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Evolution of Periodicity in Periodical Cicadas

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Evolution of Periodicity in Periodical Cicadas Ecology, 86(12), 2005, pp. 3200±3211 q 2005 by the Ecological Society of America EVOLUTION OF PERIODICITY IN PERIODICAL CICADAS NICOLAS LEHMANN-ZIEBARTH,1,2 PAUL P. H EIDEMAN,1,2 REBECCA A. SHAPIRO,1,2 SONIA L. STODDART,1,2 CHIEN CHING LILIAN HSIAO,1,2 GORDON R. STEPHENSON,1,2 PAUL A. MILEWSKI,1 AND ANTHONY R. IVES2,3 1Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706 USA 2Department of Zoology, University of Wisconsin-Madison, Madison, Wisconsin 53706 USA Abstract. Periodical cicadas present numerous puzzles for biologists. First, their period is ®xed, with individuals emerging as adults precisely after either 13 or 17 years (depending on species). Second, even when there are multiple species of either 13- or 17-year cicadas at the same location, only one or rarely two broods (cohorts) co-occur, so that periodical cicada adults appear episodically. Third, the 13- or 17-year periods of cicadas suggest there is something important about prime numbers. Finally, single broods can dominate large areas, with geographical boundaries of broods remaining generally stable through time. While previous mathematical models have been used to investigate some of these puzzles individually, here we investigate them all simultaneously. Unlike previous models, we take an explicitly evolutionary approach. Although not enough information is known about periodical cicadas to draw ®rm conclusions, the theoretical arguments favor a combination of predator satiation and nymph competition as being key to the evolution of strictly ®xed periods and occurrence of only one brood at most geographical locations. Despite ecological mechanisms that can select for strictly ®xed periods, there seem to be no plausible ecological mechanisms that select for periods being prime numbers. This suggests that the explanation for prime-numbered periods, rather than just ®xed periods, may reside in physiological or genetic mechanisms or constraints. Key words: Allee effects; evolution of periodicity; Magicicada; rock±paper±scissors competition; spatial dynamics. INTRODUCTION cicadas only emerge at a given location once or rarely twice every 13 or 17 years, causing a strikingly epi- Since the discovery of the periodical cicadas, Mag- sodic pattern of species that, when present, are strik- icicada spp., in eastern North America some 300 years ingly noticeable. Special Feature ago (Oldenburg 1666, Walsh and Riley 1868), biolo- Periodical cicadas present numerous biological puz- gists have been fascinated by their periodicity. There zles. What were the evolutionary forces that created are seven species of periodical cicadas that divide into synchrony in the emergence of broods? Not only is two categories: four species that live for 13 years, and emergence timed to be exactly 13 or 17 years, but three species that live for 17 years (Williams and Simon emergence in the spring occurs over a narrow window, 1995, Marshall and Cooley 2000). Generally, the geo- with most individuals emerging over a few days (Wil- graphical ranges of the 13- and 17-year cicadas are liams and Simon 1995), implying strong selection for nonoverlapping, with 13-year cicadas occurring to the the emergence of large numbers of cicadas together. south and west of 17-year cicadas. Periodical cicadas Why does only one brood typically dominate in a given emerge as a group in late spring, forming large and geographical location? This suggests that there are ad- noisy mating congregations for roughly a month, and vantages not only in emerging within a large brood, then the adults die. Because individuals emerge after but also in emerging periodically so that cicadas are exactly 13 or 17 years (depending on the species), the not present every year. And why are the periods of populations are divided into discrete cohorts, or broods, periodical cicadas both prime numbers? Since period that emerge together. In any one geographical location, length is evolutionarily labile, this seems hardly co- there is typically only one or rarely two broods of a incidental. The seven species actually consist of three given species, and when there are multiple species sets of sister species that are morphologically, behav- (which is often the case), their broods emerge in the iorally, and (in some cases [Martin and Simon 1988]) same years (Lloyd and Dybas 1966a, Dybas and Lloyd genetically distinct, with each of the three sets con- 1974, Williams and Simon 1995). Therefore, periodical taining one 17-year species, and one or two 13-year species (Simon et al. 2000, Cooley et al. 2003). The Manuscript received 25 October 2004; accepted 15 December difference among the species within these three sets is 2004; ®nal version received 11 February 2005. Corresponding Editor: A. A. Agrawal. For reprints of this Special Feature, see primarily period length, suggesting that period length footnote 1, p. 3137. can change evolutionarily between 13 and 17 relatively 3 Corresponding author. E-mail: [email protected] easily. 