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Introduction to Biostatistics and Bioinformatics

Phylogenetics

This Lecture

Learning Objectives

• Molecular Evolution • Calculating Distances • Clustering Algorithms • Cladistic Methods • Computer Software

• The theory of evolution is the foundation upon which all of modern biology is built.

Evolution

• From anatomy to behavior to genomics, the scientific method requires an appreciation of changes in organisms over time.

• It is impossible to evaluate relationships among gene sequences without taking into consideration the way these sequences have been modified over time

Nothing in biology makes sense except in the light of evolution.– Theodosius Dobzhansky, 1973

Similarity searches and multiple alignments of sequences naturally lead to

the question:

“How are these sequences related?”

and more generally:

“How are the organisms from which these sequences come related?”

Relationships

The purpose of a phylogenetic tree is to illustrate how a group of objects (usually genes or organisms) are related to one another

Taxonomy

• The study of the relationships between groups of organisms is called taxonomy, an ancient and venerable branch of classical biology.

• Taxonomy is the art of classifying things into groups — a quintessential human behavior — established as a mainstream scientific field by Carolus Linnaeus (1707-1778).

Phylogenetics• Evolutionary theory states that groups of similar

organisms are descended from a common ancestor.

• Phylogenetic systematics (cladistics) is a method of taxonomic classification based on their evolutionary history.

• It was developed by Willi Hennig, a German entomologist, in 1950.

Cladistics and Phenetics

• Cladistic approach: Trees are drawn based on the conserved characters

• Phenetic approach: Trees are based on some measure of distance between the leaves

• Molecular phylogenies are inferred from molecular (usually sequence) data– either cladistic (e.g. gene order) or phenetic

Cladistic Methods

• Evolutionary relationships are documented by creating a branching structure, termed a phylogeny or tree, that illustrates the relationships between the sequences.

• Cladistic methods construct a tree (cladogram) by considering the various possible pathways of evolution and choose from among these the best possible tree.

• A phylogram is a tree with branches that are proportional to evolutionary distances.

Classes of algorithm used to infer phylogeny from sequence

• Distance methods• Parsimony• Likelihood• Probabilistic methods

Molecular Evolution

• Phylogenetics often makes use of numerical data, (numerical taxonomy) which can be scores for various “character states” such as the size of a visible structure or it can be DNA sequences.

• Similarities and differences between organisms can be coded as a set of characters, each with two or more alternative character states.

• In an alignment of DNA sequences, each position is a separate character, with four possible character states, the four nucleotides.

DNA is a good tool for taxonomyDNA sequences have many advantages over classical types of taxonomic characters: – Character states can be scored

unambiguously – Large numbers of characters can be scored

for each individual – Information on both the extent and the

nature of divergence between sequences is available (nucleotide substitutions, insertion/deletions, or genome rearrangements)

A aat tcg ctt cta gga atc tgc cta atc ctg B ... ..a ..g ..a .t. ... ... t.. ... ..a C ... ..a ..c ..c ... ..t ... ... ... t.a D ... ..a ..a ..g ..g ..t ... t.t ..t t..

Each nucleotide difference is a character

• After working with sequences for a while, one develops an intuitive understanding that for a given gene, closely related organisms have similar sequences and more distantly related organisms have more dissimilar sequences. These differences can be quantified.

• Given a set of gene sequences, it should be possible to reconstruct the evolutionary relationships among genes and among organisms.

Sequences Reflect Relationships

What Sequences to Study?• Different sequences accumulate changes at

different rates - chose level of variation that is appropriate to the group of organisms being studied.– Proteins (or protein coding DNAs) are constrained by

natural selection - better for very distant relationships– Some sequences are highly variable (rRNA spacer

regions, immunoglobulin genes), while others are highly conserved (actin, rRNA coding regions)

– Different regions within a single gene can evolve at different rates (conserved vs. variable domains)

Orthologs vs. Paralogs• When comparing gene sequences, it is important

to distinguish between identical vs. merely similar genes in different organisms.

• Orthologs are homologous genes in different species with analogous functions.

• Paralogs are similar genes that are the result of a gene duplication.– A phylogeny that includes both orthologs and paralogs

is likely to be incorrect.– Sometimes phylogenetic analysis is the best way to

determine if a new gene is an ortholog or paralog to other known genes.

A

A B

A2 B2A1 B1

Duplication

Speciation

(globin)

(hemoglobin) (myoglobin)

(mouse) (human)

Ancestral gene

Disclaimers

Before describing any theoretical or practical aspects of phylogenetics, it is necessary to give some disclaimers. This area of computational biology is an intellectual minefield!¨ Neither the theory nor the practical applications of

any algorithms are universally accepted throughout the scientific community.

