The anime is a good source of information, because it gives us a view into what it would be like if Pokemon lived in our world. The game is too abstract and has limitations. True, the anime is not entirely honest (there's little to no natural carnage), and due to production limitations (read: laziness), things become less realistic the further down the line the show goes (see first Caterpie and first Metapod evolutions, and Togepi hatching vs. all subsequent cocoon evolutions and egg hatchings). But it's still factual, given that the Pokemon IP itself is so well protected that nothing associated to it is allowed to deviate from the given standards. Also, there are games that even tie into the anime, that's not something a lot of games with a cartoon on the side do.
In the Pokemon special Mewtwo Returns, there's a scene with baby Nidoqueen and baby Rhyhorn emerging from the bushes, the offspring of an adult Nidoqueen and Rhyhorn. Yes, you read that right. I said Nidoqueen had kids. See for yourself.
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And on top of that, she didn't just have Nido related children, either. While this puts to rest one thing, it unfortunately brings up another. Many people have asked why Nidoqueen gave birth to other Nidoqueen. The answer is obvious and yet everybody misses it. I knew why when I first saw it, and I was just an average kid going to a below average high school.
The heart stopping conclusion? The adult Nidoqueen is clone. The clones themselves were born as a direct result of the creature copied. Therefore, the basic stage of each cloned Pokemon is whatever stage the real Pokemon was at that time. A clone doesn't have that information about any stages prior or after what was given, so it can only produce that which it was given in the first place. That is to say, clones have limited structural information, afterall, they weren't created with time and care like Mewtwo, it was more like a photocopying machine process, and everyone knows that there's always a loss of information with each copy furthest away from the original. That said, Nidoqueen gave birth to more clones, instead of Nidoran like a natural Nidoqueen with the full genetic makeup would.
The only question left now is "given the information provided, why can't they breed in game?" A generally accepted answer is that the is a programming error in Pokemon Gold and Silver that prevented elder Nidos from breeding. At face value, I can buy that, given that the Game Boy games had such messy codes (MissingNo is marginal compared to every collective programming error in the 1st generation games). In fact, the gender in G/S was determined by the values of the attack stat. If you wanted to max out stats via a cheating device, your Pokemon would always be male, even if it started out female, unless that Pokemon was 100% female. I will eventually look into the hex values myself and experiment regarding any unseen miscalculations. If I find anything, I'll make a note of it.
There you have it. Realistically, Nidorina and Nidoqueen can breed. Oh, and clones have clones as children. Want to know what's ironic? If the programming error (or even miscommunication in the office) is fact, of all things not retconned in each subsequent game of the Poke-verse, they kept a possible error as standard. What does this say about Game Freak's priorities?