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An individual is characterized by its position on the lattice,
j
, and by its geno-
type,
g
j
, which is a double string (of 32 positions) of 0's and 1's. It could have
the form
0010110
...
0101101
...
g
j
=
We have decided on using one pair of homologous chromosomes since increasing
their number with the same number of loci in the genome and the same re-
combination rate per chromosome would increase the overall, already very high,
recombination rate. It could not produce any effect of linkeage. It should be
noted that in the model one recombination per generation equals one recombi-
nation per 32 loci.
From the genotype the phenotype,
f
j
, of the individual is constructed, as a sin-
gle string (vector) of the same length, according to the following rule. For each
position (locus) of the genotype the product of the two values is taken and the
result is put at the corresponding place of the phenotype. In biological terms it
means that 0 corresponds to a dominant, and 1 to a recessive allele:
(00)
,
(01)
,
(10)
→
0
,
(11)
→
1
.
(1)
Hence the phenotype corresponding to the genotype presented above would be
f
j
=
{
0000100
...}.
(2)
Moreover each individual is also characterized by its age,
a
j
, which at birth is
set equal to 1 and is increased during the simulations (see below). This feature
makes the model more realistic by diminishing the survival probability of an
individual with its age and also by eliminating perfectly adapted individuals,
who otherwise could live forever and eventually dominate the population.
In constructing our model we aimed at maximum simplicity, within the class
describing population dynamics with recombination and phenotype following
from the genotype. Suggestions for this type of models were given in [14]. How-
ever in almost all biological papers describing evolution, individuals are charac-
terized simply by their phenotypes.
3.2 Algorithm of Model B
The algorithm governing the dynamics of our system has the following structure:
1. Chose an individual, for example on a site
j
,
2. Calculate its survival probability
p
j
, according to the rule
p
j
= exp(
−s · a
j
/z
j
)
,
(3)
where
s
is a parameter characterizing the selection pressure and
z
j
is the
fitness of the
j
individual, defined as the agreement between the optimal
phenotype (”climate”)
F
and the individual's phenotype
32
1
−
(
f
j
− F
i
)
2
.
z
j
=
1
32
(4)
i
=1