¨ The application of different software packages to a data set is very likely to give different answers; minor changes to a data set are also likely to profoundly change the result.

A modern revision of the seals and sea lions

Genes vs. Species

• Relationships calculated from sequence data represent the relationships between genes, this is not necessarily the same as relationships between species.

• Your sequence data may not have the same phylogenetic history as the species from which they were isolated

• Different genes evolve at different speeds, and there is always the possibility of horizontal gene transfer (hybridization, vector mediated DNA movement, or direct uptake of DNA).

Cladistic vs. Phenetic

Within the field of taxonomy there are two different methods and philosophies of building phylogenetic trees: cladistic and phenetic

– Phenetic methods construct trees (phenograms) by considering the current states of characters without regard to the evolutionary history that brought the species to their current phenotypes.

– Cladistic methods rely on assumptions about ancestral relationships as well as on current data.

Darwin was a Cladist

“The natural system based on descent with modification … the characters that naturalists consider as showing true affinity are those which have been inherited from a common parent, and in so far as all true classification is genealogical; that community of descent is the common bond that naturalists have been seeking.”

- Charles Darwin, Origin of Species, 1859

Phenetic Methods

• Computer algorithms based on the phenetic model rely on Distance Methods to build of trees from sequence data.

• Phenetic methods count each base of sequence difference equally, so a single event that creates a large change in sequence (insertion/deletion or recombination) will move

two sequences far apart on the final tree. • Phenetic approaches generally lead to faster algorithms and

they often have nicer statistical properties for molecular data.• The phenetic approach is popular with molecular

evolutionists because it relies heavily on objective character data (such as sequences) and it requires relatively few assumptions.

Distances Measurements

• It is often useful to measure the genetic distance between two species, between two populations, or even between two individuals.

• The entire concept of numerical taxonomy is based on computing phylogenies from a table of distances.

• In the case of sequence data, pairwise distances must be calculated between all sequences that will be used to build the tree - thus creating a distance matrix.

• Distance methods give a single measurement of the amount of evolutionary change between two sequences since divergence from a common ancestor.

Distance methodsCalculate the distance CORRECTING FOR MULTIPLE HITS

The Distance Matrix 7 Rat Mouse Rabbit Human Opossum Chicken Frog

Rat 0.0000 0.0646 0.1434 0.1456 0.3213 0.3213 0.7018Mouse 0.0646 0.0000 0.1716 0.1743 0.3253 0.3743 0.7673Rabbit 0.1434 0.1716 0.0000 0.0649 0.3582 0.3385 0.7522Human 0.1456 0.1743 0.0649 0.0000 0.3299 0.2915 0.7116Oppossum 0.3213 0.3253 0.3582 0.3299 0.0000 0.3279 0.6653Chicken 0.3213 0.3743 0.3385 0.2915 0.3279 0.0000 0.5721Frog 0.7018 0.7673 0.7522 0.7116 0.6653 0.5721 0.0000

Computing a Distance MatrixReading sequences... gtr1_human: 548 total, 548 read gtr2_human: 548 total, 548 read gtr3_human: 548 total, 548 read gtr4_human: 548 total, 548 read gtr5_human: 548 total, 548 read

Computing distances using Kimura method... 1 x 2: 48.61 1 x 3: 45.50 1 x 4: 65.74 1 x 5: 107.70 2 x 3: 61.53 2 x 4: 74.57 2 x 5: 113.82 3 x 4: 68.93 3 x 5: 104.43 4 x 5: 110.86

Matrix 1 1 2 3 4 5 ____________________________________________________________ .. | 1 | 0.00 48.61 45.50 65.74 107.70 | 2 | 0.00 61.53 74.57 113.82 | 3 | 0.00 68.93 104.43 | 4 | 0.00 110.86 | 5 | 0.00

DNA Distances

• Distances between pairs of DNA sequences are relatively simple to compute as the sum of all base pair differences between the two sequences. – this type of algorithm can only work for pairs of sequences that are

similar enough to be aligned

• Generally all base changes are considered equal• Insertion/deletions are generally given a larger weight than

replacements (gap penalties).• It is also possible to correct for multiple substitutions at a

single site, which is common in distant relationships and for rapidly evolving sites.

Correction for multiple hits• Only differences can be observed directly – not distances• All distance methods rely (crucially) on this• A great many models used for nucleotide sequences (e.g.

