Prime Survival – Food, Sex and Death
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Prime Survival – Food, Sex and Death David G. Roberts (Image source: http://www.cicadamania.com/cicadas/cicadas-and-prime-numbers/) Background Mathematicians have been fascinated by prime numbers for millennia. And, for great reason, prime numbers provide the building blocks for all of the natural numbers. Indeed, every positive number greater than one is itself a prime or composite number. Prime numbers are only divisible by themselves and one, whereas it is possible to disassociate composite numbers into a unique set of ‘other’ numbers. As it turns out, those ‘other’ numbers or factors, as they are known in mathematics, are always prime numbers. Eratosthenes of Cyrene (ca. 275 – 194 BC), a prominent Greek scholar, and at that time, head of the Alexandrian Library, made contributions to many fields of learning, including poetry, astronomy, history, geography and mathematics. The mathematical contributions for which he is most well-known include approximation of the circumference of Earth, and a method with which to distinguish between prime and composite numbers up to a designated limit. This method of finding prime numbers is known as the ‘sieve of Eratosthenes’17. However, at the time of Eratosthenes’ discovery, a biological- mathematical generator of prime numbers, even if only of the small ones close to zero, was already in existence elsewhere in the world23&24 (Figure 1), and probably in Greece too20. 6&12 Indeed, periodical cicadas provide a fascinating example of ‘primes in nature’ . “An insect is said to be periodical if the life cycle has a fixed length of k years (k > 1) and if adults do not appear every year but only every kth year”7. Biologists and mathematicians alike, have attempted to explain this phenomenon for decades, even suggesting the occurrence of periodical cicadas as one of only a few genuine applications of mathematics as explanatory of a natural phenomenon2,3,4,5&22. Figure 1. A fossilised cicada wing from the Mesozoic Era, a period of geological time from about 252 to 66 million years ago, found in 24 Australia . Cicadas are a type of insect found on every continent in the world except Antarctica. Their quintessential songs have been playing for orders of magnitude longer than there have been humans on Earth to hear them24. With its Mediterranean climate, it would have been a very rare ancient Greek indeed, not to have heard the rampant love songs of cicadas8. While today cicada songs do not always make favourable impressions13, they seemingly captivated the ancient Greeks, who revered the little beasts. According to Rory B. Egan, an eminent Greek historian and languages expert turned cultural entomologist, cicada manifestations were many and varied through Greek antiquity, including in literature, the visual arts, philosophy, religion and scientific writing9. For example, they were considered a symbol of death and rebirth, even immortality, as inferred from the story of Tithonus, presumably due to their intermittent emergence and apparent birth from Earth, a consequence of their partially hidden lifecycle (refer below). Aristotle, the great Greek polymath, wrote about their lifecycle and periodic emergence in his book Historia Animaliumcited in 9. While other examples abound, a translation by Egan of a poem from Anacreontea, a collection of largely unknown authored works from between 100 BC and 600 AC, probably encapsulates best the feelings the ancient Greeks had for cicadas: We know that you are royally blest Cicada when, among the tree-tops, You sip some dew and sing your song; For every single thing is yours That you survey among the fields And all the things the woods produce. The farmers’ constant company, You damage nothing that is theirs; Esteemed you are by every human As the summer’s sweet-voiced prophet. Muses love you, and Apollo too, Who’s gifted you with high pitched song. Old age does nothing that can wear you, Earth’s sage and song-enamoured son; You suffer not, being flesh-and-blood-less – 9 A god-like creature, virtually. In Australia, the songs of cicadas are a harbinger of summer, and then when in full chorus, a distinctive soundtrack, to which the overwhelming majority of people are familiar. Cicadas and their songs are ubiquitous, occurring all over the continent, in bushland, in cities and in suburbia21. This is perhaps not surprising given that at any one time, in any one location, there may be several different cicada species up in the trees (or underground in the soil…but wait…their songs are loud and distinctive, as too is their urine, which floods down from the canopies of trees …surely the latter cannot be true….?). Currently, 300 species are scientifically described and formally recognised, most of which belong to a 18, 19&21 biological superfamily called the Cicadoidea . The songs, which are only vocalised by male cicadas