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So why do equal probabilities of survival and reproduction reproduce parental allele frequencies in the offspring generation?

Hopefully the answer to this question is more obvious now that you understand that an equal likelihood of surviving and producing surviving offspring is really about each individual having an equal chance of providing one of the two gametes to every fertilization event that occurs in a population and produces a surviving offspring. Nothing is operating to bias the chances of an individual contributing a gamete to each and every fertilization event and every individual's two alleles have an equal (50:50) chance of ending up in the gamete involved in fertilization. But in case its not quite clear, let's explore the issue a bit further.

To do this, re-examine the pool of potential gametes depicted as buckets in the cartoon above (which is repeated below for your benefit) and answer the questions that follow.

Population of 10 individuals. Each individual's genotype appears in its 'head'. Each individual's buckets represent the two types of gametes the individual produces in equal numbers based on its genotype for a single locus.

a. If a gamete is randomly selected from this population, as happens when each individual has an equal chance of surviving and reproducing, what is the likelihood (probability) that it contains an A allele?

b. Explain the reasoning behind your response to question a.

Much as there is a 13 in 20 chance of blindly pulling a gold chip out of a bag of 20 chips of which 13 are gold and 7 blue (and they differ in no other way), there is a 13 in 20 or 65% chance that the gamete would contain an A allele, if a a gamete were randomly selected from the population above (13/20 = 65/100 = 0.65*100 = 65%). Buckets of A alleles are nearly twice as common as buckets of a alleles. Consequently when reproduction is random, as happens when every individual has an equal probability of surviving and reproducing, any randomly selected parent is nearly twice as likely to be carrying an A allele as opposed to an a allele.

Now consider the following questions.

a. If 15 random matings took place in this population, requiring a total of 30 gametes to be randomly selected, what is the likelihood that each randomly selected gamete contains an A allele? How about an a allele?

b. Explain the reasoning supporting your response to question a.

c. Imagine all 30 of the gametes resulting from 15 random matings displayed on a piece of paper in front of you, how frequently would you expect the A allele to occur in this collection? The a allele? Why? Please explain.

d. Review your responses to questions a and c. What do they tell you about how likely (frequently) the A allele is to appear in the offspring population? The a allele? Why? Please explain.

Ideally, your responses to questions a and c were identical. For each of the 15 random mating events, the probability that a contributed gamete contains an A allele is 13/20 (65%) and an a allele 7/20 (35%). This is true because each gamete selection event is independent; the allele one gamete contains does not in anyway influence what allele the second gamete of a fertilization event will contain if mating is random. (This is not true is mating is not random. Can you provide an example?)

Since the above is true for each individual mating event, the overall allelic composition of the resulting offspring generation will simply reflect the probability associated with picking each allele during each random gamete selection event summed for all 30 events. Therefore, on average 65% of the 30 alleles will be A and 35% a in the offspring generation if mating is truly random.

Questions & Answers

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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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