Introduction toMolecular Evolution

Mike ThomasOctober 3, 2002

What we can learn from multiple sequence alignments

• An alignment is a hypothesis about the relatedness of a set of genes

• This information can be used to reconstruct the evolutionary history of those genes

• The history of the genes can provide us with information about the structure and function, and significance of a gene or family of genes

• We can also use the reconstructed history to test hypotheses about evolution itself:– Rates of change

– The degree of change

– Implications of change, etc

• We can then pose and test hypotheses about the evolution of phenomena unrelated to the genes– Evolution of flight in insects

– Evolution of humans

– Evolution of disease

Assumptions made by phylogenetic methods:

• The sequences are correct

• The sequence are homologous

• Each position is homologous

• The sampling of taxa or genes is sufficient to resolve the problem of interest

• Sequence variation is representative of the broader group of interest

• Sequence variation contains sufficient phylogenetic signal (as opposed to noise) to resolve the problem of intereest

• Each position in the sequence evolved independently

How do you extract this information from an alignment?

Haeckel’s Tree of Life

“Higher” organisms

“Lower” organisms

Answer: a tree

A phylogenetic tree is a hierarchical, graphical representation of relationships

Other Ways to Represent Phylogenies

(a) Cladogram showing the phylogenetic relationships between four species.

(b) Relationships of the same four species represented as a set of nested parentheses.

(c) Evolutionary relationships of the same four species with nine synapomorphies (shared, derived characters) plotted on the branches.

Using Phylogeny to Understand Gene Duplication

and Loss

A. A gene tree.B. The gene tree superimposed on a species tree,

allowing identification of the duplication and loss events.

Problems with Phylogenetic Inference

1. How do we know what the potential candidate trees are?

2. How do we choose which tree is (most likely) the true tree?

Number of Possible Trees

Number of taxa or genes

Number of possible rooted trees

3 3

4 15

5 105

7 10,395

B A C

A B C

C B A

Recipe for reconstructing a phylogeny

1. Select an optimality criterion2. Select a search strategy3. Use the selected search

strategy to generate a series of trees, and apply the selected optimality criterion to each tree, always keeping track of the “best” tree examined thus far

Search strategy: Which is the right tree?

• When m is the number of taxa, the number of possible trees is:– [(2m-3)!]/[2m-2(m-2)!]

– For 10 taxa, the number of trees is 34,459,425

• Many trees can be discarded because they are obviously wrong

• Sometimes, there is a general or even specific grouping that can serve as a start for the tree search

• There are a number of approaches to tree searches that can be used

Search Strategies

Strategy Type• Stepwise addition Algorithmic• Star decomposition Algorithmic• Exhaustive Exact• Branch & bound Exact• Branch swapping Heuristic• Genetic algorithm Heuristic• Markov Chain Monte Carlo heuristic

But, we still need to evaluate the trees in order to identify the one most likely to be the true tree

Choose an optimality criterion to evaluate trees

Commonalities can be found, but how can these be used to evaluate a tree?

General differences between optimality criteria

Minimum evolution

Maximum Parsimony

Maximum Likelihood

Model based “Model free” Model based

Can account for many types of sequence substitutions

Assumes that all substitutions are equal

Can account for many types of sequence substitutions

Works well with strong or weak sequence similarity

Works only when sequence similarity is high

Works well with strong or weak sequence similarity

Computationally fast Computationally fast Computationally slow

Well understood statistical properties (easy to test)

Poorly understood statistical properties (hard to test)

Well understood statistical properties (easy to test)

Can accurately estimate branch lengths (important for molecular clocks)

Cannot estimate branch lengths accurately

Can estimate branch lengths with some degree of accuracy

Maximum Parsimony

1. The parsimony score is the minimum number of required changes, or steps

2. Only shared, derived characters are used

3. The score for each character (site) is called the character score

4. Site lengths added over all sites is the tree length

5. The tree (out of all examined trees) with the lowest tree length is the most parsimonious tree… and most likely to be the true tree

Example: Maximum Parsimony

4 toes

20 teeth

10 ribs, 5 toes, round lobes, long legs

oval lobes, 16 teeth, 25 verts,8 ribs, 3 toes, short legs

XFHG

4 toes, short legs, 8 ribs, 16 teeth, oval lobes

20 teeth, 5 toes, 10 ribs, round lobes, long legs

3 toes, round lobes

round lobes, 20 teeth, 25 verts,10 ribs, 5 toes, long legs

FGHX

1

4

1

Tree length: 6 steps

5

2

5

Tree length: 12 steps

Simple example of parsimony with sequence data

Another example with nucleotide data

(a) Alignment of four hypothetical DNA sequences.

(b) Most parsimonious rooted cladogram for this alignment.

(c) Corresponding unrooted cladogram.

Issues & problems with parsimony

• Multiple trees may be the most parsimonious (have the same tree length)– A consensus tree can be constructed to visualize

the congruity & discontinuity between these

• Branch lengths (and, therefore, rates of change) cannot be accurately estimated

• No explicit model of change is used, even when one might be well supported– The most parsimonious tree(s) may not be the

true tree

Minimum Evolution (Distance)

1. All data are used, even though some may not be shared, derived characters

2. The branch lengths represent distance between a taxon and an ancestor, given an assumed model of evolution

3. The pairwise distances are calculated for each pair of taxa, given an assumed model of evolution

4. The tree length is the sum of branch length across a tree

5. The tree (out of all examined trees) with the lowest tree length is the minimum evolution tree… and most likely to be the true tree

The tree is different than a parsimony tree

(a) Hypothetical evolutionary relationships between three DNA sequences, in which the horizontal branch lengths are proportional to the number of character-state changes along the branches.

