1. Introduction to Molecular Evolution
Mike Thomas
October 3, 2002

2. 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

3. 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

4. How do you extract this information from an alignment?

5. Answer: a tree Haeckel’s Tree of Life
“Higher” organisms
Haeckel’s Tree of Life
“Lower” organisms
A phylogenetic tree is a hierarchical, graphical representation of relationships

6. Other Ways to Represent Phylogenies
Cladogram showing the phylogenetic relationships between four species.
Relationships of the same four species represented as a set of nested parentheses.
Evolutionary relationships of the same four species with nine synapomorphies (shared, derived characters) plotted on the branches.

7. Using Phylogeny to Understand Gene Duplication and Loss
A gene tree.
The gene tree superimposed on a species tree, allowing identification of the duplication and loss events.

8. Problems with Phylogenetic Inference
How do we know what the potential candidate trees are?
How do we choose which tree is (most likely) the true tree?

9. Number of Possible Trees
Number of taxa or genes
Number of possible rooted trees 3 4 15 5
105 7
10,395 A B C B A C C B A

10. Recipe for reconstructing a phylogeny
Select an optimality criterion
Select a search strategy
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

11. 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

12. Search Strategies Strategy Type Stepwise addition Algorithmic
Star decomposition
Exhaustive
Exact
Branch & bound
Branch swapping
Heuristic
Genetic algorithm
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

13. Choose an optimality criterion to evaluate trees
Commonalities can be found, but how can these be used to evaluate a tree?

14. General differences between optimality criteria Minimum evolution
Maximum Parsimony
Maximum Likelihood
Model based
“Model free”
Can account for many types of sequence substitutions
Assumes that all substitutions are equal
Works well with strong or weak sequence similarity
Works only when sequence similarity is high
Computationally fast
Computationally slow
Well understood statistical properties (easy to test)
Poorly understood statistical properties (hard 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

15. Maximum Parsimony
The parsimony score is the minimum number of required changes, or steps
Only shared, derived characters are used
The score for each character (site) is called the character score
Site lengths added over all sites is the tree length
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

16. Example: Maximum Parsimony
Tree length: 6 steps
Tree length: 12 steps X H G G H F F X 5 1
20 teeth, 5 toes, 10 ribs, round lobes, long legs 2 4
20 teeth 1 5
3 toes, round lobes
10 ribs, 5 toes,
round lobes, long legs
4 toes, short legs, 8 ribs, 16 teeth, oval lobes
4 toes
round lobes, 20 teeth, 25 verts,
10 ribs, 5 toes, long legs
oval lobes, 16 teeth, 25 verts,
8 ribs, 3 toes, short legs

17. Simple example of parsimony with sequence data

18. Another example with nucleotide data
Alignment of four hypothetical DNA sequences.
Most parsimonious rooted cladogram for this alignment.
Corresponding unrooted cladogram.

19. 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

20. Minimum Evolution (Distance)
All data are used, even though some may not be shared, derived characters
The branch lengths represent distance between a taxon and an ancestor, given an assumed model of evolution
The pairwise distances are calculated for each pair of taxa, given an assumed model of evolution
The tree length is the sum of branch length across a tree
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

21. The tree is different than a parsimony tree
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.
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.

22. Models of evolution: choosing parameters
Factors that Affect Phylogenetic Inference
Relative base frequencies (A,G,T,C)
Transition/transversion ratio
Number of substitutions per site
Number of nucleotides (or amino acids) in sequence
Different rates in different parts of the molecule
Synonymous/non-synonymous substitution ratio
Substitutions that are uninformative or obfuscatory
Parallel substitutions
Convergent substitutions
Back substitutions
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.

23. 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

24. 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 A T C G - α -α

25. 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 rate
These are treated the same for long divergence times.

26. 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

27. 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

28. 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)

29. 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

30. Example: The evolution of flight in stoneflies
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
Defined outgroup taxa
Scale, in substitutions/site

31. Maximum Likelihood
The site likelihoods represent probability of data for one site given an assumed model of evolution
Overall likelihood is the product of the site likelihoods
Trees are evaluated by comparing log-likelihood scores
Likelihood scores are comparable across models as well as trees, so it provides a way of testing the goodness of fit of a model
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

32. All material through next Tuesday (10/8) will be covered by the exam
Examples of phylogenetic reconstructions
Uses of phylogenetic trees
Other research using molecular evolution
Next Thursday: exam 1
All material through next Tuesday (10/8) will be covered by the exam