Nonrandom Mating
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© 1997
David H.A. Fitch
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Lecture notes

Deviations from the null hypotheses:  Inbreeding

I.  Inbreeding coefficient

A.  Autozygous:  not only homozygous, but both gene copies are identical by descent (i.e., can be traced to the same ancestral gene copy)

B.  Inbreeding coefficientF is the probability that an individual is autozygous (or the fraction of the population that is autozygous); i.e., F is the probability that a gene copy is Fixed.

C.  For example, what is F for an individual, I, that results...

  1. from a sib mating?
    F = Prob. (I is autozygous for one allele A* from a grandparent) = Prob.(both parents have an allele A* that is identical by descent) And Prob.( I has inherited A* homozygously)
    = (1/2 * 1/2) * 1/4 = 1/16 for A*
    There are 4 such gene copies in the grandparents, so F = 4 * 1/16 = 1/4
     
  2. from selfing?
    F = Prob. (I is autozygous for one allele A* from the single selfing parent) = the Mendelian 1/4 for A*
    There are 2 such gene copies in the parent, so F = 2 * 1/4 = 1/2
     
  3. from cloning?
     
  4. from random mating in a Mendelian population?

D.  Allozygous fraction of the population is  the non-autozygous fraction of the population (1 - F)

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II.  Correction of the Hardy Weinberg theorem for Inbreeding

A.  Assume the population is divided into an Autozygous fraction and an Allozygous fraction

  1. Of the allozygous fraction (1 - F), the frequency of genotype AA (i.e., D) in the next generation is predicted by HW:  (1 - F)p2
    Of the autozygous fraction (F), D is the same as the probability that an individual carries an A allele (because they are autozygous, such individuals will only contribute A alleles to the next generation)

    Thus, D = (1-F)p2 + Fp
     
  2. Similarly, R = (1-F)q2 + Fq
     
  3. However, heterozygotes can only result from matings in the allozygous fraction of the population, so

    H = (1-F)2pq
     
  4. Thus, D + H + R = [(1-F)p2 + Fp] + (1-F)2pq + [(1-F)q2 + Fq] = 1
    = [p2 + Fpq] + (1-F)2pq + [q2 + Fpq] = 1

B.  Predictions:

  1. If F = 0, then D = p2 ; H = 2pq ; R = q2 (i.e., the HW equilibrium!)
  2. If F = 1, then D = p ; H = 0 ; R = q
  3. If F = 1/2, then D = (1/2)p2 + (1/2)p ; H = (1/2)2pq ; R = (1/2)q2 + (1/2)q
  4. If there is inbreeding (F > 0), then the genotype frequencies change in successive generations and homozygosity increases
  5. But the allele frequencies do NOT change (inbreeding by itself does not cause evolution)

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III.  Heterozygosity

A.  Heterozygosity is the proportion of heterozygotes in a population inbred to an extent FHF = (1-F)2pq

B.  Predictions:

  1. For exclusively self-fertilizing populations, H decreases by 1/2 each generation
  2. If there is some fraction of matings among unrelated individuals, F and H will reach equilibrium values

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IV.  Application to 2 loci

A.  For 2 loci, any existing linkage disequilibrium will decay at a slower rate in an inbred population

B.  This is because the frequency of heterozygotes is lower (and recombinants can only result from recombination in heterozygotes)

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V.  Application to quantitative loci

A.  For additive loci, inbreeding does not change the phenotypic mean, but increases the phenotypic variance around the mean (there are more alleles distributed in the extreme homozygotes)

B.  For dominant (or overdominant loci), inbreeding not only increases the phenotypic variance, but also changes the phenotypic mean = Inbreeding Depression
1.  If recessive alleles cause lower fitness, they are eliminated more rapidly from an inbreeding population
2.  This selection will result in lower variation in inbred populations

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Exercises

  1. In an animal population, 20% of the individuals have genotype AA, 60% are Aa and 20% are aa.  Assume that allele A is dominant to a.  [This problem is borrowed with slight modification from Suzuki, Griffiths and Lewontin (1981, An Introduction to Genetic Analysis, Freeman, New York).]

    a.  What are the allele frequencies?

    b.  In this population, mating is always between like phenotypes.  What genotype and allele frequencies will prevail in the next generation?  (Such "assortative mating" is common in animal populations.)

    c.  Another type of assortative mating is that which occurs only between unlike phenotypes.  What genotype and allele frequencies will prevail in the next generation under this type of nonrandom mating?

    d.  For part c, what are the predicted equilibrium frequencies of alleles and genotypes after several generations?

    e.  Has evolution occurred in either case?  Why or why not?
     
  2. The frequencies of gametes AB, Ab, aB and ab are, respectively, 0.1, 0.2, 0.3 and 0.4.  [This exercise is borrowed with slight modification from J. Maynard Smith (1989, Evolutionary Genetics, Oxford Univ. Press, Oxford).]

    a.  What is the value of the disequilibrium coefficient, D?

    b.  What will be the value of D after 4 generations if the recombination rate between the A and B loci is 0.1?

    c.  If instead the recombination rate between A and B is 0.2, what will be the value of D after 4 generations?

    d.  Now suppose that mating is assortative such that like gametes only associate.  What will happen to the rate of change of D?  Why?

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Simulations

By clicking here, go to a directory to download Joe Felsenstein's PopGen (for Mac) or SIMUL8 (for PC).

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 Nonrandom
Mating  Genetic
Drift  Selection:
One Locus  Selection:
Many Loci
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[Nonrandom Mating] [Genetic Drift] [Selection: One Locus] [Selection: Many Loci]

[Natural Deviations from Null Hypotheses]

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