The authors have declared that no competing interests exist.

The problem of natural selection against recessive homozygotes in a population is investigated. It is shown that natural selection of mutant alleles linked with the

In

However in genetics there are the processes resulting in the nonlinear differential equations. These processes concern to nonlinear genetics.

The problem of mutant allele natural selection has been mentioned for a family tree in

Fitness of a genotype characterizes ability (probability) of the given genotype to a reproduction.

We accept the ratio of fitnesses of genotypes

1:1:(1 - s). ……..(1)

In the formula (1)

In

In the given article we shall solve a problem of selection in a population using a standard way of transition from finite-differential equation characteristic for a family tree to the differential equation correct for a population

As well as in

In

……...(2)

Genotypes linked to the

……….(3)

Taking into account that

……..(4)

we find the sum of the genotypes frequencies in formula (3): 1 - q_{m}_{(n-}_{1)}q_{f}_{(n-1)}^{s}.

Further, using a standard rule of an alleles frequency finding in the following generation (half of heterozygotes frequency plus of homozygotes frequency) and the formula (3) we calculate the frequency of recessive alleles

………..(5)

Let's transform the formula (5) using p_{m(n-1)} = 1 - q_{m}_{(n-1)} and p_{f(n-1)} = 1 - q_{f}_{(n-1)}. For recessive allele frequency at women in

……..(6)

Besides it is necessary to take into account the major condition that allele frequency in the _{m} in the following generation. For recessive allele

The condition (7) is caused the

Substituting (7) in (6) we find:

……..(8)

By simple algebraic transformations of the formula (8) we shall find:

Let’s consider the differential equation:

……..(10)

where η and α are some constants. Differentiation in (10) goes on dimensionless time

Let’s pass in (10) to finite-differential form of derivatives:

……..(11)

Transforming (11) by analogy to

……...(12)

Let’s identify the equation (12) with the equation (9). In

Hence, the differential equation (10) can be written down as:

........(13)

At transition to a population the number of generation of a role does not play therefore, we shall receive:

The nonlinear differential equation (14) allows calculate frequency q

For convenience of calculation it is used in (14) new independent variable

In view of the new independent variable the equation (14) will be transformed to the kind:

……...(15)

where it is designated Ԑ=3/√2s. At variation of a selection standard parameter 0≤

The nonlinear differential equation (15) can be solved only numerically.

Initial conditions, first of all, are necessary for the solution of the differential equation (15): initial frequency q_{0} or (d_{0}.

Initial frequency q_{0} = -0.6 or (d_{0 }=-0.165. The step of calculation on a variable

On

In conclusion we shall consider the some general-biological questions connected to functioning of natural selection.

There is very high degree of nonlinearity - the third - of the differential equation (15) describing natural selection in populations. It has important general-biological importance. The degree of nonlinearity of natural selection defines its opportunities, i.e.power of selection. We did not was success to find out the equations of mutational processes with higher degree of nonlinearity. The inbred mutational processes have the second degree of nonlinearity

Other mutational processes, for example, resulting to hemophilia or induced mutagenesis under action of radiation have the first degree of nonlinearity or in other words these processes are linear. It means that any mutational processes in populations of the Earth can be levelled by natural selection. From this point of view the hypothesis of H. Muller

Damage of a genome by mutational processes in earthly populations can cause destruction of a considerable part of individuals, including people. It is the extremely unpleasant and with it is necessary to resist in the various ways: creation of new medical products, protection from ionizing radiations, etc. But as a whole these negative processes practically do not threaten populations, since natural selection gradually restores genetic norm in a population.

But it is possible to assume a fantastic situation that to the Earth there arrive some technologically high-civilized individuals from other planet able to operate genic mechanisms. These individuals can start mutational process in a human population of fourth or higher order of nonlinearity. Now it is difficult to assume concrete character of such process. However, completely clearly that the natural selection generated in the earthly conditions cannot reset similar mutational influence. Earthly populations will begin to die out completely and the faster the higher the degree of nonlinearity of the given hypothetical mutational process. And to intervene in this process the populations with lower technological capabilities of a manipulating the genofund is not capable.