V13 Prediction of Phylogenies based on single genes

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V13 Prediction of Phylogenies based on single
genes
Material of this lecture taken from - chapter 6,
DW Mount Bioinformatics and from Julian
Felsensteins book.

A phylogenetic analysis of a family of related
nucleic acid or protein sequences is a
determination of how the family might have been
derived during evolution. Placing the sequences
as outer branches on a tree, the evolutionary
relationships among the sequences are depicted.
Phylogenies, or evolutionary trees, are the basic
structures to describe differences between
species, and to analyze them statistically. They
have been around for over 140 years. Statistical,
computational, and algorithmic work on them is
ca. 40 years old.
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3 main approaches in single-gene phylogeny
- maximum parsimony - distance - maximum
likelihood

Popular programs PHYLIP (phylogenetic inference
package J Felsenstein) PAUP (phylogenetic
analysis using parsimony Sinauer Assoc
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Methods for Single-Gene Phylogeny
Choose set of related sequences
Obtain multiple sequence alignment
Is there strong sequence similarity?
Maximum parsimony methods
Yes

No
Yes
Is there clearly recogniza-ble sequence
similarity?
Distance methods
No
Analyze how well data support prediction
Maximum likelihood methods
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Parsimony methods
Edwards Cavalli-Sforza (1963) that
evolutionary tree is to be preferred that
involves the minimum net amount of
evolution. ? seek that phylogeny on which, when
we reconstruct the evolutionary events leading to
our data, there are as few events as
possible. (1) We must be able to make a
reconstruction of events, involving as few events
as possible, for any proposed phylogeny. (2) We
must be able to search among all possible
phylogenies for the one or ones that minimize the
number of events.

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A simple example
Suppose that we have 5 species, each of which
has been scored for 6 characters
?(0,1) We will allow changes 0 ? 1 and
1 ? 0. The initial state at the root of a tree
may be either state 0 or state 1.

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Evaluating a particular tree
To find the most parsimonious tree, we must have
a way of calculating how many changes of state
are needed on a given tree. This tree
represents the phylogeny of character
1. Reconstruct phylogeny of character 1 on this
tree.

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Evaluating a particular tree
There are 2 equally good reconstructions, each
involving just one change of character
state. They differ in which state they assume at
the root of the tree, and they differ in which
branch they place the single change.

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Evaluating a particular tree
3 equally good reconstructions for character 2,
which needs two changes of state.

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Evaluating a particular tree
A single reconstruction for character 3,
involving one change of state.

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Evaluating a particular tree
on the right 2 reconstructions for character 4
and 5 because these characters have identical
patterns. single reconstruction for
character 6, one change of state.

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Evaluating a particular tree
The total number of changes of character state
needed on this tree is 1 2 1 2 2 1
9 Reconstruction of the changes in state on this
tree

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Evaluating a particular tree
Alternative tree with only 8 changes of
state. The minimum number
of changes of state would be 6, as there are 6
characters that can each have 2 states. Thus, we
have two extra changes ? called homoplasmy.

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Evaluating a particular tree

Figure right shows another tree also requiring 8
changes. These two most parsimonious trees are
the same tree when the roots of the tree are
removed.
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Methods of rooting the tree
There are many rooted trees, one for each branch
of this unrooted tree, and all have the same
number of changes of state. The number of
changes of state only depends on the unrooted
tree, and not at all on where the tree is then
rooted. Biologists want to think of trees as
rooted ? need method to place the root in an
otherwise unrooted tree. (1) Outgroup
criterion (2) Use a molecular clock.

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Outgroup criterion
Assumes that we know the answer in
advance. Suppose that we have a number of great
apes, plus a single old-world monkey. Suppose
that we know that the great apes are a
monophyletic group. If we infer a tree of these
species, we know that the root must be placed on
the lineage that connects the old-world monkey
(outgroup) to the great apes (ingroup).

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Molecular clock
If an equal amount of changes were observed on
all lineages, there should be a point on the tree
that has equal amounts of change (branch lengths)
from there to all tips. With a molecular clock,
it is only the expected amounts of change that
are equal. The observed amounts may not be. ?
using various methods find a root that makes the
amounts of change approximately equal on all
lineages.

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Branch lengths
Having found an unrooted tree, locate the changes
on it and find out how many occur in each of the
branches. The location of the changes can be
ambiguous. ? average over all possible
reconstructions of each character for which there
is ambiguity in the unrooted tree. F
ractional numbers in some branches of left tree
add up to (integer) number of changes (right)

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Open questions
Particularly for larger data sets, need to know
how to count number of changes of state by use of
an algorithm. need to know algorithm for
reconstructing states at interior nodes of the
tree. need to know how to search among all
possible trees for the most parsimonious ones,
and how to infer branch lengths. sofar only
considered simple model of 0/1 characters. DNA
sequences have 4 states, protein sequences 20
states. Justification is it reasonable to use
the parsimony criterion? If so, what does it
implicitly assume about the biology? What is
the statistical status of finding the most
parsimonious tree? Can we make statements how
well-supported it is compared to other trees?

