Lab 4: Inbreeding and Kinship

Inbreeding

• Reduces heterozygosity• Does not change allele frequencies

Inbreeding: Breeding between closely related individuals.

.2

1pqHf f

Hf= Heterozygosity observed in a population experiencing inbreeding

)1(222 fpqpqfpqHf

The inbreeding coefficient (f) can be calculated by:

1. Probability that two homologous alleles in an individual are IBD.

2. Value of “f” ranges from 0 to 1.

Inbreeding coefficient (f)

A1A2 A2A2

A1A2 A1A2

A1A1IBD

A1A2 A1A2

A1A2 A1A2

A1A1 Not IBD

EHOHEH

EHOHF

1

The inbreeding coefficient (f) can be calculated using the fixation index (F), assuming the departure from HWE is entirely due to inbreeding.

HO > HE, negative F-value.HO < HE, positive F-value.

Selfing: The most extreme form of inbreeding

• Many plants, and some animals, are capable of self-fertilization

• Some only self, while others have a mixed mating systemo Selfing rate So Outcrossing rate T

At inbreeding equilibrium, there is no change in heterozygosity i.e. Ht = Ht-1 = Heq

.2

2 1 tt

HSpqTH

.2

4)1(2

4SpqS

SpqTH eq

.22

1SS

pqH

f eqeq

Rate of self-fertilization (S) can be estimated from the relationship:

SS

HHH

FE

OE

2

Assumptions:

1.Population is in inbreeding equilibrium.

2.Deviation from HWE is entirely due to self-

fertilization.

Problem 1. Mountain dwarf pine (Pinus mugo) typically grows at high elevations in Southern and Central Europe. Relatively little is known about the population genetics of this species, with most of the available information coming from several studies based on allozyme markers. The data from one of these studies is available on the laboratory page of the class website.

Download the data (file pmugo_allozymes.xls), analyze them using GenAlEx, and use the output of your analyses to answer the following questions:

a) Are most populations and loci in HWE? If not, are departures generally due to heterozygote excess or deficiency?

b) How do you explain differences among loci in departures from HWE? Do some loci tend to show more departures than others?

c) How do you explain differences among populations?

d) P. mugo has a mixed mating system. Assuming that the observed level of inbreeding can be accounted for by self-fertilization alone, what is the estimated rate of self-fertilization S?

e) The rate of self-fertilization can be estimated more reliably if the genotypes of the progeny are compared to the genotypes of their mothers for multiple loci. An estimate of the average rate of self-fertilization using this approach is S = 0.15. How would you explain the difference between this estimate and the one you calculated in d)? Please consider the biology of this organism in your response.

Example 1: Estimate the inbreeding coefficient of progeny resulting from mating between half-first cousins.

Half first-cousins share one grandparent.

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

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

CAA1A2

B C

D E

PA2A2

P(A2)= 1/2

CAA1A2

B C

D E

P

.641

21

21

21

21

21

21)11( AAP .

641

21

21

21

21

21

21)22( AAP

Overall probability that the two alleles in the offspring will be IBD is:

f = P(A1A1) + P(A2A2) = 1/64 + 1/64 = 1/32

P(A2)= 1/2 P(A2)= 1/2

P(A2)= 1/2

P(A2)= 1/2 P(A2)= 1/2

Chain- Counting Technique:

1

2

3

4

5

N

f

21

Where, N= # of individuals in the chain.

321

21 5

f

Chain for half-first cousin: D-B-CA-C-E

CA1

B C

D E

P

CA2CA1

B C

D E

P

CA2

Example 2: Estimate the inbreeding coefficient of progeny P.

m= # of common ancestors = 2Chain 1: D-B-CA1-C-E Chain 2: D-B-CA2-C-EN1= 5N2= 5

m

i

Ni

f1 2

1

161

21

21

21 55

1

m

i

N i

f

When common ancestors are inbred :

)1( 21

)(1

iCA

m

i

N

ffi

Where, fCA(i) is the inbreeding coefficient of the i- th common ancestor.

Estimation of Kinship coefficient

A1A2 A3A4

A1A3 A2A3

A3A3 A2A3

Inbreeding coefficient (f): Probability that two homologous alleles in an individual are IBD.

Kinship coefficient (fxy): Probability that two alleles, one randomly chosen from each individual are IBD.

X Y

A1A2 A3A4

A1A3 A2A3

A3A3 A2A3

HA3A3

Estimation of Kinship coefficient

Kinship coefficient between two individuals X and Y (fXY)

= inbreeding coefficient (f) of a hypothetical offspring from X and Y.

X Y

Problem 2. Assuming that all common ancestors have fCA = 0.01, determine the kinship coefficients for the following relationships:

a. Half-sibs (i.e., siblings that share one parent).

b. Full first cousins (offspring of full siblings)

c. GRADUATE STUDENTS ONLY: Monozygotic twins (Hint: Do not use the

chain counting technique for this case. Think about the strict definition

of the kinship coefficient).

d. Parent and offspring.

e. Grand-uncle and grand-niece (daughter of niece).

f. Grandmother and granddaughter.

g. GRADUATE STUDENTS ONLY: First cousins twice removed (i.e. a

cousin compared to the grandchild of a cousin).

http://z.about.com/d/multiples/1/0/i/E/blgal481.jpghttp://www.babiestoday.com/graphics/ds027.jpg

Problem 3. You have decided to do some targeted sequencing to determine actual genotype distributions for the locus controlling flower color in the Mountain Laurel population. You obtain the following results:

Genotype Count

PP 343

PR 87

PW 62

RR 248

RW 57

WW 223

a. Quantitatively evaluate the null hypothesis that this population does not deviate from Hardy Weinberg expectations.

b. Assuming the departure from HWE results entirely from inbreeding, what is the inbred fraction of this population?

c. Develop a biological hypothesis to explain your results.

IBD

F 1HOHE