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Population Genetics:
The 5 Factors of Evolution
Laurence Loewe
Laboratory of GeneticsWisconsin Institute of Discovery
University of Wisconsin-Madison
Nov, 15, 2013, Biocore 301 PopGen Unit Lecture 2-preB
Questionsare
welcome!
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2
Population Genetics Unit Overview
Date Lecture Topic
W Nov 13 PopGen: science of the future
F Nov 15 Five factors of evolution
M Nov 17 Adaptation, selection, fitness landscapes
W Nov 20 Mutation, selection drift at one locus
F Nov 22 Multi-locus population genetics
M Nov 25 Mechanism of speciation
W Nov 27 Phylogenetic Trees
Office hours
Discovery Buildingat a table nearreception desk
Thursday,Nov 14, 2-3pm,
Thursday,Nov 21, 2-3pm,
Assignment
due Mon Nov 25
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5 Factors of Evolution
Modeling
Absence of all
Presence of Individual Factors
Combinations
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Evolution as a Unifying TheoryFITNESSABSTRACTIONALLOWSSEPARATIONOFCONCERNS
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Summary
A Mini-Guide to
Modeling
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Math
Models
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http://co
mmons.wikimedia.org/wiki/File:28_-
_New_
York_-_Octobre_
2008.jpghttp://upload.wikimedia.org/wikipedia/commons/2/20/New_
York_
16.jpg
Renew?or Ruin?
Modeling power
responsibilitybrings
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map
sto
Reality
Math
Models
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Linkstorealitymakethemodelre
levantforbiology
Linksareshapeda
roundaQuestion
Statisticsoftennee
dedforgoodlinks!
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10
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map
sto
Reality
mustsim
plifywell
Math
Models
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Occams Razor
Make modelsas simple
as possible,but not simpler.
William of Occam,
Franciscan Friar,1287-1347
Free paraphrase of Albert Einsteinsinterpretation of Occams Razor
http://en.wikipedia.org/wiki/William_of_Ockham
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W
ikipedia/File:Ancient_warded_loc
k_
key_
transparent.png
Wikipedia-ile:English_-_Mortise_
Lock_with_
Key_-_Walters_
52173.jpg
Question
Abstration
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All models
are wrong,
but some
are useful.
George Box
Professor of Statistics,
UW-MadisonWikipedia: Glass-of-water.jpg
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map
sto
Reality
mustsim
plifywell
mustc
onserve
Math
Models
16
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Bad Models often Violate a
Conservation Principle
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map
sto
Reality
mustsim
plifywell
mustc
onserve
m
ust
earn
trust
Models
18
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You will encounter Models
with different levels of maturity
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Life of A Model
Life event Meaning for a Model Model Quality
Conception New Question without a good answer Subconscious
Birth First Idea how an answer might even look like Speculation
Toddler Noise about this is heard by more people Speculation
Wikipedia/File:Learning_to_walk_by_pushing_wheeled_toy.jpg
20
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Life of A Model
Life event Meaning for a Model Model Quality
Conception New Question without a good answer Subconscious
Birth First Idea how an answer might even look like Speculation
Toddler Noise about this is heard by more people Speculation
Teens First Tests using a reasonable Null-Hypothesis Weak HypothesisTwenties First Supporting Evidence and many conflicts Hypothesis
Thirties 50% Majority Support among key researchers Strong Hypothesis
Wikipedia:Marine_da_nang.jpgWiki
pedia:Japan0
8.07_Shi
buya_Myb
estfriend
s.jpg Wikipedia:Teens_sharing_a_song.jpg
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Life of A Model
Life event Meaning for a Model Model Quality
Conception New Question without a good answer Subconscious
Birth First Idea how an answer might even look like Speculation
Toddler Noise about this is heard by more people Speculation
Teens First Tests using a reasonable Null-Hypothesis Weak HypothesisTwenties First Supporting Evidence and many conflicts Hypothesis
Thirties 50% Majority Support among key researchers Strong Hypothesis
Forties 80% Majority Support among key researchers,may still be called hypothesis (historic reasons)
Young Theory
>Fifties Doubters lack new evidence; enter textbooks Theory,Principle,Law, Dogma, ...>Nineties Death of last scientist from era before
Fossilized Death by boredom; all agree; no questions left Everybody knows
Immortal Now New Discipline: fountain of good questions Institutionalized
Death Death by data: can & does happen any time Case for history
Wikipedia:Charles_D
arwin_
by_
Julia_
Margaret_Cameron_
2.jp
g
Wikipedia:Lord_Ke
