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of adaptation in which the only source of genetic variation was a gene trans-
position rate
p
gt
of 0.2 and a gene recombination rate
p
gr
of 0.2. This means
that the only source of novelty consisted, in this case, of moving around the
genes already present in the initial population (for a comparison, the initial
population is also shown in Figure 3.22). It is worth noticing how genes got
scattered throughout the chromosome, occupying all the positions available
to them. It is worth emphasizing that only gene transposition is capable of
moving genes around in the chromosome. Indeed, several events of gene
transposition had to occur in order to shuffle the genes so thoroughly. Such
an event is illustrated below:
012345678900123456789001234567890
AOabccbbabcAOabccbbabc
ANAANacbaba
-[m] = 7
ANAANacbaba
AOabccbbabcAOabccbbabc-[d] = 7
Here, gene 3 in the mother chromosome (chromosome 3 of generation 7)
moved to the beginning of the chromosome, forming chromosome 5 of gen-
eration 8 (see Figure 3.22). Structurally, these chromosomes are different
from one another but, mathematically, they encode equivalent expressions.
What is important is that chromosomes with the same kind of gene in differ-
ent positions can recombine and give rise to new chromosomes with dupli-
cated genes (note, however, that in this particular case of sub-ETs linked by
OR, one of the duplicated genes is neutral). For instance, the perfect solution
found in generation 8 (chromosome 3) has a duplicated gene. Indeed, as
shown in Figure 3.22, several chromosomes have duplicated genes (chromo-
somes 0 and 3 in generation 7 and chromosomes 1, 3, and 5 in generation 8).
Curiously enough, one of these chromosomes is a perfect solution to the
majority function problem. Its expression is shown in Figure 3.23.
Although I have chosen to illustrate the combined effect of gene transpo-
sition and gene recombination with an example that also resulted in the dis-
covery of a perfect solution to the majority function problem, the transform-
ing power of these operators is, however, very limited, especially when the
population sizes are very small (say, up to 500 individuals). It is worth em-
phasizing that, by themselves, these operators are unable to create new genes:
they only move existing genes around and recombine them in different ways.
A system creating diversity as such, could only evolve good solutions to
complex problems if it used gigantic populations, as all its genes would have
to be present in the initial population (see the Evolutionary Studies of chap-
ter 12 for a discussion).
