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— The choice of how to represent the search space for a genetic algorithm (GA) is critical to the GA's performance. Representations are usually engineered by hand and fixed for the duration of the GA run. Here a new method is described in which the degrees of freedom of the representation — i.e. the genes – are increased incrementally. The phenotypic(More)
The evolution of new genes is distinct from evolution through allelic substitution in that new genes bring with them new degrees of freedom for genetic variability. Selection in the evolution of new genes can therefore act to sculpt the dimensions of variability in the genome. This " constructional " selection effect is an evolutionary mechanism, in(More)
Holland's Schema Theorem is widely taken to be the foundation for explanations of the power of genetic algorithms (GAs). Yet some dissent has been expressed as to its implications. Here, dissenting arguments are reviewed and elaborated upon, explaining why the Schema Theorem has no implications for how well a GA is performing. Interpretations of the Schema(More)
The evolution of genetic systems has been analyzed through the use of modifier gene models, in which a neutral gene is posited to control the transmission of other genes under selection. Analysis of modifier gene models has found the manifestations of an "evolutionary reduction principle": in a population near equilibrium, a new modifier allele that scales(More)
Feldman and Karlin conjectured that the number of isolated fixed points for deterministic models of viability selection and recombination among n possible haplotypes has an upper bound of 2(n)-1. Here a proof is provided. The upper bound of 3(n-1) obtained by Lyubich et al. (2001) using Bézout's Theorem (1779) is reduced here to 2(n) through a change of(More)
A model of mutation rate evolution for multiple loci under arbitrary selection is analyzed. Results are obtained using techniques from Karlin (Evolutionary Biology, vol. 14, pp. 61-204, 1982) that overcome the weak selection constraints needed for tractability in prior studies of multilocus event models.A multivariate form of the reduction principle is(More)
The spectral bound, s(αA + βV), of a combination of a resolvent positive linear operator A and an operator of multiplication V, was shown by Kato to be convex in β ∈ R. Kato's result is shown here to imply, through an elementary "dual convexity" lemma, that s(αA + βV) is also convex in α > 0, and notably, ∂s(αA + βV)/∂α ≤ s(A). Diffusions typically have(More)
McNamara and Dall (2011) identified novel relationships between the abundance of a species in different environments , the temporal properties of environmental change, and selection for or against dispersal. Here, the mathematics underlying these relationships in their two-environment model are investigated for arbitrary numbers of environments. The effect(More)