Buffl

Altklausur

BK
by Benjamin K.

Consider two populations of equal size with the following genotype frequencies AA, Aa and aa.

Pop 1: 5, 10, 5.

Pop 2: 3, 10, 7.


FIS (inbreeding coefficient)

FST is the proportion of the total genetic variance contained in a subpopulation (the S subscript) relative to the total genetic variance (the T subscript)


What is FIS for population 1 and 2 and FST (FIS_1/FIS_2/FST, rounded to two digits)?

Population 1:

  • Genotype frequencies: AA = 5, Aa = 10, aa = 5. Total individuals = 20

  • Allele frequencies:

    • p = (2 * AA + Aa) / (2 * Total) = (2 * 5 + 10) / (2 * 20) = 20 / 40 = 0.5

    • q = (2 * aa + Aa) / (2 * Total) = (2 * 5 + 10) / (2 * 20) = 20 / 40 = 0.5

  • Observed heterozygosity (Ho): Ho = Number of Aa / Total = 10 / 20 = 0.5

  • Expected heterozygosity (He): He = 2pq = 2 * 0.5 * 0.5 = 0.5

  • FIS: FIS = (He - Ho) / He = (0.5 - 0.5) / 0.5 = 0

Population 2:

  • Genotype frequencies: AA = 3, Aa = 10, aa = 7. Total individuals = 20

  • Allele frequencies:

    • p = (2 * 3 + 10) / (2 * 20) = 16 / 40 = 0.4

    • q = (2 * 7 + 10) / (2 * 20) = 24 / 40 = 0.6

  • Observed heterozygosity (Ho): Ho = 10 / 20 = 0.5

  • Expected heterozygosity (He): He = 2 * 0.4 * 0.6 = 0.48

  • FIS: FIS = (0.48 - 0.5) / 0.48 = -0.04166... ≈ -0.04 (rounded to two decimal places)

FST Calculation:

To calculate FST, we need the total allele frequencies and the average expected heterozygosity within subpopulations (Hs).

  • Total allele frequencies:

    • pT = (5 + 3 + 10) / (20 + 20) = 18 / 40 = 0.45

    • qT = (5 + 7 + 10) / (20 + 20) = 22 / 40 = 0.55

  • Total expected heterozygosity (HT): HT = 2 * 0.45 * 0.55 = 0.495

  • Average expected heterozygosity within subpopulations (HS): HS = (He1 + He2) / 2 = (0.5 + 0.48) / 2 = 0.49

  • FST: FST = (HT - HS) / HT = (0.495 - 0.49) / 0.495 = 0.005 / 0.495 ≈ 0.0101 ≈ 0.01 (rounded to two decimal places)

Final Answer: 0.00, -0.04, 0.01

Inversions often stably maintain allelic combinations of genes in so-called supergenes. In a large population, two inversion types (A and B) segregate. Individuals heterozygous for the inversions (AB) have a survival advantage, while individuals homozygous for either type (AA or BB) have reduced survival.

In a population with the following genotype frequencies among adult individuals:

  • AA (n = 10)

  • AB (n = 190)

  • BB (n = 200)

What are the selection coefficients for the respective inversion types A and B (rounded to two decimal places)?

Step 1: Define Fitness Values

Let the relative fitnesses be:

  • Fitness of AA = 1 - s_A

  • Fitness of AB = 1 (reference)

  • Fitness of BB = 1 - s_B

Step 2: Calculate Observed Genotype Frequencies

Total population size: N = 10 + 190 + 200 = 400

Observed genotype frequencies:

  • f(AA) = 10 / 400 = 0.025

  • f(AB) = 190 / 400 = 0.475

  • f(BB) = 200 / 400 = 0.50

Step 3: Estimate Allele Frequencies

  • p (frequency of A) = f(AA) + (0.5 × f(AB)) = 0.025 + (0.5 × 0.475) = 0.2625

  • q (frequency of B) = 1 - p = 1 - 0.2625 = 0.7375

Step 4: Calculate Expected Hardy-Weinberg Frequencies

  • Expected frequency of AA = p² = (0.2625)² = 0.069

  • Expected frequency of AB = 2pq = 2 × (0.2625) × (0.7375) = 0.387

  • Expected frequency of BB = q² = (0.7375)² = 0.544

Step 5: Compute Selection Coefficients

The selection coefficient for each inversion type is given by:

  • 1 - s_A = (observed frequency of AA) ÷ (expected frequency of AA) = 0.025 ÷ 0.069 = 0.30

  • 1 - s_B = (observed frequency of BB) ÷ (expected frequency of BB) = 0.50 ÷ 0.544 = 0.75

Solving for s_A and s_B:

  • s_A = 1 - 0.30 = 0.70

  • s_B = 1 - 0.75 = 0.25

Final Answer:

s_A = 0.70, s_B = 0.25


Dobzhansky-Muller incompatibilities (DMIs) ... (choose the best answer)


explain how reproductive isolation, and ultimately speciation, can arise between populations.


A) can explain how assortative mating can evolve in the face of gene flow

B) can explain how hybrid sterility can arise

C) will reduce population fitness

D) rely on chromosomal rearrangements

E) explain why male hybrids are more often infertile than female hybrids

How it Works:

  1. Independent Evolution: Imagine two populations of the same species that become geographically separated. Over time, each population accumulates different mutations. Crucially, some of these mutations may become fixed (common) within each population because they are beneficial in that specific genetic background.  


  2. Epistasis: Epistasis is when the effect of one gene depends on the presence of other genes. In the context of DMIs, this means that the effect of a particular allele at one locus depends on which allele is present at another locus.  


  3. Incompatibility: The problem arises when individuals from these two populations hybridize. The hybrid offspring inherit a mix of alleles from both parents. The combinations of alleles that were beneficial in their original populations may now clash in the hybrid. For example, an allele at locus A from population 1 might work fine with the allele at locus B also from population 1. But when that same allele at locus A is paired with the allele at locus B from population 2, it might result in a harmful interaction, leading to hybrid sterility or inviability.  


B)


Author

Benjamin K.

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