The situation presents an example of disruptive selection. In disruptive selection, organisms with an intermediate phenotype are selected against. This means that individuals with the intermediate phenotype will decrease in prevalence in the population, while organisms on either end of the phenotype spectrum will increase in prevalence. In this case, the trait being discussed is crab size. The smallest and largest crabs survive, but those with an intermediate (middle-sized) phenotype are eaten. 

Stabilizing selection is a type of natural selection in which the extremes of phenotype are selected against. In other words, individuals with traits on either end of the phenotypic spectrum are more likely to die, or less likely to produce offspring, than those in the middle of the spectrum. This selection against both extremes favors individuals with an intermediate phenotype, and therefore reduces the diversity of the population. The only scenario in which the intermediate phenotype is selected for is the situation describing the cats and the mice. The smallest mice and the largest mice are both eaten by the cats, but medium-sized mice can both run fast enough to escape the cats and fit in the nooks and crannies, making them more evolutionarily fit for survival in this particular situation.

The scenario describing rattlesnakes presents an example of directional selection. Smaller rattlesnakes benefit from being able to fit into burrows. Based on this information alone, smaller rattlesnakes may have more offspring than larger rattlesnakes, and the rattlesnake population may eventually select for a smaller body size.

The scenario describing elk and antler size is also an example of directional selection. Male elk that have larger antlers are more likely to have more offspring, so the average antler size of the male elk in the population is likely to increase over time.

In the example describing hawks, the largest and smallest hawks each benefit from their body sizes, but medium-sized hawks do not. In this situation, disruptive selection is likely to take place, dividing the population over time into two predominant phenotypes. Given enough time, the hawk population might eventually split into two distinct species, one larger and one smaller.

The situation describing the moths being blown to an island in a storm describes a founder event, not any type of selection. We don't know anything about the makeup of the population of moths, so we can't say that any particular type of selection is taking place.

Allopatric speciation occurs when two populations are separated geographically and diverge over time due to natural selection, genetic drift, and mutations. This may be due to a mountain range forming, a river, or any sort of geographic barrier. Sympatric speciation involves populations diverging without any sort of geographical barrier. Both occur today and both likely occurred in the past as well.

All of the given are assumptions made for Hardy-Weinberg equilibrium except "mutations are non-lethal." In the Hardy-Weinberg model, there is an assumption of no mutations, as mutations would introduce new alleles that would distort the ratios predicted for a population in Hardy-Weinberg equilibrium. 

The correct answer is "sympatric." Speciation often occurs after a group of individuals becomes geographically isolated from its original population, as occurs in allopatric and peripatric specition. In parapatric speciation, there is a very small overlap in the area of the diverging population during and after speciation. In sympatric speciation, a new species evolves without the individuals ever leaving the area of the ancestral species. "Convergent" is a type of evolution where two different species adapt similar phenotypes.

The definition of species states that once two groups of animals are no longer able to breed with one another, they are considered members of different species. Allopatric speciation describes speciation that happens when two groups of organisms become separated by a geographic barrier that prevents interbreeding. In this question, the river is the geographic barrier separating the organisms in the mountains from those in the forest. Over time, these two groups of organisms acquire differences. Once these differences are enough to prevent the members of these two groups from being able to mate with one another, they are considered different species and allopatric speciation has occurred. 

A bat's wing and a bird's wing are analogous structures, as the development of these structures does not share an evolutionary history. The common ancestor of bats and birds did not have wings, therefore these traits arose independently. Therefore, they are not homologous, but represent convergent evolution, as similar traits arose from different lineages due to environmental pressures.

Mutation, migration, natural selection, and genetic drift all change the presence and proportion of alleles in a given population, contributing to evolution. An unchanging environment would not contribute to changes in alleles and, therefore, does not contribute to evolution.

We see natural selection because those chickens that are entirely immune to the disease produce more offspring than those chickens who were infected but survive. The gene(s) that offers protection against contracting the disease is retained at a greater rate than the gene(s) that protects the chicken from dying of the disease. If the genetic diversity of the population is reduced generations later, this suggests that the chickens experienced a population bottleneck when the population number dropped to half of its original number.

The founder effect is when genetic variability is lost due to a small number of individuals from a larger population forming a new population. The smaller population only breeds with each other and is not genetically representative of the larger group from which it was founded. Thus, the humans on a deserted island are an example of this. The hurricane might be an example of a population bottle neck and the breeder might be causing a population bottleneck by only breeding certain dogs, but the humans are a better example of the deliberate formation of a new breeding population.