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User bonneuil
title The Mathematics of maintenance and acquisition
Authors Noël Bonneuil
Source In: Ecosystem Ecology Research Trends Editors: J. Chen and C. Guo, pp. 153-175
ISBN 978-1-60456-183-8 2008 Nova Science Publishers, Inc.
Year 2008
Type Book chapter
Type of publication ISC-PIF scholar

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Abstract Modelling dynamic systems commonly focusses on asymptotic behavior. Is the
search for asymptotic patterns appropriate for modelling maintenance and acquisition?
In biology, where variability and surprise prevail, moment-by-moment time, not
limit sets , matters. Taking the state of a particular system at a particular moment into
account requires the substitution and replacement of many of the concepts usual to
asymptotic analysis: the replacement of probability by set membership; the replacement
of trajectories by attainable sets; the replacement of limit sets by the C-viability
kernel or capture domain. Rather than convergence to an attractor and dominance of
an optimal or evolutionary stable strategy, the focus here is on identifying the right
strategy at the right moment that allows a living system to have at least some possibility
of perpetuation or collapse. Basic models of ecosystem and population genetics
are revisited from this perspective. Notably, rather than proposing a mechanism and
examining how it behaves under various constraints, here the constraints are incorporated
in the dynamic system from the start through C-viability multipliers. Case studies
reveal that even without using the theoretical tools of C-viability, some experimenters
have empirically invoked C-viability multipliers or explored C-viability domains.
Created Tuesday 11 December, 2012 11:40:19

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