Roaming has become a popular addition to the metagame strategy, wherein one player does not lane nor jungle, but rather simply moves through the jungle/river to initiate ganks on lanes from level 1 and onward, until the teamfight portion of the game begins.
A roamer essentially guarantees that you're either running a solo lane, or two solo lanes if you have a roamer and a jungler. I've also seen a double roamer game played, though this tends to be less effective as enemies who are wise start playing defensively and reduce the effectiveness of your roamers, which put them behind in both CS and levels.
The qualities of a roamer can vary, but the general requirements are that they are mobile, can do burst damage, and have a strong stun or position altering (push, throw, etc.) ability. Taric, Evelynn and Alistar are all very popular choices for roaming. I've also seen Sion and Blitz play roaming effectively, but they were both out of a lack of a jungle spot on the team and normally suit better in a lane.
This strategy is similar to the "double jungle" mindset in that you get three solo lanes, with the exception that there is extra pressure on getting early kills to succeed. A definite risk vs. reward tossup, as successful roamers will quickly catapult your laners ahead in level / CS as well as demoralize your opponents, but unsuccessful roamers will fall just as far behind due to the lack of their presence in the laning phase.
AP champions scale best off of levels so by putting them in a solo lane they earn the most experience. Mid lane is the shortest lane so it is easy to escape compared to top, which is generally the realm of bruisers who can survive ganks and have gap-closers.
Some APs are excellent roamers and having them in mid allows them to influence the other lanes. Ahri, Sion, and Leblanc are all vicious roamers that can quickly get kills in other lanes due to their burst/CC.
AD champions scale best off of gold so they get a support to help them farm safely. A lot of the times the support gives sustain to make this farming easier.
Having two people in bottom lane also allows for control over dragon, which is a very important objective early on. Baron doesn't normally become an issue until well after laning phase is over.
However, sometimes you will see pro teams throwing a solo champion bottom if the champion can handle fighting two people at once and still farm. They do this so their AD carry can abuse the enemy top lane and free farm.
Best Answer
The metagame is established generally through the thousands of games played. Usually, teams will get together and decide to try a team composition and success will lead them to keep trying it. Obviously, over just a few games everyone's performance will vary widely and no meta will save you on your bad days...
...But over thousands of games with hundreds of thousands of players, individual skill becomes averaged out and what you're left with is what strategies tend to work. Now, we need to distinguish a strategy from a meta to make a lot of sense here. I'll do it very briefly: The metagame is a framework in which you insert individual pieces (champions and builds, where builds are item/mastery/rune combos) that fit the framework. In our current state, the "meta" is usually a high-survivability (but not usually tank) in top who can solo and scales well with items and experience; mid is a character that scales best with experience; bot is a character who scales best with items and needs either baby-sitter or someone to setup kills; the jungler is highly variable, but often is prized for their ganking abilities. So, take any "pieces" that fit inside that framework, and you have a particular strategy within the meta. For instance, an AoE heavy composition is a strategy within the current meta.
Strategies are handed down from pro players (usually, but not always), but the meta is determined by all of us. It's less a "choice" that people get to make and more a mathematical optimization realized over a ridiculous number of games (millions). Metas will usually stabilize without some dramatic changes in terms of patches and champions, which is what has happened in LoL. More casual players will tend to emulate what they see the pro players do, which makes sense in terms of the number of games played per person.