JC, K2P, HKY, Rev, Maximum Likelihood)• aa sequences are infinitely more complicated!• Can take account of different rates of evolution at sites

(e.g. gamma distribution)• Accuracy falls off drastically for highly divergent

sequences

Amino Acid Distances• Distances between amino acid sequences are a bit more

complicated to calculate. • Some amino acids can replace one another with relatively little

effect on the structure and function of the final protein while other replacements can be functionally devastating.

• From the standpoint of the genetic code, some amino acid changes can be made by a single DNA mutation while others require two or even three changes in the DNA sequence.

• In practice, what has been done is to calculate tables of frequencies of all amino acid replacements within families of related protein sequences in the databanks: i.e. PAM and BLOSSUM

The PAM 250 scoring matrix A R N D C Q E G H I L K M F P S T W Y VA 2R -2 6N 0 0 2 D 0 -1 2 4

C -2 -4 4 -5 4 Q 0 1 1 2 -5 4 E 0 -1 1 3 -5 2 4 G 1 -3 0 1 -3 -1 0 5 H -1 2 2 1 -3 3 1 -2 6 I -1 -2 -2 -2 -2 -2 -2 -3 -2 5 L -2 -3 -3 -4 -6 -2 -3 -4 -2 2 6 K -1 3 1 0 -5 1 0 -2 0 -2 -3 5 M -1 0 -2 -3 -5 -1 -2 -3 -2 2 4 0 6 F -4 -4 -4 -6 -4 -5 -5 -5 -2 1 2 -5 0 9 P 1 0 -1 -1 -3 0 -1 -1 0 -2 -3 -1 -2 -5 6 S 1 0 1 0 0 -1 0 1 -1 -1 -3 0 -2 -3 1 3 T 1 -1 0 0 -2 -1 0 0 -1 0 -2 0 -1 -2 0 1 3 W -6 2 -4 -7 -8 -5 -7 -7 -3 -5 -2 -3 -4 0 -6 -2 -5 17 Y -3 -4 -2 -4 0 -4 -4 -5 0 -1 -1 -4 -2 7 -5 -3 -3 0 10 V 0 -2 -2 -2 -2 -2 -2 -1 -2 4 2 -2 2 -1 -1 -1 0 -6 -2 4

Dayhoff, M, Schwartz, RM, Orcutt, BC (1978) A model of evolutionary change in proteins. in Atlas of Protein Sequence and Structure, vol 5, sup. 3, pp 345-352. M. Dayhoff ed., National Biomedical Research Foundation, Silver Spring, MD.

Clustering Algorithms

Clustering algorithms use distances to calculate phylogenetic trees. These trees are based solely on the relative numbers of similarities and differences

between a set of sequences. – Start with a matrix of pairwise distances

– Cluster methods construct a tree by linking the least distant pairs of taxa, followed by successively more distant taxa.

Minimum Evolution

• The total length of all branches in the tree should be a minimum

• It has been shown that the minimum evolution tree is expected to be the true tree provided branch lengths are corrected for multiple hits

UPGMA

• The simplest of the distance methods is the UPGMA (Unweighted Pair Group Method using Arithmetic averages)

• The PHYLIP programs DNADIST and PROTDIST calculate absolute pairwise distances between a group of sequences. Then the GCG program GROWTREE uses UPGMA to build a tree.

• Many multiple alignment programs such as PILEUP use a variant of UPGMA to create a dendrogram of DNA sequences which is then used to guide the multiple alignment algorithm.

Neighbor Joining

• The Neighbor Joining method is the most popular way to build trees from distance measurements

(Saitou and Nei 1987, Mol. Biol. Evol. 4:406) – Neighbor Joining corrects the UPGMA method for its (frequently

invalid) assumption that the same rate of evolution applies to each

branch of a tree. – The distance matrix is adjusted for differences in the rate of

evolution of each taxon (branch).

– Neighbor Joining has given the best results in simulation studies and it is the most computationally efficient of the distance algorithms (N. Saitou and T. Imanishi, Mol. Biol. Evol. 6:514 (1989)

Neighbour Joining

87

6

54

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8

7

6

5

23

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1

Cladistic Methods

• For character data about the physical traits of organisms (such as morphology of organs etc.) and for deeper levels of taxonomy, the cladistic approach is almost certainly superior.

• Cladistic methods are often difficult to implement with molecular data because all of the assumptions are generally not satisfied.

Cladistic methods

• Cladistic methods are based on the assumption that a set of sequences evolved from a common ancestor by a process of mutation and selection without mixing (hybridization or other horizontal gene transfers).

