The net reproductive value and stability in matrix population models

J. M. Cushing, Yicang Zhou Yicang

Research output: Contribution to journalArticlepeer-review

130 Scopus citations


The net reproductive value n is defined for a general discrete linear population model with a non-negative projection matrix. This number is shown to have the biological interpretation of the expected number of offspring per individual over its life time. The main result relates n to the population's growth rate (ie the dominance eigenvalue λ of the projection matrix) and shows that the stability of the extinction state (the trivial equilibrium) can be determined by whether n is less than or greater than 1. Examples are given to show that explicit algebraic formulas for n are often derivable, and hence available for both numerical and parameter studies of stability, when no such formulas for λ are available. -Authors

Original languageEnglish (US)
Pages (from-to)297-333
Number of pages37
JournalNatural Resource Modeling
Issue number4
StatePublished - 1994
Externally publishedYes

ASJC Scopus subject areas

  • Modeling and Simulation
  • Environmental Science (miscellaneous)


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