Tuesday, May 14, 2013

Prime Time with Magicicada!

That’s right folks. We have a very special guest with us this summer: the 17-year periodical cicadas!

All rights to Wikipedia something something.
Tell us a little about yourselves.

Zeeeeee Tick Zeeeeee Tick (Warning: offensive)

Fascinating. So, some interesting factoids about cicadas of which I was previously unaware: When the 13- and 17-year cycle cicadas are underground, they’re still alive, feeding off the root systems of trees. Also, they remain in an immature, but mostly anatomically complete state the entire time—just like humans.

There are plenty of other cicadas out there, but only eastern North America has the famed 13- and 17-year broods. The genus of which these several cicada species are a part is known as Magicicada, which near as I can tell means magic tree cricket.

Anywho, as far as I’m concerned the most interesting fact about cicadas is that their cycles correspond to prime numbers. I’m not the only person who finds this interesting, and there have been a number of studies investigating this rather curious phenomenon.

So what’s the verdict? The best current hypothesis is that it’s a confluence of three separate factors: predator satiation, the last ice age, and hybridization.

The first factor is a common adaptation not unique to the periodical cicadas. As the name implies, the trait involves satisfying the hunger of those that wish to eat you. The gist is that if every single cicada emerges and breeds at the same time, then there are only so many predators that can eat said cicadas, and the vast majority won’t be eaten. If they came out piecemeal throughout the year or over the years, then their predators would have time to get hungry again, and their survival rate would go down.

Okay, so that accounts for why they all come out at once, but it doesn’t account for why they have such long cycles. This is where the ice age factor comes in. Cicadas are used to the nice warm temperatures underground and they’re only able to fly around and mate when the surface temperature is similarly suitable. So they wait until the soil temperature has reached a comfortable 63 °F and then erupt from the ground en masse.

But during glacial periods there is no guarantee that the temperature will stay that high for the 3 or 4 weeks cicadas need to successfully reproduce. What this means is that when the cicadas decide to come out, they’re taking a gamble. If the temperature drops too low during their emergence, then the brood dies off without reproducing. So the best bet is to hold off and only emerge every decade or two, reducing the odds that they hit a cold spell.

(This might seem specious, because you’d think that (ideally) one summer’s temperatures are not correlated with another’s, so no matter when you pop your head above the soil, there’s an equal chance it ends up not being warm enough to breed. More on this later.)

Now we need the final piece of the puzzle: prime numbers. What could possibly account for the appearance of prime numbers in insect reproductive cycles? It turns out the answer is hybridization. Say you’ve got your cicadas emerging en masse every decade or so. There are separate broods of cicadas emerging at different intervals, which means that every once in a while broods will come out at the same time. When that happens, they will interbreed, and the resultant brood will be hybridized.

If this different mix of genes changes the length of the cicada life cycle, the effect is to smear out the arrival times of the cicadas. This smearing out, however, reduces the population density of cicadas on any given summer, which reduces the effectiveness of the predator satiation strategy, which ultimately reduces the number of cicadas that get to breed. So hybridization is a bad strategy. The best strategy is to make sure there is as little overlap as possible in the cycles of various cicada broods.

For example, if you have one brood on a 4-year cycle and another brood on a 16-year cycle, there’s going to be a lot of overlap because 4 is a factor of 16. So we want cycles with few or preferably no factors. We want prime numbers.

I think it’s important to point out here that a lot of talk about evolutionary strategies can be quite misleading. It sounds as if a species is getting together and deciding the best way to reproduce and then carrying out that plan. But that’s not what is happening. In fact, if that were happening, very different reproductive strategies would emerge.

If cicadas wanted to get together and come up with the best strategy, they might decide to evolve faster flight and the ability to survive warmer temperatures. But they’re not given that choice. Species don’t decide what mutations they get. They are stuck with what nature selects for them.

To see how this works out, imagine there are dozens of different cicada broods with a variety of different cycle lengths and patterns of reproduction. If some broods emerge piecemeal and others as one, we know that due to predator satiation, the broods emerging together are more likely to breed. Thus, over a long enough period of time, we’re not going to see the piecemeal broods anymore because they will have been selected against.

So now we have broods that emerge in unison but do so at varying intervals. The question we have to ask ourselves again is, after a very long time, which broods are we most likely to see? We could see the broods that emerge every year or those that emerge every 20 years. Both broods might have their luck run out after 50 cycles, but that corresponds to 50 years for the first batch and 1000 years for the second batch. So after a long enough period of time, we’re only going to see the 20-year broods. This isn’t a strategy; it’s a consequence.

Now we’re left with only long-period cicadas. Again, the cicadas don’t choose to make their cycles prime numbers. What we see isn’t a choice; it’s statistics. Because prime-numbered cycles correspond to higher reproductive fitness, after a long enough period of time non-prime-numbered cycles die off, and the end result is that we only see those cycles that survived for thousands of years. We see those cicadas that breed all at once on large prime number cycles.

Sorry, no physics in this post, just stamp collecting. I really am going to follow up on the lawnmower post at some point. Really.

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