Selection, majorization and replicators

We examine the role of selection in evolution-based approaches using results drawn from majorization theory and replicator models. Analyzing selection in this framework has several advantages: the availability of convergence results from the theory of inhomogeneous doubly stochastic Markov chains, and a generalized fundamental theorem from replicator models. We show that pre-ordering a sequence of vectors by the majorization relation necessarily implies replicator dynamics. We also give sufficient conditions for a converse result. We present arguments for using majorization operators in evolutionary algorithms