The University of Southampton
University of Southampton Institutional Repository

The importance of timescales for the emergence of environmental self-regulation

The importance of timescales for the emergence of environmental self-regulation
The importance of timescales for the emergence of environmental self-regulation
Models which explore the possibilities of emergent self-regulation in the Earth system often assume the timescales associated with changes in various sub-systems to be predetermined. Given their importance in guiding the fixed point dynamics of such models, relatively little formalism has been established. We analyse a classic model of environmental self-regulation, Daisyworld, and interpret the original equations for model temperature, changes in insolation, and self-organisation of the biota as an important separation of timescales. This allows a simple analytical solution where the model is reduced to two states while retaining important characteristics of the original model. We explore the consequences of relaxing some key assumptions. We show that increasing the rate of change of insolation relative to adaptation of the biota shows a sharp transition between regulating, and lifeless states. Additionally, in slowing the rate of model temperature change relative to the adapting biota we derive expressions for the damping rate of fluctuations, along with a threshold beyond which damped oscillations occur. We relax the assumption that seeding occurs globally by extending this analysis to solve a two-dimensional cellular automata Daisyworld. We conclude by reviewing a number of previous Daisyworld models and make explicit their respective timescales, and how their behaviour can be understood in light of our analysis
0022-5193
172-180
Weaver, Iain S.
07d26f51-efdd-442b-8504-3c86b19e6106
Dyke, James G.
e2cc1b09-ae44-4525-88ed-87ee08baad2c
Weaver, Iain S.
07d26f51-efdd-442b-8504-3c86b19e6106
Dyke, James G.
e2cc1b09-ae44-4525-88ed-87ee08baad2c

Weaver, Iain S. and Dyke, James G. (2012) The importance of timescales for the emergence of environmental self-regulation. Journal of Theoretical Biology, 313, 172-180. (doi:10.1016/j.jtbi.2012.07.034). (PMID:22902427)

Record type: Article

Abstract

Models which explore the possibilities of emergent self-regulation in the Earth system often assume the timescales associated with changes in various sub-systems to be predetermined. Given their importance in guiding the fixed point dynamics of such models, relatively little formalism has been established. We analyse a classic model of environmental self-regulation, Daisyworld, and interpret the original equations for model temperature, changes in insolation, and self-organisation of the biota as an important separation of timescales. This allows a simple analytical solution where the model is reduced to two states while retaining important characteristics of the original model. We explore the consequences of relaxing some key assumptions. We show that increasing the rate of change of insolation relative to adaptation of the biota shows a sharp transition between regulating, and lifeless states. Additionally, in slowing the rate of model temperature change relative to the adapting biota we derive expressions for the damping rate of fluctuations, along with a threshold beyond which damped oscillations occur. We relax the assumption that seeding occurs globally by extending this analysis to solve a two-dimensional cellular automata Daisyworld. We conclude by reviewing a number of previous Daisyworld models and make explicit their respective timescales, and how their behaviour can be understood in light of our analysis

Other
YJTBI_7011.PDF - Other
Download (1MB)

More information

Published date: 21 November 2012
Organisations: Agents, Interactions & Complexity

Identifiers

Local EPrints ID: 342026
URI: http://eprints.soton.ac.uk/id/eprint/342026
ISSN: 0022-5193
PURE UUID: 3b549446-0223-4721-8138-d935b1c6b6bb
ORCID for James G. Dyke: ORCID iD orcid.org/0000-0002-6779-1682

Catalogue record

Date deposited: 09 Aug 2012 18:11
Last modified: 14 Mar 2024 11:46

Export record

Altmetrics

Contributors

Author: Iain S. Weaver
Author: James G. Dyke ORCID iD

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×