The Hardy-Weinberg principle is a mathematical model proposing that, under certain conditions, the allele frequencies and genotype frequencies in a sexually reporoducing population will remain constant over generations. For this principle to hold true, evolution must essentially be stopped. The conditions to maintain the Hardy-Weinberg equilibrium are: no mutation, no gene flow, large population size, random mating, and no natural selection.

The Hardy-Weinberg equilibrium can be disrupted by deviations from any of its five main underlying conditions. Therefore mutation, gene flow, small population, nonrandom mating, and natural selection will disrupt the equilibrium.

Differentiation is the process whereby relatively unspecialized cells become specialized into particular tissue types. This is a standard process in organismal development, and is generally unrelated to evolutionary principles.

All of the answer choices are assumptions made when considering Hardy-Weinberg equilibrium. Thus, the model is not very realistic in nature, since these conditions are rarely met. Also, no natural selection is assumed to occur.

All the factors listed are factors that can change the genetic equilibrium of a population. Genetic drift is a random change in the frequency of alleles, as in this question—at first, there were more red-spotted fish than spotless fish (a 2:1 ratio), but once the random fishing took place, there were fewer red-spotted fish than spotless fish (a 1:3 ratio). This selection by chance is genetic drift.

Gene flow is the movement of alleles into or out of a population, generally due to patterns of migration.

Migration is the physical departure or arrival of organisms between different populations or geographical locations.

Natural selection is the increased prevalence of "favorable" traits and genes, and the decline in prevalence of "unfavorable" traits and genes.

Mutation is a genetic alteration that results in a new DNA sequence. Mutation is responsible for the creation of new alleles, traits, and phenotypes.

For Hardy-Weinberg equilibrium to be in effect, five conditions must be met:

1. Large Population

2. Isolated populations (no immigration or emigration)

3. No spontaneous mutations

4. Mating is random

5. No natural selection

Hardy-Weinberg equilibrium describes no change in genotypic frequencies over multiple generations. This is not likely to be seen in nature due to multiple factors, but it can be a useful theory for scientists. Hardy-Weinberg equilibrium requires no immigration or emigration, a large population, random mating, and no spontaneous mutations (all of which are virtually unavoidable in nature). Natural selection would violate these conditions.

Hardy-Weinberg equilibrium describes no change in the genotypic frequencies of a population. After one generation, assuming random mating, a closed system, a large population, and no random mutations, the genotypic frequencies of the population will not change.     

Since the population is in Hardy-Weinberg equilibrium, we can use the following equation to determine the genotypic frequencies for the allele in question:

In this equation,  represents the frequency of the dominant allele and  represents the frequency of the recessive allele. The  portion of the expression represents the frequency of heterozygotes in the population. Using the allelic frequencies given in the question, we can calculate the percentage of heterozygous individuals.

32% of the population is heterozygous for the trait.

We can use the Hardy-Weinberg equations to solve this question:

We know that the black allele (B) is dominant and the brown allele (b) is recessive.

Using these two equations, we know that 0.25 are homozygous recessive (brown). This value will be equal to .

We can then solve as follows:

Therefore, we know that the frequency of each allele is equal to 0.5.

In the Hardy-Weinberg equation, the value of the term  is the percentage of homozygous dominant (BB) individuals in a population. Thus, to answer this question we will need to solve for .

With the information we are given, we can calculate , which is the percentage of the population that is homozygous recessive (bb). We know the total number of homozygous recessive rabbits (306 white rabbits) and the total number of rabbits in the population (306 + 544 = 850). We can thus divide the number of white rabbits by the population total to find :

36% of the population is homozygous recessive. We then take the square root of  to find :

This value tells us that 60% of all the alleles in the population are recessive (b).  

The Hardy-Weinberg equation is based off the idea that the total number of alleles in a population is the sum of the dominant and recessive alleles, as shown by this equation:

We can use this equation to solve for  using :

This value tells us that 40% of all the alleles in the population are dominant (B).

We can now square  to obtain . Recall that this will be the frequency of homozygous dominant individuals in the population:

The result is 16%, meaning 16% of the rabbits in the population are homozygous dominant. We can then multiply 16% by the total population to find the number of rabbits who are homozygous dominant:

Thus, 136 homozygous dominant rabbits would be expected in this population.

In the Hardy-Weinberg equation, the value of the term  is the percentage of heterozygous (Bb) individuals in a population. Thus, to answer this question we will need to solve for .

With the information we are given, we can calculate , which is the percentage of the population that is homozygous recessive (bb). We know the total number of homozygous recessive rabbits (76 without spots) and the total number of rabbits in the population (76+ 399= 475). We can thus divide the number of frogs without spots by the population total to find :

16% of the population is homozygous recessive. We then take the square root of  to find :

This value tells us that 40% of all the alleles in the population are recessive (b).  

The Hardy-Weinberg equation is based off the idea that the total number of alleles in a population is the sum of the dominant and recessive alleles, as shown by this equation:

We can use this equation to solve for  using :

This value tells us that 60% of all the alleles in the population are dominant (B).

Now that we have  and , we can calculate . Recall that this will be the frequency of heterozygous individuals in the population:

The result is 48%, meaning 48% of the frogs in the population are heterozygous.  We can then multiply 48% by the total population to find the number of frogs who are heterozygous::

Thus, 228 heterozygous frogs would be expected in this population.