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

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

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

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  1. 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

  2. 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

  3. 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 1 4 1 2 1 4 extreme cases: single fertilized female--->sib-mating single hermaphrodite--->selfing 1 2 1 2 64 t

  4. 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

  5. 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

  6. A A A A 1 2 3 4 A A A A 1 1 1 1 A A 1 1

  7. 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 1 4 1 2 1 4 extreme cases: single fertilized female--->sib-mating single hermaphrodite--->selfing 1 2 1 2 64 t

  8. 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

  9. 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

  10. Drift and Inbreeding May Occur in a Subdivided Population: A1A1 A1A2 A2A2 i 0.16 0.48 0.36 pi = 0.4, qi = 0.6 j 0.64 0.32 0.04 pj = 0.8, qj = 0.2 X 0.40 0.40 0.20 p = 0.6, q =0.4 exp 0.36 0.48 0.16 heterozygote deficiency

  11. Estimates of Wahlund’s fst For Bougainville Islanders fst ABO 0.0522 Rh 0.0113 Gm 0.0767 Inv 0.0777 Hp 0.0563 PHs 0.0490 MNSs 0.0430 Mean 0.0477

  12. 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.

  13. (Lerner 1954)

  14. lab studies have expected effects of inbreeding but most field studies suggest ecological rather than genetic factors cause extinction in small populations

  15. 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

  16. 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??

  17. extinct alive

  18. 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)

  19. 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)

  20. 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

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