Projection matrices in variable environments: λ1 in theory and practice

Dmitrii O. Logofet

Ecological Modelling, 2013, vol. 251, issue C, 307-311

Abstract: Perron–Frobenius theorem for nonnegative matrices, a mathematical foundation of matrix population models, applies when the projection matrix is not decomposable (or equivalently, when it is irreducible), the application yielding the dominant eigenvalue λ1>0 as a measure of the growth potential that a population with given demography possesses in a given environment. In practice, however, the projection matrix often appears to be decomposable (reducible); to calculate λ1 in this case, a principal submatrix should rather be used that corresponds to the reproductive core of the life cycle graph. I call it the reproductive submatrix and demonstrate that, when the reproductive submatrix does not coincide with the projection matrix and if this discrepancy is neglected in a case study, the resulting λ1 may happen to be overestimated. Averaging over a number of annual projection matrices eliminates the false growth rate but raises the problem of choice among the modes of averaging in the estimation of the stochastic growth rate in a stochastic environment. Computer simulation gives a method that avoids the both kinds of problem.

Keywords: Life cycle graph; Strong components; Reproductive submatrix; False growth rate; Carapa guianensis; Stochastic growth rate (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecomod:v:251:y:2013:i:c:p:307-311

DOI: 10.1016/j.ecolmodel.2012.12.028

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