Introduction to Computational Biology; an Evolutionary Approach: Genes in Populations: Backward in Time
Introduction to Computational Biology; An Evolutionary Approach: Genes in Populations: Backward in Time
Bernhard Haubold & Thomas Wiehe
ICB c 2006 Birkhäuser Verlag Genealogy of Individuals
A B
¡ ¢ £
¡ ¢ £¥¤ ¦¥§ ¨ ©
¦¥§ ¨¥© ª¥« ¬¥ ®¥¯ °¥± ²¥³ ´¥µ ¶¥·
¤¥¥ Past
¡ ¢ ¸
¡ ¥ ¥ ! " # $ % & ' ( ) * + , -
¹¥º »¥¼ ½¥¾ ¿¥À Á¥Â Ã¥Ä Å¥Æ Ç¥È É¥Ê Ë¥Ì
¡ ¢ Í
¡ . /¥0 1¥2 3 4 5 6 7 8 9 : ; < = > ? @ A B
Î¥Ï Ð¥Ñ Ò¥Ó Ô¥Õ Ö¥× Ø¥Ù Ú¥Û Ü¥Ý Þ¥ß à¥á
¡ ¢ â
¡ C D¥E F¥G H I J K L M N O P Q R S T U V W
ã¥ä å¥æ ç¥è é¥ê ë¥ì í¥î ï¥ð ñ¥ò ó¥ô õ¥ö
¡ ¢ ÷
¡ X Y¥Z [¥\ ] ^ _ ` a b c d e f g h i j k l
ø¥ù ú¥û ü¥ý þ¥ÿ ¢¡ £¢¤ ¥¢¦ §¢¨ ©¢ ¢
¡ ¢
¡ m n¥o p¥q r s t u v w x y z { | } ~
¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢!
¡ ¢ "
¡ ¥ ¥
#¢$ %¢& '¢( )¢* +¢, -¢. /¢0 1¢2 3¢4 5¢6
¡ ¢ 7
¡ ¥ ¥ ¡ ¢ £ ¤ ¥ ¦ § ¨ © ª «
8¢9 :¢; <¢= >¢? @¢A B¢C D¢E F¢G H¢I J¢K
¢ ¢
¡
¡ ¬ ¥® ¯¥° ± ² ³ ´ µ ¶ · ¸ ¹ º » ¼ ½ ¾ ¿ À
L¢M N¢O P¢Q R¢S T¢U V¢W X¢Y Z¢[ \¢] ^¢_
¢ `
¡
Â¥Ã Ä¥Å Æ Ç È É Ê Ë Ì Í Î Ï Ð Ñ Ò Ó Ô Õ ¢ Á
¡
a¢b c¢d e¢f g¢h i¢j k¢l m¢n o¢p q¢r s¢t
£
¡
¢ ¢ Ö¥× Ø¥Ù Ú Û Ü Ý Þ ß à á â ã ä å æ ç è é
¡
u¢v w¢x y¢z {¢| }¢~ ¢ ¢ ¢ ¢ ¢
¸
¡
¡ ¢ ê¥ë ì¥í î ï ð ñ ò ó ô õ ö ÷ ø ù ú û ü ý
¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢
¡ Í
¢
