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of neutral evolution, that we shall examine in Section 15.3.6. In this landscape,
evolution is just a random walk in sequence space, and one is interested in the
probability of xation of mutations in a nite populations, which corresponds to
the divergence of an isolated bunch of individuals (allopatric speciation).
A species is in general a rather stable entity, in spite of mutations. One can
assume that it occupies a niche, which corresponds to a maximum of the tness
in the phenotypic space. The presence of this niche generally depends on other
species, like for instance insects specialized in feeding on a particular ower have
their niche tied to the presence of their preferred food. An extremal case is that
of a sharp tness landscape constituted by an isolated peak. This landscape is
particular since it is not possible to guess where the top of the tness is, unless one
is exactly on it. A lineage in a at genotypic space is similar to a random walk, due
to mutations. The only possibility to nd the top is though casual encounter, but
is a high-dimensional space, this is an extremely unfavorable event.
For small mutation probability, the asymptotic distribution is a quasispecies
grouped around the peak. By increasing the mutation probability (or equivalently
the genome length), this cloud spreads. It may happen that in nite populations
no one has the right phenotype, so that the peak is lost. This is the error threshold
transition, studied in Section 15.3.3. Clearly, this transition poses the problem of
how this peak has been populated for the rst time. The idea (see Section 15.5.6),
is that the absence of population tness space is actually similar to a Swiss cheese:
paths of at tness and \holes" of unviable phenotypes (corresponding essentially
to proteins that are unable to fold). The \corrugation" of the tness is due to the
presence of other species. So for instance a highly specialized predator may become
so tied to its specic prey, that its eective tness landscape (for constant prey
population) is extremely sharp.
Another consequences of an increased mutation rate, more eective for individ-
uals with accurate replication machinery like multicellular ones, is the extinction of
the species without losing their \shape", the so-called Muller's ratchet [18{20] or
stochastic escape [21, 22], which, for nite populations, causes the loosing of tter
strains by stochastic uctuations. Muller's ratchet is studied in Section 15.3.3.
Genes that have an additive eect (non-epistatic) lead to quantitative traits,
and to smoother landscape, shaped like the Fujiyama mount. It is possible to
obtain a good approximation for the asymptotic distribution near such a maximum,
as shown in Section 15.3.4.1. Such a results will come at hand in dealing with
competition, Section 15.5.1. On a Fujiyama landscape, no error threshold transition
is present [17].
Finally, one can study the problem of the evolution in a landscape with variable
degree of roughness, a problem similar to that of disordered media in statistical
mechanics [11, 23, 24].
A rather generic formulation follows lines similar to that of disordered statistical
problems [17]. The phenotype u(x) of a genotype x = (x
1
; x
2
; : : : ; x
L
) is given by
