I have limited space for my Madagascar Hissing Cockroaches, and one of the roaches just had nymphs. Is there any natural population control that they use so that they do not overwhelm their container in sheer numbers?

Thanks!

All I know on this is that the young nymphs will die from byproducts of overcrowding (frass in food, attacks during molting, etc.). The problem is that this can wipe out most of the nymphs and leave few to keep the population going. They have no need for something like this in the wild.
What I'd recommend is to give away as many as you can, then try to find the space to separate the males from the females, and only allow one or two females to breed to continue your colony.

Thank you, those are excellent suggestions!

I use the culling approach. When they start to get overcrowded I go through and get my best stock and put them rest in a Ziploc in the freezer overnight. For some reason I don’t start to have much nymph die off even when crowded…

Thanks, that is an option, too.

It doesn't sound nice but...

Deep freezing is considered to be a non-stressful and rather humane way to put away invertebrates. It is my preferred too. Even the phorid flies have to give in....

But if other invertebrates needs food, there is also an opportunity to "adjust" the culture a little bit...

BR/
Ole

You could always get a Tarantula or something to cull them. A juvenile T thats at least an inch in legspan could easily take down a first or second instar nymph. As the T gets older and bigger, you can just adjust the size of the nymph you give them.

Get African clawed frogs.
They eat enough daily to cut any population down.