To investigate the relationship between parental and offspring generation genotype frequencies when a population is not being influenced by an agent of evolution, let’s review how offspring genotypes are formed when every potential parent is equally likely to survive and reproduce.

Under these conditions, the allele contributed by one parent does not and is not influenced in anyway by the allele contributed by the second parent; there is no sexual selection. Nor is a parent's likelihood of contributing alleles to the next generation influenced by environmental circumstances that favor survival of one parental phenotype over another or by chance events as occur during genetic drift.

Thus, if survival and reproduction are truly random events, each parent's allelic contribution to fertilization is a statistically independent event. Put differently, the genotype of the resulting offspring is the result of two independent, chance events - one chance event per allele. Imagine drawing two parents at random from a population and randomly collecting one allele from each.

Test your understanding by answering the question below.

When the independent events condition described above is met, a given genotype is expected to appear in the offspring generation with a likelihood equal to:

This is just a simple rule of probability. The likelihood that an event, composed of two or more independent events, will occur is equal to the mathematical product of the likelihood that each event will occur independently.

Review the bulleted definition above to see that it also makes biological sense. The likelihood that a given genotype will form is equal to the probability of picking first one then the second of the two alleles necessary to form it. And, the probability of picking an allele directly reflects its relative commonness (frequency) in the parental population.

Finally, note that this likelihood also represents the frequency with which we expect to observe the genotype in the offspring generation. This makes sense because how frequently we expect to see the genotype in the offspring generation is the direct result of how likely it is to form. Genotypes that have a low probability of forming, because the alleles that comprise them are relatively rare in the parental generation, will appear infrequently in the offspring generation.

There is one more thing to consider when determining the probability that given genotype will appear in the next generation; that is the number of ways a particular genotype can form.

Remember that the likelihood a particular genotype will form is equal to the probability of picking first one then the second of the two alleles necessary to form it. There is only one way to form a homozygote; both parents must donate the same allele. For example, the AA genotype can only form if, when one parent donates an A, the other does as well. Heterozygotes, in contrast, can form in two ways; 'parent one' can donate an A and 'parent two' an a or 'parent one' can donate an a and 'parent two' an A.

The fact that there are two routes to heterozygote formation must be taken into consideration when calculating the likelihood that the heterozygous genotype will occur in the offspring generation. To account for this, you must multiply the probability that a heterozygote will form by two, i.e. multiply the value described in the bulleted point above by two.

You should now have the tools to answer the question posed at the start of this module:

To answer the question titling this section and the module, let’s start by asking what you need to know. Then let’s figure out how you can get that information. To do this, review the question, the information provided in previous sections and develop a table similar to that below.

Check your outline above by working through the example below.

Figure 1

Now check your work: have you identified every possible genotype that could appear in the offspring generation when each parent has an equal chance of reproducing in the population above?

To do this, consider the following: if we have identified every possible genotype, then the frequencies calculated in question 2 will sum to 1 (i.e. 100%) because we will have accounted for 100% of the genotypes that could possibly occur in the offspring if all parents have an equal chance of reproducing and contributing alleles to the next generation.

If you have missed one, correct your response to question 2 above. Now you should have an accurate description of the offspring genotype frequencies that will materialize when every parent has an equal chance of reproducing in this population.

Now let’s confirm that random reproduction produces the offspring genotypes we predicted based on the parental allele frequencies above. To do so, we will run a simulation in which the computer will randomly pick 50 pairs of alleles to represent 50 random fertilization events.