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Inferring transient dynamics of human populations from non-normality metrics

Inferring transient dynamics of human populations from non-normality metrics
Inferring transient dynamics of human populations from non-normality metrics
In our increasingly unstable and unpredictable world, population dynamics rarely settle uniformly to long-term behaviour. However, projecting period-by-period through the preceding fluctuations is more data-intensive and analytically involved than evaluating at equilibrium. To efficiently model populations and best inform policy, we require pragmatic suggestions as to when it is necessary to incorporate short-term transient dynamics and their effect on eventual projected population size. To estimate this need for matrix population modelling, we adopt a linear algebraic quantity known as non-normality. Matrix non-normality is distinct from normality in the Gaussian sense, and indicates the amplificatory potential of the population projection matrix given a particular population vector. In this paper, we compare and contrast three well-regarded metrics of non-normality, which were calculated for over 1000 age-structured human population projection matrices from 42 European countries in the period 1960 to 2014. Non-normality increased over time, mirroring the indices of transient dynamics that peaked around the millennium. By standardising the matrices to focus on transient dynamics and not changes in the asymptotic growth rate, we show that the damping ratio is an uninformative predictor of whether a population is prone to transient booms or busts in its size. These analyses suggest that population ecology approaches to inferring transient dynamics have too often relied on suboptimal analytical tools focussed on an initial population vector rather than the capacity of the life cycle to amplify or dampen transient fluctuations. Finally, we introduce the engineering technique of pseudospectra analysis to population ecology, which, like matrix non-normality, provides a more complete description of the transient fluctuations than the damping ratio. Pseudospectra analysis could further support non-normality assessment to enable a greater understanding of when we might expect transient phases to impact eventual population dynamics.

1438-3896
Nicol-Harper, Alex
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Dooley, Claire
8caf4d90-5b57-4f92-a6e6-ff2399114af1
Packman, David
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Mueller, Markus
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Bijak, Jakub
e33bf9d3-fca6-405f-844c-4b2decf93c66
Hodgson, David
070bce7b-8af2-433d-ac48-c54b42bcedd7
Townley, Stuart
29a6f26d-c436-4b76-b310-9b5b867ecd44
Ezard, Thomas
a143a893-07d0-4673-a2dd-cea2cd7e1374
Nicol-Harper, Alex
5bd6c449-ad87-49cb-890e-332ea0363893
Dooley, Claire
8caf4d90-5b57-4f92-a6e6-ff2399114af1
Packman, David
9b41d2ec-8839-4d19-8af3-ac70723ba8e4
Mueller, Markus
9abd38e5-470e-479e-ba71-3e0a627431be
Bijak, Jakub
e33bf9d3-fca6-405f-844c-4b2decf93c66
Hodgson, David
070bce7b-8af2-433d-ac48-c54b42bcedd7
Townley, Stuart
29a6f26d-c436-4b76-b310-9b5b867ecd44
Ezard, Thomas
a143a893-07d0-4673-a2dd-cea2cd7e1374

Nicol-Harper, Alex, Dooley, Claire, Packman, David, Mueller, Markus, Bijak, Jakub, Hodgson, David, Townley, Stuart and Ezard, Thomas (2018) Inferring transient dynamics of human populations from non-normality metrics. Population Ecology. (doi:10.1007/s10144-018-0620-y).

Record type: Article

Abstract

In our increasingly unstable and unpredictable world, population dynamics rarely settle uniformly to long-term behaviour. However, projecting period-by-period through the preceding fluctuations is more data-intensive and analytically involved than evaluating at equilibrium. To efficiently model populations and best inform policy, we require pragmatic suggestions as to when it is necessary to incorporate short-term transient dynamics and their effect on eventual projected population size. To estimate this need for matrix population modelling, we adopt a linear algebraic quantity known as non-normality. Matrix non-normality is distinct from normality in the Gaussian sense, and indicates the amplificatory potential of the population projection matrix given a particular population vector. In this paper, we compare and contrast three well-regarded metrics of non-normality, which were calculated for over 1000 age-structured human population projection matrices from 42 European countries in the period 1960 to 2014. Non-normality increased over time, mirroring the indices of transient dynamics that peaked around the millennium. By standardising the matrices to focus on transient dynamics and not changes in the asymptotic growth rate, we show that the damping ratio is an uninformative predictor of whether a population is prone to transient booms or busts in its size. These analyses suggest that population ecology approaches to inferring transient dynamics have too often relied on suboptimal analytical tools focussed on an initial population vector rather than the capacity of the life cycle to amplify or dampen transient fluctuations. Finally, we introduce the engineering technique of pseudospectra analysis to population ecology, which, like matrix non-normality, provides a more complete description of the transient fluctuations than the damping ratio. Pseudospectra analysis could further support non-normality assessment to enable a greater understanding of when we might expect transient phases to impact eventual population dynamics.

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Accepted/In Press date: 10 May 2018
e-pub ahead of print date: 5 June 2018

Identifiers

Local EPrints ID: 421137
URI: https://eprints.soton.ac.uk/id/eprint/421137
ISSN: 1438-3896
PURE UUID: 4857ba16-5146-48e9-989f-ca440f24429c
ORCID for Jakub Bijak: ORCID iD orcid.org/0000-0002-2563-5040
ORCID for Thomas Ezard: ORCID iD orcid.org/0000-0001-8305-6605

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Date deposited: 23 May 2018 16:30
Last modified: 16 Jul 2019 17:17

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Contributors

Author: Alex Nicol-Harper
Author: Claire Dooley
Author: David Packman
Author: Markus Mueller
Author: Jakub Bijak ORCID iD
Author: David Hodgson
Author: Stuart Townley
Author: Thomas Ezard ORCID iD

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