¡ . þ¥ÿ ¢¡ £¥¤ ¦¥§ ¨¥© ¥ ¥ ¥ ¥ ¥
¢ ¢ ¡¢¢ £¢¤ ¥¢¦ §¢¨ ©¢ª «¢¬ ¢® ¯¢°
â
¡
¢
¡ C ¢ ¢ ¥ ¥ ¥ ¥ ¥! "¥# $¥% &¥'
±¢² ³¢´ µ¢¶ ·¢¸ ¹¢º »¢¼ ½¢¾ ¿¢À Á¢Â âÄ
÷
¡
¢
¡ X (¢) *¢+ ,¥- .¥/ 0¥1 2¥3 4¥5 6¥7 8¥9 :¥;
Å¢Æ Ç¢È É¢Ê Ë¢Ì Í¢Î Ï¢Ð Ñ¢Ò Ó¢Ô Õ¢Ö ×¢Ø
¡
¡ ¢
m <¢= >¢? @¥A B¥C D¥E F¥G H¥I J¥K L¥M N¥O
Ù¢Ú Û¢Ü Ý¢Þ ß¢à á¢â ã¢ä å¢æ ç¢è é¢ê ë¢ì
"
¡
¡ ¢
P¢Q R¢S T¥U V¥W X¥Y Z¥[ \¥] ^¥_ `¥a b¥c
í¢î ï¢ð ñ¢ò ó¢ô õ¢ö ÷¢ø ù¢ú û¢ü ý¢þ ÿ¡
7
¡
¡ ¢
d¢e f¢g h¥i j¥k l¥m n¥o p¥q r¥s t¥u v¥w
¢¡£ ¤¡¥ ¦¡§ ¨¡© ¡ ¡ ¡ ¡ ¡ ¡
¢
¡
¡ ¢
¬ x¢y z¢{ |¥} ~¥ ¥ ¥ ¥ ¥ ¥ ¥
¡ ¡ ¡ ¡ ¡ ¡! "¡# $¡% &¡' (¡)
`
¡
¡ Á ¢ ¢ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥
,¡- .¡/ 0¡1 2¡3 4¡5 6¡7 8¡9 :¡; <¡=
*¡+ Present
¢ 7 " ÷ â Í ¸ £ ¢ `
> > > > > > > > > >
¢ ¢ Á
. C X m ¬
ICB c 2006 Birkhäuser Verlag Genealogy of Genes
1
Tangled Untangled ?A@CBEDGFGHEIGJGKELGMENGOGP
§¡¨£©£ ¡ £ ¡ ££¡£¡ Past
?RQTSEUGVGWEXGYGZE[G\E]G^G_
£
?R`TaEbGcGdEeGfGgEhGiEjGkGl
" ' ! #£$ ( * ) %¡&
?Rm nGoGpEqGrGsEtGuEvGwGx
, . + 1 3 5 / 2 4 0 -
?RyTzE{G|G}E~GGEGEGG
> A @ :¡; = 7 ? 6 < 9 8
?RTEGGEGGEGEGG
F I G J L£M C E B D H K
?RTEGGEGGEGEGG
U N X V O Y W R T Q S P
?R T¡E¢G£G¤E¥G¦G§E¨G©EªG«G¬
d ] a \ c Z ` e [ b ^¡_
?RT®E¯G°G±E²G³G´EµG¶E·G¸G¹
n q g j¡k h p l£m f i o
@ º¼»E½G¾G¿EÀGÁGÂEÃGÄEÅGÆGÇ
?
u r t | v£w y£z£{ } s x
@ @ÉÈEÊGËGÌEÍGÎGÏEÐGÑEÒGÓGÔ
?
~
@ Q¼ÕEÖG×GØEÙGÚGÛEÜGÝEÞGßGà
?
