In biology, fitness measures the ability of an organism to reproduce and pass on its alleles and traits to future generations. An organism is considered more fit if many of its offspring survive and manage to reproduce, which creates more and more copies of the organism's original alleles. In this case, the deceased male still managed to pass on the most alleles since he has multiple offspring carrying his genetic information when compared to the other birds.

Darwinian evolution is often summarized as "survival of the fittest" but this does not necessarily mean "fit" in terms of being strong or athletic. "Fitness" in Darwinian terms describes the ability to survive to reproductive age and pass on genetic material to offspring. Random genetic mutations that contribute to this ability will be preserved and passed on to future generations. Darwinian fitness is typically measured by number of offspring that survive to reproductive age. While a fit organism will survive long enough to reproduce, life span alone doesn't define Darwinian fitness, nor does "speed" of evolution. The concept of passing on traits acquired during the lifetime is consistent with Lamarckian evolution, which is less commonly accepted than Darwin's principles. 

The correct answer is an individual that has more grandchildren than any other member of its population. Biological fitness is an organism’s ability to increase the frequency of their own alleles. Consuming large amounts of food, growing large, and having a long lifespan can potentially contribute to fitness, but an individual that does all those things but does not produce offspring would not be considered fit. Similarly, an individual that has a large number of offspring that are not capable of living long enough to produce their own offspring would also not be considered fit. Producing offspring that are fit enough to produce many grandchildren gives the starting individual the most chance of increasing the frequency of its own genes in its population, and is the best example of fitness.

The correct answer is "directional selection." Directional selection is when, over multiple generations, an entire population shifts its phenotype towards one extreme. Stabilizing selection is when the extremes of that trait decrease in frequency compared to the less extreme phenotypes. In the example of size, the extreme phenotypes are very small and very large. Disruptive selection is when the different extremes of a trait in a population become more frequent than the less extreme version, eventually forming different populations of organisms. If disruptive selection continues long enough, the differences between the two populations can accumulate to the point when they cannot breed with each other. This is speciation.

The question stem states that the mutation enables cells with the mutation to produce more daughter cells than the other cells around it. This is another way of saying that the mutation increases the fitness of the mutated cells. According to the principle of natural selection, an organism (or cell) with increased fitness will increase in prevalence in the population, since it can more readily reproduce than the other members of the population. Thus, the mutation will allow the cells that have the mutation to produce more daughter cells, so the mutation will become more prevalent in the population over time.

The question describes a particular trait—in this case, certain sloths' long arms—becoming advantageous given the environment. The population is now subject to new selective pressures, whereby sloths with short arms don't live as long or produce as many offspring as sloths with long arms. Since the sloths with long arms produce more offspring, more of the genes related to this trait get passed on to the next generation, so the average arm length of the sloth population increases. This natural selection is happening in a particular direction—in the direction of increasing arm length—so it is called "directional selection."

The question describes a particular trait—in this case, long arms—becoming advantageous in a given environment. The sloth population is now subject to new selective pressures, whereby sloths with shorter arms don't live as long or produce as many offspring as sloths with longer arms. Since the sloths with longer arms produce more offspring, more of the long-armed genes get passed on to the next generation, so the average arm length of the sloth population is most likely to increase.

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.