lvin_photograph.jpg
Wikipedia :Burlington_House_ILN_1873.jpg
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Life of A Model
Life event Meaning for a Model Model Quality
Conception New Question without a good answer Subconscious
Birth First Idea how an answer might even look like Speculation
Toddler Noise about this is heard by more people Speculation
Teens First Tests using a reasonable Null-Hypothesis Weak HypothesisTwenties First Supporting Evidence and many conflicts Hypothesis
Thirties 50% Majority Support among key researchers Strong Hypothesis
Forties 80% Majority Support among key researchers,may still be called hypothesis (historic reasons)
Young Theory
>Fifties Doubters lack new evidence; enter textbooks Theory,Principle,Law, Dogma, ...>Nineties Death of last scientist from era before
Fossilized Death by boredom; all agree; no questions left Everybody knows
Immortal Now New Discipline: fountain of good questions Institutionalized
Data Death by data: can & does happen any time Case for history
Improving
Quality
ofModels
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It can happen ...... any time ...
... to any model ...
Death by Data
... especially if the data is ...
... easier to understand ...
... in a simpler model...
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Model Reliability is Variable
Speculation
Facts
Science fiction Hard problems inbasic research
Appliedscience
25
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Evaluate the evidence.
... but how?
Before you believe anything in science ...
... and also after you do ...
... dont forget to:
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Intuition
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Hard Dry Math
in ratio
Controlled Labin vivo
Test Tubein vitro
Intuition
Real Lifein natura
Shoulders
of Giants
MeatySimulations
in silico
AllApproaches
need to worktogether!
by Brian Pelletier
Bloody Statisticsin estimo
27
You need a bit of modeling background for appreciating:
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Evolution = Map*
to how populations change
* Map under construction: you can hurt yourself & others if you get this wrong!
You need a bit of modeling background for appreciating:
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Evolution as a Unifying TheoryFITNESSABSTRACTIONALLOWSSEPARATIONOFCONCERNS
29
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5 Factors of Evolution
Modeling
Absence of all
Presence of Individual Factors
Combinations
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Who?
31
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What is a
Null-Model
?0
0
00
00
0
00
0
NullModel
32
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Mini-guide to constructing Null-Models:
What is the most
BORING
thing that couldpossibly happen?
33
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The Big Null Model In Evolution:
Nothing interestingever happens
in evolution.
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Evolution needs
change in allele frequencies.
What is the mostboring thingthat could happen toa collection of alleles?
You tell me...
NullModel
35
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Big Null Model In Evolution
There is no evolution
Allele frequencies
do not change
NullModel
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Big Null Model In Evolution
There is no evolution
Allele frequencies
do not change
NullModel
almost
verymuc
h
atthe
moment
37
n
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Lets find a good abstraction!
Assume only counts of different alleles matter
Track identity of allele types, ignore structure, function... 1 allele could be like 1 bean population = bean-bag!inheritance by sampling simplest diploids:
1 locus, 2 alleles Bean Bag Genetics
Abstraction
38
n
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Hardy-Weinberg Principle:
Conservation Law of Evolution
Alleles
do not appear or disappear in a population
unless some evolutionary factor is operatingon the population.
Remember: Evolution means change in allele frequencies
C
onservatio
39
n
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How does
that work?Lets do a very small simulation!
Ideal diploid population: 1 locus, 2 alleles
Question: How do genotypes and alleles change over time?
See Movie
C
onservatio
40
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Hardy-Weinberg Ratios
A Mendelian diploid locus with 2 alleles
has the equilibrium genotype frequencies
p2+ 2pq + q2= 1
that can be predicted from allele frequencies
p+ q = 1
Results
... but only if evolutionary factors are absent!
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Please close your laptops!
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CleanerX
Fantasticnewdete
rgent
Annualre
venue2.41
billion$int
hecountry
35%increaseinmarketsh
areforlaun
drydetergen
t
43
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Hardy-Weinberg-The-Movie
Have you seen it?
