Dawkins uses the 13-year and 17-year periodical cicadas as another example of convergent evolution. These remarkable creatures have a juvenile feeding stage lasting 13 or 17 years. Adults emerge at almost exactly the same time after spending 13 or 17 years underground to live in their mature stage for only a few weeks before dying. The interesting thing about periodical cicadas is that there is not a 13-year species and a 17-year species. There are in fact three and each has a different race of 13-year and 17-year cicadas, the intermediate years of 14, 15 and 16 having been avoided by all three. Dawkins noted that 13 and 17 are both prime numbers (cannot be divided evenly). He then speculates about the possibility of a predator that could make life difficult for cicadas that did not have 13 or 17-year breeding cycles. He suggests, for example, a species that swarmed every 7 years could make life difficult for a 14-year cicada but Dawkins is unaware of the existence of such a creature. In The Blind Watchmaker, p100, he writes:

The idea is that a race of animals that regularly erupts in plagues gains the benefit of alternately 'swamping' and starving its enemies, predators or parasites. And if these plagues are carefully timed to occur a prime number of years apart, it makes it that much more difficult for the enemies to synchronize their own life cycles. If the cicadas erupted every 14 years, for instance, they could be exploited by a parasite species with a 7-year life cycle.

The theory that cicadas swamp and then starve their enemy is a notion applicable to all insects that plague. For example, we are familiar with a grasshopper (or locust), easy pickings for birds that mostly keep their numbers in check. When locusts plague however their normal predators are ineffectual and they cause much damage for their synchronising the emergence of a new generation makes it possible for many more to survive. The birds feeding on them have a feast when they first appear but are quickly replete so take little interest in the bulk of the plague.

But it is difficult to see how this strategy relates to the cicada’s choice of prime numbers. What is being suggested by Dawkins is that a predator or parasite can also synchronise their breeding cycles to make it possible to exploit plagues not occurring at 13 or 17 year intervals. The first thing we should note is that it would be impossible for birds to increase their population at the same rate as insects. There would also be little point in an avian predator increasing its population to take advantage of a plague, for the new generation would soon starve once the swarm had passed and this is presumably why Dawkins suggests the unknown enemy is most likely a parasite. Parasites can increase their population rapidly and could exploit an insect plague.

Let us imagine there is a parasite with a 7-year breeding cycle that attempts to exploit a 14-year cicada. The parasite discovers the precise time of the cicada eruption and synchronises its own reproductive cycle to take advantage of the plague. When the cicadas erupt, the first generation of the parasite matures at exactly the right time to feast on the swarm. But when the second generation of the parasite erupts again in 7 years, the cicada is still in its juvenile stage and the parasite’s second generation will starve. The problem for Dawkins’ theory is that the cicada will starve the second generation of any parasite or predator with a breeding cycle shorter than its own regardless of whether it is a prime number or not.

But it is undeniable that a 14-year parasite would be very successful at exploiting a 14-year cicada. Every time the cicada erupts, a new generation of parasite would arrive to take advantage of the abundant food supply. So does this explain why the cicada moved from a 14-year to a 13-year breeding cycle? Of course not. The parasite can exploit a 13-year cycle in exactly the same way. The problem for Dawkins’ theory is that a prime number can be divided by itself as can every number. This means a parasite that can extend its breeding cycle to the same number of years as its target can exploit 12, 14, 15, 16 and 18 year cycles (non-prime numbers) just as easily as 13 and 17 year cycles.

It is unlikely therefore that a hypothetical predator forced cicadas to abandon composite numbers and adopt 13 and 17 year cycles.

Sadly, it would seem, Richard Dawkins does not understand simple prime numbers and the reason he gives for the convergence of 13 and 17-year cicadas is incorrect.

The above is an excerpt from my book; God Gametes and the Planet of the Butterfly Queen - page 315