Algebraic Properties of the Multistate Population Matrix Model

DOI

10.2991/assehr.k.200204.048How to use a DOI?

Keywords

matrix, population, spectral radius

Abstract

Discrete time population growth is often modeled by a matrix. Many growth parameters such as growth rate, reproduction rate, as well as the movement of the population are easily included in a matrix model. This paper will discuss a matrix model that describes the dynamics of a population having some stages of life and occupying some different patches. The matrix, which is the product of two matrices S and D, is often called SD matrix. The matrix S is a diagonal block matrix in which its block is a sub-stochastic column matrix. The matrix S represents the movement of a population between locations (patches). On the other hand, the matrix D is a block matrix in which its block is a nonnegative real diagonal matrix. The matrix D describes the population growth in specific patches. The paper will focus on the properties of the SD matrix from the algebraic point of view, particularly the spectral radius of the matrix. It will be shown that the spectral radius of the SD matrix is less than the spectral radius of D meanwhile the condition does not hold for the block matrices SD and D.

Copyright

© 2020, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Sisilia Sylviani
AU  - Ema Carnia
AU  - A.K. Supriatna
PY  - 2020
DA  - 2020/02/12
TI  - Algebraic Properties of the Multistate Population Matrix Model
BT  - Proceedings of the International Conference on Educational Research and Innovation (ICERI 2019)
PB  - Atlantis Press
SP  - 257
EP  - 258
SN  - 2352-5398
UR  - https://doi.org/10.2991/assehr.k.200204.048
DO  - 10.2991/assehr.k.200204.048
ID  - Sylviani2020
ER  -