To: WSFAlist at WSFA.org
Date: Sat, 15 May 2004 22:57:50 -0400
Subject: [WSFA] Cicadas and prime numbers
From: ronkean at juno.com
Reply-To: WSFA members <WSFAlist at WSFA.org>

On Sat, 15 May 2004 03:38:26 -0400 "Ted White" <twhite8 at cox.net> writes:
>

> From: <ronkean at juno.com>
> > There are 13 year cicadas, and 17 year cicadas.  Why are cicada
> cycles
> > always prime numbers of years?
>

> There was a piece in the POST about that, a week or so ago.
> Basically, so
> they don't emerge in concert with other broods and crossbreed.

...

> It's said that a climate line separates the 17-year broods from the
> 13-year
> broods, which exist further south.   There are also the more common
> cicadas
> (which we hear in late August until it freezes) which apparently
> have a
> two-year cycle.
>

Thanks for the explanation.  I remember Keith having offered some
explanation, but I had forgotten the details.  And the web sites I
googled did not provide an answer as to why 17 would be so much better
than 15, 16, or 18.

Clearly, the 13 year and 17 year varieties will seldom emerge the same
year in the same place, due to the mutual primality.  And it would be bad
for those two to interbreed, or try to interbreed.  But, as you indicate,
the 13 year and 17 year varieties do not overlap much geographically, so
it seems there should be some additional reason for the prime numbers.

Further searching with google turned up a predator-related reason for the
cycles being prime numbers of years:

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

http://www.economist.com/displaystory.cfm?story_id=2647052

Most biologists believe that the odd lifestyle of periodical cicadas is
an example of a survival strategy called \223predator satiation\224: the
insects emerge in such prodigious quantities that predators cannot
possibly eat them all. And their curious prime-numbered lifecycles may be
another anti-predator strategy.
Glenn Webb, a mathematician at Vanderbilt University in Nashville,
Tennessee, has demonstrated mathematically that prime-numbered lifecycles
could help cicadas avoid damaging \223resonances\224 with the two- and
three-year population fluctuations of their predators. These would result
in lots of predators being around in years when there were lots of prey.
Dr Webb's model shows that, over a 200-year period, average predator
populations during hypothetical outbreaks of 14- and 15-year cicadas
would be up to 2% higher than during outbreaks of 13- and 17-year
cicadas. That may not sound like much, but it is enough to drive natural
selection towards a prime-numbered life-cycle.

-=-=-==-=-=-=-=-=-=-=-=-=-=-==-=-=-=-=-=-=-=-=-=--=

.

________________________________________________________________