During the Cold War, as you learned your depressing drills about hiding underneath a chair to attempt to survive a nuclear explosion, you were probably warmed by the thought that "sure I'm a goner, but at least the cockroaches will live on and form their own society".
Roaches, along with Twinkies, have a reputation for being the ultimate survivors. It's not clear why Twinkies have this hardy reputation (they last about as long as any other cake) but cockroaches are admittedly badass. They are, for example, one of the few creatures that can survive without their heads.
For most animals, not having a head is basically the end of things. You rarely read a piece about someone who was decapitated but "went on to live a full life well into their seventies". If the blood loss didn't kill you, and the lack of control over your heartbeat and lungs didn't kill you (and both would) you'd soon find it difficult to eat enough to go on living.
Cockroaches can live for several quite confusing weeks following decapitation, as scientists have proved with alarming frequency. They survive decapitation by clotting at the neck. Their breathing takes place through little holes in their bodies called spiracles, which is not controlled by the brain. Since they're cold-blooded, they need less food than warm-blooded snowflakes like us, and can live for weeks on a meal they had before decapitation day.
What's more, they have ganglia throughout their bodies, leaving them still capable of reacting to a stimulus, such as a scientist prodding them with a pen. Distressingly, they can still stand up and move around, headless.
Meanwhile, the head can go on living too, surviving without its body for hours after the two got separated. Given nutrients, they can last even longer still, though they are not quite the same once they lack the feedback from their bodies.
"When we've tried to teach them when they had bits of them missing, it's hopeless," neuroscientist and arthropod learning expert Nick Strausfeld told Scientific American. "We have to keep their bodies completely intact."
They are, to be fair, hardy little critters. But can they survive nuclear blasts? Would they be alone to inherit the Earth following a nuclear apocalypse?
The short answer to the first question is yes, sort of. They were found among the rubble following the nuclear bombs dropped on Hiroshima and Nagasaki in 1945, though it should be noted that humans were found alive also, many of whom died of radiation sickness after the fact. However, there survives no record of anyone tracking the health of the cockroaches following their survival; understandably they had bigger things going on at the time.
Humans have, however, tested their resistance to radiation before and after those nuclear blasts, including the team from Mythbusters.
Over a month, they exposed different groups of cockroaches, fruit flie, and flour beetles to 1,000 rads (a unit of absorbed radiation dose), 10,000 rads, and 100,00 rads. After the ordeal, 10 percent of the roaches from the 10,000 rad group were still alive, which is 10 times the lethal dose for humans. However, none of them managed to survive 100,000 rads.
But, the flour beetles did. Ten percent survived a whopping 100,000 rads for the full 30 days of the experiment, proving themselves to be much tougher than the long-dead cockroaches.
However, the experiment didn't look at whether the radiated cockroaches and flour beetles could produce viable offspring. It could be that the insects survive the blast and the radiation, only to be unable to continue the species long enough to deal with the problem that the whole food chain has been wiped out anyway.
Either way, it looks like cockroaches would fare worse than many other insects if a nuclear war occurred.
"There is some evidence that they seem quite resilient to gamma rays, although they are not necessarily the most resistant across insects," evolutionary biologist Mark Elgar told EarthSky. "You could argue that some ants, particularly those that dig nests deep into the ground, would be more likely to survive an apocalypse than cockroaches."
So, to answer the second question, it doesn't look like cockroaches are inheriting the Earth after all.