A Yes.I easily followed the
explanations
B Yes.I worked through the
explanations and got it not easy
C Yes, I tried, but that was too hard
D Parts, I didnt have time for it all
E No, I have not yet watched it
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What is the annual revenue of CleanerX?
Which value comes closest?
A 2.1 million $
B 2.4 million $
C 3.5 million $
D 2.5 trillion $
E 1.9 billion $
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Hardy-Weinberg-The-Movie
What are the main results of the study?
A The twiddle-dee population is not in
Hardy Weinberg Equilibrium.
On these grounds they get the
company to change.
B The population is in
Hardy-Weinberg Equilibrium.
C The data shows that
recessive alleles at SweetLocus1
decrease in the orchard. That is why
pollination declines in the movie.
D I dont know.
E No, I have not yet watched it.
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Hardy-Weinberg-The-Movie
What are the main results of the study?
A Frank & Rose find the population isnot in Hardy Weinberg Equilibrium.
On these grounds they get the
company to change.
B The population is in
Hardy-Weinberg Equilibrium.
C The data shows that
recessive alleles at SweetLocus1
decrease in the orchard. That is why
pollination declines in the movie.
D I dont know.
E No, I have not yet watched it.
48
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CleanerX
Fantasticnewdete
rgent
Annualr
evenue2.41
billion$int
hecountry
35%increaseinmarkets
hareforlau
ndrydeterge
nt
illions 49
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You can open your laptops again ...
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0.160.25
0.48
0.5
0.360.25
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
2012 2013
AA (dominantlikes CleanerX)
Aa(heterozygotesdominant likesCleanerX)
aa (pollinatesrecessive)
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Hardy-Weinberg-The-Movie
What are the main results of the study?
A Frank & Rose find the population is
not in Hardy Weinberg Equilibrium.
On these grounds they get the
company to change.
B The population is in
Hardy-Weinberg Equilibrium.
C The data shows that
recessive alleles at SweetLocus1
decrease in the orchard. That is why
pollination declines in the movie.
D I dont know.
E No, I have not yet watched it.
53
It h
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It can happen ...... any time ...
... to any model ...
Death by Data
... especially if the data is ...... easier to understand ...
... in a simpler model...
54
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What did wenot test yet?
Were all tests donerigorously?
55
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There was this talk byProf. Karl Broman...
2013, BMI, UW-Madison
56
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Lets do a classical
Hardy-Weinberg Testfor 2013
58
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Hypothesis:
CleanerX kills Alleles that Pollinate
(If not, then CleanerX removes only allelesthat would not have pollinated anyway!)
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Genotype ObservedGenotype
Count / != Freq
Expected GenotypeEquations = Freq* != Count
Observed-Expected
Count "2
AA 7000 p2
Aa 2800 2pqaa 200 p2
Total ! p2+2pq +q2
Allele Symbol forallele frequency
Allele Counts fromGenotype Counts
Allele frequency
A p 2AA + Aa =
a q 2aa + Aa =
Computing Hardy-Weinberg Equilibrium1. Observe genotype counts (co-dominance needed, if using phenotype)
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Genotype ObservedGenotype
Count / != Freq
Expected GenotypeEquations = Freq* != Count
Observed-Expected
Count "2
AA 7000 p2
Aa 2800 2pqaa 200 p2
Total ! 10000 p2+2pq +q2
Allele Symbol forallele frequency
Allele Counts fromGenotype Counts
Allele frequency
A p 2AA + Aa =
a q 2aa + Aa =
Computing Hardy-Weinberg Equilibrium2. Computesum of genotypes
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Genotype ObservedGenotype
Count / != Freq
Expected GenotypeEquations = Freq* != Count
Observed-Expected
Count "2
AA 7000 0.70 p2
Aa 2800 0.28 2pqaa 200 0.02 p2
Total ! 10000 1 p2+2pq +q2
Allele Symbol forallele frequency
Allele Counts fromGenotype Counts
Allele frequency
A p 2AA + Aa =
a q 2aa + Aa =
Computing Hardy-Weinberg Equilibrium3. Computeobserved genotype frequencies
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Genotype ObservedGenotype
Count / != Freq
Expected GenotypeEquations = Freq* != Count
Observed-Expected
Count "2
AA 7000 0.70 p2
Aa 2800 0.28 2pqaa 200 0.02 p2
Total ! 10000 1 p2+2pq +q2
Allele Symbol forallele frequency
Allele Counts fromGenotype Counts
Allele frequency
A p 2AA + Aa = 16800 16800 /(2!) = 0.84
a q 2aa + Aa = 3200 3200 /(2!) = 0.16
Computing Hardy-Weinberg Equilibrium4. Compute observed allele frequencies
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Genotype ObservedGenotype
Count / != Freq
Expected GenotypeEquations = Freq* != Count
Observed-Expected
Count "2
AA 7000 0.70 p2 0.705
Aa 2800 0.28 2pq 0.269aa 200 0.02 p2 0.026
Total ! 10000 1 p2+2pq +q2 1
Allele Symbol forallele frequency
Allele Counts fromGenotype Counts
Allele frequency
A p 2AA + Aa = 16800 16800 /(2!) = 0.84
a q 2aa + Aa = 3200 3200 /(2!) = 0.16
Computing Hardy-Weinberg Equilibrium5. If at HWE: Compute expectedgenotype frequencies
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Genotype ObservedGenotype
Count / != Freq
Expected GenotypeEquations = Freq* != Count
Observed-Expected
Count "2
AA 7000 0.70 p2 0.705 7050
Aa 2800 0.28 2pq 0.269 2690aa 200 0.02 p2 0.026 260
Total ! 10000 1 p2+2pq +q2 1 10000
Allele Symbol forallele frequency
Allele Counts fromGenotype Counts
Allele frequency
A p 2AA + Aa = 16800 16800 /(2!) = 0.84
a q 2aa + Aa = 3200 3200 /(2!) = 0.16
Computing Hardy-Weinberg Equilibrium6. Compute expectedgenotype counts
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Genotype ObservedGenotype
Count / != Freq
Expected GenotypeEquations = Freq* != Count
Observed-Expected
Count "2
AA 7000 0.70 p2 0.705 7050 -50 0.35
Aa 2800 0.28 2pq 0.269 2690 110 4.5aa 200 0.02 p2 0.026 260 -60 13.8
Total ! 10000 1 p2+2pq +q2 1 10000 18.6
Allele Symbol forallele frequency
Allele Counts fromGenotype Counts
Allele frequency
A p 2AA + Aa = 16800 16800 /(2!) = 0.84
a q 2aa + Aa = 3200 3200 /(2!) = 0.16
Computing Hardy-Weinberg Equilibrium7. Compute "2test statistic
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Chi-Square Significance Test
1. Compute test statistic "2= 18.6
2. Determine probability that null hypotheses explains the data (P-Value):"2Table lookup, 1 degree of freedom:
P #5% "2 $3.84(P value #5% for test statistic "2 $3.84)P #0.1% "2 $10.83
P = 1.6*10-5 (computed by R command: pchisq(q=18.6,df=1,lower.tail=FALSE)
It is very unlikely that this population is in Hardy-Weinberg Equilibrium.
!Practical Conclusion: No equilibriumInterpretation:The hypothesis is back, but we still need to check if this generation is indeedspecial (i.e. something else could be going on).
!2
=
Obs!Exp( )Exp
2
all"
67
Summary
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y
How to test for Hardy Weinberg Equilibrium
1. Observe genotype counts (co-dominance needed, if using phenotype)2. Computesum of genotypes3. Computeobserved genotype frequencies
(Divide each genotype count by !Gto get its frequency.)
4. Compute observed allele frequenciesFor the first allele add the homozygous genotype frequency to half of the heterozygotefrequency. For the next, just use the relationship p + q = 1 for loci with 2 alleles.
5. If at HWE: Compute expected genotype frequenciesUse the Hardy-Weinberg relations : p2+ 2pq + q2= 1
6. Compute expectedgenotype counts7. Compute "2 test statistic. Here chsquare%8. Convert the test statistic to a P value%
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5 Factors of Evolution
Modeling
Absence of allPresence of Individual Factors
Combinations
Top Related