Fundamentals of human population genetics. History of the concept of “population”

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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 allele frequency is equal to the sum of the frequencies of homozygous individuals 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, the experiment does not study 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.

The 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 his book was published 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.

Lecture 8. Topic. Population genetics and adaptation of species. Fundamentals of evolutionary teaching. Natural selection. Artificial selection as the basis of selection. Fundamentals of modern biotechnology. Basic methods of genetic, cellular and chromosome engineering. Ecology. Biogeocenosis. Food chains and the structure of the ecological pyramid. Abiotic, biotic and anthropogenic factors. Types of biotic connections.

Population genetics.

Population – is a group of organisms of the same species that usually lives in a clearly defined area. The overall genetic response of an entire population determines its survival and is the subject of the study of population genetics.

Knowledge of the basic laws of population genetics allows us to understand the mechanisms of adaptive variability of species, help us understand practical issues of medical genetic counseling of people, and even comprehend a number of ideological problems.

Curious students are sometimes confused by the question: if the allelic genes for brown eyes dominate the genes for blue eyes, why don’t blue-eyed people disappear? The mathematical proof of this fact was first formulated independently by Hardy and Weinberg in 1908.

Each gene can exist in several different forms, called alleles. The number of organisms in a population that carry a particular allele determines the frequency of that allele (gene frequency). For example, the gene that determines the possibility of pigmentation of the skin, eyes and hair in humans is represented by a “normal” allele in 99% of cases. The second possible variant of this gene is the albinism allele, which makes pigment deposition impossible. Its frequency is 1%. In mathematics, allele frequency is expressed not as a percentage, but as parts (usually decimals) of one. In this example, the frequency of the dominant - normal allele will be 0.99, and the frequency of the recessive allele of albinism will be 0.01. In this case, the sum of allele frequencies is always equal to one (0.99 + 0.01 = 1). Genetics borrowed from the mathematical theory of probability the symbols “p” to indicate the frequency of the dominant allele and “q” to indicate the frequency of the recessive allele. In the given example with pigmentation in humans p+q = 1 (probability equation)

The meaning of this equation is that, knowing the frequency of one allele, you can find the frequency of another:

p=1-q – frequency of the dominant allele;

q=1-p – frequency of the recessive allele.

For example, if the recessive allele has a frequency of 5% or q=0.05, then the dominant allele will have a frequency of p=1-0.05=0.95 or 95%. It should be noted that allele frequency is not the frequency of manifestation of a trait in the phenotype, which depends on the combination of 2 alleles in the genotype.

For two alleles with complete dominance (pea seed color), 3 genotypes are possible: AA, Aa, aa and 2 phenotypes: 1 dominant yellow (AA, Aa); 2-recessive green (aa). Thus, individuals with the same phenotype may not have the same genotype. . Hardy-Weinberg Law states: the frequencies of dominant and recessive alleles of different generations of an ideal population are constant (an ideal population can be called an isolated population of large sizes, without new mutations, where mating occurs randomly, all genotypes are equally fertile, and generations do not overlap). This law can be expressed in Hardy-Weinberg equation

p 2 + 2pq+q 2 =1, Where

p2-frequency of dominant homozygotes (AA)

2pq-frequency of heterozygotes (Aa)

q 2-frequency of recessive homozygotes (aa)

This distribution of possible genotypes is associated with the random nature of the distribution of gametes during the process of meiosis and is based on probability theory, mathematically it is the square of the probability equation p+q=1 (probability equation), (p+q) 2 =1 2 ; (p+q)(p+q)=1;

p 2 + 2pq+q 2 =1(Hardy-Weinberg equation)

Having two equations for the probabilities of the frequency of allelic genes and observing the frequency of recessive homozygotes (q 2), it is possible to calculate the number of heterozygotes (2pq) - carriers of hidden genes and the frequency of allelic genes (p-dominant and q-recessive).

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 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 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 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 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 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 that have alleles. Let us denote the frequency of the Ai allele as pi. Since a heterozygous individual has different alleles, the allele frequency is equal to the sum of the frequencies of homozygous individuals 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 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, the experiment does not study 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 have the genotype 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 A1A3 genotype, and the male will have the A2A3 genotype. 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 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 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 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. 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.

Population genetics

Population genetics studies patterns of distribution of genes and genotypes in populations. The establishment of these patterns has both scientific and practical significance in various branches of biology, such as ecology and environmental genetics, biogeography, selection, etc. In medical practice, there is also often a need to establish quantitative relationships between people with different genotypes for a gene that includes a pathological allele, or the frequency of occurrence of this gene among the population.

Populations can be in a state of genetic equilibrium or be genetically disequilibrium. In 1908, G. Hardy and V. Weinberg proposed a formula reflecting the distribution of genotype frequencies in populations with free crossing, i.e. panmictic. If the frequency of the dominant allele R, and recessive – q, and
p + q = 1, Then r*r (A.A. ) + 2pq (Aa ) + q*q (aa ) = 0 , where p*p is the frequency of the dominant homozygous genotype, 2pq is the frequency of heterozygotes, and q*q is the frequency of recessive homozygotes.

