lateral thinking - Cryptobiology? Biocryptology?

I have a friend who is a self-proclaimed cryptobiologist. Okay, maybe I don't, but if I did, I like to think she would have presented me with this puzzle:

Find the hidden message:

441344•444422•132211 || 111313•114413•221311•221111•134422

The message is the answer to "What is my favorite recently established (though somewhat contested) idea in biology?"

Also, this "friend" of mine is a much better biologist than she is a cryptologist. In fact, she is just about as novice in the "cryptology" scene as one can get.

---

Update

Hint:

None of this is required in order to solve the puzzle, but it will probably help.

She told me "You silly chemist, to get you started, consider the elements hydrogen, nitrogen, oxygen, and the halogens; apply their strategy in your strategy. Or consider the behavior those nucleobases you're talking about.

Do you notice any pattern in the numbers? It's small, but it's there. Each number by itself won't mean much.

From there,
44 + 1 = 45
44 + 2 = 51
44 - 4 = 35
15 = E; 21 = F."

Answer

The secret message (and answer to the recently established but contested biological theory) is:

RNA WORLD (the idea that the precursors to life were self-replicating RNA molecules)

Reasoning/pitfalls below

---

Given the hints:

The number strings are perhaps better interpreted as doublets (or maybe alleles based on the Punnett square hint). If you break up the numbers into doublets, you could rewrite the string as:

44 13 44•44 44 22•13 22 11 || 11 13 13•11 44 13•22 13 11•22 11 11•13 44 22

This leaves only four possible doublets, 11, 13, 22, 44. Possibly those could map to A, C, G, T. But given the others hints, it looks like some sort of bonding may need to be used. And a Punnett square represents crosses between two individuals and the potential offspring they could have, so perhaps we're supposed to cross two individuals with these "alleles" but there are still so many possible directions...

Thanks to the nice work by Element118, we can use:

A Polybius square to translate the pairs of numbers into DNA bases:

TCT TTG CGA || ACC ATC GCA GAA CTG

Then we need to:

Transcribe the DNA (take its complementary strand as RNA, where A pairs with U and C pairs with G)

TCT TTG CGA || ACC ATC GCA GAA CTG
AGA AAC GCU || UGG UAG CGU CUU GAC

And since biology has its own:

Triplicate code for converting RNA sequences to amino acid sequences (see pic below) and since amino acids can each be represented by a single letter (again, pic below), we must then translate the RNA sequence.

Doing so, we get:

AGA AAC GCU || UGG UAG CGU CUU GAC
R N A W * R L D
Since there's no amino acid abbreviated "O", we switch the Stop codon to be an O.