(b) Topology of the parsimonious cladogram that would be constructed from the sequence similarities produced by such an evolutionary history if multiple substitutions had occurred at several sites.

Factors that Affect Phylogenetic Inference

1. Relative base frequencies (A,G,T,C)2. Transition/transversion ratio3. Number of substitutions per site4. Number of nucleotides (or amino acids) in sequence5. Different rates in different parts of the molecule6. Synonymous/non-synonymous substitution ratio7. Substitutions that are uninformative or obfuscatory

1. Parallel substitutions2. Convergent substitutions3. Back substitutions4. Coincidental substitutions

In general, the more factors that are accounted for by the model (i.e., more parameters), the larger the error of estimation. It is often best to use fewer parameters by choosing the simpler model.

Models of evolution: choosing parameters

Some distance models: p-distance

• p = nd/n, where n is the number of sites (nucleotides or amino acids), and nd is the number of differences between the two sequences examined.• Very robust when divergence times are recent and the affect of complicating phenomena is minor

Some distance models: Jukes-Cantor

• Used to estimate the number of substitutions per site

• The expected number of substitutions per site is:

• d = 3αt = -(3/4)ln[1-(4/3)p], where p is the proportion of difference between 2 sequences

• Variance can be calculated• No assumptions are made about

nucleotide frequencies, or differential substitution rates

A T C G

ATCG

-ααα

α-αα

αα-α

ααα-

Some distance models: Kimura two-parameter

• Used to estimate the number of substitutions per site

• d = 2rt, where r is the substitution rate (per site, per year) and t is the generation time; r = α + 2β, so:

• d = 2αt + 4βt• Accounts for different transition

and transversion rates• No assumptions are made about

nucleotide frequencies, variance is greater than Jukes-Cantor

C T

A G

Pyrimidines

Purines

= transition rate = transversion rateThese are treated the same for long divergence times.

Other models

• Hasegawa, Kishino, Yano (HKY): corrects for unequal nucleotide frequencies and transition/ transversion bias into account

• Unrestricted model: allows different rates between all pairs of nucleotides

• General Time Reversible model: allows different rates between all pairs of nucleotides and corrects for unequal nucleotide frequencies

• Many other models have been invented to correct for specific problems

• The more parameters are introduced, the larger the variance becomes

Ways to build trees with distance models: ME

• Minimum Evolution (ME) trees can be found by exhaustive searches or heuristic searches (starting with a reasonable tree or eliminating unlikely possible trees)

• For each tree examined, the total tree length is calculated as the sum of branch lengths calculated using a given model

• ME, like Maximum Parsimony, may generate a number of equal-scoring ME trees and may not actually result in the true tree Many other models have been invented to correct for specific problems

Ways to build trees with distance models: UPGMA

• UPGMA (unweighted pair-group method using arithmetic averages)

• Generally accurate for molecular evolution when substitution rates are relatively constant, but this can rarely be assumed to be true

• Method:– distances for each pair of taxa are computed using the

chosen distance method– The pair with the smallest value d are combined into a

single, composite taxon– The distances from this composite taxon to all other taxa

are computed– The next pair with the smallest d is chosen (including

consideration of pairings with the composite taxon)

Ways to build trees with distance models: Neighbor Joining

• Neighbor Joining (NJ) is a very robust method that is accurate even when substitution rates are not constant, and generally recovers the ME tree (although this is not always the case)

• Method:– We construct a “star” tree and compute the sum of all branches, SO

(this will be greater than the sum of all branches for the final tree, SF)

– We then pick a pair of taxa to be “neighbors”, (say, taxa 1 & 2) and compute the sum of all branches, S1,2

– All other pairs of taxa are then placed as neighbors and the sum of all branches computed

– The neighbors whose pairing results in the greatest reduction in the sum of all branches will be kept

– Then, another round of neighbor joining is conducted, including using the neighbor pair retained in the first round

Example: The evolution of flight in stoneflies

Scale, in substitutions/site

Defined outgroup taxa

•Reconstruction of the Plectoptera order (stoneflies) from 18S rRNA sequence•Kimura 2-parameter distance used•Tree rooted with known outgroup species•Neighbor-Joining tree building method used to construct first tree; tree search was conducted to ensure that the NJ was also the ME tree•Characters related to flight were then mapped onto the tree

Maximum Likelihood

1. The site likelihoods represent probability of data for one site given an assumed model of evolution

2. Overall likelihood is the product of the site likelihoods

3. Trees are evaluated by comparing log-likelihood scores

4. Likelihood scores are comparable across models as well as trees, so it provides a way of testing the goodness of fit of a model

5. The tree (out of all examined trees) with the lowest tree length is the maximum likelihood tree… and most likely to be the true tree

Next Tuesday:

1. Examples of phylogenetic reconstructions2. Uses of phylogenetic trees3. Other research using molecular evolution

Next Thursday: exam 1

All material through next Tuesday (10/8) will be covered by the exam