Information Technology Reference
In-Depth Information
can dene the species on the basis of the genotypic distance of individuals, taking
into consideration their genealogical story [54].
We shall see in Section 15.5.3 a model of how such a segregation, preparatory to
speciation, can arise. The role of genetic segregation in maintaining the structure of
the species is particularly clear in the model of Refs. [55{57]. In this model, there is
no tness selection, and one can have asexual reproduction, or sexual (recombina-
tion) one with or without a segregation based on genetic distance. Their conclusion
is that species (dened using the reproductive isolation, denition (b)) can appear
in at static landscapes provided with sexual reproduction and discrimination of
mating. In some sense these authors have identied denitions (b) and (c).
In the rst model reproduction is asexual: each ospring chooses its parent at
random in the previous generation, with mutations. In this model there are no
species, and the distribution uctuates greatly in time, even for very large popula-
tions. The addition of competition, Section 15.5.1, may stabilize the distribution.
In the second model reproduction is recombinant with random mating allowed
between any pair of individuals. In this case, the population becomes homogeneous
and the genetic distance between pairs of individuals has small uctuations which
vanish in the limit of an innitely large population. Without segregation (due to
competition and/or to genetic incompatibilities) one cannot have the formation of
stable, isolated species.
In the third model reproduction is still recombinant, but instead of random
mating, mating only occurs between individuals which are genetically similar to
each other. In that case, the population splits spontaneously into species which are
in reproductive isolation from one another and one observes a steady state with a
continual appearance and extinction of species in the population.
15.4. Ageing
A simple example of age-dependent (pleyotropic) eects of genes is given by the
Penna model [58, 59]. In this model, each individual is characterized by a genome
of length L, and an age counter. The genome is arranged in such a way that gene
x
i
is activated at age i. There are two alleles, a good one x
i
= 0 and a bad one
x
i
= 1. If a given number m of bad genes are activated, the individual dies.
The phenotype u(x; a) depends here of the genotype x and of the age a, and can
be written as
a
X
u(x; a) =
x
i
;
i=1
while the tness is sharp:
(
1
if u < m ;
A(u) =
0
otherwise :
