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

A1A2A1A2 A1A2A1A2 A1A2A1A2 A1A2A1A2 A1A1A1A1 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 look at one locus, consider an individual who is A 1 A 1 1) random combination from unrelated parents 2) identical by descent (both A 1 alleles from a common ancestor)

example—one generation of selfing start with a single heterozygous hermaphrodite A 1 A 2 H obs = 1.0 A 1 A 1 A 1 A 2 A 2 A 2 H obs = 0.5 H 1 = ( )H 0 H t = ( ) t H 0 limH t = extreme cases: single fertilized female--->sib-mating single hermaphrodite--->selfing t

A 1 A 2 A 1 A 1 A 1 AA 4 3 A 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 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 1 A 2 A 1 A 1 A 1 A 1 The chance of events occurring is again (1/2) 4 However, only two possible pathways Inbreeding coefficient = 1/8 F = 1/8

A 1 A 2 A 1 A 1 A 1 AA 4 3 A 1 A 1 A 1

example—one generation of selfing start with a single heterozygous hermaphrodite A 1 A 2 H obs = 1.0 A 1 A 1 A 1 A 2 A 2 A 2 H obs = 0.5 H 1 = ( )H 0 H t = ( ) t H 0 limH t = extreme cases: single fertilized female--->sib-mating single hermaphrodite--->selfing t

Inbreeding Reduces Heterozygosity: outbred inbred genotype fr. A 1 A 1 p 2 (1-F) + pF = P A 1 A 2 2pq(1-F) = H A 2 A 2 q 2 (1-F) + qF = Q if F=0, HWE Measuring inbreeding: Observed Heterozygosity = 2pq(1-F) or, H obs / 2pq = 1-F or, F = 1 - [H obs /H exp ]; H exp = 2pq

How Does F Change Over Time in a Population Undergoing Inbreeding? F t = (1/2N e ) (1) + (1 - (1/2N e )) (F t-1 ) F t = 1 - ( 1 - (1/2N e ) t in small pop ns, as t --> 4, [1 – (1/2N e ) --> 0, F t --> 1 but, if N e --> 4, [1 – (1/2N e ) --> 1, F t stays near 0 identical indentical by descent by chance in pop ns known to inbreed: H t = H o (1-F) t

Drift and Inbreeding May Occur in a Subdivided Population: A 1 A 1 A 1 A 2 A 2 A 2 i p i = 0.4, q i = 0.6 j p j = 0.8, q j = 0.2 X p = 0.6, q =0.4 exp heterozygote deficiency

Estimates of Wahlund’s f st For Bougainville Islanders f st ABO Rh Gm Inv Hp PHs MNSs 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

Inbreeding depression in the Glanville Fritillary, Melitea cinxia Aland Islands in southwest Finland many small, isolated populations ~1600 suitable sites ~ occupied sites Saccheri et al Nature 392:491

Model 1: Extinction Throughout Aland Islands ( ) 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 : data on heterozygosity ( 7 allozyme loci) for 42 pop ns 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 ) decreasing regional trend in butterfly density decreasing habitat patch size decreasing heterozygosity (increased inbreeding) sample model (n=42 populations; 7 extinct ) 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