Convexity in projection matrices: Projection to a calibration problem

Dmitrii O. Logofet

Ecological Modelling, 2008, vol. 216, issue 2, 217-228

Abstract: Convexity, as a fundamental property of sets and functions defined on convex sets, plays an important role in many mathematical and applied disciplines, including extremal and optimal-control problems. We prove the set of all feasible projection matrices in a general class of matrix models for stage-structured population dynamics to be convex and the dominant eigenvalue (λ1) of any projection 2×2 matrix to be either a convex, or a concave function on a simplex of the matrix first-row entries (i.e., stage-specific reproduction rates). The latter is also conjectured for the general n×n case. Though looking far from practical needs of matrix population models, this mathematical result has appeared to be quite useful in solving a practical problem to calibrate the projection matrix, i.e., to estimate all the stage-specific vital rates, from empirical data. The data from monitoring of individual life histories of marked plants on permanent sample plots during successive years enable direct calculation of the stage-specific survival and ontogenetic transition rates, but the rates of reproduction do remain uncertain as far as the parent plants can hardly be determined for the (not yet marked!) recruitment.

Keywords: Population structure; Life cycle graph; Matrix model; Vital rates; Uncertainty; Dominant eigenvalue; Adaptation principle; Constrained maximization; Potential-growth indicator; Linear programming (search for similar items in EconPapers)
Date: 2008
References: View complete reference list from CitEc
Citations: View citations in EconPapers (9)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304380008001439
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ecomod:v:216:y:2008:i:2:p:217-228

DOI: 10.1016/j.ecolmodel.2008.03.004

Access Statistics for this article

Ecological Modelling is currently edited by Brian D. Fath

More articles in Ecological Modelling from Elsevier
Bibliographic data for series maintained by Catherine Liu ().