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In this case even if such a population happens to lose its equilibrium state, i. The crossing which transforms the former equilibrium distribution of population genotypes into a new equilibrium state based on new relative concentrations of alleles is known as stablizing-cross.

It goes without saying that in real populations none of the conditions necessary for the realization of the equilibrium law is observed. It does not, however, mean that the Hardy-Weinberg law ceases to be important. The formula of the distribution of genotypes in a population is of utmost importance. Analysis of this formula allows the genetic structure of a population to be revealed by ascertaining concentrations of different alleles.

However, this formula holds only for a single frame the present generation of a continuous film with which may be compared the dynamic development of generations. This permanent development in the genetic structure of populations associated with isolations, migrations, mutations and selections is the internal side of all life processes of different units of the species in different parts of its habitat. One of the most evident characteristics of any population is the number of individuals at the given moment. Very large populations may number billions of specimens micro-organisms, algae and fish populations or less than a hundred specimens, as with populations of rare endemic plants.

The number and distribution of specimens in large populations are permanently changing and the rate of this process is varying.

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Changes in the size of the population bear various effects on its evolution. Thus the size of the population affects the tempo of random oscillations in the concentrations of alleles caused by probable disturbances characteristic of any limited group of specimens.

Dubinin, Romashov and Wright established that stationary concentrations of alleles in conditions of absence of mutations, selection and migration are impossible in principle. They showed that in any limited population, concentrations of alleles undergo quite stochastic changes which result from errors in the limited choice of gametes under the emergence of the next generation. These phenomena are known as genetic-automatic processes S. This process is based on the fact that in a limited population the given concentration of genes from generation to generation is conveyed not absolutely in the same proportion as assumed on the basis of Hardy's equilibrium law , but only as a mathematical expectancy.

In other words, in a limited population with any initial concentration of the gene, there is always a certain probability of a change in this concentration in the next generation in the positive or negative direction. The above statement is of decisive importance in the analysis of the main processes occurring in a limited population, as any change in the initial concentration is of consequence in the further destiny of the gene. This change brings the concentration to a new level which is the starting point for subsequent development.

Non-direction of changes in the concentration is often a cause of the complicated course of these changes, which as a rule take place in many successive stages of different directions. At the same time these occasional oscillations through rather a large number of generations result in a development that leads to radical changes in the structure of the population, since after a number of successive random drifts the initial concentration may greatly deviate from its initial value.

Evolution - Hardy Weinberg's Principle

As a result of this, these deviations in a limited population result either in elimination of the gene 0 percent concentration or in its domination in the population percent concentration ; i. This transformation is inevitable, because in any limited population there is ultimate probability of the whole succession of changes in the concentration the process is non-directional in each stage from any initial state to homozygous, though very often this ultimate probability is a very small value. However, this ultimate probability is always present, and if so, it must be realized throughout a large number of generations.

The inevitable realization of this probability directs the whole random motion of alleles in such a way that without mutational development or any form of selection, any limited population through the mechanism of random mating throughout a certain average number of generations comes to the homozygous state through one or another allele.


Population genetics

This process is very important for the understanding of the main phenomena taking place in gene composition of a population and may be defined as isogametation extinction of variation. Mean duration of isogametation and consequently the rate at which it occurs, i. Dubinin and Romashov carried out two series of statistical experiments with models of uniformly multiplying populations with percent initial variety of alleles.

In the first series of experiments the initial pool consisted of balls with different numbers. Each drawing comprised 25 scoopings, two balls being taken at a time. The number of the first of the two balls stood for the perishing allele and the other for the multiplying allele. Thus in each generation 25 percent of the balls were removed from the pool and the other 25 percent doubled.

Population Genetics: What It Is and Why It Matters

Drawings were carried on until all the balls in the pool had the same number, i. The second series of experiments differed from the first one in the size of the population. In this case the initial pool consisted of 10 different balls. The drawings showed that mean duration of isogametation in the first series was equal to generations. It can be seen that in the rd generation there is only one allele from the initial percent variety which seizes the whole population.

