Hardy-Weinberg states that for a population to be in equilibrium, it must not be experiencing migration, genetic drift, mutation, or selection. By this definition, population size cannot fluctuate.

Random mating must occur in the population in order for the equilibrium to remain. If nonrandom mating occurred, allele frequency in the population would change. The alleles frequency of those mating the most would increase, while that of those mating less would decrease.

Large populations must be used to minimize the effects of genetic drift. Mustations cannot occur, as these could introduce new alleles.

It is important to note that no natural populations exist in Hardy-Weinberg equilibrium. This is simply a theoretical tool.

When a population is in Hardy-Weinberg equilibrium, we can quantitatively determine how the alleles are distributed in the population. P² is equal to the proprtion of the population that is homozygous dominant based on the equation p² + 2pq + q² = 1. We also know that p + q = 1.

Since P² = 0.49 in this case, we know that p is equal to 0.7. Since there are only two alleles for this gene, we know that the other allele, q in this case, is 0.3. Since homozygous recessive is referred to as q² in the equation, we can plug in the value of 0.3 and determine that q² = 0.09. As a result, we confirm that 9% of the population is homozygous recessive.

We must remember our two equations for allele frequency, according to Hardy-Weinberg equilibrium.

We know that, in the first equation, each term represents a total percentage of homozygotes or heterozygotes.  represents the allele for red eyes and  represents white.

Using the information from the question, we can solve for and .

The frequency of each allele is 0.50.

For this question we are going to need to make use of the Hardy-Weinberg equilibrium equations. The equation we need to use is:

These numbers represent the percentages of each genotype found in a given population. We were given the values of  and  in the question.

After plugging the numbers into the equation, we can find the value of . This value will give us the frequency of homozygous dominant individuals.

We can solve this question using the Hardy-Weinberg equations:

In the second equation, corresponds to the frequency of homozygous dominant individuals, corresponds to the heterozygous frequency, and corresponds to the frequency of homozygous recessive individuals. We are given enough information to find each of these values from the question.

We can find the values of and by taking the square root of their squares.

We can solve this question using the Hardy-Weinberg equations:

is equal to the recessive allele frequency, while in the second Hardy-Weinberg equation corresponds to the frequency of the recessive phenotype.

The question tells us the number of dominant red snails and the number of recessive white snails. Using these values, we can find the frequency of the recessive phenotype.

From here, take the square root to find the value of .

Most of the information in the question is actually superfluous because we are given the final dominant allele frequency. The dominant allele frequency corresponds to the variable in the Hardy-Weinberg equations.

The question tells us that the dominant allele frequency after introduction of the predator is . Use this value in the first Hardy-Weinberg equation to solve for the recessive allele frequency, .

For a population in Hardy-Weinberg equilibrium, every trait follows the equations:

In these formulas,  represents the frequency of the dominant allele and  represents the frequency of the recessive allele.  represents the frequency of the homozygous dominant genotype,  represents the frequency of the heterozygous genotype, and  represents the frequency of the homozygous recessive genotype.

In this case, the individuals with blue eyes would be represented by the homozygous recessive genotype. Using this data, we can solve for the frequency of the recessive allele.

Use the frequency of the recessive allele to find the frequency of the dominant allele, .

It is impossible to determine the allele frequency from the given information.

The problem only tells the number of black beetles, but does not give any information that would allow us to find the total number of beetles in the population. We do not have the homozygous recessive population or the distribution of heterozygotes and homozygous dominant beetles. Given information on the number of white beetles would allow us to calculate the recessive allele frequency, and subsequently the dominant allele frequency.