Allele frequencies are the measure of an allele in relation to the total number of alleles in the given population. Introducing a predator that only preys upon homozygous dominant members will cause the number of dominant alleles to drop significantly and will, therefore, change allele frequencies. This would be an example of the bottleneck effect. Isolating a small subset of a population is going to change allele frequencies because that small subset is not likely to accurately represent the original population. This is an example of the founder effect.

Random mating is actually a factor that helps maintain allele frequencies, and is a requirement for Hardy-Weinberg equilibrium.

Of the choices, the only one that is not a Hardy-Weinberg assumption is that natural selection is occurring on the population. In fact, the exact opposite is a Hardy-Weinberg assumption. If natural selection is occurring on a population, over a large period of time, it is likely to have an effect on allele frequencies within the population.

All other answers are requirements in order for Hardy-Weinberg equilibrium to be in effect: large population size, random mating, and negligible mutation frequencies.

The Hardy-Weinberg equilibrium states that the frequency of alleles at a locus remains constant from generation to generation. In order for this to be the case, natural selection cannot affect the alleles under consideration. All other answer choices describe conditions that do need to be met for Hardy-Weinberg equilibrium to be displayed. Note that the conditions for Hardy-Weinberg equilibrium are not met in nature.

Use the two Hardy-Weinberg equations:

Above,  is the frequency of the dominant allele, and  is the frequency of the recessive allele in the isolated population. 

Since there are 20 people in total on the island, that means that there are 40 alleles for eye color. 2 of the 40 are for the blue allele:

We are looking for the blue eye phenotype, which can only result from two recessive alleles.

Use the Hardy-Weinberg equations:

The equation he will need to set up is the following:

Solve for  and substitute the first equation into the equation above.

Simplify.

Lastly, find .

The correct answer is Bb = 0.44 and bb = 0.11. 

Since we know BB = 0.45 and the equations for allele frequencies when Hardy-Weinberg equilibrium conditions are met: 

and 

We solve for B first:

Now we can solve for the homozygote recessive.

Lastly, solve for the heterozygote.

Non-random mating is not an assumption of the Hardy-Weinberg equilibrium, in fact, in order to make predictions about the next generation, random mating must be assumed. Additionally, no new mutations, no gene flow, no genetic drift, and no natural selection must also occur. If any of these phenomenon are present in a population, we can not estimate allele frequencies in subsequent generations due to chance, rather selective pressures may favor one allele over another allele. 

To solve this problem, assume Hardy-Weinberg equilibrium and use the associated equations to solve:

 is dominant allele and  is recessive allele 

To find the phenotype ratios:

 homozygous dominant 

 heterozygous 

 homozygous recessive 

The Hardy-Weinberg equilibrium does not account for genetic drift. The Hardy-Weinberg law states that genetic frequencies will remain constant in a population from generation to generation in the absence of evolutionary influences. Therefore, there is no migration, natural selection, nonrandom mating, or small populations in a Hardy-Weinberg population.

Codominance occurs when both phenotypes are displayed equally and independently in the phenotype (without blending). This is the case with blood type and the red and white spotted flower. A person with blood type AB expresses proteins that will recognize both type A and type B. The red and white spotted flower equally expresses the two color phenotypes.

The pink flower is an example of incomplete dominance (blended phenotype). Option IV describes a normal dominant-recessive hierarchy, where only one copy of the dominant allele is needed to display the dominant phenotype.