The genealogical decomposition of a matrix population model with applications to the aggregation of stages

Bienvenu, François, Akcay, Erol, Legendre, Stéphane, McCandlish, David (June 2017) The genealogical decomposition of a matrix population model with applications to the aggregation of stages. Theoretical Population Biology, 115. pp. 69-80.

URL: https://www.ncbi.nlm.nih.gov/pubmed/28476403
DOI: 10.1016/j.tpb.2017.04.002

Abstract

Matrix projection models are a central tool in many areas of population biology. In most applications, one starts from the projection matrix to quantify the asymptotic growth rate of the population (the dominant eigenvalue), the stable stage distribution, and the reproductive values (the dominant right and left eigenvectors, respectively). Any primitive projection matrix also has an associated ergodic Markov chain that contains information about the genealogy of the population. In this paper, we show that these facts can be used to specify any matrix population model as a triple consisting of the ergodic Markov matrix, the dominant eigenvalue and one of the corresponding eigenvectors. This decomposition of the projection matrix separates properties associated with lineages from those associated with individuals. It also clarifies the relationships between many quantities commonly used to describe such models, including the relationship between eigenvalue sensitivities and elasticities. We illustrate the utility of such a decomposition by introducing a new method for aggregating classes in a matrix population models to produce a simpler model with a smaller number of classes. Unlike the standard method, our method has the advantage of preserving reproductive values and elasticities. It also has conceptually satisfying properties such as commuting with changes of units.

Item Type: Paper
Subjects: bioinformatics > genomics and proteomics > genetics & nucleic acid processing
evolution
bioinformatics > genomics and proteomics > genetics & nucleic acid processing > population genetics
CSHL Authors:
Communities: CSHL labs > McCandlish lab
Depositing User: Matt Covey
Date: June 2017
Date Deposited: 18 Jan 2017 20:57
Last Modified: 08 Jun 2017 19:18
Related URLs:
URI: http://repository.cshl.edu/id/eprint/34034

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