I am sure most people will have heard this claim in some form or another:
Cockroaches are so resilient that they will survive the nuclear holocaust.
Is this true?
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Rad Roaches (2001)
In a study (Wharton and Wharton 1959), the authors conclusively demonstrated that the American cockroach was, compared with the rest of the known irradiated insect world, a wimp;
Periplaneta americana died at doses of 20,000 rads.
In comparison, it was noted that Drosophila melanogaster (Fruit fly) had an LD100 (100% probability of causing death ) of 64,000 rads and the parasitoid wasp Habrobracon an LD100 of 180,000 rads.
In retrospect, it could be argued that Periplaneta americana might have been atypically sensitive to radiation as far as cockroaches go, but it’s hard to find any subsequent studies that might have created the reputation of roaches as tops among the ranks of the radiation-resistant.
Ross and Cochran (1963) examined the effects of ionizing radiation on the German cockroach, Blattella germanica, and found that doses as low as 6,400 rads killed 93% of nymphs after 35 days, and effects on reproductive capacity could be detected at doses as low as 400 rads.
Granted, German cockroaches proved capable of surviving 10 times the dosages over the same time period that would be lethal to humans, but, in point of fact, they ultimately succumbed to dosages that don’t even disturb many other insect species.
Deinococcus radiodurans (is without doubt the most radiation-resistant organism known on the planet.
A pinkish bacterium that smells vaguely of rotten cabbage, it was isolated originally from canned meat that had spoiled despite being irradiated (it has turned up in irradiated fish and duck meat, as well as in the dung of elephants and llamas and in granite from Antarctica) (Travis 1998).
It grows happily in radioactive waste sites in the presence of levels as high as 1.5 million rads (keep in mind that’s over 1,000 times the 1,000 rads that kill humans and sterilizes American cockroaches). In a frozen state it may even be able to withstand 3 million rads.
To test whether this doomsday scenario has any legs, the MythBusters subjected German cockroaches to three levels of radioactive metal cobalt 60.
They started with a baseline exposure of 1,000 radon units (rads) of cobalt 60, capable of killing a person in 10 minutes, and followed it up with 10,000 and 100,000 rad exposures on separate guinea pig — er, roach — groups.
(As a comparison, the bomb on Hiroshima emitted radioactive gamma rays at a strength of around 10,000 rads)
Since radiation gradually destroys organisms on the cellular level, the MythBusters monitored the radiated roaches for 30 days.
After a month, half the roaches exposed to 1,000 rads were still kicking, and a remarkable 10 percent of the 10,000 rad group was alive.
The results confirmed that cockroaches can survive a nuclear explosion — but only to a point, as none of the critters in the 100,000 rad group made it through.
Taken from the Annotated MythBusters website:
To evaluate the longer term affects of the test on the insects, the MythBusters took them home along with a control group that hadn't been exposed.
They monitored the insects over the next 30 days and counted how many died.
They exposed the three different sets of bugs at 1000 rads, 10,000 rads, and 100,000 rads.
The bugs in the 1000 rads and 10,000 rads tests appeared fine but 90% of the cockroaches in the 100,000 rads group immediately died.
Based on these results, the cockroaches clearly weren't the best survivors of a nuclear blast. They are quite hardy, able to survive radiation doses at 10,000 rads, which is 10x the lethal dose for humans.
However, the flour beetles did much better and the fruit flies might have done better if their normal lifespan wasn't 30 days.
... most people (including many biologists who do not study cockroaches) are generally familiar with just a handful of “pest” cockroach species that have become associated with human habitation.
Few people realize the extent of cockroach diversity in life history, habitat, behavior, and morphology.
Cockroaches occupy a wide variety of habitats including tropical and temperate forests, deserts, grasslands, and salt marshes.
Similarly, they have a wide vertical distribution ranging from tropical rain forest canopies to deep in the soil.
The broad habitat is reflected in a number of features such as diet and foraging , morphology, physiology, reproduction, diet, circadian rhythms, and seasonal activity
Most species of roaches live in the tropics. But roaches live all over the world, including the North and South Poles.
Pest cockroaches can withstand temperatures as cold as 32°F (0°C), but will die if the temperature goes much below that.
In extremely cold places, however, they survive by moving in with humans.
What do they eat?
They feed on just about anything of vegetable origin. But cockroaches also like meat.
While they prefer starch, they thrive on grease, sweets, paper, soap, cardboard, book bindings, ink, shoe polish, and even dirty clothes.
They’ve been known to gnaw on a fingernail while people sleep and on infants’ eyelashes.
They are especially fond of beer.
Cockroaches can live for 3 months without food and for 30 days without water.
Since they taste their food before eating it, they learn to avoid chemically-treated products.
Due to the large variety of species it's hard to make a general statement about how well "a cockroach" would fare in the aftermath of a nuclear war.
But it seems they have a better chance at surviving the radiation and they are less picky eaters than we humans.
While Oliver_C's (excellent) answer look at the effects of radiation on cockroaches as an indication of whether or not they would survive a nuclear explosion, the question is about surviving a nuclear holocaust which means factors other than radiation are also an important determinant.
The National Geographic documentary Aftermath: Population Zero states that no, cockroaches would not survive without humans. The documentary states that cockroaches are imports from the tropics and only flourished due to central heating provided by humans.
Given that it is unlikely there would be central heating up and running if a nuclear holocaust were to occur, it is unlikely that cockroaches would survive outside of the tropics and even that is questionable if a nuclear winter is in place.
HowStuffWorks supports that idea, although without a reference:
One common perception is that cockroaches will outlive humans, even in the event of a full-scale nuclear war. Opinions differ about whether this is the case. Some studies have shown that cockroaches, while hardier than humans, are more susceptible to radiation than other insects. However, others believe that since roaches' cells do not constantly divide the way people's cells do, they will be more likely to survive. Regardless of whether roaches could survive the initial blast, their need for warmth and moisture makes it unlikely that they could survive nuclear winter.
A nuclear winter could vary in intensity depending on how much remaining material was in the atmosphere. Given that the question uses the term nuclear holocaust, I will assume the a worst case scenario.
In which case it is not likely that most species of cockroaches would survive because:
As such I don't think it's fair to say cockroaches would not survive a nuclear holocaust, although they would survive a nuclear explosion. Then again, I don't think most life would survive a nuclear holocaust.
1 - Not a great reference, although it supports what I found for the various different species, with the longest seeming to be 4 years.