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Counting evolutionary changes
2 related dynamic programming algorithms Fitch
(1971) and Sankoff (1975) - evaluate a phylogeny
character by character - for each character,
consider it as rooted tree, placing the root
wherever seems appropriate. - update some
information down a tree when we reach the
bottom, the number of changes of state is
available. Do not actually locate changes or
reconstruct interior states at the nodes of the
tree.

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Fitch algorithm
intended to count the number of changes in a
bifurcating tree with nucleotide sequence data,
in which any one of the 4 bases (A, C, G, T) can
change to any other. At the particular
site, we have observed the bases C, A, C, A and G
in the 5 species. Give them in the order in which
they appear in the tree, left to right.

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Fitch algorithm
For the left two, at the node that is their
immediate common ancestor, attempt to construct
the intersection of the two sets. But as C ?
A ? instead construct the union C ? A
AC and count 1 change of state. For the
rightmost pair of species, assign common
ancestor as AG, since A ? G ? and count
another change of state. .... proceed to
bottom Total number of changes 3. Algorithm
works on arbitrarily large trees.

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Complexity of Fitch algorithm
Fitch algorithm can be carried out in a number of
operations that is proportional to the number of
species (tips) on the tree. Dont we need to
multiply this by the number of sites n ? Any
site that is invariant (which has the same base
in all species, e.g. AAAAA) can be
dropped. Other sites with a single variant base
(e.g. ATAAA) will only require a single change of
state on all trees. These too can be
dropped. For sites with the same pattern (e.g.
CACAG) that we have already seen, simply use
number of changes previously computed. Pattern
following same symmetry (e.g. TCTCA CACAG) need
same number of changes ? numerical effort rises
slower than linearly with the number of sites.

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Sankoff algorithm
Fitch algorithm is very effective but we cant
understand why it works. Sankoff algorithm more
complex, but its structure is more
apparent. Assume that we have a table of the
cost of changes cij between each character state
i and each other state j. Compute the total cost
of the most parsimonious combinations of events
by computing it for each character. For a given
character, compute for each node k in the tree a
quantity Sk(i). This is interpreted as the
minimal cost, given that node k is assigned state
i, of all the events upwards from node k in the
tree.

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Sankoff algorithm
If we can compute these values for all nodes, we
can also compute them for the bottom node in the
tree. Simply choose the minimum of these
values which is the desired total cost we seek,
the minimum cost of evolution for this
character. At the tips of the tree, the S(i) are
easy to compute. The cost is 0 if the observed
state is state i, and infinite otherwise. If we
have observed an ambigous state, the cost is 0
for all states that it could be, and infinite for
the rest. Now we just need an algorithm to
calculate the S(i) for the immediate common
ancestor of two nodes.

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Sankoff algorithm
Suppose that the two descendant nodes are called
l and r (for left and right). For their
immediate common ancestor, node a, we compute

The smallest possible cost given that node a is
in state i is the cost cij of going from state i
to state j in the left descendant lineage, plus
the cost Sl(j) of events further up in the
subtree gien that node l is in state j. Select
value of j that minimizes that sum. Same
calculation for right descendant lineage ? sum of
these two minima is the smallest possible cost
for the subtree above node a, given that node a
is in state i. Apply equation successively to
each node in the tree, working downwards. Finally
compute all S0(i) and use previous eq. to find
minimum cost for whole tree.
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Sankoff algorithm
The array (6,6,7,8) at the bottom
of the tree has a minimum value of 6 minimum
total cost of the tree for this site.

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Finding the best tree by heuristic search
The obvious method for searching for the most
parsimonious tree is to consider ALL trees and
evaluate each one. Unfortunately, generally the
number of possible trees is too large. ? use
heuristic search methods that attempt to find the
best trees without looking at all possible
trees. (1) Make an initial estimate of the tree
and make small rearrangements of it find
neighboring trees. (2) If any of these
neighbors are better, consider them and continue
search.

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Nearest-neighbor interchanges

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Nearest-neighbor interchanges

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Subtree pruning and regrafting

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Branch-and-Bound
find global optimum, NP-hard problem

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Resolve Incongruences in Phylogeny
Many possible reasons that may make decisions on
how to handle conflicts in larger sets of
molecular data difficult. E.g. two genes with
different evolutionary history (e.g. owing to
hybridization or horizontal transfer) will
necessarily give incongruent pictures while still
depicting true histories. Here compare genome
sequence data for 7 Saccharomyces yeast
species S. cerevisae S. paradoxus S.
mikatae S. kudriavzevii S. bayanus S.
castelli S. kluyveri plus one outgroup fungus
Candida albicans.

