Authors

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
â†’ 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.