What percent of Fry's DNA comes from his Grandfather in Futurama?

In the episode Roswell That Ends Well Fry's abnormal parentage is revealed. During the commentary David X Cohen challenges viewers to describe that parentage. I would expect to see all possible answers to the question. Those answers would be:

In a predestinous universe, that is one where Fry always got some % of his DNA from himself; and in a multidimensional universe, where Fry would have at first gotten his DNA from his proper grandfather, but in all future universes somehow gets those same pieces of his DNA from himself. Also, please address the origin of his Y chromosome.

I have seen pieces of this puzzle discussed elsewhere online, however I haven't seen a fully-realized solution.

So, What percent of Fry's DNA really does come from himself? And where does his Y chromosome come from?

Answer

It's been a while since I watched the episode, so you'll have to forgive the fuzzy details. I believe the grandfather in question is Fry's paternal grandfather (father's father), but please correct me if I'm wrong. I have also not listened to the DVD commentary you refer to, so you may well have insight that I lack.

First, the science.

As for the genetics of family; let's talk about general chromosomes, then sex chromosomes. There are 23 pairs of chromosomes in the human body; and one half of each pair of chromosomes comes from each parent (ie 23 single chromosomes from each parent). There are exceptions and fringe cases (Down's Syndrome, for example) but these are unimportant for the purposes of this discussion.

Thus, 50% of Fry's DNA comes from Fry's father, and 50% of Fry's father's DNA comes from HIS father. What is interesting is the way in which genes mutate before they are passed on to offspring. Essentially, in each pair of chromosomes, they can swap around parts of themselves (a process known as crossing over); so that each chromosome the parent supplies to his child is a mixture of both the chromosomes of the parent. Thus a parent is extremely unlikely to pass on his father's or his mother's copy of the chromosome as he received it. This diagram from wikipedia should help visualise the process a bit.

So (excluding sex chromosomes) it is impossible to say how much of fry's DNA comes from his grandfather. But we can assume that of the DNA Fry's father passed on to him, around 50% of that will have come from Fry's grandfather, and the rest from his grandmother; although the exact percentage could be much less or more. You will note that in the wikipedia meiosis diagram, each of the 4 gametes produced has a different composition of red and blue DNA; which is what I am driving at.

But statistically speaking, around 25% of the DNA in Fry's chromosomes comes from his grandfather, or more correctly, around 50% of the DNA in the chromosomes Fry obtained from his father comes from his grandfather.

With sex chromosomes, it's a different story. Each person contains one pair of sex chromosomes; of which there are two types: X and Y. In a normal human (we will again discount rare genetic disorders, such as Kleinfelter's Syndrome), a male has an XY configuration, and a female has an XX configuration. The important part of sex chromosome inheritance is that a male's X chromosome always comes from his mother, and his Y chromosome always comes from his father. This is an important element of sex-linked genetic diseases; which tend to be much more common in males because they only have a single X chromosome. So Fry's Y chromosome will have come entirely from his father, who will have gotten his Y chromosome from HIS father; Fry's grandfather.

So, since we can assume Fry, his father, and his (original) grandfather are all normal human males, it is safe to say that Fry's Y chromosome is that of his paternal grandfather.

That is where the actual science ends. Now we turn to science fiction to deduce the identity of Fry's paternal grandfather. And that depends on the theory of time travel.

If I'm missing any major theories on time-travel please tell me, but I think these are the relevant two options.

First option is that history is fixed, and that travelling back in time to the past and changing something is impossible, because it already happened that way. In this theory, Fry is his own grandfather. Enos is irrelevant, because he never fathered Fry's father; it was Fry himself who fathered his father all along. In this version of events we quickly reach a paradox. Fry gave his Y chromosome to his son, who gave it to fry, who gave it to his son, and so on infinitely. The Y chromosome has no origin. Likewise for around 25% of Fry's DNA.

The second option is that Fry's personal history is fixed, and that changing something in the past will create a new "alternate timeline". So Enos is Fry's paternal grandfather, Fry travels back in time and kills Enos, and copulates with his paternal grandmother. The result of this copulation is irrelevant to Fry's genetics and Fry's timeline, because he has already been born; and already contains Enos's DNA. The paradox in this version of events is that if Fry returns to his original timeline, then the events of Roswell in the past are ignored completely; though this would mean that Bender was never buried there waiting to be rescued in the present. Whereas, if Fry returned to the new alternate timeline's Future, he would never have been born because he killed his grandfather; and the offspring of his encounter with his grandmother (if any) would not have been Fry's father himself.

A third option is that the original Fry came from the second theory of events; and then conceived a first theory Fry's father when he travelled into the past. The resulting Fry would then conceive another Fry's father when HE travelled into the past, and so on. This version of events seems to resolve most paradoxes. There is an ultimate origin of Fry's DNA (Enos), so we know where the original Fry's DNA came from; and we know how that first Fry would pass on that DNA to any "next generation" Fry's. We also have a "multiverse" theory allowing for the branching of timelines, which allows for a rational explanation of how Fry could in fact be his own grandfather; although the question of which timeline Fry returns to after Roswell is still not answered. If the Fry who travelled back in time returned to his own timeline, Bender would not have buried himself in New Mexico for the gang to find in the present. But if he returned to a newly-altered timeline, would he still be the genetic original Fry, or would he be a newly altered Fry who was the result of the encounter with his grandmother?

I don't believe there is (or was meant to be) a definitive answer, but puzzling it out certainly helps make it one of Futurama's strongest episodes!

If anyone can find a flaw in my science or in my time travel logic, please let me know!