David H.A. Fitch

Lecture notes

Deviations from the null hypotheses:  Selection at single loci

I.  Selection on phenotypes (genotypes) affects allele frequencies

A.  Correcting the HW model to account for selection

1.  HW model suggests that, given the genotype frequencies in reproducing adults, genotype frequencies (HW frequencies) of newborns in next generation can be predicted

2.  But in reality, there will be differential fitness among genotypes

1. Differential survival of newborns to reproductive age
2. Difference in ability to reproduce (contribute gametes)

3.  Absolute fitnesses; e.g.,

w(AA) = (2/3)[survival] x (5)[gametes contributed to the next generation]= 10/3

w(aa) = (1/2) x (4) = 2

4.  Relative Fitnesses; e.g.,

w(AA) = 1 = w(AA)/w(AA) = 1.0 [arbitrary which genotype to set to 1.0]

w(aa) = w(aa)/w(AA) = 2/(10/3) = 0.6

5.  Assume that 3 genotypes have the following fitnesses:

 Genotypes: AA Aa aa Fitnesses (as depicted in most textbooks):The "selection coefficient", s, takes on values 0 to 1 1 1 1 - s Fitnesses (an alternative formulation that is more general):By choosing h = 1, 0, 0.5 or >1, respectively, we can consider cases where an advantageous allele A is dominant, recessive, semidominant or overdominant 1 + s 1 + hs 1 Frequencies of zygotes:Predicted for the next generation, assuming random mating p2 2pq q2 Relative proportions of adults contributing to gene pool:s reflects advantage to survivorship, contribution to gene pool, or both p2(1+s) 2pq(1+hs) q2
 Exercises Consider the populations whose genotypes are shown below:
 Population AA Aa aa 1 1.0 0.0 0.0 2 0.0 1.0 0.0 3 0.0 0.0 1.0 4 0.5 0.25 0.25 5 0.25 0.25 0.5 6 0.25 0.5 0.25 7 0.33 0.33 0.33 8 0.04 0.32 0.64 9 0.64 0.32 0.04 10 0.986049 0.013902 0.000049
1. What are p and q in each population?
2. Which of the populations are in Hardy-Weinberg equilibrium?
3. In population 6, the a allele is detrimental, and the A allele is incompletely dominant such that AA is relatively the fittest, Aa has a fitness of 0.8, and aa has a fitness of 0.6.  If there is no mutation, what will p and q be in the next generation?

(The two exercises above and below were taken from Suzuki, Griffiths & Lewontin, 1981, An Introduction to Genetic Analysis, Freeman, New York.)

1. The fitnesses of three genotypes are w(AA) = 0.9, w(Aa) = 1.0, and w(aa) = 0.7.  If the population starts at allele frequency p = 0.5, what is the value of p in the next generation?  What is the predicted equilibrium frequency of p?