Big news in bug math. This is the first year since 1803 when both 13-year cicadas and 17-year cicadas will emerge from the ground simultaneously in the US!
13 and 17 are both prime. It's believed cicadas evolved to have prime-number life cycles to avoid predators that emerge more frequently, like once every 4 years or 5 years or... whatever. By showing up infrequently, with a prime number life cycle, they can starve out those predators.
And since 13 and 17 are both prime and 13 × 17 = 221, both kinds of cicadas emerge simultaneously only once every 221 years. And
1803 + 221 = 2024
so now they'll both emerge simultaneously and we'll have 𝑙𝑜𝑡𝑠 of cicadas!
Also, this year the two kinds can interbreed!
The last time the Northern Illinois Brood’s 17-year cycle aligned with the Great Southern Brood’s 13-year cycle, Thomas Jefferson was president.
https://www.nytimes.com/2024/01/19/science/cicadas-emergence-broods.html
@johncarlosbaez If they do interbreed what happens to the math?
@holothuroid - great question! I bet nobody knows. I hope the descendants have either 13-year or 17-year periods. If they get screwed up and have, say, 15-year periods they may be less fit. Though honestly I don't know any predators with 3- or 5-year life cycles.
@johncarlosbaez If it's either of the first option that would point to a single allel being a switch. Which makes sense, thinking about it, because if it was a combined effect, there would likely be more variation.
@holothuroid @johncarlosbaez It would be nice to understand the determinism for these periodicities (I want to believe there's a conserved 4-year cycle in there and a super-cycle (x3 or x4) + 1 normal seasonal cycle). According to https://cicadas.uconn.edu/broods/, spurious broods are common. It's not clear what happens to their descendants. More speculation tells me that it's possible that the large broods leave something in the environment that prevents spurious/smaller broods from being successful. That would ensure regional stability.
@holothuroid @johncarlosbaez I haven't looked at the map too closely but it looks like the 13-year and 17-year populations do not generally overlap in space, and same-period but different-phase populations don't overlap either. This would confirm that something left in the environment contributes to self-stabilizing around one particular period and phase.