In the presence of migrations, the boundaries of populations are blurred and therefore indefinable. For example, the entire population of Europe are descendants of the Cro-Magnons who settled our continent tens of thousands of years ago. The isolation between the ancient tribes, which increased as each of them developed their own language and culture, led to differences between them. But their isolation is relative. Constant wars and seizures of territory, and in Lately- gigantic migration led and is leading to a certain genetic rapprochement of peoples.

The examples given show that the word “population” should be understood as a grouping of individuals related by territorial, historical and reproductive community.

The individuals of each population are different from each other, and each of them is unique in some way. Many of these differences are hereditary, or genetic—they are determined by genes and passed on from parents to children.

The totality of genes in individuals of a given population is called its gene pool. In order to solve problems of ecology, demography, evolution and selection, it is important to know the characteristics of the gene pool, namely: how large genetic diversity in each population, what are the genetic differences between geographically separated populations of the same species and between various types how the gene pool changes under the influence of the environment, how it is transformed during evolution, how hereditary diseases spread, how effectively the gene pool of cultivated plants and domestic animals is used. The study of these issues is carried out population genetics.

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POPULATION GENETICS, a branch of genetics that studies the gene pool of populations and its changes in space and time. Let's take a closer look at this definition. Individuals do not live alone, but form more or less stable groups, jointly mastering their habitat. Such groups, if they self-reproduce over generations and are not supported only by newcomers, are called populations. For example, a school of salmon spawning in one river forms a population because the descendants of each fish tend to return to the same river, to the same spawning grounds, from year to year. In farm animals, a population is usually considered to be a breed: all individuals in it are of the same origin, i.e. have common ancestors, are kept in similar conditions and are supported by uniform selection and breeding work. Among aboriginal peoples, the population consists of members of related camps.

In the presence of migrations, the boundaries of populations are blurred and therefore indefinable. For example, the entire population of Europe are descendants of the Cro-Magnons who settled our continent tens of thousands of years ago. The isolation of the ancient tribes, which increased with the development of each of them's own language and culture, led to differences between them. But their isolation has always been relative. Constant wars and seizures of territory, and more recently, gigantic migration have led and are leading to a certain genetic rapprochement of peoples.

The examples given show that the word “population” should be understood as a grouping of individuals related by territorial, historical and reproductive community.

The individuals of each population are different from each other, and each of them is unique in some way. Many of these differences are hereditary, or genetic—they are determined by genes and passed from parents to children.

The totality of genes of all individuals of a given population is called its gene pool. In order to solve problems of ecology, demography, evolution and selection, it is important to know the features of the gene pool, namely, how much genetic diversity is in each population, what are the genetic differences between geographically separated populations of the same species and between different species, how the gene pool changes under the influence of the environment how it is transformed during evolution, how hereditary diseases spread, how effectively the gene pool of cultivated plants and domestic animals is used. Population genetics studies these issues.

BASIC CONCEPTS OF POPULATION GENETICS

Frequencies of genotypes and alleles.

The most important concept of population genetics is genotype frequency - the proportion of individuals in a population having a given genotype. Consider an autosomal gene that has k alleles, A 1 , A 2 , ..., A k . Let the population consist of N individuals, some of which have alleles A i A j . Let us denote the number of these individuals N ij . Then the frequency of this genotype (P ij) is determined as P ij = N ij /N. Let, for example, a gene have three alleles: A 1, A 2 and A 3 - and let the population consist of 10,000 individuals, among which there are 500, 1000 and 2000 homozygotes A 1 A 1, A 2 A 2 and A 3 A 3, and heterozygotes A 1 A 2, A 1 A 3 and A 2 A 3 – 1000, 2500 and 3000, respectively. Then the frequency of homozygotes A 1 A 1 is equal to P 11 = 500/10000 = 0.05, or 5%. Thus we obtain the following observed frequencies of homo- and heterozygotes:

P11 = 0.05, P22 = 0.10, P33 = 0.20,

P12 = 0.10, P13 = 0.25, P23 = 0.30.

Another important concept in population genetics is allele frequency—its proportion among those that have alleles. Let us denote the frequency of the allele A i as p i . Since a heterozygous individual has different alleles, the frequency of the allele is equal to the sum of the frequency of homozygous and half the frequencies of individuals heterozygous for this allele. This is expressed by the following formula: p i = P ii + 0.5Che j P ij. In the example given, the frequency of the first allele is p 1 = P 11 + 0.5H (P 12 + P 13) = 0.225. Accordingly, p2 = 0.300, p3 = 0.475.

Hardy–Weinberg relations.

When studying the genetic dynamics of populations, a population with random crossing, having an infinite number and isolated from the influx of migrants, is taken as a theoretical, “zero” reference point; It is also believed that the rate of gene mutation is negligible and there is no selection. It is mathematically proven that in such a population the allele frequencies of the autosomal gene are the same for females and males and do not change from generation to generation, and the frequencies of homo- and heterozygotes are expressed in terms of allele frequencies as follows:

P ii = p i 2 , P ij = 2p i p j .

This is called the Hardy-Weinberg relationship, or law, after the English mathematician G. Hardy and the German physician and statistician W. Weinberg, who simultaneously and independently discovered them: the first - theoretically, the second - from data on the inheritance of traits in humans.

Real populations can differ significantly from the ideal one described by the Hardy–Weinberg equations. Therefore, the observed genotype frequencies deviate from the theoretical values ​​calculated using the Hardy–Weinberg relationships. Thus, in the example discussed above, the theoretical frequencies of genotypes differ from the observed ones and are

P11 = 0.0506, P22 = 0.0900, P33 = 0.2256,

P12 = 0.1350, P13 = 0.2138, P23 = 0.2850.

Such deviations can be partially explained by the so-called. sampling error; after all, in reality, in an experiment they study not the entire population, but only individual individuals, i.e. sample. But the main reason for the deviation in genotype frequencies is undoubtedly the processes that occur in populations and affect their genetic structure. Let us describe them sequentially.

POPULATION GENETIC PROCESSES

Genetic drift.

Genetic drift refers to random changes in gene frequencies caused by a finite population size. To understand how genetic drift occurs, let us first consider a population of the smallest possible size N = 2: one male and one female. Let the female in the initial generation have the genotype A 1 A 2 , and the male have the genotype A 3 A 4 . Thus, in the initial (zero) generation, the frequencies of alleles A 1, A 2, A 3 and A 4 are each 0.25. Individuals of the next generation can equally likely have one of the following genotypes: A 1 A 3, A 1 A 4, A 2 A 3 and A 2 A 4. Let us assume that the female will have the genotype A 1 A 3, and the male will have the genotype A 2 A 3. Then in the first generation, allele A 4 is lost, alleles A 1 and A 2 retain the same frequencies as in the original generation - 0.25 and 0.25, and allele A 3 increases the frequency to 0.5. In the second generation, the female and male can also have any combination of parental alleles, for example A 1 A 2 and A 1 A 2. In this case, it turns out that the A 3 allele, despite its high frequency, disappeared from the population, and the A 1 and A 2 alleles increased their frequency (p 1 = 0.5, p 2 = 0.5). Fluctuations in their frequencies will eventually lead to the fact that either the A 1 allele or the A 2 allele will remain in the population; in other words, both male and female will be homozygous for the same allele: A 1 or A 2. The situation could have developed in such a way that the A 3 or A 4 allele would have remained in the population, but in the case considered this did not happen.

