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15.2.3. Mutations
During lifetime, or in the genome replication phase (when an organism reproduces),
some symbol in the genome can be changed: a mutation. Many dierent types of
mutations has been observed. The most common (either because they are actually
more common than others, or because they have less chance to cause harmful conse-
quences) are point mutations (an exchange of a basis with another. Other common
mutations are deletions (the replacement of a symbol with a \*") and insertions (the
replacement of a \*" with a basis). These mutations correspond to jumps is the
sequence space. Therefore, a given lineage can be seen as a path in sequence space.
By considering all descendants of a given individual (assuming asexual reproduc-
tion), we have a set of branching walks, where an \arm" stops when an individual
dies [7, 8].
The probability that a path comes back to an already visited sequence (disre-
garding the empty symbol) vanishes with growing L. Moreover, as we shall see,
competition will prevent the merging of dierent species.
In our model, a mutation is just a change in the sequence g, that can occur
with a probability that depends only on the sub-sequence that changes, or that
may depend on other portion of the genotype. For instance, point mutations are
the replacement of a zero with an one and vice versa. The probability of this
occurrence (g
i
!g
0
i
) may depend on the position i of the \gene". A translocation,
on the other hand, involves correlated changes in dierent positions. Considering
the interpretation of g
i
as the presence or absence of a certain genetic characteristic,
it could be represented as the simultaneous change of two locations g
i
and g
j
in the
genome, that for instance may happen only of g
i
= 1 (presence of the transposable
element). Similar representations may be interpreted as gene duplications, etc.
Point mutations correspond to base substitutions. If this happens in a coding
region, it causes the change of one codon. Due to the redundancy of genetic code,
this mutation may not aect at all the resulting protein, either because the altered
codon is read by the same tRNA as the original one, or because it is read by a dier-
ent tRNA carrying the same amino acid. The modications in the protein may also
be marginal if a amino acid is replaced by another one with similar characteristics.
A deletion or insertion in a coding region causes a \frame shift", completely
altering the resulting protein. Transpositions also causes similar damages, and the
protein is normally not working.
e
If the protein has a crucial role, this modication
lead to the death of the individual. However, it may happen that the same protein
is produced by more that one copy of the gene. This generally occurs after a gene
duplication, and is vastly more common in eukaryotes (due to the larger genome
size and less pressure towards \eciency") than in prokaryotes. In this case, the
mutation only reduces the amount of protein produced, a mutation that may be
harmful or not. In the latter case, the duplicated gene is \allowed" to mutate,
e
Some cases of partially-working proteins correspond to genetic diseases, like Huntington's corea,
that allow the survival of aected individuals for some time.
