Diapositiva 1

PAML
Phylogenetic Analysis by Maximum Likelihood
Yang Z. Computational Molecular Evolution
Yang Z. 2007
PAML 4: Phylogenetic Analysis by Maximum Likelihood.
Mol. Biol. Evol. 24, 1586-1591.
Yang Z. and Bielawski J.P. 2000
Statistical methods for detecting molecular adaptation.
TREE 15, 496-503.
http://abacus.gene.ucl.ac.uk/
http://abacus.gene.ucl.ac.uk/ziheng/ziheng.html
http://abacus.gene.ucl.ac.uk/software/paml.html
Ziheng Yang

Adaptive Evolution
• Most variation within or between species random fixation selectively neutral mutations.
• Selectively deleterious purifying selection not tolerated.
• Occasionally, mutations selective advantage positive selection (adaptive evolution) fixed in the
population at a much higher rate.
Why?
• Can indicate which amino acid sites/domains are functionally important in a molecule
• Interest in detecting whether most mutations are deleterious, advantageous or neutral
• Identification of selected loci provide insight into the events that have shaped a species’ evolution & can
indicate which genes have been particularly important in the evolution of a species.
• By screening for selective signatures associated with immunity or disease susceptibility, we may be
able to identify those genes that have been of critical importance to the development of disease
resistance.

Amino Acid Sites Subject to Positive Selection in
Mammalian a-Defensins
Red: sites predicted to be under positive selection.
Blue: sites that are 100% conserved across all OTUs.
Lynn et al., MBE 2004.

• Widely used method to detect adaptive evolution accelerated rate of d N /d s
– d N = nonsynonymous (protein changing) substitutions rates
– d S = synonymous substitutions rates
d N
ω = dS
ω < 1 → Nonsynonymous mutations are slightly deleterious
ω = 1 → Amino acid changes selectively neutral
ω > 1 → Amino acid changes selectively advantageous
Statistical Methods to Detect Positive Selection
Test whether dN is significantly higher than dS .
Approximate methods
→ Normal approximation applied to dN-dS .
ML method
→ Likelihood-ratio test.
3a: test Z
3b: confronto modelli con un likelihood ratio test
(modello zero:=1)

Metodi di Maximum Likelihood
• In PAML sfrutta le MCMC come metodo di esplorazione dello spazio dei
parametri
• Spazio dei parametri è infinito perché sono IGNOTI ed EQUIPROBABILI
• La funzione di Likelihood verifica qual è il valore del parametro che massimizza
la verosimiglianza con i dati.
X→ dati
θ→ parametro da stimare
La probabilità di osservare i dati X può essere vista come
una funzione del parametro ignoto θ dati i dati
L(θ ;X) = f (θ |X)
Il valore di θ che massimizza la likelihood è definito come
Maximum Likelihood Estimate (MLE)

PAML → CODEML
Models to detect positive selection acting on:
• Particular branches/lineages of a phylogeny (branch models).
• Particular codon (amino acid) sites (site-specific models).
Test for adaptive evolution in the VHL (Von Hippel-Lindau ) gene
• Dataset:
• Objective:
16 sequencies from different species
Test for sites evolving under positive
selection.
Identify sites by using empirical Bayes

Site-specific models Allow ω vary among sites.
H 0: uniform selective pressure among sites (M0)
H 1: variable selective pressure among sites (M3)
p p
ω ω
Likelihood ratio test (LRT)
2Δl = 2 (l 1-l 0) χ 2 distribution
SERVE PER VERIFICARE
SE ω VARIA FRA I SITI.
NON E’ CONSIDERATO UN
TEST PER VERIFICARE LA
PRESENZA/ASSENZA DI
SELEZIONE

H 0: variable selective pressure but NO positive selection (M1a)
H 1: variable selective pressure with positive selection (M2a)
Likelihood ratio test (LRT)
2Δl = 2 (l 1-l 0) χ 2 distribution
SE:
• IL MODELLO M2a SI
ADATTA MEGLIO AI DATI
• IL VALORE DI ω STIMATO
E’ >1 PER LA CLASSE DI
SITI p 2
UNA PROPORZIONE
DI SITI PARI A p2 E’
SOTTOPOSTA A
SELEZIONE
POSITIVA

H 0: Beta distributed variable selective pressure (M7)
H 1: Beta plus positive selection(M8)
Likelihood ratio test (LRT)
2Δl = 2 (l 1-l 0) χ 2 distribution
SE:
• IL MODELLO M8 SI ADATTA
MEGLIO AI DATI
• IL VALORE DI ω S STIMATO E’
>1 PER LA CLASSE DI SITI
p1
UNA PROPORZIONE
DI SITI PARI A p1 E’
SOTTOPOSTA A
SELEZIONE POSITIVA
Quando i test suggeriscono la presenza di selezione positiva si utilizzano dei metodi Bayesiani
(BEB) per calcolare la probabilità a posteriori che ciascun codone provenga dalla classe di
siti sotto selezione positiva.

