Pauses of Larval Development and Their Consequences for Stage-Structured Populations

Hermann Brunner, Stephen A. Gourley*, Rongsong Liu, Yanyu Xiao

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

7 Citations (Scopus)
12 Downloads (Pure)


This paper considers some novel predictions of a mathematical model for a stage-structured insect species that undergoes diapause if faced with strong intraspecific competition among larvae. The model consists of a system of two delay differential equations with a state-dependent time delay of threshold type. When the model has an Allee effect, we show that diapause may cause extinction in some parameter regimes even where the initial population is high. We also demonstrate that the model can have diapause-induced periodic solutions that can arise even if the birth function is strictly increasing, a situation in which solutions for the constant delay case always converge to an equilibrium.

Original languageEnglish
Pages (from-to)977-994
Number of pages18
JournalSIAM Journal on Applied Mathematics
Issue number3
Publication statusPublished - 13 Jun 2017

Scopus Subject Areas

  • Applied Mathematics

User-Defined Keywords

  • Allee effect
  • Delay
  • Diapause
  • Size structure
  • Threshold condition


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