Chapter 11Inbreeding

When the parents of an individual share one ormore common ancestors, the individual is inbred.

Inbreeding is unavoidable in small populations asall individuals become related by descent overtime.

The consequence of matings between relatives isthat offspring have an increased probability ofinheriting alleles that are recent copies of the same DNA sequence.

These recent copies of the same allele are referred to as Identical by DescentIdentical by Descent or AutozygousAutozygous.

The inbreeding coefficient (FF) is used to measure inbreeding.

As F is a probability, it ranges from 0 to 1.

Identity by descent is related to, but distinct fromhomozygosity.

Individuals carrying two alleles identical bydescent are homozygous.

However, not all homozygotes carry alleles thatare identical by descent -- homozygotes includeboth autozygous and allozygous types.

Inbreeding decreases heterozygosity and increases homozygosity thus altering genotypicratios from that expected based on Hardy-Weinberg expectations.

However, inbreeding does NOT change allele frequencies.

The reduction in heterozygosity due to inbreedingis directly related to the inbreedingcoefficient.

We can estimate the level of inbreeding bycomparing observed (Ho) heterozygosity withexpected (He) under random mating as follows:

F = 1 - (He/Ho)

Effects of population size on the level of inbreedingcan be determined by considering the probabilityof identity by descent in the idealized randomly mating population.

When the initial population is NOTNOT inbred (F0 = 0),the inbreeding coefficient in any subsequentgeneration t is:

FFtt = 1 - [1 - 1/2N = 1 - [1 - 1/2Nee]]tt

Thus, inbreeding accumulates with time in allclosed finite populations at a rate dependent upontheir population size.

If population sizes fluctuates among generations,as occurs in real populations, the expression forthe inbreeding coefficient at generation t is:

FFtt = 1 - = 1 - [1 - (1/2N[1 - (1/2Neiei)])]i=1i=1

tt

Where Nei is the effective size of the ith

generation.

Indirect Estimates of Inbreeding CoefficientsIndirect Estimates of Inbreeding Coefficients

In most populations, levels of inbreeding areunknown.

However, an estimate of the average inbreedingcan be obtained from the effective inbreedingcoefficient (FFee):

FFee = 1 - (H = 1 - (Htt/H/H00))

Gray wolves became establishedon Isle Royale in about 1949during an extreme winterwhen the lake froze.

The wolf population is assumed to have beenstarted by a single pair of individuals.

Population rose toabout 50 in 1980.

Population crashedto 14 in 1990.

Decline could have been due to:reduced availability of preyreduced availability of preydiseasediseasedeleterious effects of inbreedingdeleterious effects of inbreedingcombination of factorscombination of factors

Suggested that the island population must beinbred due to the low number of founders.

All individuals have the same rare mtDNAhaplotype.

DNA fingerprint data suggests that island wolves are as similar as sibs in a captive populationof wolves.

Allozyme heterozygosity, based on 25 loci, was3.9% for Isle Royale wolves compared to 8.7%for a captive population.

Fe = 1 - (Hisland/Hmainland) = 1 - (0.39/0.87)= 0.55

Thus, this endangered island population is highly inbred.

Gray wolves suffer reproductive fitness dueto inbreeding -- the Isle Royale population hassmaller litters and poor juvenile survival!

Pedigree Path AnalysisPedigree Path Analysis -- Once a pedigree of anindividual (say “XX”) is obtained, we can calculateits inbreeding coefficient, FFXX.

Step IStep I: Draw the pedigree so that the commonancestors appear only once.

A common ancestor is any individual related toboth parents of X, the individual for whom wewish to determine FX.

If there are no common ancestors, then FX = 0

AStep IIStep II: Determine the inbreeding coefficient.

If there is no pedigree information on the commonancestors, it is often assumed to be non-inbred

If the common ancestor is inbred, then its inbreeding coefficient, FCA, must be calculatedbefore calculating FX

Calculate FCA as you would FX as described below.

Once FCA is determined, FX can be calculated.

Step IIIStep III: Look for loops in the pedigree

A loop is a path that runs from X, through oneparent, to the common ancestor, through the otherparent, and back to X without going through anyindividual more than once.

Determine the number of steps in each path.

Step IVStep IV: Calculate the contribution of each loopto the inbreeding coefficient.

The contribution of each loop to FX is determinedas follows:

(1/2)(1/2)ii X (1 + F X (1 + FCACA))

Where FCA is the inbreeding coefficient of thecommon ancestor and i is the number of steps ineach loop as defined in step III.

Step VStep V: Sum the contribution of each loop. The summation of all the contributions will be the inbreeding coefficient of individual X.

Example I: Half-Sib Matings

X

AA B AA C

D EPedigree

AA

D E

X

Path

AA

D E

X

Loop FCA i Contribution to FX

D - A - E 0.0 3 (1/2)3 X (1 + 0.0)

FX = 0.125

Example 2 -- Full-Sib Mating

A B A B

X

AA

BB

X

C D

Loop FCA i Contribution to FX

C--AA--D 0.0 3 (1/2)3 X (1+0.0) = 0.125C--BB--D 0.0 3 (1/2)3 X (1+0.0) = 0.125

FX = 0.25

A B

C D E F

G H I J

K L

M N

O

WHAT IS FO?

A B

C D E F

G H I J

K L

M N

O

P

A

C D

G H

K L

M

What is FWhat is FMM??

A

C D

G H

K L

M

Loop FCA iK-G-C-AA-D-H-L 0.0 7 (1/2)7 0.0078K-H-C-AA-D-G-L 0.0 7 (1/2)7 0.0078K-G-D-AA-C-H-L 0.0 7 (1/2)7 0.0078K-H-D-AA-C-G-L 0.0 7 (1/2)7 0.0078K-G-CC-H-L 0.0 5 (1/2)5 0.0313K-G-DD-H-L 0.0 5 (1/2)5 0.0313[C-AA-D 0.0 3 (1/2)3 0.125][C-AA-D 0.0 3 (1/2)3 0.125]K-GG-L 0.125 3 (1/2)3 X (1.125) 0.1406K-HH-L 0.125 3 (1/2)3 X (1.125) 0.1406

FM = 0.375