Evolutionary Distances

Two ways that data is related to trees

1. Distance based approaches

2. Character based approaches

Both rely on optimality criterion

Distance Based Approached

• convert sequence data into a numerical measure of evolutionary measure

• construct a distance matrix

• use this matrix to build a tree

Character Based approaches

• use multiple sequence alignment directly

• evaluate each site (character)

Evolutionary Distance

a numerical estimate of evolutionary change

increases with dissimilarity

often correlates with time since divergence

represented as branch lengths or patristic distanced

Pairwise

an estimate

p-distance

proportion of sites at which two sequences differ

Features:

• normalised per site

• based on only observed differences in extant sequences

Multiple Hits

• more than one substitution can occur at the same site

• can occur in one lineage and both lineages

• substitutions may be superimpoed

Consequences of multiple Hits

• underestimation of evolutionary distance

• incorrect rate estimates

• increased homoplasy

Homoplasy

fixation of identical by state alleles in different lineages with independent mutational origins

can mislead phylogenetic inference by grouping taxa based on similarity rather than ancestry

When does saturation occur

most sites have undergone one or more substitutions

additional substitutions are no longer detectable

Effects of saturation

• sequences appear randomly scrambled

• alignment becomes unreliable or impossible

• correction for multiple hits becomes infeasible

• phylogenetic signal is lost

Procedure for Distance Matrix

1. Calculate pairwise distances between all sequences

2. Construct a tree from the distance matrix

What does this mean if distances are additive?

• each distance equals the sum of branch lengths connecting taxa

• the matrix perfectly summarises patristic distances

How do we address correcting multiple hits?

• estimate the number of unobserved substitutions

• attempt to recover the true revolutionary distance

Why is correction uncertain?

• we only observe end points

• we lack direct knowledge of intermediate events

Assumptions of Jukes-Cantor Model

• four nucleotides occur at equal frequency

• all substitution equally likely

• constant rate over time

• only substitutions considered (no indels)

How is the JC69 model constrained?

• each row sums to zero

• total number of character states remains constant

When is JC model good?

• when sequences are highly similar

• few substitutions have occurred

5 main approaches to phylogenetic inheritance

1. Distance methods

2. Maximum parsimony

3. Maximum likelihood

4. Bayesian inference

5. Hybrid appraoches

UPGMA

• assumes a molecular clock

• almost always inappropiate

• explicitly discouraged

Neighbour Joining

• does not assume equal rates

• efficient and widely used

• uses distance matrix to minimise total tree length