Abstract
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 language | English |
|---|---|
| Pages (from-to) | 283-301 |
| Number of pages | 19 |
| Journal | Journal of Mathematical Biology |
| Volume | 80 |
| Issue number | 1-2 |
| Early online date | 27 Apr 2019 |
| DOIs | |
| Publication status | Published - Jan 2020 |
Funding
Part of the work was done during the Mathematical Biology semester at the Mittag-Leffler Institute. We thank the organisers, in particular Torbjörn Lundh and Mats Gyllenberg, for making it such a success. We also thank two anonymous reviewers for their careful reading and suggestions to improve the manuscript.
| Funders | Funder number |
|---|---|
| Mittag-Leffler Institute |
