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Now that we know the frequency with which we expect A and a alleles to appear in the offspring generation when all individuals in a population have an equal probability of surviving and producing surviving offspring, let's explicitly and consciously compare them to the frequency with which these same alleles appear in the parent population and, finally, reflect on the question titling this section.

a. How does the probability (likelihood) that an allele will make it into the offspring generation compare to the frequency with which that allele occurs in the parental generation?

b. Compare your responses to Problems 1, 2a, 2c, and 3a. What do they suggest about the relationship between the frequency with which an allele appears in the parental generation, its probability of appearing in parental generation gametes, and ultimately its frequency in the offspring generation when mating is random? Why? Please explain.

As is hopefully now clear, when all individuals in a population have an equal probability of surviving and reproducing successfully the probability that an allele ends up in a fertilization event and thus, in the offspring generation is equal to the frequency with which that allele appears in the parent generation. That is, when no agents of evolution are acting on a population, the allele frequencies observed in the offspring generation will be the same as those observed in the population producing them.

In reality, would you expect offspring generation allele frequencies to always be perfectly identical to those of the parental generation when mating is random? Why or why not? Please explain.

Of course in practice, all populations are subject to genetic drift (an agent of evolution) where, just by chance, some individuals will reproduce more frequently than others making a disproportionate contribution to the next generation. This effect will be most pronounced in small populations, like that in the example above, and least in very large ones.

Test your understanding by returning to the scenario depicted in Problem 3 of the previous section. It turns out that the allele associated with increased fertility, referred to as H2, is found in 21% of the loci of people of European descent.

a. If this population is not evolving with respect to this allele, how frequently should this allele occur in this population 200 years from now? Why? Please explain.

b. Draw a figure (graph) illustrating your prediction from part a. Please make sure to label your axes and include a figure legend .

a. In the absence of any evolutionary processes including genetic drift operating on this population, this allele should still occur in 21% of the population 200 years from now. This is expected because the H2 allele currently occurs in 21% of the population's loci, consequently 21% of all 'buckets' in the population contain this allele, leading 21% of the gametes involved in fertilization events to contain the H2 allele, causing the H2 allele to occur in 21% of the loci in the next generation. This will be repeated generation after generation for 200 years in the absence of an evolutionary force.

Expected frequency of the H2 allele over a 200 year period if the European population is not evolving with respect to this allele.

    Definitions

  • frequency - the number of times an event or observation, for example a particular measurement or condition like blue eyes, is observed in a collection of events or observations like those comprising a sample, population or study. In this statistical sense, a frequency is equivalent to a proportion. For example, the frequency of a particular allele is equal to the number of times that allele is observed in a population over the total number of alleles for that locus in the population. Can be expressed as a fraction, a percentage, a decimal, or a probability.
  • genetic equilibrium - state of a population in which allele frequencies remain unchanged from one generation to the next.
  • legend - a one or two sentence description of the variables depicted in a figure (graph).

    Works cited

  • Stefansson, H., Helgason, A., Thorleifsson, G. et al. 2005. A common inversion under selection in Europeans. Nature Genetics . 37:129-137.

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Source:  OpenStax, Understanding the hardy-weinberg equation. OpenStax CNX. Oct 22, 2007 Download for free at http://cnx.org/content/col10472/1.1
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