Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2011-01-31
Nonlinear Sciences
Adaptation and Self-Organizing Systems
11 pages, 1 figure, 1 table
Scientific paper
The evolution of organismal populations is not typically thought of in terms of classical mechanics. However, many of the models used to approximate evolutionary trajectories have implicit parallels to dynamical physical systems. Therefore, it stands to reason that dynamical physical models can be adapted to model less explored aspects of evolutionary (biological) systems. In this paper, I will present the parallels between currently-used evolutionary models and a class of physical system known as a Hamiltonian. By comparing currently-used evolutionary modeling approaches with Hamiltonian systems, both of which use similar sets of underlying assumptions, it becomes clear that new approaches may be needed for approximating emergent phenomena. Using what is learned from this exercise, I will then introduce a new model for characterizing evolvability in living (biological) systems based on the Lagrangian Coherent Structures (LCS) approach. It is my contention that the limits of evolvability in a population can be treated in a way analogous to fronts, waves, and other aggregate formation in collective animal behavior. Ultimately, this application of the LCS approach may be able to provide insight into adaptation in a broad range of biological and social systems.
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