A Hybrid Model for the Population Dynamics of Periodical Cicadas

Variation in Avian Predation Pressure as a Driver for the Diversification of Periodical Cicada Broods

AbstractPeriodical cicadas live 13 or 17 years underground as nymphs, then emerge in synchrony as adults to reproduce. Developmentally synchronized populations called broods rarely coexist, with one dominant brood locally excluding those that emerge in off years. Twelve modern 17-year cicada broods are believed to have descended from only three ancestral broods following the last glaciation. The mechanisms by which these daughter broods overcame exclusion by the ancestral brood to synchronously emerge in a different year, however, are elusive. Here, we demonstrate that temporal variation in the population density of generalist predators can allow intermittent opportunities for new broods to invade, even though a single brood remains dominant most of the time. We show that this mechanism is consistent, in terms of the type and frequency of brood replacements, with the distribution of periodical cicada broods throughout North America today. Although we investigate one particularly charismatic case study, the mechanisms involved (competitive exclusion, Allee effects, trait variation, predation, and temporal variability) are ubiquitous and could contribute to patterns of species diversity in a range of systems.

How do cicadas emerge together? Thermophysical aspects of their collective decision-making

Periodical cicadas exhibit life cycles with durations of 13 or 17 years, and it is now accepted that large prime cycles arose to avoid synchrony with predators. Less well explored is how, in the face of intrinsic biological and environmental noise, insects within a brood emerge together in large successive swarms from underground during springtime warming. Here, we consider the decision-making process of underground cicadas experiencing random, spatially correlated thermal microclimates such as those in nature. Introducing short-range communication between insects leads to an Ising model of consensus building with a quenched, spatially correlated random magnetic field and annealed site dilution, which displays the kinds of collective swarms seen in nature. These results highlight the need for fieldwork to quantify the spatial fluctuations in thermal microclimates and their relationship to the spatiotemporal dynamics of swarm emergence.

Advances in the Evolution and Ecology of 13- and 17-Year Periodical Cicadas

Apart from model organisms, 13- and 17-year periodical cicadas (Hemiptera: Cicadidae: Magicicada) are among the most studied insects in evolution and ecology. They are attractive subjects because they predictably emerge in large numbers; have a complex biogeography shaped by both spatial and temporal isolation; and include three largely sympatric, parallel species groups that are, in a sense, evolutionary replicates. Magicicada are also relatively easy to capture and manipulate, and their spectacular, synchronized mass emergences facilitate outreach and citizen science opportunities. Since the last major review, studies of Magicicada have revealed insights into reproductive character displacement and the nature of species boundaries, provided additional examples of allochronic speciation, found evidence for repeated and parallel (but noncontemporaneous) evolution of 13- and 17-year life cycles, quantified the amount and direction of gene flow through time, revealed phylogeographic patterning resulting from paleoclimate change, examined the timing of juvenile development, and created hypotheses for the evolution of life-cycle control and the future effects of climate changeon Magicicada life cycles. New ecological studies have supported and questioned the role of prime numbers in Magicicada ecology and evolution, found bidirectional shifts in population size over generations, quantified the contribution of Magicicada to nutrient flow in forest ecosystems, and examined behavioral and biochemical interactions between Magicicada and their fungal parasites and bacterial endosymbionts.

Sharp boundary formation and invasion between spatially adjacent periodical cicada broods

Periodical cicadas, Magicicada spp., are a useful model system for understanding the population processes that influence range boundaries. Unlike most insects, these species typically exist at very high densities (occasionally >1000/ m²) and have unusually long life-spans (13 or 17 years). They spend most of their lives underground feeding on plant roots. After the underground period, adults emerge from the ground to mate and oviposit over a period of just a few days. Collections of populations that are developmentally synchronized across large areas are known as "broods". There are usually sharp boundaries between spatially adjacent broods and regions of brood overlap are generally small. The exact mechanism behind this developmental synchronization and the sharp boundary between broods remain unknown: previous studies have focused on the impacts of predator-driven Allee-effects, competition among nymphs, and their impacts on the persistence of off-synchronized emergence events. Here, we present a nonlinear Leslie-type matrix model to additionally consider cicada movement between spatially separated broods, and examine its role in maintaining brood boundaries and within-brood developmental synchrony that is seen in nature. We successfully identify ranges of competition and dispersal that lead to stable coexistence of broods that differ between spatial patches.

Bifurcations of cycles in nonlinear semelparous Leslie matrix models

This paper develops a method for studying bifurcations that occur in a neighborhood of the extinction equilibrium in nonlinear semelparous Leslie matrix models. The method uses a Lotka-Volterra equation with cyclic symmetry to detect the existence and to evaluate the stability of bifurcating equilibria and cycles. An application of the method provides sharp stability conditions for both a single-class cycle and a positive equilibrium bifurcating from the extinction equilibrium. The stability condition for a bifurcating single-class cycle confirms that the periodicity observed in periodical insects occurs if competition is more severe between than within age-classes. The developed method is also used to investigate two examples of nonlinear semelparous Leslie matrix models incorporating predator satiation. The investigation shows that a single-class cycle, which is associated with the periodicity in periodical insects, is a unique stable cycle in a neighborhood of the extinction equilibrium if the density effects in survival probabilities are identical among age-classes.

The winner takes it all: how semelparous insects can become periodical

The aim of this short note is to give a simple explanation for the remarkable periodicity of Magicicada species, which appear as adults only every 13 or 17 years, depending on the region. We show that a combination of two types of density dependence may drive, for large classes of initial conditions, all but 1 year class to extinction. Competition for food leads to negative density dependence in the form of a uniform (i.e., affecting all age classes in the same way) reduction of the survival probability. Satiation of predators leads to positive density dependence within the reproducing age class. The analysis focuses on the full life cycle map derived by iteration of a semelparous Leslie matrix.