Aggregation of variables and system decomposition: Applications to fitness landscape analysis.
In this paper we present general results on aggregation of variables, specifically as it applies to decomposable (partitionable) dynamical systems. We show that a particular class of transition matrices, namely, those satisfying an equitable partitioning property, are aggregable under appropriate decomposition operators. It is also shown that equitable partitions have a natural application to the description of mutation-selection matrices (fitness landscapes) when their fitness functions have certain symmetries concordant with the neighborhood relationships in the underlying configuration space. We propose that the aggregate variable descriptions of mutation-selection systems offer a potential formal definition of units of selection and evolution.
Shpak
Max
M
Department of Ecology and Evolutionary Biology, University of Tennessee, 37996-1610, Knoxville, TN, USA, shpak@yale.edu.
Stadler
Peter
P
Wagner
Gunter P
GP
Hermisson
Joachim
J