Darwin observed that the finches found on the Galapagos had adapted different sized beaks to eat different diets. By doing this, the birds had evolved to eat diets that would be inedible by other finches. This concept of a "niche" means that different species will exploit and use their environment in different ways.

The inheritance of traits through discrete units called alleles was not a part of Darwin's theory of evolution. A monk named Gregor Mendel developed the theory of inheritance through alleles. Darwin's theory did not propose a method of inheritance, and Darwin was unaware of Mendel’s work. The works of Darwin and Mendel were later combined by scientists to create the modern theory of evolution.

The finches' beaks are highly adapted to their preferred diet. Therefore, this is an excellent example of adaptation. Acclimation occurs on a very short-term basis and does not apply to speciation. Stabilizing selection decreases the amount of genetic diversity among a population, and does not promote speciation as seen among finches. Heredity is simply the degree to which a parent's genes are passed to its offspring and is not demonstrated by this example.

The answer is directional selection. This environmental change will cause a shift in the mean beak size of the population towards smaller beaks because their food resource was not affected. There is selection against long beak size only.

Artificial selection is a process by which humans have modified species over many generations by selecting and breeding individuals that possess desired traits. The result of such a selection is a narrowing of the traits originally present from its ancestors. The goal of artificial selection is generally to make certain desired traits fixed in the population, with an allele frequency of 100%. These traits are relatively arbitrary, and may be wild type, recessive, advantageous, or disadvantageous. The key factor is a decrease in genetic variability in a small population.

Examples of artificial selection include the derivation of individual breeds of dog and the production of genetically specific lab mice.

Disruptive selection occurs when conditions in a habitat favor individuals that are on the extremes of the phenotypic range, instead of individuals with intermediate phenotypic traits. In the example provided in the question, dark-colored moths and light-colored moths each have regions of the habitat where they gain an advantage, but intermediate grey coloring is not favored in any region of the habitat. As a result, both extremes will experience positive selection, while the intermediate will decrease, giving rise to a disruptive selection trend.

Stabilizing occurs when the intermediate phenotype is favored over either extreme. Directional selection occurs when a single extreme is favored over any other phenotype. Artificial selection is the result of human manipulation of breeding, selecting for chosen traits.

Stabilizing selection removes extreme variants, as they do not provide a survival advantage in a given environment, and increases the frequency of the intermediate phenotype. For example, the bone density of a species of bird is likely to experience stabilizing selection. Bones that are too dense will inhibit the bird's ability to fly, and bones that are too light will be brittle and prone to injury. Stabilizing selection moderates the influence of these two factors and selects for the intermediate phenotype that is neither too heavy, nor too weak.

Disruptive selection shows an increase the in the frequency of extreme traits and a decline in the intermediate trait. For example, if two extremes are white and black coloration, disruptive selection will act against grey coloration and favor both white and back. Directional selection favors only one extreme, for example favoring black over grey and grey over white. Artificial selection occurs when humans interfere with breeding habits to promote the inheritance of a specific trait.

In this example the extreme beak sizes are favored over the mean; however the mean beak size does not change. There is selection against the mean, without affecting the value of the mean. This type of selection is known as disruptive selection.

This relationship displays a frequency-dependent selection. Frequency-dependent selection occurs when the fitness of a phenotype depends on how common it is in the population. When blue-bellied lizards are preyed on the most because they are most abundant, the yellow-bellied lizard population grows quickly. However, as the blue-bellied lizard population declines, predators will begin to prey on the yellow-bellied lizards. As the yellow-bellied lizard population declines, the blue-bellied lizard population will increase, and so on. The number of blue or yellow-bellied lizards depends on the relative amount of lizards of a different phenotype, demonstrating frequency-dependent selection.  

Mutations are changes to a cell’s genome and include inversions, duplications, translocations, and deletions, among other unplanned changes to the DNA. Mutations can be harmful to the organism, but can also have beneficial or neutral impacts. Mutation is an important means of evolution because it introduces new genetic combinations into a genome, allowing for the potential of new functions.