### Abstract

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 language | English (US) |
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Pages (from-to) | 297-333 |

Number of pages | 37 |

Journal | Natural Resource Modeling |

Volume | 8 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 1994 |

### ASJC Scopus subject areas

- Modeling and Simulation
- Environmental Science (miscellaneous)

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## Cite this

*Natural Resource Modeling*,

*8*(4), 297-333. https://doi.org/10.1111/j.1939-7445.1994.tb00188.x