to attract females with which to mate, signify the final few weeks of life. It is a period in which there is a flurry of promiscuous, unadulterated sex. However, not long after it begins (or even before) they die (a Greek tragedy perhaps…?), either through natural senescence, fungal attack, to which many cicada species are highly susceptible, or predation by voracious vertebrate predators, namely birds, reptiles, and even fishes15,25&26. Yet, as much as their persistent singing (or deafening drone…?) and abundant shed nymphal skin on the ground or on the trunks of trees implies that they are eminently and conspicuously present (Figure 2), few people know anything about how they came to be up in the trees. Figure 2: The shed nymphal skin of perhaps 100 or more cicadas, a sure sign that summer has arrived in Australia. Note the adult cicada on the trunk of the tree…Can you locate it? (Image source: http://www.smh.com.au/environment/animals/suicide-song-cicada- sex-racket-risks-death-for-chance-at-love-20131230-3036d) All cicada species, irrespective of where in the world they are found, have a fascinating, multistage lifecycle. After mating in the treetops, female cicadas lay eggs in splits in tree stems, from which about a month later emerge wingless cicadas called nymphs. Nymphs disperse to the ground via gravity, and then burrow into the soil. Once underground, they tunnel through the soil until they find a plant’s roots. Then, using piercing sucking mouthparts, they attach to roots, from which they slurp sap out of the internal transport system (xylem and phloem). None of this is particularly exciting. What is remarkable is the length of time that some cicada nymphs spend underground attached to a plant’s roots (with occasional dispersion) – seventeen years! Yes, that is right, seventeen years sucking sap! That seems more like a prison sentence, than an existence! However, suddenly they all emerge en masse from the soil, every single last one of them, perfectly synchronised, shedding their subterranean skin (Figure 3), and then taking flight to the trees to eat, court (or be lured), mate and then die, completing their lifecycle18. Figure 3: An Australian green grocer cicada, Cyclochila australasiae, emerging from its subterranean skin. (Image source: https://commons.wikimedia.org/wiki/File:Green_grocer_cicada_molting.jpg) The most well-known periodical cicadas are the Magicicada species’ from North America, which spend either 13 or 17 years underground12,16&26. The eminent palaeontologist and natural historian Stephen J. Gould (1941 – 2002) hypothesised about the possible link between the mathematics of prime numbers and cicada periodical life-cycles. Gould stated: “I am most impressed by the timing of the cycles themselves. Why do we have 13 and 17 year cicadas, but no cycles of 12, 14, 15, 16, or 18? They are large enough to exceed the life cycle of any predator, but they are also prime numbers….Many potential predators have 2-5 year life cycles”11. So, are 13 and 17 year periodical cicadas in North America merely a coincidence? With many potential predators (refer above), of which any by chance may have matching reproductive cycles, which then would be a good year for cicadas to emerge and disperse to the treetops? Well, we know that prime numbers are number greater than one and only divisible by themselves and one; they cannot be further divided into smaller subsets of numbers. Therefore, any prime number year would limit contact with potential predators, irrespective of the years in which predators themselves appeared in nature. As Gould points out, many predators have lifecycles that track two to five year cycles11. Therefore, it seems that in choosing a prime life-cycle, some cicada species have arrived at an optimal strategy with which to avoid predators! So, how do cicadas distinguish the prime years? Well, they do not. They are cicadas! They know only about food and sex, and nothing at all about prime numbers! Essentially, it is a numbers game, played out over evolutionary time. The observed prime lifecycles are likely a result of Darwinian natural selection. Cicadas that emerged to complete their lifecycles in years divisible by many prime factors likely met their end at the hand of swarms of hungry predators. At this point, it is important to recall that for all living organisms, behaviours, traits, etcetera, are judged by whether or not they provide an ‘advantage’. Here, ‘advantage’ implies a greater than before chance of survival, and hence reproduction. Cicada species, which by chance acquired a gene mutation/s conveying long, prime- numbered life cycles, would have had a selective advantage. In other words, they fared best, survived the longest, and hence contributed the most offspring to the next generation. Simple right…? Possibly not so; while many cicada species have prime life-cycles, many 27 others do not; there are other competing hypotheses .