Lecture 5: Genetic Variation and Inbreeding

September 7, 2012

Announcements

 I will be out of town Thursday Sept 20 through Sunday, Sept 24

 No office hours

 Friday, Sept 21: Prof. Hawkins will give a guest lecture about transposable elements

Computer Lab Access Schedule is posted on the door and on the website

Hari will be holding his office hours in the lab

Updated hours will be on class homepage

Last Time  Hardy-Weinberg Equilibrium

 Using Hardy-Weinberg: Estimating allele frequencies for dominant loci

 Variance of allele frequencies for dominant loci

 Hypothesis testing

Measures of Diversity are a Function of Populations and Locus Characteristics

Assuming you assay the same samples, order the following markers by increasing average expected values of Ne and HE:

RAPD SSR

Allozyme

Today  More Hardy-Weinberg Calculations

 Merle Patterning in Dogs

 First Violation of Hardy-Weinberg assumptions: Random Mating

 Effects of Inbreeding on allele frequencies, genotype frequencies, and heterozygosity

Example: Merle patterning in dogs

Clarke et al. 2006 PNAS 103:1376

 Merle or “dilute” coat color is a desired trait in collies, shetland sheepdogs (pictured), Dachshunds and other breeds

 Homozygotes for mutant gene lack most coat color and have numerous defects (blindness, deafness)

  Caused by a retrotransposon insertion in the SILV gene

Example: Merling Pattern in collies Homozygous wild-type

N=6,498 M1M1

Heterozygotes

N=3,500 M1M2

Homozygous mutants

N=2 M2M2

  Is the Merle coat color mutation dominant, semi-dominant (incompletely dominant), or recessive?

 Do the Merle genotype frequencies differ from those expected under Hardy-Weinberg Equilibrium?

Why does the merle coat coloration occur in some breeds

but not others?

How did we end up with so many dog breeds anyway?

Nonrandom Mating: Inbreeding   Inbreeding: Nonrandom mating

within populations resulting in greater than expected mating between relatives

 Assumptions (for this lecture): No selection, gene flow, mutation, or genetic drift

  Inbreeding very common in plants and some insects

  Pathological results of inbreeding in animal populations

 Recessive human diseases   Endangered species

http://i36.photobucket.com/albums/e4/doooosh/microcephaly.jpg

Important Points about Inbreeding   Inbreeding affects ALL LOCI in genome

  Inbreeding results in a REDUCTION OF HETEROZYGOSITY in the population

  Inbreeding BY ITSELF changes only genotype frequencies, NOT ALLELE FREQUENCIES and therefore has NO EFFECT on overall genetic diversity within populations

  Inbreeding equilibrium occurs when there is a balance between the creation (through outcrossing) and loss of heterozygotes in each generation

Inbreeding can be quantified by probability (f) an individual contains two alleles that are

Identical by Descent

A1A2 A3A4

A1A3 A2A3

A3A3 A2A3

A1A2 A3A4

A1A3 A2A3 A3A5

A3A3 A2A3

Identical by descent (IBD) Identical by state (IBS) Identical by descent (IBD)

P

F1

F2

Nomenclature  D=X=P: frequency of AA or A1A1 genotype

 R=Z=Q: frequency of aa or A2A2 genotype

 H=Y: frequency of Aa or A1A2 genotype

 p is frequency of the A or A1 allele

 q is frequency of the a or A2 allele

 All of these should have circumflex or hat when they are estimates:

p̂

Effect of Inbreeding on Genotype Frequencies

  fp is probability of getting two A1 alleles IBD in an individual

  p2(1-f) is probability of getting two A1 alleles IBS in an individual

  Inbreeding increases homozygosity and decreases heterozygosity by equal amounts each generation

  Complete inbreeding eliminates heterozygotes entirely

)1(2 fpfpD −+=

fpqpD += 2

22 fppfpD −+=22 fpfppD −+=

)1(2 pfppD −+=

fpqqR += 2

fpqpqH 22 −=

Fixation Index  The difference between observed and expected

heterozygosity is a convenient measure of departures from Hardy-Weinberg Equilibrium

E

O

E

OE

HH

HHHF −=

−= 1

Where HO is observed heterozygosity and

HE is expected heterozygosity (2pq under Hardy-Weinberg Equilibrium)

 Assume completely inbred fraction (f) and noninbred fraction (1-f) in population

)0()1(2 ffpqH +−=

!

H = 2pq(1" f )

!

f =1" H2pq

  If departures from Hardy Weinberg are entirely due to inbreeding, f can be estimated from Fixation Index, F

!

F =1" HO

HE

IBD IBS

Effects of Inbreeding on Allele Frequencies

 Allele frequencies do not change with inbreeding

  Loss of heterozygotes exactly balanced by gain of homozygotes

00201 qfppD +=

!

H1 = 2p0q0 " 2 fp0q0

iii HDp21

+=

!

p1 = (p02 + fp0q0) +

12(2p0q0 " 2 fp0q0)

!

= p02 + p0q0

!

= p02 + p0(1" p0)

!

= p02 + p0 " p0

2

!

p1 = p0

Extreme Inbreeding: Self Fertilization   Common mode of

reproduction in plants: mate only with self

 Assume selfing newly established in a population

  ½ of heterozygotes become homozygotes each generation

 Homozygotes are NEVER converted to heterozygotes

Self Fertilization

AA

aa

Aa

Aa

A

a

a A Aa Self-Fertilizations

AA

AA

AA

AA

A

A

A A AA Self-Fertilizations

½ Aa each generation ½ AA or aa (allele fixed

within lineage)

http://www.life.illinois.edu/ib/335/BreedingSystems/BreedingSystems.html

Decline of Heterozygosity with Self Fertilization

 Steady and rapid decline of heterozygosity to zero 01 2

1 HH =

121

−= tt HH

.21

0HHt

t ⎟⎠

⎞⎜⎝

⎛=

AA or aa

Aa

Partial Self Fertilization

 Mixed mating system: some progeny produced by selfing, others by outcrossing (assumed random)

  Rate of outcrossing = T

  Rate of selfing = S

 T+S=1

 Heterozygosity declines to equilibrium point

.2

2 1−+= tt

HSpqTH

aa

AA

Aa

What determines the equilibrium frequency of heterozygotes in a population with mixed selfing and

outcrossing?