The process of genetic drift described by us takes place in any population of finite size, with the only difference that events develop at a much lower speed than with a population of two individuals. Genetic drift has two important consequences. First, each population loses genetic variation at a rate inversely proportional to its size. Over time, some alleles become rare and then disappear altogether. In the end, only one allele remains in the population, which one is a matter of chance. Secondly, if a population divides into two or more new independent populations, then genetic drift leads to an increase in differences between them: some alleles remain in some populations, and others remain. Processes that counteract the loss of variability and genetic divergence of populations are mutations and migrations.

Mutations.

During the formation of gametes, random events occur - mutations, when the parent allele, say A 1, turns into another allele (A 2, A 3 or any other), which was or was not previously present in the population. For example, if in the nucleotide sequence “...TCT TGG...”, encoding a section of the polypeptide chain “...serine-tryptophan...”, the third nucleotide, T, as a result of mutation was passed on to the child as C, then in the corresponding section of the amino acid chain of the protein synthesized in the body child, alanine would be located instead of serine, since it is encoded by the TCC triplet ( cm. HERITANCE). Regularly occurring mutations have formed, in a long series of generations of all species living on Earth, the gigantic genetic diversity that we now observe.

The probability with which a mutation occurs is called the frequency, or rate, of mutation. The rate of mutation of different genes varies from 10 –4 to 10 –7 per generation. At first glance, these values ​​seem insignificant. However, it should be taken into account that, firstly, the genome contains many genes, and, secondly, that the population can have a significant size. Therefore, some gametes always carry mutant alleles, and in almost every generation one or more individuals with mutations appear. Their fate depends on how strongly these mutations affect fitness and fertility. The mutation process leads to an increase in the genetic variability of populations, counteracting the effect of genetic drift.

Migrations.

Populations of the same species are not isolated from each other: there is always an exchange of individuals—migration. Migrating individuals, leaving offspring, pass on to the next generations alleles that might not exist at all in this population or they might be rare; This is how gene flow is formed from one population to another. Migrations, like mutations, lead to an increase in genetic diversity. In addition, gene flow connecting populations leads to their genetic similarity.

Crossing systems.

In population genetics, crossing is called random if the genotypes of individuals do not affect the formation of mating pairs. For example, based on blood groups, crossing may be considered random. However, coloring, size, and behavior can greatly influence the choice of a sexual partner. If preference is given to individuals of a similar phenotype (i.e., with similar individual characteristics), then such positive assortative crossing leads to an increase in the proportion of individuals with the parental genotype in the population. If, when selecting a mating pair, preference is given to individuals of the opposite phenotype (negative assortative crossing), then new combinations of alleles will be presented in the genotype of the offspring; Accordingly, individuals of either an intermediate phenotype or a phenotype that is sharply different from the phenotype of the parents will appear in the population.

In many regions of the world, the frequency of consanguineous marriages (for example, between first and second cousins) is high. The formation of marriage pairs based on kinship is called inbreeding. Inbreeding increases the proportion of homozygous individuals in a population because it is more likely that the parents have similar alleles. As the number of homozygotes increases, the number of patients with recessive hereditary diseases also increases. But inbreeding also promotes a higher concentration of certain genes, which can provide better adaptation of a given population.

Selection.

Differences in fertility, survival, sexual activity, etc. lead to the fact that some individuals leave more sexually mature offspring than others - with a different set of genes. The different contributions of individuals with different genotypes to the reproduction of a population are called selection.

Nucleotide changes may or may not affect the gene product - the polypeptide chain and the protein it forms. For example, the amino acid serine is encoded by six different triplets - TCA, TCG, TCT, TCC, AGT and AGC. Therefore, a mutation can change one of these triplets into another without changing the amino acid itself. On the contrary, the amino acid tryptophan is encoded by only one triplet - THG, and therefore any mutation will replace tryptophan with another amino acid, for example, arginine (CHG) or serine (TCG), or even lead to the termination of the synthesized polypeptide chain if the so-called mutation appears as a result of the mutation . stop codon (TGA or TAG). Differences between variants (or forms) of a protein may not be noticeable to the body, but can significantly affect its functioning. For example, it is known that when in the 6th position of the beta chain of human hemoglobin, instead of glutamic acid, there is another amino acid, namely valine, this leads to a severe pathology - sickle cell anemia. Changes in other parts of the hemoglobin molecule lead to other forms of pathology called hemoglobinopathies.

Even greater differences in fitness are observed in genes that determine the size, physiological characteristics and behavior of individuals; there can be many such genes. Selection, as a rule, affects them all and can lead to the formation of associations of alleles of different genes.

Genetic parameters of the population.

When describing populations or comparing them with each other, a number of genetic characteristics are used.

Polymorphism.

A population is called polymorphic at a given locus if two or more alleles occur in it. If a locus is represented by a single allele, we speak of monomorphism. By examining many loci, it is possible to determine the proportion of polymorphic ones among them, i.e. estimate degree polymorphism, which is an indicator of the genetic diversity of a population.

Heterozygosity.

An important genetic characteristic of a population is heterozygosity - the frequency of heterozygous individuals in the population. It also reflects genetic diversity.

Inbreeding coefficient.

This coefficient is used to estimate the prevalence of inbreeding in a population.

Gene association.

Allele frequencies of different genes can depend on each other, which is characterized by coefficients associations.

Genetic distances.

Different populations differ from each other in allele frequencies. To quantify these differences, metrics called genetic distances have been proposed.

Various population genetic processes have different effects on these parameters: inbreeding leads to a decrease in the proportion of heterozygous individuals; mutations and migrations increase, and drift decreases, the genetic diversity of populations; selection changes the frequencies of genes and genotypes; genetic drift increases, and migration decreases genetic distances, etc. Knowing these patterns, it is possible to quantitatively study the genetic structure of populations and predict its possible changes. This is facilitated by the solid theoretical basis of population genetics - population genetic processes are mathematically formalized and described by dynamic equations. Statistical models and criteria have been developed to test various hypotheses about genetic processes in populations.

