From Ron:
in this problem, if you understand PARALLELISM, then you don't really have to worry about those distinctions.
the comparison must be made between individuals of one genetic composition and individuals of another genetic composition.

therefore, (a) and (e) are wrong because "that" is singular; we're supposed to be comparing individuals (plural).
(b) and (c) are wrong because "other"/"another" refers to another genetic composition; therefore, these are faulty comparisons, because there's no word to suggest individuals (we MUST compare individuals to other individuals, not to a composition).

that leaves (d).

--

as for the distinctions:

"the other" is used when there are only two things.
i chose one of the two dinner options; my date chose the other.

"another" is used for another of an indefinite number of things.
usually, i'll order one entree and my date will order another, so that we can each try some of both.

"each other" refers to interaction between exactly two things or people.
my date and i usually sit next to each other, rather than across from each other.

"one another" also refers to interaction, but there may be more than two things/people.
the holiday season offers many occasions for people who have not seen one another in many months to reunite.