selection theory 2 - amazon s3 · selection theory ii chris kempes ... j =1 x j f j q j,i x i x i...
TRANSCRIPT
![Page 1: selection theory 2 - Amazon S3 · Selection Theory II Chris Kempes ... j =1 x j f j q j,i x i x i Frequency of a given sequence i Fitness of a given sequence i (e.g. relative growth](https://reader035.vdocument.in/reader035/viewer/2022081402/5f0ef4f87e708231d441c5c7/html5/thumbnails/1.jpg)
Selection Theory II
Chris Kempes
![Page 2: selection theory 2 - Amazon S3 · Selection Theory II Chris Kempes ... j =1 x j f j q j,i x i x i Frequency of a given sequence i Fitness of a given sequence i (e.g. relative growth](https://reader035.vdocument.in/reader035/viewer/2022081402/5f0ef4f87e708231d441c5c7/html5/thumbnails/2.jpg)
• What are the basic ways in which we think about evolution?
•
![Page 3: selection theory 2 - Amazon S3 · Selection Theory II Chris Kempes ... j =1 x j f j q j,i x i x i Frequency of a given sequence i Fitness of a given sequence i (e.g. relative growth](https://reader035.vdocument.in/reader035/viewer/2022081402/5f0ef4f87e708231d441c5c7/html5/thumbnails/3.jpg)
Fitness Landscape00
0...0
000.
..110
0...0 ......
sequence
fitness
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Quasispecies equationdxi
dt=
nX
j=1
xjfjqj,i � �xi
xi Frequency of a given sequence i
Fitness of a given sequence i (e.g. relative growth rate)fi
Probability of mutating from sequence i to sequence j
qi,j
� =nX
i=1
xifi
![Page 5: selection theory 2 - Amazon S3 · Selection Theory II Chris Kempes ... j =1 x j f j q j,i x i x i Frequency of a given sequence i Fitness of a given sequence i (e.g. relative growth](https://reader035.vdocument.in/reader035/viewer/2022081402/5f0ef4f87e708231d441c5c7/html5/thumbnails/5.jpg)
Steady State Solutions
f0f1
![Page 6: selection theory 2 - Amazon S3 · Selection Theory II Chris Kempes ... j =1 x j f j q j,i x i x i Frequency of a given sequence i Fitness of a given sequence i (e.g. relative growth](https://reader035.vdocument.in/reader035/viewer/2022081402/5f0ef4f87e708231d441c5c7/html5/thumbnails/6.jpg)
Steady State Solutions
f0
f0 > 1
f1 = 1
f1
![Page 7: selection theory 2 - Amazon S3 · Selection Theory II Chris Kempes ... j =1 x j f j q j,i x i x i Frequency of a given sequence i Fitness of a given sequence i (e.g. relative growth](https://reader035.vdocument.in/reader035/viewer/2022081402/5f0ef4f87e708231d441c5c7/html5/thumbnails/7.jpg)
Steady State Solutions
f0
f0 > 1 q0,0 = (1� u)L
f1 = 1
f1
![Page 8: selection theory 2 - Amazon S3 · Selection Theory II Chris Kempes ... j =1 x j f j q j,i x i x i Frequency of a given sequence i Fitness of a given sequence i (e.g. relative growth](https://reader035.vdocument.in/reader035/viewer/2022081402/5f0ef4f87e708231d441c5c7/html5/thumbnails/8.jpg)
Steady State Solutions
f0
f0 > 1 q0,0 = (1� u)L
q0,1 = 1� q0,0f1 = 1
f1
![Page 9: selection theory 2 - Amazon S3 · Selection Theory II Chris Kempes ... j =1 x j f j q j,i x i x i Frequency of a given sequence i Fitness of a given sequence i (e.g. relative growth](https://reader035.vdocument.in/reader035/viewer/2022081402/5f0ef4f87e708231d441c5c7/html5/thumbnails/9.jpg)
Steady State Solutions
f0
f0 > 1 q0,0 = (1� u)L
q1,1 = 1
q0,1 = 1� q0,0
q1,0 = 0f1 = 1
f1
![Page 10: selection theory 2 - Amazon S3 · Selection Theory II Chris Kempes ... j =1 x j f j q j,i x i x i Frequency of a given sequence i Fitness of a given sequence i (e.g. relative growth](https://reader035.vdocument.in/reader035/viewer/2022081402/5f0ef4f87e708231d441c5c7/html5/thumbnails/10.jpg)
dxi
dt=
nX
j=1
xjfjqj,i � �xi
� =nX
i=1
xifi
Steady State Solutions
![Page 11: selection theory 2 - Amazon S3 · Selection Theory II Chris Kempes ... j =1 x j f j q j,i x i x i Frequency of a given sequence i Fitness of a given sequence i (e.g. relative growth](https://reader035.vdocument.in/reader035/viewer/2022081402/5f0ef4f87e708231d441c5c7/html5/thumbnails/11.jpg)