By applying these approaches and methods to the study of populations of humans, animals, plants and microorganisms, it is possible to solve many problems of evolution, ecology, medicine, selection, etc. Let us consider several examples demonstrating the connection of population genetics with other sciences.

POPULATION GENETICS AND EVOLUTION

It is often thought that Charles Darwin's main merit is that he discovered the phenomenon of biological evolution. However, this is not at all true. Even before the publication of his book Origin of species(1859), biologists agreed that old species give rise to new ones. There were disagreements only in the understanding of how exactly this could happen. The most popular was the hypothesis of Jean Baptiste Lamarck, according to which during life each organism changes in a direction corresponding to the environment in which it lives, and these useful changes (“acquired” characteristics) are transmitted to descendants. For all its attractiveness, this hypothesis has not been tested by genetic experiments.

In contrast, evolutionary theory, developed by Darwin, stated that 1) individuals of the same species differ from each other in many ways; 2) these differences can provide adaptation to different environmental conditions; 3) these differences are hereditary. In terms of population genetics, these provisions can be formulated as follows: a greater contribution to the next generations is made by those individuals who have the genotypes most suitable for a given environment. If the environment changes, the selection of genes that are more appropriate to the new conditions will begin. Thus, from Darwin's theory it follows that gene pools evolve.

Evolution can be defined as the irreversible change in the gene pools of populations over time. It is accomplished through the accumulation of mutational changes in DNA, the emergence of new genes, chromosomal transformations, etc. An important role in this is played by the fact that genes have the ability to double (duplicate), and their copies are integrated into chromosomes. As an example, let's look again at hemoglobin. It is known that the alpha and beta chain genes originated by duplication of a certain ancestral gene, which, in turn, descended from the ancestor of the gene encoding the protein myoglobin, the oxygen carrier in the muscles. Evolutionarily, this led to the emergence of hemoglobin, a molecule with a tetrameric structure consisting of four polypeptide chains: two alpha and two beta. After nature “found” the tetrameric structure of hemoglobin (in vertebrates), other types of structures for oxygen transport turned out to be practically uncompetitive. Then, over the course of tens of millions of years, the best variants of hemoglobin arose and were selected (each evolutionary branch of animals had its own), but within the framework of a tetrameric structure. Today's selection for this trait in humans has become conservative: it “protects” the only variant of hemoglobin that has passed through millions of generations, and any replacement in any of the chains of this molecule leads to disease. However, many vertebrate species have two or more equivalent hemoglobin variants - selection has favored them equally. And humans have proteins for which evolution has “left” several options.

Population genetics allows us to estimate the time when certain events occurred in evolutionary history. Let's go back to the hemoglobin example. Let, for example, it is desirable to estimate the time when the separation of the ancestral genes of the alpha and beta chains occurred and, consequently, such a respiratory system arose. We analyze the structure of these polypeptide chains in humans or any animal and, by comparing them, determine how different the corresponding nucleotide sequences are from each other. Since at the beginning of their evolutionary history both ancestral chains were identical, then, knowing the rate of replacement of one nucleotide by another and the number of differences in the compared chains, one can find out the time from the moment of their duplication. Thus, here proteins act as a kind of “molecular clock”. Another example. By comparing hemoglobin or other proteins in humans and primates, we can estimate how many millions of years ago our common ancestor existed. Currently, “silent” DNA sections that do not code for proteins and are less susceptible to external influences are used as molecular clocks.

Population genetics allows us to look back into the depths of centuries and sheds light on events in the evolutionary history of mankind that would be impossible to determine from modern archaeological finds. Thus, quite recently, comparing the gene pools of people from different parts of the world, most scientists agreed that the common ancestor of all races of modern man arose approximately 150 thousand years ago in Africa, from where he settled across all continents through Western Asia. Moreover, by comparing the DNA of people in different regions of the Earth, it is possible to estimate the time when human populations began to grow in numbers. Research shows that this happened several tens of thousands of years ago. Thus, in the study of human history, population genetic data are beginning to play as important a role as data from archaeology, demography and linguistics.

POPULATION GENETICS AND ECOLOGY

The species of animals, plants and microorganisms living in each region form an integral system known as an ecosystem. Each species is represented in it by its own unique population. The ecological well-being of a given territory or water area can be assessed using data characterizing the gene pool of its ecosystem, i.e. the gene pool of its constituent populations. It is he who ensures the existence of the ecosystem in these conditions. Therefore, changes in the ecological situation of a region can be monitored by studying the gene pools of populations of species living there.

When developing new territories and laying oil and gas pipelines, care should be taken to preserve and restore natural populations. Population genetics has already proposed its own measures, for example, the identification of natural genetic reserves. They must be large enough to contain the main gene pool of plants and animals in a given region. The theoretical apparatus of population genetics makes it possible to determine the minimum number that is necessary to maintain the genetic composition of the population so that it does not contain the so-called. inbreeding depression so that it contains the main genotypes inherent in a given population and can reproduce these genotypes. Moreover, each region should have its own natural genetic reserves. It is impossible to restore the ruined pine forests of the North of Western Siberia by importing pine seeds from Altai, Europe or the Far East: after decades it may turn out that the “outsiders” are genetically poorly adapted to local conditions. That is why environmentally sound industrial development of a territory must necessarily include population studies of regional ecosystems, making it possible to identify their genetic uniqueness.

This applies not only to plants, but also to animals. The gene pool of a particular fish population is evolutionarily adapted precisely to the conditions in which it lived for many generations. Therefore, the introduction of fish from one natural reservoir to another sometimes leads to unpredictable consequences. For example, attempts to breed Sakhalin pink salmon in the Caspian Sea were unsuccessful; its gene pool was unable to “develop” the new habitat. The same pink salmon, introduced into the White Sea, left it and went to Norway, forming temporary herds of “Russian salmon” there.

One should not think that the main objects of concern for nature should be only economically valuable species of plants and animals, such as tree species, fur-bearing animals or commercial fish. Herbaceous plants and mosses, small mammals and insects - their populations and their gene pools, along with all others, ensure the normal life of the territory. The same applies to microorganisms - thousands of their species inhabit the soil. The study of soil microbes is a task not only for microbiologists, but also for population geneticists.

Changes in the gene pool of populations due to gross interventions in nature are not immediately detected. Decades may pass before the consequences become apparent in the form of the disappearance of some populations, followed by others associated with the first.

POPULATION GENETICS AND MEDICINE

One of the most pressing questions of humanity is how to treat hereditary diseases. However, until recently, the very posing of such a question seemed fantastic. We could only talk about the prevention of hereditary diseases in the form of medical and genetic counseling. An experienced geneticist, studying the patient’s medical history and examining how often the hereditary disease manifested itself among his close and distant relatives, gave an opinion on whether the patient could have a child with such a pathology; and if so, what is the probability of this event (for example, 1/2, 1/10, or 1/100). Based on this information, the spouses themselves decided whether to have a child or not.

