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Inferring transient dynamics of human populations from matrix non-normality.

Alex Nicol-Harper¹, Claire Dooley¹, David Packman²

¹1Ocean and Earth Science, National Oceanography Centre, University of Southampton Waterfront Campus, Southampton, UK.

Population Ecology

|July 17, 2018

Summary

Population projection models need to account for short-term dynamics. Matrix non-normality, a measure of amplification potential, helps predict population booms or busts, improving ecological modeling.

Keywords:

Damping ratio Europe Eurostat Human demography Population projection matrix Pseudospectra

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Area of Science:

Population Ecology
Mathematical Biology
Demography

Background:

Population dynamics are often unstable, making long-term projections difficult.
Projecting period-by-period is data-intensive and analytically complex.
Understanding when to include short-term dynamics is crucial for policy and modeling.

Purpose of the Study:

To assess the necessity of incorporating short-term transient dynamics in population modeling.
To evaluate matrix non-normality as a tool for estimating the need for transient dynamics analysis.
To compare existing non-normality metrics and introduce pseudospectra analysis for population ecology.

Main Methods:

Calculated three non-normality metrics for over 1000 human population projection matrices (1960-2014, 42 European countries).
Standardized matrices to isolate transient dynamics from asymptotic growth rate changes.
Introduced and applied pseudospectra analysis to population projection matrices.

Main Results:

Matrix non-normality increased over time, correlating with transient dynamics peaking around the millennium.
The damping ratio was found to be an uninformative predictor of population volatility.
Pseudospectra analysis offers a more comprehensive description of transient fluctuations than the damping ratio.

Conclusions:

Current population ecology methods may rely on suboptimal tools for inferring transient dynamics.
Matrix non-normality and pseudospectra analysis provide better insights into population projection matrix behavior.
These methods can help determine when transient phases significantly impact eventual population dynamics.