Rokas et al. Nature 425, 798 (2003)
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Resolve Incongruences in Phylogeny
Identify orthologous genes to serve as
phylogenetic markers 106 genes which are
distributed throughout the S. cerevisae genome on
all 16 chromosomes and comprise a total length of
127026 nt 42342 amino acids corresponding to
roughly 1 of the genomic sequence and 2 of the
predicted genes. Criteria to select genes spaced
ca. every 40 kb (1) genes have homologous
sequence in each of the 8 species (2) genes have
at least two homologous flanking syntenic
genes (3) genes can be aligned over most of the
protein. 3 types of analysis - maximum
likelihood (ML) analysis of nucleotide data -
maximum parsimony (MP) analysis of nucleotide
data - MP of the amino acid data

Rokas et al. Nature 425, 798 (2003)
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Resolve Incongruences in Phylogeny
Align individual genes with ClustalW. Edit
manually to exclude indels and areas of uncertain
alignment ? left with 76 of the sequence of each
gene on average. Tree construction with PAUP by
branch-and-bound algorithm which guarantees to
find the optimal tree. Estimate tree reliability
using non-parametric bootstrap re-sampling. Analy
sis of the 106 genes gave more than 20
alternative ML or MP trees. Generate 50
majority-rule consensus trees by
bootstrapping. Next slide shows several strongly
supported trees.

Rokas et al. Nature 425, 798 (2003)
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Bootstrap analysis.
A method for testing how well a particular data
set fits a model. E.g. the validity of the
branch arrangement in a predicted phylogenetic
tree can be tested by resampling columns in a
multiple sequence alignment to create many new
alignments. The appearance of a particular
branch in trees generated from these resampled
sequences can then be measured. Alternatively,
a sequence may be left out of an analysis to
determine how much the sequence influences the
results of an analysis. Here swap individual
nucleotide sites or positions of genes (bootstrap
replicas).
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Alternative Tree topologies

Rokas et al. Nature 425, 798 (2003)
Single-gene data sets generate multiple, robustly
supported alternative topologies. Representative
alternative trees recovered from analyses of
nucleotide data of 106 selected single genes and
six commonly used genes are shown. The trees are
the 50 majority-rule consensus trees from the
genes YBL091C (a), YDL031W (b), YER005W (c),
YGL001C (d), YNL155W (e) and YOL097C (f). These 6
genes were selected without consideration of
their function. Maybe commonly used, well known
genes of important functions provide a better
resolution?
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Alternative Tree topologies

Results from the commonly used genes actin (g),
hsp70 (h), ?-tubulin (i), RNA polymerase II (j)
elongation factor 1-? (k) and 18S rDNA (l).
Numbers above branches indicate bootstrap values
(ML on nucleotides/MP on nucleotides). ? Same
problem of alternative topologies as before.
Rokas et al. Nature 425, 798 (2003)
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Explanations?
The alternative phylogenies could have resulted
from a number of different scenarios (1) most
genes could have weakly supported most
phylogenies and strongly supported only a few
alternative trees, (2) most genes could have
strongly supported one phylogeny and a few genes
strongly supported only a small number of
alternatives, (3) there could have been some
combinations of these scenarios so that each
branch among alternative phylogenies had either
weak or strong support depending on the gene. To
distinguish between these possibilities, identify
all branches recovered during single-gene
analyses, record each bootstrap value with
respect to the gene and method of analysis. ? 8
branches were shared by all three analyses with
multiple instances of bootstrap values gt 50.

Rokas et al. Nature 425, 798 (2003)
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Common Branches

The distribution of bootstrap values for the
eight prevalent branches recovered from 106
single-gene analyses highlights the pervasive
conflict among single-gene analyses. a,
Majority-rule consensus tree of the 106 ML trees
derived from single-gene analyses. Across all
analyses, there were eight commonly observed
branches the five branches in the consensus tree
(numbers 15 a) and the three branches (numbers
68) shown in b.
Rokas et al. Nature 425, 798 (2003)
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Bootstrap Values of Common Branches
Only branches 1 and 4 are supported by a majority
of genes.

c, For each of the eight branches, the ranked
distribution of per cent bootstrap values
recovered from the three analyses of 106 genes is
shown. Results from ML (blue) and MP (red)
analyses of nucleotide data sets, and MP analyses
of amino acid data sets (black), are shown. For
each branch, the mean bootstrap value and 95
confidence intervals from the ML analyses and the
percentage of ML trees supporting this branch (in
parentheses) are indicated below each graph.
Although the ranked distributions of bootstrap
values from the three analyses are remarkably
similar for most branches, on a gene-by-gene
basis there is no tight correspondence between
bootstrap values from ML and MP analyses
Rokas et al. Nature 425, 798 (2003)
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How different are the trees?
The degree of conflict among the trees could be
relatively minor. Determine how many taxa
(genes) would need to be removed to make two
trees congruent (deckungsgleich).