The rapid development of molecular biology has brought us significantly closer to our cherished goal - the treatment of hereditary diseases. To do this, first of all, it is necessary to find among the many human genes the one that is responsible for the disease. Population genetics helps solve this difficult problem.

Genetic marks are known - the so-called. DNA markers that allow you to mark, say, every thousandth or ten thousandth “bead” in a long DNA strand. By studying the patient, his relatives and healthy individuals from the population, it is possible to determine which marker is linked to the disease gene. Using special mathematical methods, population geneticists identify the section of DNA in which the gene of interest is located. After this, molecular biologists get involved in the work, analyzing this piece of DNA in detail and finding a defective gene in it. The genes of most hereditary diseases have been mapped in this way. Now doctors have the opportunity to directly judge the health of the unborn child in the first months of pregnancy, and parents have the opportunity to decide whether or not to continue the pregnancy if it is known in advance that the child will be born sick. Moreover, attempts are already being made to correct the mistakes made by nature, to eliminate “breakdowns” in genes.

Using DNA markers, you can not only search for disease genes. Using them, they carry out a kind of certification of individuals. This type of DNA identification is a common type of forensic medical examination, allowing one to determine paternity, identify children mixed up in a maternity hospital, and identify the identity of participants in a crime, victims of disasters and military operations.

POPULATION GENETICS AND SELECTION

According to Darwin's theory, selection in nature is aimed only at immediate benefit - to survive and reproduce. For example, a lynx's coat is smoky-fawn, while a lion's coat is sandy-yellow. Coloring, like camouflage clothing, serves to ensure that the individual blends in with the area. This allows predators to sneak up on prey unnoticed or wait. Therefore, although color variations appear constantly in nature, wild cats with this “mark” do not survive. Only a person with his taste preferences creates all the conditions for the life of domestic cats of the most diverse colors.

Transitioning to a sedentary lifestyle, people moved away from hunting animals and collecting plants to their reproduction, sharply reducing their dependence on natural disasters. By breeding individuals with the desired traits for thousands of years and thereby selecting the appropriate genes from the gene pools of populations, people gradually created all the varieties of domestic plants and breeds of animals that surround us. This was the same selection that nature had been carrying out for millions of years, but only now man, guided by reason, acted in the role of nature.

With the beginning of the development of population genetics, i.e. Since the mid-20th century, selection has followed a scientific path, namely the path of predicting the response to selection and choosing the optimal options for breeding work. For example, in cattle breeding, the breeding value of each animal is calculated immediately based on many characteristics of productivity, determined not only in this animal, but also in its relatives (mothers, sisters, descendants, etc.). All this is reduced to a general index that takes into account both the genetic determination of productivity traits and their economic significance. This is especially important when assessing producers whose own productivity cannot be determined (for example, bulls in dairy cattle breeding or roosters of egg breeds). With the introduction of artificial insemination, a need arose for a comprehensive population assessment of the breeding value of sires when used in different herds with different levels of feeding, housing and productivity. In plant breeding, the population approach helps to quantify the genetic ability of lines and varieties to produce promising hybrids and predict their fitness and productivity in regions of different climates and soils.

Meaning of POPULATION GENETICS: BASIC CONCEPTS OF POPULATION GENETICS in Collier's Dictionary

POPULATION GENETICS: BASIC CONCEPTS OF POPULATION GENETICS

To the article POPULATION GENETICS

Frequencies of genotypes and alleles. The most important concept of population genetics is genotype frequency - the proportion of individuals in a population having a given genotype. Consider an autosomal gene with k alleles, A1, A2, ..., Ak. Let the population consist of N individuals, some of which have alleles Ai Aj. Let us denote the number of these individuals as Nij. Then the frequency of this genotype (Pij) is determined as Pij = Nij/N. Let, for example, a gene have three alleles: A1, A2 and A3 - and let the population consist of 10,000 individuals, among which there are 500, 1000 and 2000 homozygotes A1A1, A2A2 and A3A3, and heterozygotes A1A2, A1A3 and A2A3 - 1000, 2500 and 3000 respectively. Then the frequency of A1A1 homozygotes is P11 = 500/10000 = 0.05, or 5%. Thus we obtain the following observed frequencies of homo- and heterozygotes:

P11 = 0.05, P22 = 0.10, P33 = 0.20,

P12 = 0.10, P13 = 0.25, P23 = 0.30.

Another important concept in population genetics is allele frequency - its proportion among those with alleles. Let us denote the frequency of the Ai allele as pi. Since a heterozygous individual has different alleles, the frequency of the allele is equal to the sum of the frequency of homozygous and half the frequencies of individuals heterozygous for this allele. This is expressed by the following formula: pi = Pii + 0.5??jPij. In the example given, the frequency of the first allele is p1 = P11 + 0.5?(P12 + P13) = 0.225. Accordingly, p2 = 0.300, p3 = 0.475.

Hardy-Weinberg relations. When studying the genetic dynamics of populations, a population with random crossing, having an infinite number and isolated from the influx of migrants, is taken as a theoretical, “zero” reference point; It is also believed that the rate of gene mutation is negligible and there is no selection. It is mathematically proven that in such a population the allele frequencies of the autosomal gene are the same for females and males and do not change from generation to generation, and the frequencies of homo- and heterozygotes are expressed in terms of allele frequencies as follows:

Pii = pi2, Pij = 2pi pj.

This is called the Hardy-Weinberg relationship, or law, after the English mathematician G. Hardy and the German physician and statistician W. Weinberg, who simultaneously and independently discovered them: the first - theoretically, the second - from data on the inheritance of traits in humans.

Real populations can differ significantly from the ideal one described by the Hardy-Weinberg equations. Therefore, the observed genotype frequencies deviate from the theoretical values ​​calculated from the Hardy-Weinberg relationships. Thus, in the example discussed above, the theoretical frequencies of genotypes differ from the observed ones and are

P11 = 0.0506, P22 = 0.0900, P33 = 0.2256,

P12 = 0.1350, P13 = 0.2138, P23 = 0.2850.

Such deviations can be partially explained by the so-called. sampling error; after all, in reality, in an experiment they study not the entire population, but only individual individuals, i.e. sample. But the main reason for the deviation in genotype frequencies is undoubtedly the processes that occur in populations and affect their genetic structure. Let us describe them sequentially.

