###Probably not.

The Rule of Two served two functions:

1. Stop infighting amongst many Sith vying for power. With only two Sith, they had to work together.
2. Strengthen the Sith Master over time, since each Master would be defeated by his successor and thus the succeeding Master was theoretically stronger for having defeated his predecessor.

The first and primary function is articulated well on Darth Bane's (archived) page from starwars.com:

An ancient and legendary Sith Lord, it was Darth Bane who saw that the Sith traditions of old were ultimately a dead end. All too often, squabbling Sith in their bid for power upended carefully laid plans and planted the seeds of their own defeat. After the Sith were decimated by the Jedi Knights of a thousand years ago, Bane enacted the Sith rule of two: there would be only two active Sith at one time -- a Dark Lord to embody the power, and an apprentice to crave it.

The second function is obvious from the nature of the Rule of Two, but is best articulated in Legends:

Under [Bane's] leadership the Sith had been reborn. Now they numbered only two—one Master and one apprentice; one to embody the power of the dark side, the other to crave it. Thus would the Sith line always flow from the strongest, the one most worthy. Bane’s Rule of Two ensured that the power of both Master and apprentice would grow from generation to generation until the Sith were finally able to exterminate the Jedi and usher in a new galactic age.

_{Dynasty of Evil, p. 9 (Legends novel)}

It's true that the second function sounds vaguely like natural selection. For example, Encyclopaedia Britannica says that

In natural selection, those variations in the genotype that increase an organism’s chances of survival and procreation are preserved and multiplied from generation to generation at the expense of less advantageous ones.

However, the second function follows from the first: the Rule of Two was instituted to stop infighting, and the practice of the apprentice killing the Master was mostly a consequence of the drastic reduction in the numbers of the Sith. The first/primary function doesn't have anything to do with natural selection, so it doesn't look like the Rule of Two was based on natural selection.

Furthermore, the Sith Order's behavior prior to the Rule of Two arguably looked like natural selection as well -- some Sith were "selected" by the Force to be stronger, and these stronger Sith were able to kill off the weaker ones. And there's no reason why a Sith Order composed of many Sith Lords couldn't institute a rule that each Sith apprentice must kill his Master so as to strengthen each Sith from "generation to generation".

Lastly, I can find no mention of natural selection in the context of the Rule of Two in any Star Wars source (various novels about the Sith, Wookieepedia, starwars.com, etc.).

Probably not.

The Rule of Two served two functions:

1. Stop infighting amongst many Sith vying for power. With only two Sith, they had to work together.
2. Strengthen the Sith Master over time, since each Master would be defeated by his successor and thus the succeeding Master was theoretically stronger for having defeated his predecessor.

The first and primary function is articulated well on Darth Bane's (archived) page from starwars.com:

An ancient and legendary Sith Lord, it was Darth Bane who saw that the Sith traditions of old were ultimately a dead end. All too often, squabbling Sith in their bid for power upended carefully laid plans and planted the seeds of their own defeat. After the Sith were decimated by the Jedi Knights of a thousand years ago, Bane enacted the Sith rule of two: there would be only two active Sith at one time -- a Dark Lord to embody the power, and an apprentice to crave it.

The second function is obvious from the nature of the Rule of Two, but is best articulated in Legends:

Under [Bane's] leadership the Sith had been reborn. Now they numbered only two—one Master and one apprentice; one to embody the power of the dark side, the other to crave it. Thus would the Sith line always flow from the strongest, the one most worthy. Bane’s Rule of Two ensured that the power of both Master and apprentice would grow from generation to generation until the Sith were finally able to exterminate the Jedi and usher in a new galactic age.

_{Dynasty of Evil, p. 9 (Legends novel)}

It's true that the second function sounds vaguely like natural selection. For example, Encyclopaedia Britannica says that

In natural selection, those variations in the genotype that increase an organism’s chances of survival and procreation are preserved and multiplied from generation to generation at the expense of less advantageous ones.

However, the second function follows from the first: the Rule of Two was instituted to stop infighting, and the practice of the apprentice killing the Master was mostly a consequence of the drastic reduction in the numbers of the Sith. The first/primary function doesn't have anything to do with natural selection, so it doesn't look like the Rule of Two was based on natural selection.

Furthermore, the Sith Order's behavior prior to the Rule of Two arguably looked like natural selection as well -- some Sith were "selected" by the Force to be stronger, and these stronger Sith were able to kill off the weaker ones. And there's no reason why a Sith Order composed of many Sith Lords couldn't institute a rule that each Sith apprentice must kill his Master so as to strengthen each Sith from "generation to generation".

Lastly, I can find no mention of natural selection in the context of the Rule of Two in any Star Wars source (various novels about the Sith, Wookieepedia, starwars.com, etc.).