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

The aim of the lecture 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. In joint work with Bob Planqué it is shown that a combination of two types of density dependence may drive, for large classes of initial conditions, all but one year class to extinction. Competition for food creates 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.