In a genetically equilibrium population, the frequencies of genes and genotypes do not change from generation to generation. This, in addition to panmixia, i.e. the absence of special selection of pairs based on any individual characteristics contributes to:

Large population size;

The absence of outflow or influx of genes into it due to the migration of individuals;

Absence of mutation pressure that changes the frequency of any allele of a given gene or leads to the appearance of new alleles;

The absence of natural selection, which may result in unequal viability or unequal fertility of individuals with different genotypes.

The action of any of these factors may cause a violation of the genetic balance in a given population, i.e. the dynamics of its genetic structure or its change in time (from generation to generation) or in space. Such a population may be evolving.

Using the Hardy-Weinberg formula, you can perform a number of calculations. For example, based on the known frequencies of phenotypes whose genotypes are known, it is possible to calculate the allele frequencies of the corresponding genes. Knowing the frequency of a dominant or recessive homozygous genotype in a given population, it is possible to calculate the parameters of the genetic structure of this population, namely, the frequencies of genes and genotypes. In addition, based on the Hardy-Weinberg formula, it is possible to determine whether a given population with a certain ratio of genotype frequencies is genetically equilibrium. Thus, analysis of populations from the standpoint of the main provisions of the Hardy-Weinberg law allows us to assess the state and direction of variability of a particular population.

The Hardy-Weinberg law also applies to genes represented by multiple alleles. If a gene is known in three allelic forms, the frequencies of these alleles are expressed, respectively, as p, q and r, and the Hardy-Weinberg formula, reflecting the ratio of the frequencies of the genotypes formed by these alleles, takes the form:

p*p + q*q + r*r + 2pq + 2pr + 2qr = 1

1. In one isolated human population, approximately 16% of people have Rh negative blood (a recessive trait). Determine the number of heterozygous carriers of the Rh-negative blood gene.

2. Does the following ratio of homozygotes and heterozygotes in the population correspond to the Hardy-Weinberg formula: 239 AA:79 Ahh: 6 ahh?

3. Gout occurs in 2% of people and is caused by an autosomal dominant gene. In women, the gout gene does not manifest itself; in men, its penetrance is 20% (V.P. Efroimson, 1968). Determine the genetic structure of the population based on the analyzed trait based on these data.

4. The frequency of blood group genes according to the AB0 system among the European population is given below (N.P. Bochkov, 1979).

Population Gene Frequencies

Russians 0.249 0.189 0.562

Buryats 0.165 0.277 0.558

English 0.251 0.050 0.699

Determine the percentage of people with I, II, III and IY blood groups among Russians, Buryats and English.

Homework:

1. In one of the panmictic populations, the allele frequency b is equal to 0.1, and in the other – 0.9. Which population has more heterozygotes?

2. In European populations, there is 1 albino per 20,000 people. Determine the genetic structure of the population.

3. The island's population descended from several individuals from a population characterized by the frequency of occurrence of the dominant allele B(brown eyes) equal to 0.2, and a recessive allele b(blue eyes) equal to 0.8. For this island population, determine the percentage of people with brown and blue eyes in the first generation. Will this ratio of individuals by phenotype and the gene pool of the population change after changes of several generations, provided that the population is panmictic in nature, and there were practically no mutations in eye color in it.

4. In the United States, about 30% of the population perceives the bitter taste of phenylthiourea (PTC); 70% of people do not distinguish its taste. The ability to taste FTC is determined by a recessive gene A. Determine allele frequency A And A and genotypes AA, Ahh And ahh in this population.

5. There are three genotypes for the albinism gene in the population: A in ratio: 9/16 A.A., 6/16 Aa and 1/16 ahh. Is this population in a state of genetic equilibrium?

6. Congenital hip dislocation is inherited dominantly, the average penetrance is 25%. The disease occurs with a frequency of 6: 10,000 (V.P. Efroimson, 1968). Determine the number of homozygous individuals for the recessive gene.

7. Find the percentage of heterozygous individuals in the population:

8. See task 4 - Buryats and British. Compare.

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 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 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 group 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 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 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.

CHANGES IN ALLELE FREQUENCIES DURING DRIFT. The results of modeling the process of genetic drift in two populations of N = 25 and two populations of N = 250, with an allele frequency of 0.5 in the initial generation, are presented. Under the influence of drift, the frequency of a given allele changes chaotically from generation to generation, with frequency “jumps” being more pronounced in smaller populations. Over 50 generations, drift led to the fixation of the allele in one population of N = 25, and to its complete elimination in another. In larger populations, this allele is still at intermediate frequencies, but the populations are already noticeably different from each other starting from the 60th generation.

Collier's Encyclopedia. - Open Society. 2000 .