54406741 molecular evolution

7/24/2019 54406741 Molecular Evolution

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Introduction toMolecular Evolution

Mike Thomas

October 3, 2002


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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 evolutionitself:

Rates of change

The degree of change

mplications of change, etc

We can then pose and test hypotheses about the evolution of phenomenaunrelated to the genes

!volution of flight in insects

!volution of humans

!volution of disease


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Assumptions made by phylogenetic methods:

The sequences are correct

The sequence are homologous

!ach position is homologous

The sampling of ta"a or genes is sufficient to resolve the

problem of interest #equence variation is representative of the broader group of

interest

#equence variation contains sufficient phylogenetic signal $as

opposed to noise% to resolve the problem of intereest !ach position in the sequence evolved independently


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How do you extract this inormation rom an ali!nm


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Haeckel#s Tree o $ie

%Hi!her& or!anisms

%$ower& or!anisms

'nswer( a tree

' )hylo!enetic tree isa hierarchical,!ra)hicalre)resentation o

relationshi)s


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Other *ays to +e)resent hylo!eni

-a. /lado!ram showin!the )hylo!eneticrelationshi)s betweenour s)ecies

-b. +elationshi)s o thesame our s)eciesre)resented as a set onested )arentheses

-c. Evolutionaryrelationshi)s o thesame our s)ecies withnine syna)omor)hies-shared, derived

characters. )lotted onthe branches


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Using Phylogeny toUnderstand Gene Duplication

and Loss

' ' !ene tree1 The !ene tree su)erim)osed on a s)ecies tree,

allowin! identication o the du)lication and lossevents


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roblems with hylo!enetic Inerence

How do we know what the)otential candidate trees are"

2 How do we choose which treeis -most likely. the true tree"


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4umber o ossible Trees

4umber otaxa or !enes

4umber o)ossible rootedtrees

3 3

5 6

6 06

7 0,386

1 ' /

' 1 /

/ 1 '


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+eci)e or reconstructin! a )hylo!eny

9elect an o)timality criterion2 9elect a search strate!y

3 :se the selected searchstrate!y to !enerate a serieso trees, and a))ly theselected o)timality criterion

to each tree, always kee)in!track o the %best& treeexamined thus ar

9 h t t *hi h i th i ht


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9earch strate!y( *hich is the ri!httree"

When

m

is the number of ta"a, the number ofpossible trees is:

&$'m()%*+&'m('$m('%*+

-or ./ ta"a, the number of trees is )0,012,0'1

3any trees can be discarded because they areobviously wrong

#ometimes, 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


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9earch 9trate!ies

Strategy Type;Stepwise addition Algorithmic

; 9tar decom)osition 'l!orithmic

;Exhaustive Exact;1ranch < bound Exact

;Branch swapping euristic

; =enetic al!orithm Heuristic;Markov /hain Monte /arlo heuristic

1ut, we still need to evaluate the trees in order to

identiy the one most likely to be the true tree


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/hoose an o)timality criterion to evaluate t

/ommonalities can be ound, but how

can these be used to evaluate a tree"


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=eneral di>erences between o)timality crite

Minimumevolution

Maximumarsimony

Maximum$ikelihood

Model based %Model ree& Model based

/an account or manyty)es o se?uence

substitutions

'ssumes that allsubstitutions are e?ual

/an account or manyty)es o se?uence

substitutions

*orks well with stron! orweak se?uence similarity

*orks only when se?uencesimilarity is hi!h

*orks well with stron!or weak se?uencesimilarity

/om)utationally ast /om)utationally ast /om)utationally slow

*ell understood statistical)ro)erties -easy to test.

oorly understoodstatistical )ro)erties -hardto test.

*ell understoodstatistical )ro)erties-easy to test.

/an accurately estimatebranch len!ths -im)ortantor molecular clocks.

/annot estimate branchlen!ths accurately

/an estimate branchlen!ths with somede!ree o accuracy


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Maximum arsimony

The )arsimony score is theminimum number o re?uiredchan!es, or ste)s

2 Only shared, derived characters are

used3 The score or each character -site.is called the character score

5 9ite len!ths added over all sites is

the tree length6 The tree -out o all examined trees.

with the lowest tree len!th is themost parsimonious tree@ and

most likely to be the true tree


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Exam)le( Maximum arsimony

5 toes

20 teeth

0 ribs, 6 toes,round lobes, lon! le!s

oval lobes, A teeth, 26 verts,B ribs, 3 toes, short le!s

XFHG

5 toes, short le!s, Bribs, A teeth, ovallobes

20 teeth, 6toes, 0ribs, roundlobes, lon!le!s

3 toes, roundlobes

round lobes, 20 teeth, 26

verts,0 ribs, 6 toes, lon! le!s

FGHX

5

Tree len!th( A ste)s

6

2

6

Tree len!th( 2 ste)s


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#imple e"ample of parsimony with sequence data


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'nother exam)le with nucleotide da

-a. 'li!nment o ourhy)othetical C4'se?uences

-b. Most )arsimoniousrooted clado!ram orthis ali!nment

-c. /orres)ondin! unrootedclado!ram


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ssues 4 problems with parsimony

3ultiple trees may be the mostparsimonious $have the same tree length%A consensus tree can be constructed to visuali5e

the congruity 4 discontinuity between these 6ranch lengths $and, therefore, rates of

change% cannot be accurately estimated

7o e"plicit model of change is used, evenwhen one might be well supportedThe most parsimonious tree$s% may not be the

true tree


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Minimum Evolution -Cistance.