Branch-site models
Allow ω vary among branches. Likelihood ratio test (LRT)
• LRT based on χ 2 can be powerful
2Δl = 2 (l 1-l 2) χ 2 distribution
Alternative model (estimated ω 2>1)
Null model (fixed ω 2=1)
• Power is affected by (i) sequence divergence, (ii) number of lineages, and (iii) strength of positive selection
• The most efficient way to increase power is to add lineages
Anisimova, Bielawski, and Yang, 2001, Mol. Bio. Evol. 18:1585-1592.

Requirements for PAML Analysis
• A coding DNA sequence alignment in PAML format.
• A treefile in newick-like format.
• codeml.ctl parameter file.
• PAML installed on your machine!
Searching DNA sequences
Download of coding sequences from different species by querying databases such as:
• UniProt (http://www.uniprot.org/)
• NCBI Entrez Gene (http://www.ncbi.nlm.nih.gov/sites/entrez?db=gene)
• Genome browser Ensembl (http://www.ensembl.org/).

1. Tradurre in proteine
2. Allineare
3. Esportare un file *.meg, e un file *.fas

Coding DNA sequence alignment in PAML format
Number of sequences
Length of alignment
N.B.→ Remove TGA at the end of sequences

Treefile
• Tree must be trifurcated NOT rooted.
• The tree is likely to represent the true relationship among the species
• NCBITaxonomy (http://www.ncbi.nlm.nih.gov/guide/taxonomy/ ).
• Tree exported in *.phy.
• Converted from rooted to unrooted as suggest the author with Retree tools of Phylip.
MEGA4 - http://www.megasoftware.net/
Phylip - http://evolution.genetics.washington.edu/phylip.html
Abbreviazioni:
PCA: Procavia capensis
PVA: Pteropus vampyrus
MLU: Myotis lucifugus
BTA: Bos taurus
SSC: Sus scrofa
TTR: Tursiops truncatus
FCA: Felis catus
CFA: Canis familiaris
STO: Spermophilus tridecemlineatus
RNO: Rattus norvegicus
MUS: Mus musculus
OPR: Ochotona princeps
PAB: Pongo abelii
HOM: Homo sapiens
GGO: Gorilla gorilla
CJA: Callithrix jacchus

CODEML.ctl parameter file
• Ziheng Yang: Computational Molecular Evolution
• PAML User Guide
k → transition/transversion rate ratio
π → codon frequency
• Yang Z, Nielsen R. Estimating synonymous and nonsynonymous substitution rates under realistic evolutionary
models. Mol Biol Evol 2000; 17: 32-43
• Yang Z. PAML 4: phylogenetic Analysis by Maximum Likelihood. Mol Biol Evol 2007; 24: 1586-1591
• F EQUAL: each codon has the same frequency
• F1X 4: codon frequency are expected from the
frequencies of four nucleotides.
• F3 X 4: codon frequencies are expected from 3
sets of nucleotide frequencies for the three
codon positions.
• F61: all codon frequnecies as parameters

1. Create a directory to run analysis.
2. Copy the codeml.ctl file, the “file.fas” and treefile “file.nwk” into this directory.
3. To open command prompt in windows XP start Run type “cmd”
4. Open folder: “cd” and folder path
5. To run CODEML: “Codeml.exe”
Running process…

Output Files
Several different output files produced:
• rst
• Rst1
• Rub
• Lnf
• 2NG.ds
• 2NG.dn
• 2NG.t
• mlc → Main output file

Modello N°
Parametri
liberi
k lnL Parametri stimati
M0 1 2,86312 -2617,14 ω= 0,12877
M1 2 2,99216 -2547,89 p0= 0,85808 ω0=0,04165
(p1=0,14192) (ω1=1)
M2 4 3,02129 -2547,47 p0=0,85768 ω0=0,04237
p1=0,13527 (ω1=1)
(p2=0,00705) ω2=2,70033
M3 5 2,91362 -2538,98 p0=0,78851 ω0=0,02312
p1=0,19543 ω1=0,47991
(p2= 0,01606) ω2=2,20475
M7 2 2,89921 -2543,01 p=0,14942 q=0,87349
M8 4 2,9211 -2539,62 p=0,18576 q=1,38392
p0=0,98448 (p1=0,01552) ω=2,21316
Modelli testati 2∆ℓ df P-Value
M0 vs M3 156,3233 4 8,98 * 10 -33
M1 vs M2 0 2 0,6545
M7 vs M8 6,782778 2 0,0336