Duke Nukem starts off as a 2D sidescrolling platformer. In this platformer, when he jumps he does a sort of flipping animation similar to Sonic's spinball jumps. His first villain is Dr. Proton, a brilliant scientist but also a cyborg madman dreaming of conquering the world with his army of robots. After Duke destroys his Earth base, Proton opts to rule from a new base in space. He is ultimately thwarted by Duke Nukem and escapes into the future where Duke follows, seemingly defeats (but fails to double check) him a second time, and then Duke returns to his own time.

Duke Nukem 2 occurs where Duke is abducted by aliens, escapes, and discovers more aliens have invaded Earth while he was away, cue Duke Nukem 3D. 

In Duke 3D, we discover aliens have the ability to turn people into anthropormorphic animals, which the invading force primarily is using at this point in the timeline to turn police into pig-men to bolster their army while shrinking Earth's fighting force with the Shrinker. Fortunately, Duke Nukem is a one-man army, and he works for the Earth Defense Force, an army for the entire planet, so he stops the alien threat.

Now here is where things get interesting, because Duke Nukem Forever is a timeline split. There's the 2001 version and the 2011 version. 2001 edition was never released, but it's the timeline where things transition into Sonic. 2011 is the timeline where the franchise ends because the 2011 version is terrible and killed the series, but that is another discussion. 

Okay so what was happening in the 2001 game? Well, it wasn't released and the build that leaked somewhat recently wasn't the latest build of that version of the game. There's a build that's more fleshed out, but we don't have access to it. Anyways, from what trailers show us, Duke Nukem Forever would have involved a new alien invasion. We aren't sure if these are the same aliens or another race entirely, but it seems like whatever the case may be, Duke Nukem 3D aliens are a less common sight than before. Primarily Duke is fighting a type of alien that burrows into a host and mind-controls them, turning them into some type of monster in the process. Very System Shock 2-y and Half-Life Headcrabby. There's even some similarities to the enemies in Resident Evil 4. 

Anyways! As General Graves tells us and as footage and leaks confirm, The Earth Defense Force is compromised, turning its soldiers into hosts for the aliens. The thing is, you don't always know if someone is being controlled or not! General Graves tells us not to trust anyone, and from the radio chatter the soldiers have, they sound normal! The only clue something is wrong is A) They shoot the good guys, B) sometimes tentacles pop out of them (especially when shot) and C) their eyes sometimes roll to the back of their head. Once the situation is complete, the EDF is finished. World saved or not nobody is going to be able to trust this organization anymore, and nobody would want to be associated with it either. But they're still needed! So they rebrand. Reform. Whatever. Into what? I say they become known as the Guardian Units of Nations.

Time passes. Society advances, and the alien technology is reverse engineered. We see glimses of this with the Shrink Ray in the 2001 version of Duke Nukem Forever being powered by the brain of the enemy from 3D that could shrink you, but now it's much more widespread. Amongst the technology reverse engineered, tweaked, and repurposed is the tech that turned people into the pig cops. It becomes possible to transform yourself into an animal person without the brainwashing and with a far wider variety of animals than just boars. Time passes some more. You can't guarantee an animal person is actually transformed anymore, they could have been born that way. Probability is fairly high that they were, actually. Animal people are just a fact of life now.

Of course, an evil maniacal cyborg scientist with an army of robots is causing havoc again. Sounds like a fairly familiar foe, who Generations ago traveled to the future, which may now finally be the present. There seems to be a new hero stepping up to face him, however. A certain blue hedgehog. Whatever happened to Duke himself? Did he get old and die over the generations? Does he have any descendants? Has he traveled into the future again? We don't know. All we do know is that Big the Cat is voiced by the same VA as Duke - Jon St. John. Is Big a descendant of Duke? Perhaps Duke got experimental one day and hooked up with a cat lady? "This is not the kind of pussy I had in mind," Duke would say. Or perhaps Big the Cat IS Duke? This aspect of his character is even referenced in Duke Forever 2011 where he sees an alien with giant tits and says "I'd still hit it!" Duke isn't afraid to experiment. Or perhaps he did travel into the future. He retired, got fat, and perhaps fell prey to someone seeking to ensure Duke couldn't come out of retirement and stop them. They used the technology to transform Duke into a cat person, and not only that, but cloud his mind in the process. But joke's on them, cause there's a certain blue hedgehog these days filling the void Duke leaves behind.

Want to hear some more theory spitting?
In the 2001 DNF trailer, General Graves mentions that the aliens have kidnapped "the president". Duke and the EDF have jurisdiction over the planet. You would think he'd say "the US President" if that's who he was referring to, but he doesn't. He just says "the president". The president of Earth? Is there a New World Order in effect?

Sonic Adventure 2 and Shadow the Hedgehog. "The President" is a character. Again, no reference to what he's president to, but GUN is working under him implying that he is indeed president of the planet. These are different characters of course, and the time jump makes sense of that, but interesting that both these series may have the same governmental body in place!

ANOTHER THING! Duke Nukem Manhattan Project. A sidescrolling game that came out between Duke Nukem 3D and Duke Nukem Forever. Forever was still in an earlier state than the 2011 version. The game's antagonist is Dr Mech Morphix, a budget Dr. Proton (that was originally going to be Proton but Forever was potentially going to use Proton in some form (and there's a super unfinished boss fight in the leak that's apparently meant to be Proton) and they didn't want continuity to clash). His presence shows that there's room for more robot genius scientist dictators in the Duke Nukem universe, but more importantly he does something very interesting. Not only does he use robots, but remember how I said Earth starts reverse engineering the aliens' ability to turn people into animal people? Dr. Morphix has the G.L.O.P.P. mutagen, and its ability mutates animals into humanoid forms. It is also used on humans to transform them into animal people with a wider variety of options than just pigs. Supported by canon, my theory is.

ONE MORE THING! Bean the Dynamite from Sonic the Fighters, Archie Sonic, and Sonic Mania. Modeled after the Sega game Dynamite Duxs. Interestingly enough we learn in the Master System version of this game that these ducks are actually TRANSFORMED HUMANS, further contributing to this theory.