11 15 13 Images-5 Factors of Evolution

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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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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

[email protected]


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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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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

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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

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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

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Life of A Model





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







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







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

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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

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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

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Modeling

Absence of all

Presence of Individual Factors

Combinations

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Who?

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What is a

Null-Model

?0

0

00

00

0

00

0

NullModel

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Mini-guide to constructing Null-Models:

What is the most

BORING

thing that couldpossibly happen?

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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

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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

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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

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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

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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

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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

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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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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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A Frank & Rose find the population isnot in Hardy Weinberg Equilibrium.


company to change.







D I dont know.


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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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A Frank & Rose find the population is

not in Hardy Weinberg Equilibrium.


company to change.







D I dont know.


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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...

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What did wenot test yet?

Were all tests donerigorously?

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There was this talk byProf. Karl Broman...

2013, BMI, UW-Madison

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Lets do a classical

Hardy-Weinberg Testfor 2013

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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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Count / != Freq


Observed-Expected

Count "2

AA 7000 p2

Aa 2800 2pqaa 200 p2

Total ! 10000 p2+2pq +q2



Allele frequency

A p 2AA + Aa =

a q 2aa + Aa =

Computing Hardy-Weinberg Equilibrium2. Computesum of genotypes

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Count / != Freq


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 frequency

A p 2AA + Aa =

a q 2aa + Aa =

Computing Hardy-Weinberg Equilibrium3. Computeobserved genotype frequencies

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Count / != Freq


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 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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Count / != Freq


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 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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Count / != Freq


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 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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Count / != Freq


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 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"

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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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Modeling

Absence of allPresence of Individual Factors

Combinations

Documents

11 15 13 Images-5 Factors of Evolution