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rate in the unigenic system (
c
= 29) is only 1%, whereas in the less compact
two-genic system (
c
= 58) it is 73%. Again, a plateau is observed where
systems are most efficient, showing that a certain amount of redundancy is
fundamental for evolution to occur efficiently. Indeed, it is intuitively under-
stood that a certain room to experiment, not only by forming new building
blocks but also by rejecting existing ones, is essential to come up with some-
thing new and useful. If no room is there to play, only costly (if ever) one
comes up with a good solution to the problem at hand. Again, note that highly
redundant systems are more efficient than extremely compact ones. For in-
stance, the 10-genic system used in the function finding problem (
c
= 130),
has a success rate of 61% compared to only 2% obtained with the most com-
pact organization (
c
= 13). The same behavior can be observed in the se-
quence induction problem where the highly redundant 10-genic system with
a chromosome length of 290 performs slightly better than the extremely com-
pact one (
c
= 29) (1% and 11%, respectively).
The comparison of Figures 12.11 and 12.12 also shows that multigenic
systems perform considerably better than unigenic ones (see also section
12.5, The Higher Organization of Multigenic Systems). For instance, in the
function finding problem, from two-genic to six-genic systems (correspond-
ing to chromosome lengths 26 through 78) the success rates are in all cases
above 94% and the best has a success rate of 100% (see Figure 12.12), whereas
the best chromosome length in the unigenic system (
c
= 37 and
h
= 18) achieved
only 76% (see Figure 12.11). The same phenomenon can be observed in the
sequence induction problem in which from two-genic to five-genic sys-
tems (corresponding to chromosome lengths 58 through 145) the suc-
cess rates are above 60% and the best has a success rate of 79% (see
Figure 12.12) whereas the best chromosome length in the unigenic system
(
c
= 79 and
h
= 39) achieved only 43% (see Figure 12.11).
The structural analysis of compact solutions and less compact ones can
also provide some insights into the role of redundancy in evolution. For in-
stance, the following perfect solutions to the sequence induction problem
were obtained, respectively, for systems with one, three, and five genes:
(a) 01234567890123456789012345678
**a+a*a++/+/+/aaaaaaaaaaaaaaa
(b) 01234567890123456789012345678
**a+/*+a//++//aaaaaaaaaaaaaaa
/*a+/*+a//++//aaaaaaaaaaaaaaa
-*a+/-*a//++aaaaaaaaaaaaaaaaa
