I love this theory from Jon Negroni that all of the Pixar movies take place in the same universe and are all connected.
Centuries later, the animals from Brave that have been experimented on by the witch have interbred, creating a large-scale population of animals slowly gaining personification and intelligence on their own.
There are two progressions: the progression of the animals and the progression of artificial intelligence. The events of the following movies set up a power struggle between humans, animals, and machines.
The stage for all-out war in regards to animals is set by Ratatouille, Finding Nemo, and Up, in that order. Notice I left out A Bug’s Life, but I’ll explain why later.
Update: And for the very reading-averse, here’s a video explanation: