Open AccessTHE NET REPRODUCTIVE VALUE AND STABILITY IN MATRIX POPULATION MODELS
Author(s) -
Cushing J.M.,
Yicang Zhou
Publication year - 1994
Publication title -
natural resource modeling
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.28
H-Index - 32
eISSN - 1939-7445
pISSN - 0890-8575
DOI - 10.1111/j.1939-7445.1994.tb00188.x
Subject(s) - mathematics , stability (learning theory) , eigenvalues and eigenvectors , population , net (polyhedron) , matrix (chemical analysis) , algebraic number , projection (relational algebra) , value (mathematics) , reproductive value , discrete time and continuous time , interpretation (philosophy) , mathematical economics , statistics , computer science , offspring , biology , mathematical analysis , algorithm , physics , demography , genetics , pregnancy , geometry , materials science , quantum mechanics , machine learning , sociology , composite material , programming language
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 (i.e. the dominant 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.