Lecture 6: Inbreeding

September 4, 2015

Last Time

Calculations

Measures of diversity and Merle patterning in dogs

Excel sheet posted

First Violation of Hardy-Weinberg assumptions: Random Mating

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

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

Today

Self-fertilization and mixed mating systems

Inbreeding equilibrium

Estimating inbreeding coefficients from pedigrees

Relatedness and kinship

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

H

H

H

HHF

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

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

IBDIBS

Effects of Inbreeding on Allele Frequencies

Allele frequencies do not change with inbreeding

Loss of heterozygotes exactly balanced by gain of homozygotes

00201 qfppD

iii HDp2

1

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

aA

Aa Self-Fertilizations

AA

AA

AA

AA

A

A

AAAA Self-

Fertilizations

½ Aa each generation

½ AA or aa (allele fixed within lineage)

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

Changes in Genotype Frequencies under Self-Fertilization

Decline of Heterozygosity with Self Fertilization

Steady and rapid decline of heterozygosity toward zero01 2

1HH

12

1 tt HH

.2

10HH

t

t

AA or aa

Aa

If the population is infinite, how long will it take to eliminate

heterozygotes in a population that becomes completely self-

fertilizing?

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

aa

AA

Aa

H-W Expectation

Selfing Effect(from

previous slide)

Inbreeding Equilibrium Production of

heterozygotes by outcrossing balances loss of heterozygotes by selfing

For any value of p and S, there is a characteristic equilibrium point, regardless of starting genotype frequencies

Inbreeding coefficient also reaches equilibrium point, purely a function of selfing rate

Deq

Heq

Req

.22

1S

S

pq

Hf eqeq

See lab notes for derivations

Outcross Combinations That Produce Heterozygotes AA x aa

AA x Aa

aa x Aa

Aa x Aa

gain

loss

Estimating Selfing in Populations

Level of selfing can be readily estimated from allele frequencies and observed heterozygosity:

E

O

H

HF 1

.2

1S

S

H

HF

E

Oeq

OE

OE

HH

HHS

2

)(2

What are the assumptions of this calculation?

CA

CB

D E

P

CA

B C

D E

P

CA

CB

D E

P

CA

B C

D E

P

CA

B C

D E

P

Estimating Inbreeding from Pedigrees

Most accurate estimate of f derived from direct assessment of relationships among ancestors

CA

CB

D E

P

CA

B C

D E

P

CA

CB

D E

P

CA

B C

D E

P

CA

B C

D E

P

Half First-Cousins

CA: Common Ancestor

Estimating Inbreeding from Pedigrees

Probability P contains two A1 alleles IBD

Overall:

There are two alleles in the common ancestor, so there are two possibilities to inherit different alleles IBD

Probability P contains any alleles IBD is therefore:

P(A1) = ½

CAA1A2

B C

D E

PA1A1

P(A1) = ½

P(A1) = ½ P(A1) = ½

P(A1) = ½ P(A1) = ½

P(A1) = ½

CAA1A2

B C

D E

PA1A1

P(A1) = ½

P(A1) = ½ P(A1) = ½

P(A1) = ½ P(A1) = ½

8

1

2

1

2

1

2

1Pr

1

fromDA 8

1

2

1

2

1

2

1Pr

1

fromEA

64

1

8

1

8

1Pr

1

IBDA

32

1

64

1

64

1Pr fIBD

P(A1) = ½

CAA1A2

B C

D E

PA1A1

P(A1) = ½

P(A1) = ½ P(A1) = ½

P(A1) = ½ P(A1) = ½

P(A1) = ½

CAA1A2

B C

D E

PA1A1

P(A1) = ½

P(A1) = ½ P(A1) = ½

P(A1) = ½ P(A1) = ½

Chain Counting Count links to Common Ancestor starting with one parent of inbred individual and continuing down to other parent

D-B-CA-C-E

N=5 links

32

1

2

1

2

15

N

f

For multiple common ancestors, m:

.2

1

1

m

i

N i

f

If common ancestors are inbred as well:

)1(2

1

1

m

iCA

N

i

i

ff

Where fCAi is inbreeding coefficient of common ancestor i

Kinship Coefficient

CA2CA1

D

B C

E

Estimate of relationship between two individuals in a population, D and E

Probability a randomly selected allele from each is Identical by Descent

Easiest to estimate as f of hypothetical progeny, p

P )1(2

1

1

m

iCA

N

PDE i

i

ffk

Relatedness Sewall Wright revolutionized

study of inbreeding in 1922

Defined coefficient of relationship (r)

Shared alleles between related individuals result in genetic correlation

Also the fraction of alleles that two individuals share IBD

Can be estimated as twice the inbreeding coefficient of possible offspring (i.e., twice the kinship)

http://www.harvardsquarelibrary.org/unitarians/wright-

sewall.html fr 2

Relatedness Relatedness is twice the

probability that two alleles, one chosen randomly from each individual, are IBD

CA1

B C

D E

P

CA2CA1

B C

D E

P

CA2

PDEDE fkr 22 r=0.5 for parent–offspring and full sibsr=0.25 for half-sibs, andr=0.125 for first cousins.

Can be estimated from sharing of alleles conditioned on allele frequencies

Estimating Relatedness Without a Pedigree Molecular markers provide indication of relatedness of

individuals based on shared alleles

More polymorphic markers are preferable: microsatellites

Source: SilkSatDB

Allozymes

Microsatellites

Lowe, Harris, and Ashton 2004

Estimating Relatedness Without a Pedigree In many cases, relationships among samples are

unknown

Relationships can be estimated using multiple, highly polymorphic loci

Queller and Goodnight (1999, Mol Ecol. 8:1231) developed a program, KINSHIP, that estimates relatedness based on likelihood ratios (explained in more detail later)

Number of Microsatellites Required to Distinguish Relationships

Relatedness in Natural Populations White-toothed shrew

inbreeding (Crocidura russula) (Duarte et al. 2003, Evol. 57:638-645)

Breeding pairs defend territory

Some female offspring disperse away from parents

How much inbreeding occurs?

12 microsatellite loci used to calculate relatedness in population and determine parentage

17% of matings from inbreeding

Num

ber

of

mati

ngs

Relatedness

Parental Relatedness

Off

spri

ng H

ete

rozy

gosi

ty