Population dependent Fourier decomposition of fitness landscapes over recombination spaces: Evolvability of complex characters

Citation
Pf. Stadler et al., Population dependent Fourier decomposition of fitness landscapes over recombination spaces: Evolvability of complex characters, B MATH BIOL, 62(3), 2000, pp. 399-428
Citations number
71
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Multidisciplinary
Journal title
BULLETIN OF MATHEMATICAL BIOLOGY
ISSN journal
0092-8240 → ACNP
Volume
62
Issue
3
Year of publication
2000
Pages
399 - 428
Database
ISI
SICI code
0092-8240(200005)62:3<399:PDFDOF>2.0.ZU;2-5
Abstract
The effect of recombination on genotypes can be represented in the form of P-structures, i.e., a map from the set of pairs of genotypes to the power s et of genotypes. The interpretation is that the P-structure maps the pair o f parental genotypes to the set of recombinant genotypes which result from the recombination of the parental genotypes. A recombination fitness landsc ape is then a function from the genotypes in a P-structure to the real numb ers. In previous papers we have shown that the eigenfunctions of (a matrix associated with) the P-structure provide a basis for the Fourier decomposit ion of arbitrary recombination landscapes. Here we generalize this framework to include the effect of genotype frequen cies, assuming linkage equilibrium. We find that the autocorrelation of the eigenfunctions of the population-weighted P-structure is independent of th e population composition. As a consequence we can directly compare the perf ormance of mutation and recombination operators by comparing the autocorrel ations on the finite set of elementary landscapes. This comparison suggests that point mutation is a superior search strategy on landscapes with a low order and a moderate order of interaction p < n/3 (n is the number of loci ). For more complex landscapes I-point recombination is superior to both mu tation and uniform recombination, but only if the distance among the intera cting loci (defining length) is minimal. Furthermore we find that the autocorrelation on any landscape is increasing as the distribution of genotypes becomes more extreme, i.e., if the: popul ation occupies a location close to the boundary of the frequency simplex. L andscapes are smoother the more biased the distribution of genotype frequen cies is. We suggest that this result explains the paradox that there is lit tle epistatic interaction for quantitative traits detected in natural popul ations if one uses variance decomposition methods while there is evidence f or strong interactions in molecular mapping studies for quantitative trait loci. (C) 2000 Society for Mathematical Biology.