hypothetical most recent common ancestors u Edges length - “time” from one speciation to the next AardvarkBisonChimpDogElephant

Phylogenetic Tree u Topology: bifurcating Leaves - 1…N Internal nodes N+1…2N-2 leaf branch internal node

Example: Primate evolution mya mya mya

How to construct a Phylogeny? u Until mid 1950’s phylogenies were constructed by experts based on their opinion (subjective criteria) u Since then, focus on objective criteria for constructing phylogenetic trees l Thousands of articles in the last decades u Important for many aspects of biology l Classification (systematics) l Understanding biological mechanisms

Morphological vs. Molecular u Classical phylogenetic analysis: morphological features l number of legs, lengths of legs, etc. u Modern biological methods allow to use molecular features l Gene sequences l Protein sequences u Analysis based on homologous sequences (e.g., globins) in different species

Dangers in Molecular Phylogenies u We have to remember that gene/protein sequence can be homologous for different reasons: u Orthologs -- sequences diverged after a speciation event u Paralogs -- sequences diverged after a duplication event u Xenologs -- sequences diverged after a horizontal transfer (e.g., by virus)

Dangers of Paralogues Speciation events Gene Duplication 1A 2A 3A3B 2B1B

Dangers of Paralogs Speciation events Gene Duplication 1A 2A 3A3B 2B1B u If we only consider 1A, 2B, and 3A...

Types of Trees u A natural model to consider is that of rooted trees Common Ancestor

Types of Trees u Depending on the model, data from current day species does not distinguish between different placements of the root vs

Types of trees u Unrooted tree represents the same phylogeny with out the root node

Positioning Roots in Unrooted Trees u We can estimate the position of the root by introducing an outgroup: l a set of species that are definitely distant from all the species of interest AardvarkBisonChimpDogElephant Falcon Proposed root

Types of Data u Distance-based l Input is a matrix of distances between species l Can be fraction of residues they disagree on, or -alignment score between them, or … u Character-based l Examine each character (e.g., residue) separately

Simple Distance-Based Method Input: distance matrix between species Outline: u Cluster species together u Initially clusters are singletons u At each iteration combine two “closest” clusters to get a new one

UPGMA Clustering  Let C i and C j be clusters, define distance between them to be  When combining two clusters, C i and C j, to form a new cluster C k, then

Molecular Clock u UPGMA implicitly assumes that all distances measure time in the same way

Additivity u A weaker requirement is additivity l In “real” tree, distances between species are the sum of distances between intermediate nodes a b c i j k

Consequences of Additivity u Suppose input distances are additive u For any three leaves u Thus a b c i j k m

u Can we use this fact to construct trees? u Let where Theorem: if D(i,j) is minimal (among all pairs of leaves), then i and j are neighbors in the tree Neighbor Joining

 Set L to contain all leaves Iteration:  Choose i,j such that D(i,j) is minimal  Create new node k, and set  remove i,j from L, and add k Terminate: when |L| =2, connect two remaining nodes Neighbor Joining i j m k

Distance Based Methods u If we make strong assumptions on distances, we can reconstruct trees u In real-life distances are not additive u Sometimes they are close to additive