A metapopulation model with discrete size structure

Maia Martcheva, Horst Thieme

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We consider a discrete size-structured meta-population model with the proportions of patches occupied by n individuals as dependent variables. Adults are territorial and stay on a certain patch. The juveniles may emigrate to enter a dispersers' pool from which they can settle on another patch and become adults. Absence of colonization and absence of emigration lead to extinction of the metapopula-tion. We define the basic reproduction number R 0 of the metapopulation as a measure for its strength of persistence. The metapopulation is uniformly weakly persistent if R 0 > 1. We identify subcritical bifurcation of persistence equilibria from the extinction equilibrium as a source of multiple persistence equilibria: It occurs, e.g., when the immigration rate, into occupied patches, exceeds the colonization rate (of empty patches). We determine that the persistence-optimal dispersal strategy which maximizes the basic reproduction number is of bang-bang type: If the number of adults on a patch is below carrying capacity all the juveniles should stay, if it is above the carrying capacity all the juveniles should leave.

Original languageEnglish (US)
Pages (from-to)379-413
Number of pages35
JournalNatural Resource Modeling
Issue number4
StatePublished - Dec 2005

ASJC Scopus subject areas

  • Modeling and Simulation
  • Environmental Science (miscellaneous)


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