Periodic matrix models for seasonal dynamics of structured populations with application to a seabird population

J. M. Cushing, Shandelle M. Henson

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


For structured populations with an annual breeding season, life-stage interactions and behavioral tactics may occur on a faster time scale than that of population dynamics. Motivated by recent field studies of the effect of rising sea surface temperature (SST) on within-breeding-season behaviors in colonial seabirds, we formulate and analyze a general class of discrete-time matrix models designed to account for changes in behavioral tactics within the breeding season and their dynamic consequences at the population level across breeding seasons. As a specific example, we focus on egg cannibalism and the daily reproductive synchrony observed in seabirds. Using the model, we investigate circumstances under which these life history tactics can be beneficial or non-beneficial at the population level in light of the expected continued rise in SST. Using bifurcation theoretic techniques, we study the nature of non-extinction, seasonal cycles as a function of environmental resource availability as they are created upon destabilization of the extinction state. Of particular interest are backward bifurcations in that they typically create strong Allee effects in population models which, in turn, lead to the benefit of possible (initial condition dependent) survival in adverse environments. We find that positive density effects (component Allee effects) due to increased adult survival from cannibalism and the propensity of females to synchronize daily egg laying can produce a strong Allee effect due to a backward bifurcation.

Original languageEnglish (US)
Pages (from-to)1689-1720
Number of pages32
JournalJournal of mathematical biology
Issue number6-7
StatePublished - Dec 1 2018


  • Allee effect
  • Animal behavior
  • Bifurcations
  • Cannibalism
  • Discrete-time population dynamics
  • Periodic orbits
  • Periodically-forced matrix equations
  • Reproductive synchrony
  • Seabird population dynamics
  • Stability
  • Structured population dynamics
  • Tipping point

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


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