[cheryl j (OP)]

The journal Nature (May 30) says that the 17 and 13 year cycles of cicadas allow them to overwhelm predators with large numbers at once, but also hypothesized that cycles based on prime numbers might help circumvent predators from timing their cycles to cicadas' emergence, which I thought was interesting. This post should probably go under entomology,  but I was wondering if any mathematicians here know of other roles prime numbers might play in biology.

[Lmnre]

Don't know about biology, but in botany, bamboo flowers at intervals. Wikipedia says —

Most bamboo species flower infrequently. In fact, many bamboos only flower at intervals as long as 65 or 120 years. These taxa exhibit mass flowering (or gregarious flowering), with all plants in a particular species flowering worldwide over a several-year period. The longest mass flowering interval known is 130 years, and is found for all the species Phyllostachys bambusoides (Sieb. & Zucc.). In this species, all plants of the same stock flower at the same time, regardless of differences in geographic locations or climatic conditions, and then the bamboo dies. The lack of environmental impact on the time of flowering indicates the presence of some sort of “alarm clock” in each cell of the plant which signals the diversion of all energy to flower production and the cessation of vegetative growth. This mechanism, as well as the evolutionary cause behind it, is still largely a mystery.

[evan_au]

There are a few lonely cicadas that appear in off-cycle years - they are highly unlikely to find a mate, and highly likely to be eaten.

There are broods that arrive with different prime-number intervals - this must be a clock with a strong genetic basis.
If the broods appear at intervals which are relatively prime, then the interval between simultaneous emergences will be the product of the individual intervals (and a prime number is automatically relatively prime to every other number). So the interval between clashes of a 13-year and 17-year brood will be 13x17=221 years.

I have not heard that the basis of this clock has been identified, but presumably cross-breeds could appear in years that are different from either parent brood - and thus be at risk of predation. Their clock cycle may be intermediate between the parent broods - so a 13 & 17 year brood may produce offspring with a 15-year cycle, while an 11 & 13 year brood might produce offspring with a 12 year cycle. Unfortunately, these are not relatively prime (having a common factor of 3), and so are more likely to "clash", producing more smaller hybrid broods that then go extinct.

If the stragglers have a mutation in their genetic clock, this might be a possible basis for identifying the gene(s) behind the clock, by comparing the DNA of stragglers with the DNA of those that appear in the "right" year?

See: http://project.wnyc.org/cicadas/
http://www.sciencefriday.com/segment/05/03/2013/17-year-cicadas-primed-to-emerge.html
http://www.sciencefriday.com/segment/05/20/2011/every-thirteen-years-brood-nineteen-is-back.html