dxi
dt=
nX
j=1
xjfjqj,i � �xi
� =nX
i=1
xifi
Steady State Solutionsf0 > 1
f1 = 1
![Page 12: selection theory 2 - Amazon S3 · Selection Theory II Chris Kempes ... j =1 x j f j q j,i x i x i Frequency of a given sequence i Fitness of a given sequence i (e.g. relative growth](https://reader035.vdocument.in/reader035/viewer/2022081402/5f0ef4f87e708231d441c5c7/html5/thumbnails/12.jpg)
dxi
dt=
nX
j=1
xjfjqj,i � �xi
� =nX
i=1
xifi
Steady State Solutionsf0 > 1
q1,1 = 1
q1,0 = 0
f1 = 1
q0,0 = (1� u)L ⌘ q
q0,1 = 1� q
![Page 13: selection theory 2 - Amazon S3 · Selection Theory II Chris Kempes ... j =1 x j f j q j,i x i x i Frequency of a given sequence i Fitness of a given sequence i (e.g. relative growth](https://reader035.vdocument.in/reader035/viewer/2022081402/5f0ef4f87e708231d441c5c7/html5/thumbnails/13.jpg)
dxi
dt=
nX
j=1
xjfjqj,i � �xi
� =nX
i=1
xifi
Steady State Solutionsf0 > 1
q1,1 = 1
q1,0 = 0
f1 = 1
q0,0 = (1� u)L ⌘ q
q0,1 = 1� q
dx0
dt= x0f0q � x0�
![Page 14: selection theory 2 - Amazon S3 · Selection Theory II Chris Kempes ... j =1 x j f j q j,i x i x i Frequency of a given sequence i Fitness of a given sequence i (e.g. relative growth](https://reader035.vdocument.in/reader035/viewer/2022081402/5f0ef4f87e708231d441c5c7/html5/thumbnails/14.jpg)
dxi
dt=
nX
j=1
xjfjqj,i � �xi
� =nX
i=1
xifi
Steady State Solutionsf0 > 1
q1,1 = 1
q1,0 = 0
f1 = 1
q0,0 = (1� u)L ⌘ q
q0,1 = 1� q
dx0
dt= x0f0q � x0�
dx1
dt= x0f0 (1� q) + x1 � x1�
![Page 15: selection theory 2 - Amazon S3 · Selection Theory II Chris Kempes ... j =1 x j f j q j,i x i x i Frequency of a given sequence i Fitness of a given sequence i (e.g. relative growth](https://reader035.vdocument.in/reader035/viewer/2022081402/5f0ef4f87e708231d441c5c7/html5/thumbnails/15.jpg)
dxi
dt=
nX
j=1
xjfjqj,i � �xi
� =nX
i=1
xifi
Steady State Solutionsf0 > 1
q1,1 = 1
q1,0 = 0
f1 = 1
q0,0 = (1� u)L ⌘ q
q0,1 = 1� q
dx0
dt= x0f0q � x0�
dx1
dt= x0f0 (1� q) + x1 � x1�
� = f0x0 + x1
![Page 16: selection theory 2 - Amazon S3 · Selection Theory II Chris Kempes ... j =1 x j f j q j,i x i x i Frequency of a given sequence i Fitness of a given sequence i (e.g. relative growth](https://reader035.vdocument.in/reader035/viewer/2022081402/5f0ef4f87e708231d441c5c7/html5/thumbnails/16.jpg)
Steady State Solutionsdx0
dt= x0f0q � x0�
dx1
dt= x0f0 (1� q) + x1 � x1�
� = f0x0 + x1
![Page 17: selection theory 2 - Amazon S3 · Selection Theory II Chris Kempes ... j =1 x j f j q j,i x i x i Frequency of a given sequence i Fitness of a given sequence i (e.g. relative growth](https://reader035.vdocument.in/reader035/viewer/2022081402/5f0ef4f87e708231d441c5c7/html5/thumbnails/17.jpg)
Steady State Solutionsdx0
dt= x0f0q � x0�
dx1
dt= x0f0 (1� q) + x1 � x1�
� = f0x0 + x1
x0 + x1 = 1
![Page 18: selection theory 2 - Amazon S3 · Selection Theory II Chris Kempes ... j =1 x j f j q j,i x i x i Frequency of a given sequence i Fitness of a given sequence i (e.g. relative growth](https://reader035.vdocument.in/reader035/viewer/2022081402/5f0ef4f87e708231d441c5c7/html5/thumbnails/18.jpg)
Steady State Solutionsdx0
dt= x0f0q � x0�
dx1
dt= x0f0 (1� q) + x1 � x1�
� = f0x0 + x1
x0 + x1 = 1
dx0
dt= x0 [f0q � 1� x0 (f0 � 1)]
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Steady State Solutionsdx0
dt= x0 [f0q � 1� x0 (f0 � 1)]
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Steady State Solutionsdx0
dt= x0 [f0q � 1� x0 (f0 � 1)]
x⇤0 =
f0q � 1
f0 � 1
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Steady State Solutionsdx0
dt= x0 [f0q � 1� x0 (f0 � 1)]
x⇤0 =
f0q � 1
f0 � 1
f0q > 1x⇤0 > 0
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Error Threshold
f0f1
f0q > 1 log (f0) > �L log (1� u)
u <log (f0)
L