POPULATION GENETIC PROCESSES

Genetic drift. Genetic drift refers to random changes in gene frequencies caused by a finite population size. To understand how genetic drift occurs, let us first consider a population of the smallest possible size N = 2: one male and one female. Let the female in the initial generation have the genotype A1A2, and the male - A3A4. Thus, in the initial (zero) generation, the frequencies of alleles A1, A2, A3 and A4 are each 0.25. Individuals of the next generation are equally likely to have one of the following genotypes: A1A3, A1A4, A2A3 and A2A4. Let's assume that the female will have the genotype A1A3, and the male - A2A3. Then in the first generation, the A4 allele is lost, the A1 and A2 alleles retain the same frequencies as in the original generation - 0.25 and 0.25, and the A3 allele increases the frequency to 0.5. In the second generation, the female and male can also have any combination of parental alleles, for example A1A2 and A1A2. In this case, it turns out that the A3 allele, despite its high frequency, disappeared from the population, and the A1 and A2 alleles increased their frequency (p1 = 0.5, p2 = 0.5). Fluctuations in their frequencies will eventually result in either the A1 or A2 allele remaining in the population; in other words, both male and female will be homozygous for the same allele: A1 or A2. The situation could have developed in such a way that the A3 or A4 allele would have remained in the population, but in the case considered this did not happen.

The process of genetic drift described by us takes place in any population of finite size, with the only difference that events develop at a much lower speed than with a population of two individuals. Genetic drift has two important consequences. First, each population loses genetic variation at a rate inversely proportional to its size. Over time, some alleles become rare and then disappear altogether. In the end, only one allele remains in the population, which one is a matter of chance. Secondly, if a population is divided into two or more new independent populations, then genetic drift leads to an increase in differences between them: in some populations some alleles remain, and in others - others. Processes that counteract the loss of variation and genetic divergence of populations are mutations and migrations.

Mutations. During the formation of gametes, random events occur - mutations, when the parent allele, say A1, turns into another allele (A2, A3 or any other), which was or was not previously present in the population. For example, if in the nucleotide sequence “...TCT TGG...”, encoding a section of the polypeptide chain “...serine-tryptophan...”, the third nucleotide, T, as a result of a mutation was passed on to the child as C, then in the corresponding In the section of the amino acid chain of the protein synthesized in the child’s body, alanine would be located instead of serine, since it is encoded by the TCC triplet (see HERITANCE). Regularly occurring mutations have formed, in a long series of generations of all species living on Earth, the gigantic genetic diversity that we now observe.

The probability with which a mutation occurs is called the frequency, or rate, of mutation. The rate of mutation of different genes varies from 10-4 to 10-7 per generation. At first glance, these values ​​seem insignificant. However, it should be taken into account that, firstly, the genome contains many genes, and, secondly, that the population can have a significant size. Therefore, some gametes always carry mutant alleles, and in almost every generation one or more individuals with mutations appear. Their fate depends on how strongly these mutations affect fitness and fertility. The mutation process leads to an increase in the genetic variability of populations, counteracting the effect of genetic drift.

Migrations. Populations of the same species are not isolated from each other: there is always an exchange of individuals - migration. Migrating individuals, leaving offspring, pass on to the next generations alleles that might not exist at all in this population or they might be rare; This is how gene flow is formed from one population to another. Migrations, like mutations, lead to an increase in genetic diversity. In addition, gene flow connecting populations leads to their genetic similarity.

Crossing systems. In population genetics, crossing is called random if the genotypes of individuals do not affect the formation of mating pairs. For example, based on blood groups, crossing may be considered random. However, coloring, size, and behavior can greatly influence the choice of a sexual partner. If preference is given to individuals of a similar phenotype (i.e., with similar individual characteristics), then such positive assortative crossing leads to an increase in the proportion of individuals with the parental genotype in the population. If, when selecting a mating pair, preference is given to individuals of the opposite phenotype (negative assortative crossing), then new combinations of alleles will be presented in the genotype of the offspring; Accordingly, individuals of either an intermediate phenotype or a phenotype that is sharply different from the phenotype of the parents will appear in the population.

In many regions of the world, the frequency of consanguineous marriages (for example, between first and second cousins) is high. The formation of marriage pairs based on kinship is called inbreeding. Inbreeding increases the proportion of homozygous individuals in a population because it is more likely that the parents have similar alleles. As the number of homozygotes increases, the number of patients with recessive hereditary diseases also increases. But inbreeding also promotes a higher concentration of certain genes, which can provide better adaptation of a given population.

Selection. Differences in fertility, survival, sexual activity, etc. lead to the fact that some individuals leave more sexually mature offspring than others - with a different set of genes. The different contributions of individuals with different genotypes to the reproduction of a population are called selection.

Nucleotide changes may or may not affect the gene product - the polypeptide chain and the protein it forms. For example, the amino acid serine is encoded by six different triplets - TCA, TCG, TCT, TCC, AGT and AGC. Therefore, a mutation can change one of these triplets into another without changing the amino acid itself. On the contrary, the amino acid tryptophan is encoded by only one triplet - THG, and therefore any mutation will replace tryptophan with another amino acid, for example, arginine (CHG) or serine (TCG), or even lead to the break of the synthesized polypeptide chain if the mutation results in the so-called . stop codon (TGA or TAG). Differences between variants (or forms) of a protein may not be noticeable to the body, but can significantly affect its functioning. For example, it is known that when in the 6th position of the beta chain of human hemoglobin, instead of glutamic acid, there is another amino acid, namely valine, this leads to a severe pathology - sickle cell anemia. Changes in other parts of the hemoglobin molecule lead to other forms of pathology called hemoglobinopathies.

Even greater differences in fitness are observed in genes that determine the size, physiological characteristics and behavior of individuals; there can be many such genes. Selection, as a rule, affects them all and can lead to the formation of associations of alleles of different genes.

Genetic parameters of the population. When describing populations or comparing them with each other, a number of genetic characteristics are used.

Polymorphism. A population is called polymorphic at a given locus if two or more alleles occur in it. If a locus is represented by a single allele, we speak of monomorphism. By examining many loci, it is possible to determine the proportion of polymorphic ones among them, i.e. assess the degree of polymorphism, which is an indicator of the genetic diversity of the population.

Heterozygosity. An important genetic characteristic of a population is heterozygosity - the frequency of heterozygous individuals in the population. It also reflects genetic diversity.

Inbreeding coefficient. This coefficient is used to estimate the prevalence of inbreeding in a population.

Gene association. Allele frequencies of different genes can depend on each other, which is characterized by association coefficients.

Genetic distances. Different populations differ from each other in allele frequencies. To quantify these differences, metrics called genetic distances have been proposed.

Various population genetic processes have different effects on these parameters: inbreeding leads to a decrease in the proportion of heterozygous individuals; mutations and migrations increase, and drift decreases, the genetic diversity of populations; selection changes the frequencies of genes and genotypes; genetic drift increases, and migration decreases genetic distances, etc. Knowing these patterns, it is possible to quantitatively study the genetic structure of populations and predict its possible changes. This is facilitated by the solid theoretical basis of population genetics - population genetic processes are mathematically formalized and described by dynamic equations. Statistical models and criteria have been developed to test various hypotheses about genetic processes in populations.