?A@ `¼áEâGãGäEåGæGçEèGéEêGëGì
£ £ ¡
@
? m¼íEîGïGðEñGòGóEôGõEöG÷Gø
ª ¦ ¥ ¨ ¬ ¢ © « ¤ § £
@
? y¼ùEúGûGüEýGþGÿ¡ £¢¡¤£¥£¦
¸ ° ² ¶ ¹ ± µ ³£´ · ®£¯ Present
1 2 3 4 5 6 7 8 9 10 11 12 11 3 5 9 12 4 8 6 7 10 1 2
ICB º c 2006 Birkhäuser Verlag Sample Genealogy
»½¼¿¾½À½Á¿Â½Ã½Ä¿Å½Æ½Ç¿È Past
É Ñ Ó Ë Í¿Î Ê Ì Ð Ï Ò Ô
Ø Ý × Ö Ù¿Ú Þ à Õ ß Û¿Ü
ã å â è ê ì æ á é ë ç ä
õ ø ÷ ñ½ò ô î ö í ó ð ï
ý þ ¡ £¥¤ ú ü ù û ÿ ¢
¦ § © ¨
¥
' * "$# ) %¥& ! (
. + - 5 /¥0 2$3¥4 6 , 1
@ ; = : > < 9 ? 8 7 A
B E M F K H C I L D G J
T X U$V O S Q$R P Y N W
b ^ ] ` e d Z a c \ _ [
p h j n q i m k¥l o f¥g Present 11 3 5 9 12 4 8 6 7 10 1 2
ICB r c 2006 Birkhäuser Verlag The Coalescent
Past MRCA
T2
x CA
T3
w CA
T4
t u v Present s 4 8 2 1
ICB c 2006 Birkhäuser Verlag Coalescent Trees
n y 2:
z z z
~ ~ ~
| }~ | }~ | }~
{ { {
z z z
n y 10:
z z z
~ ~ ~
| }~ | }~ | }~
{ { {
z z z
n y 50:
z z z
~ ~ ~
| }~ | }~ | }~
{ { {
z z z
ICB c 2006 Birkhäuser Verlag Coalescent vs. Phylogeny
Feature Phylogeny Coalescent Level of comparison Inter-species gene history Intra-species gene history Purpose Reconstruct the true Simulate sets of potential species history gene histories Observation of interest Tree topology Frequency spectrum and distribution of segregating sites Data source Comparative data Model parameters Multiplicity Single Many
ICB c 2006 Birkhäuser Verlag Genealogy & Polymorphisms
genealogical history MRCA of a sample
of two genes
present day sequence comparison
PSfrag replacements Seq 1 Seq 2
ICB c 2006 Birkhäuser Verlag TMRCA
10 2
)
¡
)
1
of
¡
of (units 1 alue v 0.5 (units PSfrag replacements ariance V Expected
0 0.2 10 100 1000
sample size ( )
ICB c 2006 Birkhäuser Verlag Topology & Frequency Spectrum
MRCA MRCA
¢ ¢¤£
£
¢¥
¥ ¢
PSfrag replacements
¢¤¦ ¢¤¦
ICB c 2006 Birkhäuser Verlag Coalescent and SNPs
6 6 6 4 4 4
count 2 2 2
0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 6 number of pairwise differences 1.0 1.0 1.0 0.6 0.6 0.6 0.3 0.3 0.3 proportion 1 2 3 1 2 3 1 2 3 number
ICB c 2006 Birkhäuser Verlag SNPs § Recombination
no recombination 0.04 with recombination
0.03
0.02
0.01
0 0 20 40 60 80 segregating sites
ICB c 2006 Birkhäuser Verlag Coalescent with Recombination
past
º»¼·½¿¾ À Á
µ ¶ sampled chromosomes: «¬®°¯²±´³ segment a segment b
chromosome not contained in sample:
º»²¼·½¾  Á
«
¬®·¯²±´³ ¸ ¶
¨©¨©¨©¨©¨©¨©¨©¨©¨©¨ ª©ª©ª©ª©ª©ª©ª©ª©ª©ª
recombination x «¹ PSfrag replacements
present
ICB c 2006 Birkhäuser Verlag Selective Sweep
fB 0 0.5 1.0 past al
neutr à al neutr present
ICB c 2006 Birkhäuser Verlag Recombination & Selection
1.0 R a4
fB a3 0.5 MRCA a2
a1
0.0 Ä past present
ICB c 2006 Birkhäuser Verlag Recombination & Genetic Diversity in D. melanogaster
9 É È locus ÅÇÆ 10 reference
X-linked loci Yellow,Achaete 0.429 0.0008 [3] Pgd 1.466 0.0030 [3] Z,Tko 2.114 0.0044 [1] Per 4.952 0.0014 [3] White 13.30 0.0090 [13] Notch 11.54 0.0050 [14] Vermilion 5.619 0.0010 [4] Forked 4.330 0.0020 [9] Zw 4.619 0.0007 [6] Su(F) 0.476 0.0000 [9]
autosomal loci Gpdh 5.714 0.0078 [15] Adh 4.621 0.0060 [10] Ddc 1.314 0.0050 [4] Amy 3.107 0.0080 [11] Pu 5.129 0.0040 [15] Est6 4.314 0.0050 [7] MtnA 0.593 0.0010 [8] Hsp70A 0.493 0.0020 [12] Ry 3.364 0.0030 [2] CiD 0.000 0.0000 [5]
