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Inbreeding if population is finite, and mating is random, there

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Inbreeding

if population is finite, and mating is random, there

is some probability of mating with a relative

effects of small population size, mating with

related individuals are similar

drift, inbreeding, population subdivision all

reduce within population genetic variance

more likely if population size is small

consequence is assortative mating over entire genome

--deviations from expected heterozygosity

(vs. HWE expectations) over all genes

A1A2

A1A2

A1A2

A1A2

A1A1

look at one locus, consider an individual who is A1A1

1) random combination from unrelated parents

2) identical by descent (both A1 alleles from a

common ancestor)

F = inbreeding coefficient

= probability that an individual that is

homozygous carries two alleles that

are identical by descent, i.e., from

a common ancestor

when a population is totally outbred, F = 0

when a population is totally inbred, F = 1

example—one generation of selfing

start with a single heterozygous hermaphrodite

A1A2Hobs = 1.0

A1A1 A1A2 A2A2 Hobs = 0.5

H1 = ( )H0 Ht = ( )tH0 limHt = 0

1

4

1

2

1

4

extreme cases:

single fertilized female--->sib-mating

single hermaphrodite--->selfing

1

2

1

2

64

t

A

A

A

A

1

2

3

4

A

A

1

1

A

A

1

1

Calculating Inbreeding Coefficients from Genealogies

What is the chance of a individual

Becoming homozygous due to alleles

From the same source?

p = 1/2

p = 1/2

p = 1/2

p = 1/2

Chance of all events occurring = (1/2) 4

However, there are four possible alleles that could be

Made homozygous due to inbreeding, therefore the

Probability of homozygosity due to inbreeding is 4(1/2) 4= 1/4

Inbreeding coefficient

A

A

1

2

A

A

1

1

A

A

1

1

The chance of events occurring is again (1/2) 4

However, only two possible pathways

Inbreeding coefficient = 1/8

F = 1/8

A

A

A

A

1

2

3

4

A

A

A

A

1

1

1

1

A

A

1

1

example—one generation of selfing

start with a single heterozygous hermaphrodite

A1A2Hobs = 1.0

A1A1 A1A2 A2A2 Hobs = 0.5

H1 = ( )H0 Ht = ( )tH0 limHt = 0

1

4

1

2

1

4

extreme cases:

single fertilized female--->sib-mating

single hermaphrodite--->selfing

1

2

1

2

64

t

Inbreeding Reduces Heterozygosity:

outbred inbred genotype fr.

A1A1 p2(1-F) + pF = P

A1A2 2pq(1-F) = H

A2A2 q2(1-F) + qF = Q

if F=0,

HWE

Measuring inbreeding: Observed Heterozygosity = 2pq(1-F)

or, Hobs / 2pq = 1-F

or,

F = 1 - [Hobs/Hexp]; Hexp = 2pq

How Does F Change Over Time in a Population Undergoing Inbreeding?

Ft = (1/2Ne) (1) + (1 - (1/2Ne)) (Ft-1)

Ft = 1 - ( 1 - (1/2Ne)t

in small popns, as t --> 4, [1 – (1/2Ne) --> 0, Ft --> 1

but, if Ne --> 4, [1 – (1/2Ne) --> 1, Ft stays near 0

identical indentical

by descent by chance

in popns known to inbreed: Ht = Ho(1-F)t

Drift and Inbreeding May Occur in a Subdivided Population:

A1A1 A1A2 A2A2

i 0.16 0.48 0.36pi = 0.4, qi = 0.6

j 0.64 0.32 0.04pj = 0.8, qj = 0.2

X 0.40 0.40 0.20p = 0.6, q =0.4

exp 0.36 0.48 0.16

heterozygote

deficiency

Estimates of Wahlund’s fst For Bougainville Islanders

fst

ABO0.0522

Rh0.0113

Gm0.0767

Inv0.0777

Hp0.0563

PHs0.0490

MNSs0.0430

Mean0.0477

Predicted Effects of Inbreeding

1) inbred populations become genetically uniform;

no longer respond to selection

2) inbred populations may become phenotypically

more uniform due to loss of genetic variance

3) inbreeding depression—fixation of deleterious

recessives and loss of selectively favored

heterozygotes leads to decreased fertility,

viability, etc.

(Lerner 1954)

lab studies have expected effects of inbreeding

but most field studies suggest ecological rather than

genetic factors cause extinction in

small populations

Saccheri et al. 1998 Nature 392:491

Inbreeding depression in the

Glanville Fritillary,

Melitea cinxia

Aland Islands in southwest

Finland

many small, isolated populations

~1600 suitable sites

~350-500 occupied sites

Model 1: Extinction Throughout Aland Islands (1993-94)

risk of extinction increases with:

decreasing population size

decreasing density of butterflies in the

neighborhood of the focal population

decreasing regional trend in butterfly density

modelling extinction risk 1995-96:

data on heterozygosity ( 7 allozyme loci) for 42 popns

336 additional populations with only ecological data

does genetic data improve model’s ability to predict

extinction??

extinct

alive

Effects of inbreeding on M. cinxia

probability of extinction is affected by:

global model (n=336 populations; 185 extinct 1995-96)

decreasing regional trend in butterfly density

decreasing habitat patch size

decreasing heterozygosity (increased inbreeding)

sample model (n=42 populations; 7 extinct 1995-96)

small size in 1995

decreasing density of butterflies in the area

surrounding the focal population

decreasing abundance of flowers

decreasing heterozygosity (increased inbreeding)

Consequences of Inbreeding in M. cinxia

reduced rate of egg hatching

reduced rate of larval survival

longer pupal period--->increased risk of

being parasitized

shortened female lifespan (lower female

fecundity)

Inbreeding Results in the Loss of Heterozygosity

more likley to occur in small populations (inbreeding

and drift may both contribute to loss of genetic

variation)

in previously outbred populations, habitat fragmentation

(and smaller population size) may lead to inbreeding

and subsequent extinction

in species that routinely inbreed (e.g., parasitic wasps)

inbreeding is not deleterious