By applying these approaches and methods to the study of populations of humans, animals, plants and microorganisms, it is possible to solve many problems of evolution, ecology, medicine, selection, etc. Let us consider several examples demonstrating the connection of population genetics with other sciences.

Collier. Collier's Dictionary. 2012

See also interpretations, synonyms, meanings of the word and what POPULATION GENETICS is: BASIC CONCEPTS OF POPULATION GENETICS in Russian in dictionaries, encyclopedias and reference books:

• GENETICS
  (from the Greek genesis - origin) - the science of the laws of heredity and variability of organisms. The most important task G. - development of management methods...
• GENETICS in Collier's Dictionary:
  a science that studies heredity and variability - properties inherent in all living organisms. The endless diversity of plant, animal and microorganism species is maintained by...
• GENETICS in the Big Encyclopedic Dictionary:
  (from the Greek genesis - origin) the science of the laws of heredity and variability of organisms and methods of controlling them. Depending on the object...
• BASIC
  FUNCTIONS OF THE CUSTOMS BODIES OF THE RF - 1) participation in the development of the customs policy of the Russian Federation and the implementation of this policy; 2) ensuring compliance with legislation, ...
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  MEANS - means of labor for production and non-production purposes. Characteristic feature O. s. is participation in the production process long time, V …
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  STATE LAWS OF THE RUSSIAN EMPIRE - a set of laws relating to common principles political system Russia. First codified under the leadership of M.M. Speransky in ...
• GENETICS in the Encyclopedia Biology:
  , the science of heredity and variability of living organisms. Since these properties are inherent in all organisms without exception, they represent the most important...
• GENETICS in the Lexicon of Sex:
  (from genesis), the science of the laws of heredity and variability of organisms and methods of management...
• GENETICS in the Popular Medical Encyclopedia:
  - the science of the laws of heredity and variability...
• GENETICS in Medical terms:
  (Greek genetikos relating to birth, origin) a science that studies the patterns of heredity and variability...
• GENETICS in the Great Soviet Encyclopedia, TSB:
  scientific journal of the USSR Academy of Sciences. Published in Moscow since 1965. The magazine contains articles, reviews, reports on issues of molecular, chemical and...
• GENETICS in the Modern Encyclopedic Dictionary:
  
• GENETICS
  (from the Greek genesis - origin), the science of the laws of heredity and variability of organisms and methods of controlling them. Depending on the object...
• GENETICS in the Encyclopedic Dictionary:
  , and, plural no, w. The science of the laws of heredity and variability of organisms. Geneticist is a specialist in genetics. Genetic - related...
• GENETICS in the Encyclopedic Dictionary:
  [ne], -i, f. The science of the laws of heredity and variability of organisms. II adj. genetic...
• BASIC
  PRIMARY COLORS, three colors, by mixing them in different proportions you can get any color. Number of possible systems O.c. endlessly. Often O.c. ...
• BASIC in the Big Russian Encyclopedic Dictionary:
  BASIC MATERIALS, raw materials or materials constituting ch. material content of the manufactured product. In planning and accounting of production costs O.m. stand out in...
• BASIC in the Big Russian Encyclopedic Dictionary:
  BASIC DYES, organic salts. bases that dissociate in water to form a colored and colorless cation. anion. According to chemistry the structure of ch. arr. ...
• BASIC in the Big Russian Encyclopedic Dictionary:
  BASIC STATE LAWS of Russia. empire, a set of laws relating to the general principles of state. building Russia. For the first time codified under hand. MM. Speransky in...
• BASIC in the Big Russian Encyclopedic Dictionary:
  BASIC ROCKS, igneous. horn rocks relatively poor in silica (44-53% SiO 2) and rich in magnesium and calcium (gabbro, basalts...
• GENETICS in the Big Russian Encyclopedic Dictionary:
  "GENETICS", monthly. scientific Journal of the Russian Academy of Sciences, since 1965, Moscow. Founders (1998) - Department of General Biology, Department of Biochemistry, Biophysics and Physiological Chemistry ...
• GENETICS in the Big Russian Encyclopedic Dictionary:
  GENETICS (from the Greek genesis - origin), the science of the laws of heredity and variability of organisms and methods of controlling them. Depending on the …
• GENETICS in the Complete Accented Paradigm according to Zaliznyak:
  genetics, genetics, genetics, genetics, genetics, genetics, genetics, genetics, genetics, genetics, genetics, genetics, …
• GENETICS in the Popular Explanatory Encyclopedic Dictionary of the Russian Language:
  [n"e], -i, only units, g. The science of the laws of heredity and variability of organisms. Molecular genetics. Population genetics. Develop theory and...

The species of living beings inhabiting the earth form communities, that is, spatiotemporal associations. One of the types of communities is a population - a community of one species occupying a certain territory. Population genetics studies the laws of gene distribution among the population.

Genetic characteristics populations makes it possible to establish the gene pool of a population, factors and patterns that determine the preservation of the gene pool or its change over generations. Study of distribution features mental properties in different populations makes it possible to predict the prevalence of these properties in subsequent generations. The genetic characterization of a population begins with an assessment of the prevalence of the property or trait being studied in the population. Based on data on the prevalence of a trait, the frequencies of genes and corresponding genotypes in the population are determined.

Main characteristics genetic population are:

• individuals belonging to the same species,
• spatiotemporal similarity,
• similarity environmental needs,
• the ability to randomly and freely interbreed with each other - panmixia. Panmixia may be disrupted if pair formation does not occur by chance. For example, in human populations there is a tendency towards a non-random selection of married couples based on height, intelligence, interests, etc. Such a non-random selection of couples is called assortativity.

A population that is closed geographically or for religious reasons, in which there is no exchange of individuals with other populations, is called an isolate.

Hardy-Weinberg Law

The relationships between allele frequencies and genotype frequencies in generations were first described in 1908 independently by the English mathematician G. Hardy and German doctor V. Weinberg (Fig. 5.1). This law defines the relationship between allele frequencies in the original population and genotype frequencies in the next generation.

Figure 5.1.

The Hardy-Weinberg law considers an ideal population. In fact, the real population will not fully correspond this law, since processes occur in it that influence changes in allele frequencies in the population, such as mutations, migrations, genetic drift, selection, and in human populations, assortativity.

Let's consider these factors separately.

Mutations and types of mutations

Mutations- sudden and sustainable change genotype. The term "mutation" was proposed in 1901 by the Dutchman Hugo de Vries. Mutations are the main source of genetic variation, but their frequency is low. It will take a very long time for mutations to lead to significant changes in allele frequencies.

