ODO DIEKMANN
	"DESTOBIO 2000" August 23-27, 2000 West Lafayette, Indiana, USA

"Dynamics of Semelparous Populations."

ABSTRACT: A species is called "semelparous" if individuals reproduce only once (and then die, like, e.g., Pacific Salmon). If, in addition, individuals live for exactly k years, there are k reproductively isolated subpopulations, which we call year classes. These do, in general, interact with each other via an environmental feedback mechanism: their survival probability and reproductive output depends on the environmental conditions (like food availability) and these ,in turn, are affected by the presence or absence of other individuals.

Motivated by the Cicada Phenomenon we focus on Missing Year Classes by asking the typical invasibility question: can a rare invader grow in the environment as set by the ubiquitous resident? We do so in the context of a caricatural model in which the "environmental condition" is a one-dimensional quantity. We shall find a degenerate bifurcation phenomenon (a non-local exchange of stability between an interior and a boundary attractor). In addition we pinpoint several open mathematical questions.

Echoing early results by Bulmer (Am. Nat. 111(1977) 1099-1117) and later work by Ebenman, Cushing, Li, Nisbet, ..., our main biological conclusion is that a single year class may very well monopolize the world.

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