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In genecology, it is usually supposed that dominance is inherited by
interaction of gene locus. At each gene locus, two alleles are separated, and
dominant value increases by one, while the other decreases by one.
Individual's phenotypic value is expressed as:
P
i,j
=
Ⱥ
+
G
i
+
E
i,j
+ (
GE
)
i,j
where
Ⱥ
is the average of dominant value,
G
i
denotes the
i
-th phenotype,
E
i,j
is the
i
-th gene in the
j
-th individual, GE denotes the interaction of genotype and
environment.
The complex relationship prevents population directly accessing some “best
phenotypes”. This relationship constrains the selection. The important constraint
has no genetic variation, interaction of genes and nonlinear transformation from
genotype to phenotype.
In the theory of evolutionary gamete, each individual can suit
N
strategies.
Suppose that
p
i
is the frequency of strategy
i
in the next generations,
E
i,j
is the
profit of strategy
i
resisting strategy
j
. The quality of strategy
i
is
=
Ã
Q
p E i j
( ,
)
i
i
j
The average fitness of population is
=
Ã
Q
p Q
i
i
i
Suppose that the number of asexual reproduction individuals is proportional
to their fitness. This can be expressed by the familiar selection equation:
Q
p
′ =
p
i
(13.12)
i
i
Q
Evolution gamete theory requires dynamical attractors, which are called
evolutionarily stable strategy(ESS). For
p
i
, p
j
¬
0ESS is characterized by
Q
i
=
Q
j
.
13.3 Darwin's Evolutionary Algorithm
According to quantitative genetics, Darwin's evolutionary algorithm uses simple
mutation/selection kinetics. Darwin's algorithm can be formalized as follows:
(
Ⱥ
/
Ⱦ
ȹ
) (
Ⱥ
/
Ⱦ
+
ȹ
) (13.13)
where
Ⱥ
is the number of the parents,
ȹ
is the number of offspring. Integer
Ⱦ
is
called “hybrid” number. If two parents' genes are mixed, then
Ⱦ
= 2. Individuals