'll data are used, even thou!h some maynot be shared, derived characters

2 The !ranch lengths re)resent distancebetween a taxon and an ancestor, !iven an

assumed model o evolution3 The pairwise distancesare calculated oreach )air o taxa, !iven an assumed modelo evolution

5 The tree lengthis the sum o branch

len!th across a tree6 The tree -out o all examined trees. with the

lowest tree len!th is the minimumevolution tree@ and most likely to be the

true tree


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The tree is di>erent than a )arsimony tree

-a. Hy)othetical evolutionaryrelationshi)s between threeC4' se?uences, in which thehoriDontal branch len!ths are)ro)ortional to the number o

characterstate chan!esalon! the branches

-b. To)olo!y o the )arsimoniousclado!ram that would beconstructed rom the

se?uence similarities)roduced by such anevolutionary history imulti)le substitutions hadoccurred at several sites


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Factors that '>ect hylo!enetic Inerence

+elative base re?uencies -',=,T,/.2 TransitionGtransversion ratio3 4umber o substitutions )er site5 4umber o nucleotides -or amino acids. in se?uence6 Ci>erent rates in di>erent )arts o the molecule

A 9ynonymousGnonsynonymous substitution ratio7 9ubstitutions that are uninormative or obuscatory

arallel substitutions2 /onver!ent substitutions3 1ack substitutions

5 /oincidental substitutions

In !eneral, the more actors that are accounted orby the model -ie, more )arameters., the lar!er theerror o estimation It is oten best to use ewer

)arameters by choosin! the sim)ler model

Models o evolution( choosin! )arame


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9ome distance models( )distance

;) ndGn, where n is the number o sites

-nucleotides or amino acids., and ndis the

number o di>erences between the two

se?uences examined;ery robust when diver!ence times arerecent and the a>ect o com)licatin!)henomena is minor


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9ome distance models( Jukes/antor

8sed to estimate the number ofsubstitutions per site

The e"pected number of

substitutions per site is:

d 9 )t 9 ($)0%ln&.($0)%p+,

where p is the proportion of

difference between ' sequences

;ariance can be calculated 7o assumptions are made about

nucleotide frequencies, or

differential substitution rates

' T / =

'

T/=

(

(

(

(

9ome distance models( Kimura two


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9ome distance models( Kimura two)arameter

8sed to estimate the number of

substitutions per site

d 9 'rt, where r is thesubstitution rate $per site, peryear% and t is the generation timet

Accounts for different transition

and transversion rates 7o assumptions are made aboutnucleotide frequencies, varianceis greater than ?u@es(antor

C T

A G

Pyrimidines

Purines

= transition rate= transversion rateThese are treated the

same for long divergence

times.


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Bther models

Casegawa, Dishino, Eano $CDE%: corrects forunequal nucleotide frequencies and transitiontransversion bias into account

8nrestricted model: allows different rates between

all pairs of nucleotides Feneral Time Reversible model: allows different

rates between all pairs of nucleotides and correctsfor unequal nucleotide frequencies

3any other models have been invented to correctfor specific problems

The more parameters are introduced, the larger thevariance becomes


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Ways to build trees with distance models: 3!

3inimum !volution $3!% trees can be found by

e"haustive searches or heuristic searches $starting

with a reasonable tree or eliminating unli@ely

possible trees%

-or each tree e"amined, the total tree length iscalculated as the sum of branch lengths calculated

using a given model

3!, li@e 3a"imum Garsimony, may generate a

number of equal(scoring 3! trees and may not

actually result in the true tree 3any other models

have been invented to correct for specific problems


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Ways to build trees with distance models: 8GF3A

8GF3A $unweighted pair(group method usingarithmetic averages%

Fenerally accurate for molecular evolution whensubstitution rates are relatively constant, but this canrarely be assumed to be true

3ethod: distances for each pair of ta"a are computed using the chosen

distance method

The pair with the smallest value d are combined into a single,

composite ta"on The distances from this composite ta"on to all other ta"a are

computed

The ne"t pair with the smallest d is chosen $includingconsideration of pairings with the composite ta"on%


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Ways to build trees with distance models: 7eighbor ?oining

7eighbor ?oining $7?% is a very robust method that is accurate

even when substitution rates are not constant, and generally

recovers the 3! tree $although this is not always the case%

3ethod:

We construct a HstarI tree and compute the sum of all branches, #B

$this will be greater than the sum of all branches for the final tree, #-%

We then pic@ a pair of ta"a to be HneighborsI, $say, ta"a . 4 '% and

compute the sum of all branches, #.,'

All other pairs of ta"a 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 @ept

Then, another round of neighbor Joining is conducted, including using

the neighbor pair retained in the first round


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!"ample: The evolution of flight in stoneflies

9cale, in substitutionsGsite

Cened out!rou) taxa

;+econstruction o the

lecto)tera order -stoneLies.rom B9 r+4' se?uence

;Kimura 2)arameterdistance used

;Tree rooted with knownout!rou) s)ecies

;4ei!hborJoinin! treebuildin! method used toconstruct rst tree treesearch was conducted toensure that the 4J was alsothe ME tree

;/haracters related to Li!htwere then ma))ed onto thetree


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Maximum $ikelihood

The site li"elihoods re)resent )robabilityo data or one site !iven an assumedmodel o evolution

2 Overall likelihood is the )roduct o the site

likelihoods3 Trees are evaluated by com)arin! log#

li"elihoodscores5 $ikelihood scores are com)arable across

models as well as trees, so it )rovides away o testin! the !oodness o t o amodel

6 The tree -out o all examined trees. withthe lowest tree len!th is the maximumli"elihood tree@ and most likely to be


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4ext Tuesday(

Exam)les o )hylo!enetic reconstructions2 :ses o )hylo!enetic trees3 Other research usin! molecular evolution

4ext Thursday( exam

'll material throu!h next

Tuesday -0GB. will be coveredby the exam

54406741 molecular evolution

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