Rokas et al. Nature 425, 798 (2003)
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Reversal distance problem
Extensive incongruence between trees derived from
the 106 individual-gene data sets. Pairwise
comparisons between 50 majority-rule consensus
trees from 106 single-gene ML analyses of
nucleotide data (black bars), MP analyses of
nucleotide data (white bars), and MP analyses of
amino acid data (grey bars) were categorized on
the basis of the minimum number of taxa that need
to be removed for two trees to reach congruence
(x axis). For each of the analyses, the
majority of pairwise comparisons require the
removal of two or more taxa before congruence is
attained.
Rokas et al. Nature 425, 798 (2003)
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What leads to incongruence?
Many factors were checked that could lead to
incongruence between single-gene phylogenies -
outgroup choice repeat all analyses without C.
albicans - number of variable sites significant
ly correlated with - number of parsimony-informati
ve sites bootstrap values for some - gene
size branches - rate of evolution -
nucleotide composition - base compositional
bias - genome location - gene ontology no
parameters can systematically account for or
predict the performance of single genes!

Rokas et al. Nature 425, 798 (2003)
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Can incongruence be overcome?
Although we do not know the cause(s) of
incongruence between single-gene phylogenies, the
critical question is how this incongruence
between single trees might be overcome to arrive
at the actual species tree. Can single gene
trees be concatenated into one large data set?
Rokas et al. Nature 425, 798 (2003)
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Concatenation of single genes gives a single tree!
Phylogenetic analyses of the concatenated data
set composed of 106 genes yield maximum support
for a single tree, irrespective of method and
type of character evaluated. Numbers above
branches indicate bootstrap values (ML on
nucleotides/MP on nucleotides/MP on amino acids).

All alternative topologies were rejected. This
level of support for a single tree with 5
internal branches is unprecedented. This tree can
now be referred to as species tree.
Rokas et al. Nature 425, 798 (2003)
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How much data is required?
The concatanated data recovered a tree with
maximum support on all branches, despite
divergent levels of support for each branch among
single-gene analyses. ? At what size did the
data set arrive at the species tree?

Rokas et al. Nature 425, 798 (2003)
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Convergence on single tree

branch 3 branch 5
A minimum of 20 genes is required to recover gt95
bootstrap values for each branch of the species
tree. a, b, The bootstrap values for branches 3
(a) and 5 (b) were constructed from the
concatenation of randomly re-sampled orthologous
nucleotides (left) or random subsets of genes
(right). The species tree is recovered with
robust support (gt95 bootstrap values in all
branches at 95 confidence interval) by analyses
of a minimum of 20 concatenated genes. All
analyses were performed using MP.
Rokas et al. Nature 425, 798 (2003)
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Independent evolution?
It has been suggested that nucleotides within a
given gene do not evolve independently. Re-sample
subset of orthologous nucleotides from the total
data set. Only 3000 randomly chosen nucleotide
positions (corresponding to less than three
concatenated genes) are sufficient to generate
single tree with gt 95 confidence. This
indicates that nucleotides in genes have not
evolved independently (because when using
complete genes more than 20 genes are necessary
to generate single tree).

Rokas et al. Nature 425, 798 (2003)
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Implications for resolution of phylogenies
Unreliability of single-gene data sets stems from
the fact that each gene is shaped by a unique set
of functional constraints through
evolution. Phylogenetic algorithms are sensitive
to such constraints. Such problems can be
avoided with genome-wide sampling of
independently evolving genes. In other cases the
amount of sequence information needed to resolve
specific relationships will be dependent on the
particular phylogenetic history under
examination. Branches depicting speciation
events separated by long time intervals may be
resolved with a smaller amount of data, and those
depicting speciation events separated by shorter
invtervals may be much harder to resolve.

Rokas et al. Nature 425, 798 (2003)
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Summary
Robust strategies exist for phylogenies built on
single-gene comparisons (maximum parsimony,
distance, maximum likelihood). Problem of
incongruence of phylogenies derived from
individual genes. Can be resolved by integrative
analysis of multiple (here gt 20) genes. It is
desirable to combine results from phylogenies
constructed from local sequence information with
trees constructed from genome rearrangement. The
power of genome rearrangement studies is the
construction of ancestral genomes. Then one can
derive the speed of evolution at different times,
disect mutation biases at different times from
the influence of genomic context ... and possibly
derive the driving forces of biological evolution.