© 1997
David H.A. Fitch
all rights reserved

Click on the topic you wish to review:

• Lecture notes
• Correcting the HW model to account for selection
• How might polymorphism be maintained in natural populations?
• Sewall Wright's "adaptive landscape" model of interacting evolutionary forces
• Exercises
• Simulations

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:

 Thus, the total contribution to the gene pool:

    p2(1+s) + 2pq(1+hs) + q2 = 1 + s(p2 + 2hpq)

(Note that the total contribution to the gene pool is NOT 1, because of the effect of the fitness coefficients)

(Note that the 1 in the right side of the equation results from the HW equation: p2 + 2pq + q2 = 1)

Frequencies of particular alleles in the next generation, n, can then be calculated:

     f(A)_n = p_n = (D + (H/2)) / total contribution of alleles
     = [p2(1+s) + pq(1+hs)] / [1 + s(p2 + 2hpq)]

If A is partially or wholly dominant, p is:

    p_n ~= p₀e^shn

B.  Predictions

1.  If A rare and dominant, initial increase is rapid
2.  If A rare and recessive, initial increase is very slow (shielded from selection by heterozygotes)
3.  Deleterious alleles are never completely eliminated (in the assumed infinitely large population)

C.  Examples

1.  Evolution of industrial melanism in the peppered moth, Biston betularia (Kettlewell 1955)

1. Melanism is generally due to a dominant allele (Why?)
2. Selection due to differential predation, as shown by marked-release and recapture experiments (How are such experiments performed?)

2.  Spread of insecticide resistance (DDT) (Bennett 1960)

1. Performed "sib-selection" experiments-selection of mating population based on the resistance of sibs to DDT
2. Not only showed this to be a dominant trait (why?), but also showed that adaptation has a genetic, non-Lamarckian basis

II.  How is polymorphism maintained in natural populations? Several alternative hypotheses:

A.  The genotypes have identical fitnesses, and (neutral) allele frequencies fluctuate by drift (But what have we learned about drift that argues against this being an adequate explanation for maintenance of variation?)
 

B.  The locus is not yet at monomorphic equilibrium, and the observed polymorphisms are transient (i.e., in the midst of a dynamic process)

C.  Fixation by selection is "balanced" by mutation (like fixation due to drift being balanced by mutation)

D.  Fixation by selection is balanced by gene flow between populations that might exist in different conditions (e.g., urban vs. rural environments)

1. Selection and gene flow may be 2 opposing forces that establish an equilibrium frequency for an allele from another population
2. Again, the immigrant allele may even be deleterious in population A's environment
3. Example: Mytilus edulis-see Futuyma, pp. 161-162

E.  Selection acts by itself on the locus to balance polymorphism

1.  Heterozygous advantage-("Overdominance, or heterosis,for fitness")
One of the few proven examples:  sickle-cell anemia

2. Frequency-dependent selection:  Fitness is variable and depends on a genotype's or allele'sfrequency

1. Positive dependence (but tends toward monomorphism)
   For example, APOSEMATIC Coloration-Warning colors are only effective when they are common (so predators associate particular patterns or colors with distastefulness)
2. Inverse dependence-(maintains polymorphism)
   For example, Batesian mimicry-palatable mimics are only protected by their mimicry if their frequency is low in the population-fitness is highest for the rarest alleles!
3. Also, frequency-dependent selection works whenever there is competition for different resources for which different genotypes are better adapted-the RARER genotype will have less competition! (Doesn't this sound very much like Darwin's chapter 4?)

3.  Heterogeneous temporal or spatial environments:  if the different environments provide two or more consistent niches

1. Polymorphisms will only persist if the selection coefficients are fairly large
2. For example, two different color patterns for the catepillars of Papilo demodocus are associated with different host plants

III.  The "Adaptive Landscape"

A.  There are 4 "forces" that shape the allele frequencies in a population: selection, mutation, gene flow (all "deterministic") and drift ("stochastic")

B.  The "adaptive landscape" is Sewall Wright's visualization for the interaction of these forces to produce particular allele (gene) frequencies; i.e., Sewall Wright's "SHIFTING BALANCE THEORY" (see Futuyma, pp. 170-174):

1.  There is a particular "landscape" for each environment

2.  Genetic drift is a larger force for shifting allele frequencies in smaller populations than in larger populations

3.  It is thus possible for drift to cause allele frequencies to shift to a "valley" on the "adaptive landscape"
Subsequent selection could then carry the allele frequencies up to another adaptive peak

(NOTE: A population is NOT necessarily driven by natural selection to the most adaptive possible genetic composition!)

4.  Shifting environments could also cause "peak shifts" (by shifting the "landscape" itself)

(NOTE: If the Environment changes, the Peaks are likely to change, and the Allele frequencies will change, probably to the CLOSEST peak-not necessarily the highest, most fit, peak)

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Exercises

1. Consider the populations whose genotypes are shown below:
    

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.)

2. 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?

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Simulations

By clicking here, you can go to a directory to download Joe Felsenstein's PopGen (for Mac) or SIMUL8 (for PC).  (Use the Back button of your browser to come back to this page.)

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[Deviations from the null hypotheses]