Mutations can be classified on various grounds. So, there are mutations:

• spontaneous and induced, i.e. arising under the influence of mutagens - a) physical radiation; b) chemicals; c) biological - the influence of viruses, for example, the rubella virus;
• genetic, cytoplasmic, chromosomal and genomic (changes in the number of chromosomes);
• depending on the effect on viability - negative, neutral and positive (the role of the mutation has been identified in resistance to diseases such as HIV and sickle cell anemia);
• depending on the type of inheritance - dominant and recessive;
• somatic or reproductive (gametic).

Gametic mutations are mutations that occur in germ cells, for example, breast cancer. According to the forecast, for women born after 1980, the risk of developing the disease before the age of 80 is 12%, that is, one in eight will get the disease. A mutated gene on chromosomes 13 and 17 causes 5 to 10% of breast cancer cases. The gene is transmitted according to Mendelian laws.

The JAL1 gene, which is responsible for genetic forms of breast cancer, can now be called the Angelina Jolie gene, since it has become known to the general public thanks to her recent actions and public statements. This gene and its role in the development of cancer have been known since the mid-90s of the last century. Moreover, A. Jolie is far from the first who came up with the idea of ​​​​carrying out a preventive mastectomy. There is evidence that in the UK during 2010-2011. carried out about 1,500 such operations for preventive purposes.

It must be emphasized that purely genetic cancer, that is, one that arose only because of an inherited specific “bad” gene, is rare. As already mentioned, no more than 10% of cases of breast and ovarian cancer are hereditary, and 50% of them are responsible for LLCL genes. The frequency of the mutant allele of the VYASL1 gene is 0.06%, among Ashkenazi Jews it is higher - 2.6%. Several tests have been developed that, using special computer program calculate cancer risk based on analysis of LLCL genes and individual information. For A. Jolie, the program calculated highest risk breast cancer - 86%.

Somatic - the remaining 80% of mutations associated with breast cancer occur in somatic cells.

Let's consider separately types of chromosomal and genomic mutations (Fig. 5.2).

Figure 5.2.

To chromosomal mutations include divisions, duplications, inversions, translocations:

• division - loss of a section of a chromosome;
• duplication - doubling;
• translocation - transfer of a chromosome section to another;
• inversion - a 180-degree rotation of a certain section of a chromosome.

Genomic mutations characterized by changes in the number of chromosomes. Genomic mutations are described in several types. In humans, polyploidy (including tetraploidy and triploidy) and aneuploidy are known (Fig. 5.3).

Figure 5.3.

Polyploidy- an increase in the number of sets of chromosomes, a multiple of the haploid one (3p, 4p, 5p, etc.). That is, the number of chromosomes becomes equal to 69, 92, etc. The causes of polyploidy are double fertilization and the absence of the first meiotic division. In humans, polyploidy, as well as most aneuploidies, lead to the formation deaths immediately after birth or before birth (spontaneous miscarriages).

Aneuploidy- change (decrease - monosomy or increase - trisomy) the number of chromosomes in a diploid set, that is, the number of chromosomes that is not a multiple of the haploid one (2n+1, 2n-1, etc.). The number of chromosomes becomes equal to 45, 47, 48, etc. The mechanisms of occurrence of aneuploidy are different: non-disjunction of chromosomes (chromosomes move to one pole, while each gamete has one an extra chromosome there is another - without one chromosome) and “anaphase lag” (in anaphase, one of the moving chromosomes lags behind all the others).

Trisomy- the presence of three homologous chromosomes in the karyotype (for example, on the 21st pair, which leads to the development of Down syndrome; on the 18th pair - Edwards syndrome; on the 13th pair - Patau syndrome).

Monosomy- the presence of only one of two homologous chromosomes. With monosomy for any of the autosomes normal development embryo is impossible. The only monosomy compatible with life in humans - on the X chromosome - leads to the development of Shereshevsky-Turner syndrome (45, X0).

One of the factors causing mutations is inbreeding. Inbreeding- consanguineous marriages, for example between first cousins. Marriages between genetic relatives increase the likelihood of producing offspring with recessive traits. We will illustrate the genetic consequences of such marriages using the example of a number of hereditary diseases in populations of Europe and the USA. For example, among the white population of the United States, only 0.05% of the population undergoes consanguineous marriages. total number marriages and at the same time 20% of cases of albinism.

However, the consequences of inbreeding are not negative in all populations. U rural population In India, China and Japan, consanguineous marriages are quite common, but negative effects(number of deformities, stillbirths) were not detected. Most likely, in these countries where consanguineous marriages are allowed by culture, over the course of many generations, recessive homozygotes were produced that had reduced vitality.

Migration and genetic drift

Migration is the movement of individuals from one population to another with the subsequent formation of marriage ties between migrants and members of the original population. Migration leads to a change in the genetic composition of the population due to the arrival of new genes. For example, the distribution of blood group B in Europe is a consequence of the movement of the Mongols into westward from the maternal population between the 6th and 15th centuries. Therefore, in Europe, the frequency of allele B is consistently decreasing, starting from the borders with Asia and ending with Spain and Portugal. The exchange of genes between populations can have significant medical consequences. Thus, until recently, Rh-conflict was practically not encountered in China, since all Chinese women are Rh-positive.

However, migration processes, Americans moving to China, and interracial marriages introduced the Rh-negative allele into Chinese populations. And if in the first generation the offspring of American men and Chinese women did not experience a Rh conflict, in subsequent generations its frequency increased, as Rh-negative women appeared who married Rh-positive men.

Due to the limited number of individuals forming a population, random changes in gene frequencies are possible, which are called genetic drift. Over a series of generations, if other factors do not act, genetic drift can lead to the fixation of one allele and the disappearance of another.

S. Wright experimentally proved that in small populations the frequency of the mutant allele changes quickly and randomly. His experiment was simple: in test tubes with food he placed two females and two males of Drosophila flies, heterozygous for the A gene (their genotype can be written Aa). In these artificially created populations, the concentration of normal (A) and mutation (a) alleles was 50%. After several generations, it turned out that in some populations all individuals became homozygous for the mutant allele (a), in other populations it was completely lost, and, finally, some populations contained both a normal and a mutant allele. It is important to emphasize that, despite the decrease in the viability of mutant individuals and, therefore, contrary to natural selection, in some populations the mutant allele completely replaced the normal one. This is the result random process- genetic drift.

Natural selection is the process of selective reproduction of offspring by genetically different individuals in a population. Natural selection manifests itself in the fact that individuals with different genotypes leave an unequal number of offspring, that is, they make an unequal genetic contribution to the next generation.

