Cicadas and Prime Numbers

Australian summers are usually filled with the deafening sound of cicadas but there are the occasional years where there seem to be no cicadas.  I remember one summer (1967?) when I was a child there were huge numbers of cicadas.  One weekend, along with two friends (Jimmy and Peter), we collected over one hundred of at least four different varieties.  (Kids had given names to the different types based on their colour, like Black Prince, Green Grocer, etc.)  Not only was this a fun time for kids but the birds were enjoying a feast too.  Many times each day you would hear the monotonous sound of the cicadas interrupted by the intermittent and panicked sound of a cicada that had been caught by a bird.

Someone told me at the time that every seven years there are a lot of cicadas but I do not recall ever having seen so many in any year since.  Several summers later I noticed that were no cicadas at all that year.  This started me thinking about the variation in cicada numbers from year to year and I came across some information on the life-cycle of cicadas.

Life-Cycle of Cicadas

Apparently, the different varieties we had found were different species most of which had different life spans.  (If you don't know, cicadas spend many years underground sucking on the sap from tree roots before emerging and mating for a few months before dying.)  The life span of various species varies from 3 years to as long as 17 years.  I had just learnt of prime numbers at that time and it occurred to me that the life span (in years) of any particular species was always a prime number.  The most common varieties spend seven years in the ground but others spend 3, 5, 11, 13 and even 17 years underground.

Now it was obvious why some years there were few or even no cicadas and very occasionally there were a huge number.  Obviously the numbers of each variety varied from year to year either through some form of collusion or due to different environment factors (weather conditions, prevalence of predators, etc) in certain years.  If a variety has a life-cycle of seven years then the peaks and troughs in their numbers would tend to follow a seven year cycle, though I guess there could be several peaks in one cycle.

Why Prime?

Since different varieties have different cycles then only occasionally would the peaks coincide.  I believe the "year of the cicada" I experienced happened when the peaks of at least three types coincided or at least came close to coinciding.  This probably happens only once, or a few times, every 105 (3 x 5 x 7) years.  By my calculations there may be another peak in 2019 and/or 2020 (1967 + 52/53), though this may be localised to the Lower Blue Mountains area.

But why would the life cycle of cicadas always be a prime number?  I believe cicadas have evolved to have these life spans for the very reason that it makes their numbers unpredictable from year to year.  If there were always the same number of cicadas each year, birds would come to depend on this and the number of birds that hunted cicadas would increase.  The fact that different varieties have different life spans is the key to this strategy working.  I believe that this is an example of inter-species cooperation.  (Inter-species cooperation is something you never hear of and I believe it is far more common than biologists are currently aware.)

Clarification (Oct 11): I should clarify my last comment.  Obviously, symbiotic relationships between species have been extensively studied.  I simply meant that I feel there is a lot of more subtle inter-species cooperation that is yet to be discovered.