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generating varied proteins that, inserted in the biochemical network of the cell, may
induce new functions (although in general it simply increases the amount of \junk"
genetic material). This is supposed to be one of the main \motors" of evolution,
together with the horizontal transfer of DNA among individuals (possibly belonging
to dierent species) by retroviruses.
f
In non-coding regions (essentially eukaryotes), the substitutions, insertions and
deletions may have \smoother" eects, unless they destroy the promoter region of
a gene.
In general, we may say that genetic modications are either lethal, or almost
neutral, at least at the level of proteins and biochemical networks. How these
almost-neutral modications (like for instance a change of pigmentation) corre-
spond to the alteration of survival characteristics, depends on their inuence on the
phenotype, and in how phenotypes of dierent individuals (and species) interact.
Thus, in many cases one can get rid of the genotypic space: for large scale
evolution (formation of species) one can assume that mutations induces a diusion
in the phenotypic space, while for small scale evolution (asymptotic distribution of
intra-specic traits) one can assume that mutations are able to generate all possible
phenotypic traits.
For simplicity we assume that all point mutations are equally likely, while in
reality they depend on the identity of the symbol and on its positions on the genome.
For real organisms, the probability of observing a mutation is quite small. We
assume that at most one mutation is possible per generation. We denote with
s
the probability of having one point mutation per generation.
The probability to have a point mutation from genotype y to genotype x is given
by the short-range mutation matrix M
s
(x; y) which is
8
<
1
s
if x = y ;
s
L
M
s
(xjy) =
(15.1)
if d(x; y) = 1 ;
:
0
otherwise :
Other mutations correspond to long-range jumps in the genotypic space. A very
rough approximation consists in assuming all mutations are equally probable. Let
us denote with
`
the probability per generation of this kind of mutations. The
long-range mutation matrix, M
`
, is dened as
8
<
:
1
`
if x = y ;
M
`
(xjy) =
(15.2)
`
2
L
1
otherwise :
f
Transposable elements and gene duplications are often the eects of viral elements, still able to
manipulate the genome, but \trapped" into the genome by mutations that have destroyed their
capability of producing the protective cap.
