Class 9: Phylogenetic Trees


Andrés Aravena

December 14, 2024

We know sequences today.
We want to know how they come to be

Let’s think about bacteria

If an organism X evolves into two new organisms A and B, both new organisms share something in common

If we had a time machine…

We would see evolution like this

But we do not have a time machine

So we only see the modern organisms

The question is

How to reconstruct the original tree, given the modern sequences?

How evolution works

See it working

in YouTube

How evolution works

  • Random mutations
  • Selection
  • Competition for the environment
    • Bottleneck effect
  • Coevolution

Random mutations

DNA replication is not 100% perfect

Mutations can be

  • Substitutions
  • Insertions
  • Deletions
  • Reorganizations


  • Not all mutations are “accepted”

  • Probably most mutations are lethal

  • We only see mutations that keeps the organism alive

    • Some mutations can give an advantage

    • Other mutations are neutral


  • In the short term, all viable organisms are alive

  • In the long term, and when resources are scarce, some organisms do not survive

  • For example, some organisms may be more efficient in capturing food or using energy

    • Some organisms have higher “fitness”
  • If the environment changes, the “fitness” changes

    • There may be bottleneck effects


  • Evolution is more complex for sexual organisms

  • Some individuals do not pass their genes to the next generation, due to mate-selection

  • Mate-selection also evolves

  • We say that phenotype and peer-selection co-evolve

Coevolution between predator and prey

  • “Every morning in Africa, a gazelle wakes up, it knows it must run faster than the fastest lion or it will be killed.

  • “Every morning in Africa, a lion wakes up, it knows it must run faster than the slowest gazelle, or it will starve.

  • “It doesn’t matter whether you’re the lion or a gazelle-when the sun comes up, you’d better be running.”

Molecular evolution

Looking at only one gene

For this class we will consider the 16S gene in bacteria

  • Approx. 1500 nucleotides
  • Highly conserved
    • Most mutations are lethal
    • Cell viability depends on 16S structure
  • Asexual reproduction

Unrooted trees

Looking only at the modern data, we cannot know which sequence existed before

That is, we cannot put an arrow between two nodes

We put a link, undirected, between nodes

These trees are called unrooted

Outgroups point to the root

Since we only see leaves, we cannot put arrows

So we cannot tell which internal node is the root

But, if we include a leave that we know is very distant from all the others, then we can find the root.

Illustration: Unrooted tree

Illustration: Unrooted tree with outgroup

Illustration: Rooted tree

Essence of a tree

The same tree can be drawn in several ways

The drawing is not important

The only important things are

  • The tree topology. That is, who is connected to who

  • The length of each arc (or edge)

Reconstructing the tree

There are basically three approaches

  • Maximum parsimony
    • smallest tree that explains all mutations
  • Maximum likelihood
    • most probable tree, using a probabilistic model
  • Distance based
    • forget the sequences, use only their distances

In all cases the input is a multiple alignment of all sequences

Maximum parsimony

If we know the tree topology, we can count how many mutations are needed to match our data

Based on Bininda-Emonds et al (1998) “Properties of Matrix Representation with Parsimony Analyses”. Systematic Biology, 47(3), 497–508.

So we just have to test all trees and see which is the best one

There are too many trees

But the number of trees is HUGE


So the search has to be done with heuristics

Other problem with parsimony methods

  • In some simulations the predicted tree may be very different from the real one

    • We only know “the real tree” when we create it
  • It can be statistically inconsistent

    • That is, adding more sequences sometimes makes a worse tree

Maximum likelihood

An alternative is to find the most probable tree, given the available data

This method needs:

  • A probabilistic model of evolution
  • Looking at all the trees

So, again, we need an heuristic

Distance methods

We already discussed them


  • Neighbor Joining

Here we use the Hamming or Levenstein distance between sequences after Multiple sequence alignment

Distance and time

Hamming Distance is not time

Mutation rate is not proportional to time

Multiple substitutions of the same base cannot be observed


So we underestimate the divergence time

Max DNA mutation ≈ 75%

Substitution model

There are different models to find time given distance

The simplest one is Jukes-Cantor (1969)

Kimura (1980)

Tamura (1992)

Real v/s observed mutations

According to the Jukes Cantor model

\[R = -\frac{3}{4}\ln\left(1-\frac{4}{3}D/L\right)\]

Here \(D/L\) is the percentage of sites with different nucleotides
(Hamming Distance over Length)

\(R\) is the expected number of mutations that really happened

In summary

It is hard to build time machines, and we only get an approximate answer