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450
400
350
300
250
200
EXTINCT
150
100
ALIVE
50
0
54
56
58
60
62
64
66
68
70
72
s*1000
Fig. 2.
Phase diagram in the selection-mutation plane.
that the dependence of the average time of extinction on the mutation rate can
be fitted into a dependence
<t
ext
>≈ p
mut
.
where
α
varies with the
selection pressure
s
. Since however the data covers rather narrow range, it would
be di
?
cult to claim that we have here a true power law.
Our results [12] can be interpreted as follows. For strong selection the pop-
ulation has really no chance to develop and changing the mutation rate has no
marked effect. Any individual which is not well fit has a very low chance of sur-
vival. Therefore the time to extinction increases with growing mutation rate in
more or less the same way. If the selection is weaker, then it matters whether
the mutation rate is low or high. If it is low, the population has enough time to
grow, since at the beginning there are few mutations. Afterwards the mutations
accumulate and the population dies. This behavior is reflected as the upper part
of the
t
ext
versus
p
mut
curve. If the mutation rate is high, then the population
very quickly acquires enough mutations and behaves similarly as in the case of
strong selection, and this is the lower part of the
t
ext
versus
p
mut
dependence.
Similar kind of dependence of the average extinction time on the selection and
mutation could be deduced from the data presented in Ref. [16]. It should be
noted that the role of the selection pressure is realized in our model via the sur-
vival probability of an individual, and since it depends explicitly on its fitness,
it it impossible to describe the model in terms of global variables.
Because in order to produce offspring an individual has to move, find a part-
ner and find the place for the progeny, there is no need to introduce outside
restrictions on the population growth, like the Verhulst factor, see e.g. Ref.[19].
Summarizing,wehavepresentedamicroscopicmodeldescribingthebehavior
of a population under selection pressure and mutational load living in a changing
environment. The population is confronted with a choice - either adapt to new
conditions or follow the climate and colonize new territories. We have found that
if the selection pressure is not high, the population will be spread with similar
densities all over the three regions. With increasing selection pressure and rate
of mutations the first region will become depleted and the regions II and III will