3200 December 2005 EMPIRICALLY MOTIVATED ECOLOGICAL THEORY 3201 These questions have a mathematical component, might suggest a very long-term effect of the previous and it was for this reason that periodical cicadas were emergence, although this pattern was far less striking selected as a topic for an undergraduate summer re- than the short-lived increase in abundance of other spe- search program involving all of the authors. The goal cies following emergence. of this program was to give undergraduate students Nymphs feed on xylem from the roots of a variety experience in research at the interface of biology and of deciduous tree species (White and Strehl 1978). In mathematics. Because the question of periodical cicada a study investigating underground survival, Karban periodicity is inherently both biological and mathe- (1997) found high nymph mortality in the ®rst two matical, it gave a compelling empirical problem to years following egg laying, but subsequent low mor- demonstrate the value of mathematics in the biological tality until emergence. Furthermore, early mortality sciences. Developing ecological theory to address spe- was apparently density dependent; from ®ve study ci®c empirical problems±the theme of this Special Fea- sites, the two with much higher density than the others ture±may be useful not just in research, but also in also had higher mortality. This could be explained by education. competition among nymphs for food (Williams and Si- Below, we ®rst review the biology of periodical ci- mon 1995). Nymphs grow through ®ve instars, and cadas. We then give an overview of previous theoretical once they have reached the last nymph instar, growth models addressing periodical cicadas, showing that our is arrested even if this occurs several years before their understanding of the evolution of cicada's periodicity timed emergence at 13 or 17 years (White and Lloyd is far from complete. Using a mathematical model that 1975). Arrested growth suggests strong evolutionary incorporates and generalizes features from many pre- forces underlying the strict periodicity of emergence. vious models, we investigate different mechanisms that Occasionally, however, ``mistakes'' are made, in which could be responsible for the evolution of strict peri- case a 17-year cicada generally emerges at 13 years, odicity. We then investigate the more speci®c problem although rarer mistakes are made in which emergence of explaining prime-numbered periods. Finally, we de- is off by only one year (Williams and Simon 1995). velop a spatial model of periodical cicada dynamics, Several authors argue that the phenotypic differentia- Special Feature which gives a strong argument in favor of one of the tion between 13- and 17-year periods may be governed several mechanisms that could lead to cicada period- by a single, diallelic locus (Lloyd et al. 1983, Cox and icity. Carlton 1988), suggesting that there is a genetic switch mechanism between prime-numbered periods. STUDY SYSTEM The life cycle and key ecological features of peri- THEORETICAL APPROACH odical cicadas are reviewed in depth by Lloyd and Dy- Previous models bas (1966a, b) and Williams and Simon (1995); here we present an abbreviated overview to explain the con- Numerous theoretical models have been used to in- struction of models. The adult stage starts as a given vestigate mechanisms that could create cicada peri- brood of nymphs digs its way from the ground at night odicity. Here we review some of the key models that to emerge over a 7±10 d period (Heath 1968, Williams explore different facets of periodicity. et al. 1993). After mating in large congregations, fe- Hoppensteadt and Keller (1976) and Bulmer (1977) males lay up to 600 eggs. Nymphs then hatch, drop to investigated mechanisms that could drive periodicity. the forest ¯oor, and burrow to underground roots. The Both investigations demonstrated that a combination total adult life span is roughly 2±6 weeks. Adult mor- of nymph competition and predator satiation could lead tality from bird predation can be high (Karban 1984), to one or a few broods dominating other broods and although birds become satiated when emerging broods driving them to extinction. Nymph competition acts are large (Karban 1982, Williams et al. 1993). Ander- across broods, with high enough densities of one brood son (1977) and Nolan and Thompson (1975) both re- leading to the suppression of other broods in following corded an increase in ¯edging success of birds during years. This process is exacerbated by predator satiation years of cicada emergence, showing that cicadas rep- (Bulmer 1977). When there is predator satiation, large resent an important food source for some species of broods are favored over small broods, since by satiating birds. In a recent study, Koenig and Liebhold (2005) their predators large broods have higher per capita sur- analyzed 37 years of North American Breeding Bird vival. Thus, once a brood is diminished to levels at Count data for 24 species that potentially eat cicadas. which predator satiation is no longer strong, the brood Of these, 15 showed some population abundance re- will be extinguished.
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