ICB c 2006 Birkhäuser Verlag PSfrag
Quantifying Selectionreplacements
0.012 autosomal X−linked
0.008 Ê
0.004
0
0 4e−09 8e−09 1.2e−08 Ë
ICB c 2006 Birkhäuser Verlag References
M. Aguadé, N. Miyashita, and C. H. Langley. Restriction map variation at the zeste–tko region in natural populations of Drosophila melanogaster. Molecular Biology and Evolution, 6:123–130, 1989. C. F. Aquadro, K. M. Lado, and W. A. Noon. The rosy region of Drosophila melanogaster and Drosophila simulans. I. Contrasting levels of naturally occuring DNA restriction map variation and divergence. Genetics, 119:875–888, 1988. D.J. Begun and C. F. Aquadro. Molecular population genetics of the distal portion of the X chromosome in Drosophila: Evidence for genetic hitchhiking of the yellow–achaete region. Genetics, 129:1147–1158, 1991. D.J. Begun and C. F. Aquadro. Levels of naturally occuring DNA polymorphism are correlated with recombination rates in Drosophila melanogaster. Nature, 356:519–520, 1992. A. J. Berry, J. W. Ajioka, and M. Kreitman. Lack of polymorphism on the Drosophila fourth chromosome resulting from selection. Genetics, 129:1111–1117, 1991. W. F. Eanes, J. W. Ajioka, J. Hey, and C. Wesley. Restriction map variation associated with the G6pd polymorphism in natural populations of Drosophila melanogaster. Molecular Biology and Evolution, 6:384–397, 1989. A. Y. Game and J. G. Oakeshott. The association between restriction site polymorphism and enzyme activity variation for Esterase6 in Drosophila melanogaster. Genetics, 126:1021–1031, 1990. B. W. Lange, C. H. Langley, and W. Stephan. Molecular evolution of Drosophila metallothionein genes. Genetics, 126:921–932, 1990. C. H. Langley. The molecular population genetics of Drosophila. In N. Takahata and J. F. Crow, editors, Population Biology of Genes and Molecules, pages 75–91. National Academy of Sciences, Baifukan, Japan, 1990. C. H. Langley, E. A. Montgomery, and W. F. Quattlebaum. Restriction map variation in the Adh region of Drosophila. Proceedings of the National Academy of Sciences, USA, 79:5631–5635, 1982. C. H. Langley, A. E. Shrimpton, T. Yamazaki, N. Miyashita, Y. Matsuo, and C. F. Aquadro. Naturally occuring variation in the restriction map of the Amy region of Drosophila melanogaster. Genetics, 119:619–629, 1988. A. J. Leigh-Brown. Variation of the 87A heat shock locus in Drosophila melanogaster. Proceedings of the National Academy of Sciences, USA, 80:5350–5354, 1983. N. Miyashita and C. H. Langley. Molecular and phenotypic variation of the white locus region in Drosophila melanogaster. Genetics, 120:199–212, 1988. S. W. Schaeffer, C. F. Aquadro, and C. H. Langley. Restriction map variation in the Notch region of Drosophila melanogaster. Molecular Biology and Evolution, 5:30–40, 1988. T. S. Takano, S. Kusakabe, and T. Mukai. The genetic structure of natural populations of Drosophila melanogaster. XXII. Comparative study of DNA polymorphisms in northern and southern natural populations. Genetics, 129:753–761, 1991.
ICB c 2006 Birkhäuser Verlag