Inbreeding if population is finite, and mating is random, there is some probability of mating with a...

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

A1A2A1A2

A1A1

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 = 0when a population is totally inbred, F = 1

look at one locus, consider an individual who is A1A1

1) random combination from unrelated parents2) identical by descent (both A1 alleles from a

common ancestor)

example—one generation of selfing

start with a single heterozygous hermaphrodite

A1A2 Hobs = 1.0

A1A1 A1A2 A2A2 Hobs = 0.5

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

14

14

12

extreme cases:single fertilized female--->sib-matingsingle hermaphrodite--->selfing

12

12

t

A1A2

A1

A1A1

A A4 3

A1

Calculating Inbreeding Coefficients from Genealogies

What is the chance of a individualBecoming 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 beMade homozygous due to inbreeding, therefore the Probability of homozygosity due to inbreeding is 4(1/2) 4 = 1/4

Inbreeding coefficient

A1A2

A1

A1A1

A1

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

However, only two possible pathwaysInbreeding coefficient = 1/8

F = 1/8

A1A2

A1

A1A1

A A4 3

A1

A1 A1

example—one generation of selfing

start with a single heterozygous hermaphrodite

A1A2 Hobs = 1.0

A1A1 A1A2 A2A2 Hobs = 0.5

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

14

14

12

extreme cases:single fertilized female--->sib-matingsingle hermaphrodite--->selfing

12

12

t

Inbreeding Reduces Heterozygosity:

outbred inbred genotype fr.

A1A1 p2(1-F) + pF = PA1A2 2pq(1-F) = HA2A2 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 --> , [1 – (1/2Ne) --> 0, Ft --> 1

but, if Ne --> , [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 0.36 pi = 0.4, qi = 0.6j 0.64 0.32 0.04 pj = 0.8, qj = 0.2

X 0.40 0.40 0.20 p = 0.6, q =0.4exp 0.36 0.48 0.16

heterozygote deficiency

Estimates of Wahlund’s fst For Bougainville Islanders

fst

ABO 0.0522Rh 0.0113Gm 0.0767Inv 0.0777Hp 0.0563PHs 0.0490MNSs 0.0430

Mean 0.0477

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 deleteriousrecessives 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 insmall populations

Inbreeding depression in the Glanville Fritillary, Melitea cinxia

Aland Islands in southwestFinland

many small, isolated populations~1600 suitable sites~350-500 occupied sites

Saccheri et al. 1998 Nature 392:491

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

risk of extinction increases with:decreasing population sizedecreasing density of butterflies in the

neighborhood of the focal populationdecreasing 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 predictextinction??

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 densitydecreasing habitat patch sizedecreasing heterozygosity (increased inbreeding)

sample model (n=42 populations; 7 extinct 1995-96)small size in 1995decreasing density of butterflies in the area

surrounding the focal populationdecreasing abundance of flowersdecreasing heterozygosity (increased inbreeding)

Consequences of Inbreeding in M. cinxia

reduced rate of egg hatching

reduced rate of larval survival

longer pupal period--->increased risk ofbeing parasitized

shortened female lifespan (lower femalefecundity)

Inbreeding Results in the Loss of Heterozygosity

more likley to occur in small populations (inbreedingand drift may both contribute to loss of geneticvariation)

in previously outbred populations, habitat fragmentation(and smaller population size) may lead to inbreedingand subsequent extinction

in species that routinely inbreed (e.g., parasitic wasps)inbreeding is not deleterious