How are Gridiron and Association football related? What was their common ancestor and how did the split? Is North American football a mutation of Rugby, or do they share a common ancestor that resembled the two sports but was actually different? I am basically wondering how these games evolved and how they relate to one another. If one were to make a phylogenetic chart, like a species family tree, what might it look like?
The game of football goes back to the middle ages, but that game bears no resemblance to any modern code.
Incidentally the various codes are all called football because they're played on foot, as opposed to on horseback.
Basically, two sides would meet, designate a "ball" (which could be an inflated pig or sheep bladder, or could even be something like a chunk of wood wrapped in leather), and designate two goals, which could be anything -- think the steps in front of a church as one goal and a tree several hundred meters away as the other.
Whoever got the "ball" to their goal first won the match. Beyond that, there weren't really any rules -- no time limit, no set number of players, no fouls, etc.
In practice, this game more closely resembled a riot then a sport, and serious injuries and death were not uncommon. The game was banned several times in English history.
In the mid 19th century, being consummate organizers, the Victorians began to standardize the game around a number of codes.
The code that arose in Rugby called for an oblong ball and allowed the use of hands, while the Sheffield and Cambridge codes used a round ball and were primarily played with the feet.
Association football was formed primarily out of the Cambridge code, which from the beginning had concepts like offside, hand-ball, goalkeepers, and fouls baked in.
Gridiron games, Aussie rules, Rugby League, etc all derive from the original Rugby.