What is the "theme" of the Farcry Series?

Let me start by saying I've never played a Farcry game before. I remember watching some dedicated gaming channel (not G4) that did an entire series playing through the first one, so I know about how the story turns and jumps at least five sharks before the end of the game. I'm familiar with the "Heart of Darkness" theme of the second one in Africa, and I know that the third one has something to do with "Insanity".

All three games narratively independent, with no crossovers that I am aware. For those that have played this series, could you explain what links these games together as part of a series. What exactly defines a "Farcry" game?

Tropical Vistas? Over-the-top gun fights? or something else?