• These methods work best if a specific tree, or at least an ancestral sequence, is already known so that comparisons can be made between a finite number of alternate trees rather than calculating all possible trees for a given set of sequences.

Parsimony

• Parsimony is the most popular method for reconstructing ancestral relationships.

• Parsimony allows the use of all known evolutionary information in building a tree

– In contrast, distance methods compress all of the differences between pairs of sequences into a single number

Building Trees with Parsimony

• Parsimony involves evaluating all possible trees and giving each a score based on the number of evolutionary changes that are needed to explain the observed data.

• The best tree is the one that requires the fewest base changes for all sequences to derive from a common ancestor.

• Check each topology• Count the minimum number of changes required

to explain the data• Choose the tree with the smallest number of

changes• Usually performs well with closely related

sequences – but often performs badly with very distantly related sequences

• With distantly related sequences homoplasy becomes a major problem

Parsimony Example

• Consider four sequences: ATCG, TTCG, ATCC, and TCCG

• Imagine a tree that branches at the first position, grouping ATCG and ATCC on one branch, TTCG and TCCG on the other branch.

• Then each branch splits, for a total of 3 nodes on the tree (Tree #1)

Tree #1 Tree #2

Compare Tree #1 with one that first divides ATCC on its own branch, then splits off ATCG, and finally divides TTCG from TCCG (Tree #2).

Trees #1 and #2 both have three nodes, but when all of the distances back to the root (# of nodes crossed) are summed, the total is equal to 8 for Tree #1 and 9 for Tree #2.

Maximum Likelihood

• Require a model of evolution• Each substitution has an associated

likelihood given a branch of a certain length

• A function is derived to represent the likelihood of the data given the tree, branch-lengths and additional parameters

• Function is minimized

Maximum Likelihood• The method of Maximum Likelihood attempts to

reconstruct a phylogeny using an explicit model of evolution.

• This method works best when it is used to test (or improve) an existing tree.

• Even with simple models of evolutionary change, the computational task is enormous, making this the slowest of all phylogenetic methods.

Models can be made more parameter rich to increase their realism

• The most common additional parameters are:– A correction to allow different substitution rates

for each type of nucleotide change– A correction for the proportion of sites which are

unable to change– A correction for variable site rates at those sites

which can change

• The values of the additional parameters will be estimated in the process

Ancestral Sequences• Maximum likelihood predicts ancestral sequences

– at branch points in the tree (nodes) • can provide information about the timing of the

acquiring of a novel trait or mutation• PAML (Phylogenetic Analysis using Maximum

Likelihood)– Confidence intervals provided– Selection can be inferred

Assumptions for Maximum Likelihood

• The frequencies of DNA transitions (C<->T,A<->G) and transversions (C or T<->A or G).

• The assumptions for protein sequence changes are taken from the PAM matrix - and are quite likely to be violated in “real” data.

• Since each nucleotide site evolves independently, the tree is calculated separately for each site. The product of the likelihood's for each site provides the overall likelihood of the observed data.

The Molecular Clock

For a given protein the rate of sequence evolution is approximately constant across lineages

Zuckerkandl and Pauling (1965)

This would allow speciation and duplication events to be dated accurately based on molecular data

Local and approximate molecular clocks more reasonable

Rooting the Tree

• In an unrooted tree the direction of evolution is unknown

• The root is the hypothesized ancestor of the sequences in the tree

• The root can either be placed on a branch or at a node

• You should start by viewing an unrooted tree

Rooting Using an Outgroup

• The outgroup should be a sequence (or set of sequences) known to be less closely related to the rest of the sequences than they are to each other

• It should ideally be as closely related as possible to the rest of the sequences while still satisfying condition 1

• The root must be somewhere between the outgroup and the rest (either on the node or in a branch)

Newick Format for Trees• Describes a tree as a set of nodes using nested parentheses.

(A:0.1,B:0.2,(C:0.3,D:0.4)E:0.5)F;

• An ‘informal’ standard established by Felsenstein, Maddison, Swofford, et al. at a dinner meeting at Newick’s Lobster House, Dover, NH.<http://evolution.genetics.washington.edu/phylip/newicktree.html>

Making Pretty Trees

• Options in MEGA• Phylodendron (start with tree generated by any phylogenetic

method in Newick format)

Are there Correct trees??• Despite all of these caveats, it is actually quite simple to

use computer programs calculate phylogenetic trees for data sets.

• Provided the data are clean, outgroups are correctly specified, appropriate algorithms are chosen, no assumptions are violated, etc., can the true, correct tree

be found and proven to be scientifically valid? • Unfortunately, it is impossible to ever conclusively state

what is the "true" tree for a group of sequences (or a group of organisms); taxonomy is constantly under revision as new data is gathered.

Is my tree correct?

Bootstrap values Bootstrapping is a statistical technique that can use

random re-sampling of data to determine sampling error for tree topologies

• Leave-one-out methods– (leave out a row, not a species)

• Agreement among the resulting trees is summarized with a majority-rule consensus tree

• Each branch of the tree is labelled with the % of bootstrap trees where it occurred.

• 80% is good, less than 50% is bad

Non-Synonymous Substitutions

• There is MORE information hidden in alignments• For each DNA substitution, we can observe if it

changes the corresponding amino acid• due to the redundancy of the genetic code, a

SYNONYMOUS (Ks) substitution does not change the AA

• a NON-SYNONYMOUS (Ka) substitution changes the AA at that codon

• [Need to correct the # of observed Ka and Ks for the possible number of each kind of changes that could occur in each codon]

Ka/Ks

• Neutral mutations will changes all bases at an equal rate, so Ka/Ks = 1

• Conserved sequences will have Ka/Ks <1 [this is true for the vast majority of protien coding seqences]

• Ka/Ks >1 is a signature for selection (AA changes occur at a faster rate than expected by chance)– discovery of a gene under positive selection by Ka/Ks>1 is a very big

deal

[The K(A)/K(S) ratio test for assessing the protein-coding potential of genomic regions: an empirical and simulation study.Nekrutenko A, Makova KD, Li WH. Genome Res. 2002 Jan;12(1):198-202.]

Ka/Ks varies within a gene

Computer Software for Phylogenetics Due to the lack of consensus among evolutionary biologists about basic principles for phylogenetic analysis, it is not surprising that there is a wide array of computer software available for this purpose.– PHYLIP is a free package that includes 30 programs

that compute various phylogenetic algorithms on different kinds of data. Command line only - hard to use.(Several free web servers provide a fuctional user interface)

– CLUSTALX is a multiple alignment program that includes the ability to create tress based on Neighbor Joining. Very easy to use, but NJ may not always be the best method to handle your data.

Other useful software• Mega - (free, Windows only) alignment, build trees,

estimate rates of evolution, • Mesquite - (free Mac & Win) advanced analysis of trees

created by other programs• Phylowin - (free Mac & Win) builds trees from a distance

matrix (NJ, parsimony, max likelihood)• PAUP - (Commercial, Mac & Win)

– sophisticated, but fairly easy to use– Includes NJ, Parsimony, and Max. Likelihood– Also does bootstrapping

• Phylodendron - (web) redraw trees

Other Web Resources• Joseph Felsenstein (author of PHYLIP) maintains a

comprehensive list of Phylogeny programs at: http://evolution.genetics.washington.edu/phylip

/software.html

• Introduction to Phylogenetic Systematics,Peter H. Weston & Michael D. Crisp, Society of Australian Systematic Biologists

http://www.science.uts.edu.au/sasb/WestonCrisp.html

• University of California, Berkeley Museum of Paleontology (UCMP)http://www.ucmp.berkeley.edu/clad/clad4.html

Software Hazards• There are a variety of programs for Macs and PCs,

but you can easily tie up your machine for many hours with even moderately sized data sets (i.e. fifty 300 bp sequences)

• Moving sequences into different programs can be a major hassle due to incompatible file formats.

• Just because a program can perform a given computation on a set of data does not mean that that is the appropriate algorithm for that type of data.

ConclusionsGiven the huge variety of methods for computing phylogenies, how can the biologist determine what is the best method for analyzing a given data set?– Published papers that address phylogenetic issues generally

make use of several different algorithms and data sets in order to support their conclusions.

– In some cases different methods of analysis can work synergistically

• Neighbor Joining methods generally produce just one tree, which can help to validate a tree built with the parsimony or maximum likelihood method

– Using several alternate methods can give an indication of the robustness of a given conclusion.

Summary

0 1 2 3 4 5A: -0.19 1.46 -1.42 -1.42 -1.42 -1.42C: 1.25 -1.42 1.52 -1.42 -1.42 -1.42G: -1.42 -1.00 -1.42 1.52 -1.42 1.52T: -1.42 -1.42 -1.42 -1.42 1.52 -1.42

• Restriction sites• Finding genes in DNA sequences• Regulatory sites in DNA• Protein signals (transport and processing)• Protein functional domains & motif

databases• Regular Expressions• Position Specific Scoring Matrix

& Hidden Markov Models

Next Lecture: Analysis of Variance