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In case of sexual reproduction, the evolution may lead to other non-optimal
stable patterns, represented by the run-o development of sexual characters. This
phenomenon if particularly evident in a model by Dieckmann and Doebeli [65].
In this model, the space plays no role (no spatial niches, sympatric speciation).
The tness in phenotypic space presents a smooth maximum, so in the absence of
other ingredients, the asymptotic distribution is a quasispecies peaked around this
maximum. The introduction of a nite-range competition broadens the distribution,
but in the absence of assortativity (preference in mating), no speciation occurs [29].
In the model, the assortativity is coded in a portion of the genotype, and is
related to a phenotypic character either related to the tness or acting just like an
arbitrary marker. In both cases, speciation may occur (depending on the parame-
ters), even if in the second case the dierentiation takes longer (since it is due to
genetic drift).
Sex and recombination have important consequences also in the evolution over
simple landscapes, like the sharp peak one. In Ref. [66] it is shown that while for
asexual reproduction the error threshold is driven by the average mutation prob-
ability per unit of genome, , in recombinant organisms it depends on the total
mutation rate L, and the transition is near L = 1. This observation poses a limit
to the maximum length of genomes for a given accuracy of replication.
15.5.4. Game theory
Up to now, we have supposed that there is an instantaneous response to the en-
vironment. Considering only binary interactions, the contribution to the score of
phenotype x given by an encounter with phenotype y, W (xjy), can schematically
be grouped as
W (xjy) < 0 & W (yjx) < 0 :
competition ;
W (xjy) > 0 & W (yjx) < 0 :
predation or parasitism of y on x ;
(15.30)
W (xjy) < 0 & W (yjx) > 0 :
predation or parasitism of x on y ;
W (xjy) > 0 & W (yjx) > 0 :
cooperation :
However, the actual interactions among individuals with memory and strategy
are more complex, may depend on the past encounters and on the environment
status.
A more sophisticated modeling follows the ideas of game theory: the genotype
of an individual is read as a small program, and the score of an encounter depends
on the running of the programs of the participants [67].
In order to reduce this complexity, let us assume that there are only binary
encounters, and that the participants can assume only two external status: zero
and one, that traditionally are called cooperation or defection. We assume also
that the encounter is divided into rounds (hands), and that the number of hands
depends on external factors (one could alternatively have a three-letter alphabet like
