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where g denotes genotype and p denotes phenotype. The possible value of gene
g
i
is called allele. In Mendel' s genetics, it is assumed that there are finite alleles in
each gene.
Genetic
operator
Epigenetic
environment
Selection
environment
p
g
Fig. 13.2. Major processes of evolution
Given a set of epigenetic environment:
EP
= {
EP
1
, …, EP
k
}
and transformation function:
f
:
GS × EP
ŗ
PS
(g, EP). (13.3)
In fact, the transformation function presents a model, which shows that the
change of phenotype is due to the interaction of gene with environment and this
change is higher-order nonlinear. The final phenotype has all the characteristics,
while the initial one just has a simple one-to-one correspondence. Quality
function q expresses the quality of phenotype in a given selection environment
ES
i
, and it is defined as follows:
p
=
f
)
ŗ
IR
+
(13.4)
This quality function is in fact a fitness function, which is used for Darwinian
selection. So far, there are three general models:
(1) Mendel's genetics;
(2) Genecology;
(3) Evolutionary gamete;
In Mendel's genetics, genotype is modeled detailed, but phenotype and
environment are almost left in the basket. In genecology, the case is just the
opposite. The theory of evolutionary gamete is a model induced from
sociobiology.
Let's first discuss the selection model in Mendel's genetics. For simplicity,
assume that there are n alleles a
1
,···, an in a gene. Double-genotype is expressed
as a 2-tuple (
q
(
p
ES
i
,
t
a
i
,a
j
), and
p
i,j
is defined as the frequency of genotype (
a
i
,a
j
) in
