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

R. Planque, O. Diekmann*

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


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.

Original languageEnglish
Pages (from-to)283-301
Number of pages19
JournalJournal of Mathematical Biology
Issue number1-2
Early online date27 Apr 2019
Publication statusPublished - Jan 2020


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