What mechanism accounts for the cicadas' 17-year-life cycle? How are the years counted?

There are quite a few broods; twenty-three by major count. Some are extinct, which is the real oddity to me. Here’s a very good page on the broods and cycles.

I totally understand this, and even why this makes prime numbers advantageous.

I was asking about the OTHER posited explanation, that the prime numbered cycles are an adaptation to avoid occasional cold summers during the glaciation period (and NOT an adaptation to counter predators). I’m not sure exactly how this is supposed to work, or why the predation hypothesis isn’t sufficient.

I can only read the abstract linked above, and it’s not very clear to me. Is there anybody who can explain it?

Read my link. Prime numbers are good because they mean that any two broods with different prime-number breeding times will rarely appear in the same year (if they are in the same area). A 13-year and a 17-year brood will only appear in the same year once in 221 years. On the other hand, a 16-year and a 24-year brood will appear together once in 48 years.

Wait, why? It doesn’t affect the weather in any way, and I figure the odds of emerging during a cold summer are roughly the same for any given year, right? I mean they’d see less cold summers only as an effect of seeing less summers overall. But the percentage should be the same given that the odds of a bad summer are roughly the same for any given year, right?

Yeah – I’ve read that scientists think exactly such “splitting” has occasionally caused a new brood to form out-of-synch with the original brood.

Probably the above-mentioned splitting. Historical accident gets the new brood on a different 17-year cycle. The factors that make 17 years an effective cycle should work for any given 17 years, and keep each of the now-separate broods on its own 17-year cycle.

I apologize. I once read a brilliant explanation of how the prime-number cycles reduce the odds of cold summers killing them off, but can not find it now. The math was dramatic – according to my memory, over some long period (either 1,000 years or the whole 10,000 year period since the glaciers) the odds of a brood being wiped out by cold summers was something like 90% for annual emergence, 50% for a ten-year cycle, and only 1-3% for a 17-year cycle…or something like that (I am pulling these numbers out of thin air, but the numbers in the article made a big impression on me and were not very far from these figures). The math, assuming the author was accurate, immediately made clear that the 17-year strategy (and to a lesser extant, the 13-year one) would have indeed increased the odds of a brood surviving, even if the details were inobvious to the mathematically-challenged.

Even if your expected number of generations of survival is constant, a longer dormant period will result in survival for a longer amount of time.

I’m just wondering what the methodology there is. Maybe you can’t find a cite but do you remember any of the math, even vaguely? It’s just that, if I bury myself now, why would I have more luck emerging in any given summer than any other? It should be like flipping a coin, every new toss has roughly the same odds as the one before.