Thus, the Hardy-Weinberg law is a law of population genetics, which states that in a population there is an infinite big size, in which there is no selection, no mutation process, no exchange of individuals with other populations, no genetic drift, all crossings are random - the frequencies of genotypes for any gene (if there are two alleles of this gene in the population) will be be maintained constant from generation to generation and correspond to the equation:

Where R- the proportion of homozygotes for one of the alleles; R- frequency of this allele;

¥^ - the proportion of homozygotes for the alternative allele; I- frequency of the corresponding allele; - proportion of heterozygotes.

In the process of evolution of living organisms, there is a clear tendency towards one form or another of integration, which manifests itself starting from molecular level organization and ends with the biosphere. Integration allows for the division of functions between individual elements of the system, which makes the system itself more labile, viable and economical. One level of integration that exists between an individual and a species is represented by a population.

Population- a group of individuals of the same species united commonplace a habitat. It develops under the influence of living conditions based on the interaction of three factors: heredity, variability and selection. Individuals within a population have a similar system of adaptations to environmental conditions and reproduce basic adaptive traits from generation to generation.

Population is the basic unit of evolution. The population assumed this role thanks to the following features:

1. A population is a self-reproducing system, capable of long-term existence in time and space, in contrast to an individual, whose life is limited to a narrow time frame and who may not leave offspring. The reproduction of a population is based on the process of reproduction of its constituent individuals.
2. The population is authorized representative kind, because its gene pool includes all the main species-level genes. At the same time, new genes and their combinations are tested in it, due to which the species gene pool is enriched.
3. In a population, as a result of crossings, an exchange occurs genetic information between individuals, which changes the genotypic structure of the population, allowing it to adequately respond to a variety of influences.

Main characteristics of the population are: its gene pool, numbers, habitat and genotypic structure. All of them are dynamic, subject to temporary, sometimes very significant, fluctuations. Dynamic processes leading to changes in the genetic structure of old and the formation of new populations are designated by the term microevolution.

Research in the field of population genetics began in the early years of the twentieth century. The founder of this direction is considered to be the Danish geneticist V. Johansen, who developed the doctrine of populations and pure lines. Studying the inheritance of quantitative traits in bean populations, Johansen came to the conclusion that selection is ineffective in pure lines and effective in populations, which is based on the genetic homogeneity of the former and the heterogeneity of the latter. Johannsen's discovery, along with Mendel's laws, contributed to the creation scientific foundations selection.

Most populations of animals and plants are formed on the basis of free crossing of individuals - Panmixia. These are the so-called Mendelian, or panmictic, populations of dioecious animals and cross-plants, in which there is a constant exchange of genetic information between its members. Another type of population is formed by organisms that are characterized by self-fertilization or vegetative reproduction. In this case, the exchange of genes between individuals is either completely excluded or difficult. These are so-called closed populations (self-pollinating plants, hermaphrodite animals), which are formed as groups of individuals of the same species, having common origin, common gene pool and common system adaptations. And finally intermediate type characteristic of plant populations in which self-pollination alternates with cross-pollination, and sexual reproduction with apomixis (facultative apomicts) or vegetative propagation. Such populations are usually characterized by a complex genetic structure.

Human populations occupy a special position in wildlife. Action biological factors, changing the genetic structure of the population, primarily natural selection, changed as a result of the activities of man himself. With the help of advances in science, culture, ethics and medicine, people make significant adjustments to the process of constructing populations, trying to minimize the risk of the spread of “harmful” genes. However, the existence of human populations is subject to the same laws that operate in other populations.

Basic law of population genetics was formulated in 1908 by mathematician J.G. Hardy in England and physician W. Weinberg in Germany, independently of each other, based on data relating to human populations. The main postulate of this law is that the gene frequency does not change from generation to generation, and the distribution of genotypes in each generation corresponds to the Newton binomial formula, i.e. determined by squaring the sum of the frequencies of two alleles.

Let us consider the procedure for deriving this law. Let’s take a fairly large Mendelian population in which two alleles of one gene are present: A And A. In such a population there will be three genotypes: AA, Ahh And ahh. Let us denote the frequency of the dominant allele by p, and recessive through q. In the case of free combination of gametes A And A the frequency of each of the three genotypes will be equal to: A.A. = p · p = p 2 ; aa = q q = q 2. Genotype Ahh can arise in two ways: by receiving a gene A- from the mother, and the gene A from the father, or vice versa. The probability of each of them is equal pq, and thus the overall genotype frequency Aa = pq + pq = 2pq.

Geometric image Hardy-Weinberg law can be represented as a Punnett lattice.

p 2 + 2pq + q 2 = 1

(p + q) 2 = 1

Individuals with a genotype AA will form one type of gamete with the gene A with frequency p 2. In individuals with the genotype Ahh two types of gametes will be formed: half with A (pq) and half with A (pq). Individuals with a genotype ahh will give all gametes of the same type with the gene A with frequency q 2. Total frequency of gametes with gene A, thus, will be equal p 2 + pq = p(p + q) = 1 = p, and the gametes with the gene A: q 2 + pq = q(q + p) = q· 1 = q.

Consequently, the frequency of gametes, and therefore the population structure (the ratio of different genotypes) in it and in the next generation will be the same. In this case, the population is said to be in a state of equilibrium.

The Hardy-Weinberg law is fundamental. Its formula allows you to calculate the frequency of different genotypes in a population based on phenotypic analysis. For example, let's say that in a population of cows, animals with a recessive red color make up 16%, the remaining 84% have a dominant black color. Therefore, the frequency of homozygous recessive q 2 = 0.16, a q, accordingly, is equal to 0.4. Because p + q= 1, then p= 0.6. Thus, the frequency of homozygous black animals p 2 = 0.36, and heterozygous 2 pq= 2 · 0.4 · 0.6 = 0.48.

One of the interesting consequences that follows from the Hardy-Weinberg law is that rare genes are present in a population mainly in a heterozygous state. So, if the frequency of a recessive allele q= 0.01, then its frequency in homozygotes q 2 = 0.0001, and the frequency in heterozygotes pq= 0.01 · 0.99 ≈ 0.01, i.e. in the heterozygous state there are 100 times more alleles than in the homozygous state.

It follows from this that it is almost impossible to eliminate a harmful recessive mutation from a population: there will always be a zone of heterozygotes where it will hide under the cover of a dominant gene.

The Hardy-Weinberg formula is applicable for calculations under the following conditions:

1) if one pair of alleles is taken into account;

2) the mating of individuals and the combination of gametes is carried out randomly, i.e. no restrictions on panmixation;

3) mutations occur so rarely that they can be neglected;

4) the population is quite large;

5) individuals with different genotypes have the same viability.

It is unlikely that even one of them can meet the above conditions. natural population. The law is valid for the so-called ideal population. But this in no way detracts from its significance. There are periods in the life of each population when it is in a state of equilibrium in the frequencies of individual genes. And if this balance is disturbed for any reason, the population quickly restores it.