Simon-Ando decomposability and fitness landscapes |
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Authors: | Email author" target="_blank">Max?ShpakEmail author Peter?Stadler Gunter?P?Wagner Lee?Altenberg |
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Institution: | (1) Department of Ecology and Evolutionary Biology, University of Tennessee, 37996 Knoxville, TN, USA;(2) Institute of Bioinformatics, University of Leipzig, Kreuzstrasse 7b, D-04103 Leipzig, Germany;(3) Department of Ecology and Evolutionary Biology, Yale University, 06520-8106 New Haven, CT, USA;(4) Department of Information and Computer Sciences, University of Hawaii, 96753 Manoa, HI, USA |
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Abstract: | In this paper, we investigate fitness landscapes (under point mutation and recombination) from the standpoint of whether the
induced evolutionary dynamics have a “fast-slow” time scale associated with the differences in relaxation time between local
quasi-equilibria and the global equilibrium. This dynamical hevavior has been formally described in the econometrics literature
in terms of the spectral properties of the appropriate operator matrices by Simon and Ando (Econometrica 29 (1961) 111), and
we use the relations they derive to ask which fitness functions and mutation/recombination operators satisfy these properties.
It turns out that quite a wide range of landscapes satisfy the condition (at least trivially) under point mutation given a
sufficiently low mutation rate, while the property appears to be difficult to satisfy under genetic recombination. In spite
of the fact that Simon-Ando decomposability can be realized over fairly wide range of parameters, it imposes a number of restriction
on which landscape partitionings are possible. For these reasons, the Simon-Ando formalism does not appear to be applicable
to other forms of decomposition and aggregation of variables that are important in evolutionary systems. |
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Keywords: | Fitness landscapes Aggregation of variables Decomposability Mutation Selection Dynamical systems |
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