In the second series of experiments, which differed from the first in that the size of the population was 10 times less, the mean duration of isogametation was equal to 29 generations. Isogametation in the given case goes through 20 generations. In conditions of uneven multiplication, genetic-automatic processes occur most intensively. The general scheme of uneven multiplication in stationary conditions from generation to generation and the numerical size of a population may be described in the following way.

Each mating parent pair leaves a very great number of zygotes whose independent probability of survival is very low. Ultimately on the average only one pair of the offspring of a parent pair manage to survive in the next generation. But this is only an average estimation and the actual importance of various pairs for the next generation is different. There are pairs which leave no offspring and there are those that leave one, two, three or more offspring. This form of reproduction, which is dominant in a population with a stationary numerical size, was mathematically analysed by Fisher and Wright Fisher has proved that in this case with small concentrations of genes varying from individual genes to concentrations giving rise to homozygous forms it is possible, with a certain approximation, to apply Poisson's series.

On the basis of this series it proved possible to calculate the rate of elimination and replacement of genes. Table 2 shows that with this form of multiplication the number of mutant genes lost by the population in each generation is equal to 37 percent in evenly multiplying populations this amount comprises 25 percent.

This value also affects replacement and multiplication development of other genes.


Probability of elimination and preservation of individual mutations in an unevenly multiplying population with a stationary numerical size calculated according to Poisson's series. According to Fisher, with a great number of generations the probability of preservation for an individual mutation is , and the mean number of mutations preserved in n generation is.

In small populations genetic-automatic processes may be of essential importance and in large populations they may be insignificant. For instance, in a population numbering 50 specimens these processes will be times more intensive than in a population numbering 5 specimens.

Population Genetics, Selection, and Evolution

This example relates to the multiplying part of the population, which is the group of mature specimens of the given generation which are able to produce offspring. For instance, Fig. The difference in the rate of isogametation in both populations is very great and is in inverse relation to the value of their multiplying parts.

In the four populations shown in Fig. So it is possible to conclude that genetic-automatic processes continue throughout the life of a population. They take place in populations of stationary numerical size.

Population Genetics and Evolution

They are especially intensive in periods when the multiplying part of the population decreases. This period is characterized by an abrupt change in the whole genetic composition of the population.

The same processes take place with increasing numerical size of the population. Even though in this case they are very slow, they facilitate uninterrupted differentiation of the hereditary content of the species, and determine the continuous development of the genetic composition. Thus the study of genetic-automatic processes radically changed the conception that inside a population there is a stationary ratio of genes based only on the equilibrium properties of the genotypes surviving throughout any number of generations.

One of the interesting consequences of the theory of genetic-automatic processes is the analysis of the processes taking place when populating new territories by a limited group of migrants or even by one fertilized female. Mayr formulated the so-called principle of the founders of the population. According to him the population that forms due to the populating of a new territory has only the alleles that were brought by the migrants that founded the population. These alleles are only a small part of the total genes of the initial large population. As a result of this, in individual colonies, in populations at the periphery of a species, habitat, etc.

The role of such populations in the evolution of the species may be considerable. One of the properties of a population, which is not characteristic of its organisms, is distribution in space. Generally speaking, the distribution area is the minimum geographical area including all territories which in usual conditions are populated by the given organisms.

Populating of a territory by different organisms is uneven. Unevenness of geographical distribution of specimens is usually accounted for by inter-relations of the organisms with animate and inanimate components of the environment. Of basic importance for the dynamics and history of the hereditary pattern of populations of a species are different forms of isolation and, contrarily, the migrations connected with the mixing of populations.

In reality there are no species which are of united intra-breeding populations. Within the ecological-geographical area each species, due to various factors of both complete and incomplete isolation, falls into a great number of populations that comprise a species.

Isolation factors determining the segregation of the species into more or less independent populations are of great variety. For instance, very frequent are isolations caused by physical barriers such as mountains, islands, etc. Of interest is isolation of generations in time. Then we should mention physiological isolation.