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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
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