title: Single generation cycles and delayed feedback cycles are not separate phenomena.
abstract: We study a simple model for generation cycles, which are oscillations with a period of one or a few generation times of the species. The model is formulated in terms of a single delay-differential equation for the population density of an adult stage, with recruitment to the adult stage depending on the intensity of competition during the juvenile phase. This model is a simplified version of a group of models proposed by Gurney and Nisbet, who were the first to distinguish between single-generation cycles and delayed-feedback cycles. According to these authors, the two oscillation types are caused by different mechanisms and have periods in different intervals, which are one to two generation times for single-generation cycles and two to four generation times for delayed-feedback cycles. By abolishing the strict coupling between the maturation time and the time delay between competition and its effect on the population dynamics, we find that single-generation cycles and delayed-feedback cycles occur in the same model version, with a gradual transition between the two as the model parameters are varied over a sufficiently large range. Furthermore, cycle periods are not bounded to lie within single octaves. This implies that a clear distinction between different types of generation cycles is not possible. Cycles of all periods and even chaos can be generated by varying the parameters that determine the time during which individuals from different cohorts compete with each other. This suggests that life-cycle features in the juvenile stage and during the transition to the adult stage are important determinants of the dynamics of density limited populations.
authors.affiliation: Institute of Condensed Matter Physics, Hochschulstraße 6, 64289 Darmstadt, Germany. Electronic address: pfaff@fkp.tu-darmstadt.de.
authors.forename: T
authors.initials: T
authors.lastname: Pfaff
authors.affiliation: Institute of Condensed Matter Physics, Hochschulstraße 6, 64289 Darmstadt, Germany. Electronic address: andreasbrechtel@googlemail.com.
authors.forename: A
authors.initials: A
authors.lastname: Brechtel
authors.affiliation: Institute of Condensed Matter Physics, Hochschulstraße 6, 64289 Darmstadt, Germany. Electronic address: drossel@fkp.tu-darmstadt.de.
authors.forename: B
authors.initials: B
authors.lastname: Drossel
authors.affiliation: Institute for Biodiversity and Ecosystem Dynamics, P.O. Box 94248, 1090 GE Amsterdam, The Netherlands. Electronic address: c.p.guill@uva.nl.
authors.forename: C
authors.initials: C
authors.lastname: Guill
mesh_terms: D000818:Animals; D003163:Competitive Behavior / Q000502:physiology*; D003198:Computer Simulation; D004463:Ecology / Q000379:methods; D017753:Ecosystem; D008018:Life Cycle Stages / Q000502:physiology*; D008954:Models, Biological; D011157:Population Dynamics; D012098:Reproduction / Q000502:physiology*; D016019:Survival Analysis
keywords: Delay differential equation; Delayed feedback cycles; Generation cycles; Single generation cycles; Structured population model