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Human genetics with the basics of general genetics [ Tutorial] Kurchanov Nikolai Anatolievich
8.1. population genetics
8.1. population genetics
Population genetics postulates that the unit of the evolutionary process must be an indivisible unity and be able to change in a number of generations. Neither species nor individual satisfies these criteria. The elementary unit of the evolutionary process is the population.
Population - this is isolated group individuals of the same species, connected by a common territory and origin. This term was proposed by W. Johannsen in 1909.
The idea of a population as a unit of evolution was formed almost immediately after the advent of Darwinism. A population is a continuous series of generations, it is characterized by both heredity and variability. The concept of a population is applicable to both sexually reproducing and non-sexually reproducing organisms.
During the formation of population genetics, it was believed that the genetic variability of natural populations is very small, most loci contain dominant alleles (alleles wild type) and only a few loci contain mutant alleles. It turned out that the “normal” genotype of an individual in nature is homozygous for almost all loci.
At present, the so-called balance theory of populations, proposed by F. Dobzhansky (Dobzhansky T., 1937), is accepted. According to it, the variability of natural populations is very high, the individuals that make up the population are heterozygous for most loci, there are no “wild type” alleles. It emphasizes that there is no "normal" genotype. gene pool population, which includes all the alleles of all individuals inhabiting the population, is very diverse. A measure of the genetic variability of a population is such a thing as heterozygosity.
Population heterozygosity shows the average frequency of individuals heterozygous for certain loci. To calculate heterozygosity, first determine the frequencies of heterozygotes for each locus, and then calculate the average of the results. How large quantity loci will be investigated, the more accurate assessment of population variability will be obtained. Studies have shown that for a rough estimate, it is enough to analyze about 20 loci.
Heterozygosity is a reliable indicator of variability. It determines the probability that any two alleles of one locus from the gene pool of a population, taken at random, will be different. The average heterozygosity of human populations is 6.7% (Ayala F., Kaiger J., 1988).
Thus, a population is a collection of genotypes that differ in many loci. Most loci are characterized by multiple alleles. This phenomenon is called polymorphism. The quantitative expression of population polymorphism is polymorphism(P) showing the proportion of polymorphic loci. So, if in the studied population of 40 loci, 8 loci turned out to be polymorphic (represented by several alleles), and 32 were monomorphic (represented by one allele), then P = 0.2, or 20%.
Polymorphism does not fully express the degree of genetic variability of a population. All loci with more than one allele will be equal when calculating P. However, one locus may have 2 alleles in the population, and the other 20. P does not change the relative frequency of alleles with the same number of alleles. Alleles can be more or less evenly represented in the population, or there can be a clear prevalence of one allele over all the others.
As in the case of many other genetic terms, the difference between the concepts of "mutation" and "polymorphism" is rather arbitrary. Usually, if any DNA sequence occurs more often than in 1% of cases, then they talk about polymorphism, if less than 1%, then about a mutation. In the human genome, the average number of variations for each gene is 14 (Tarantul V.Z., 2003). The number of different repeats is also characterized by significant polymorphism, which plays an important diagnostic role in humans.
The most important characteristic of a population is the allele and genotype frequencies of its constituent individuals. They can be calculated by the key law of population genetics - Hardy-Weinberg law. It states that with random crossing and the absence of external factors, the allele frequency in the population is constant.
To designate allele frequencies in population genetics, special symbols are used: R– allele frequency A; q– allele frequency a; then p+ q= 1.
To calculate the frequencies of genotypes, the binomial square formula is used:
(p+ q) 2 = p 2 + 2pq+ q 2 ,
where p 2 – AA genotype frequency; 2 pq– Aa genotype frequency; q 2 – aa genotype frequency.
The application of the Hardy–Weinberg law to calculate allele frequencies in humans provides a clear example of autosomal recessive diseases. Knowing the frequency of occurrence genetic disease, using the Hardy-Weinberg formula, we can calculate the allele frequency (adjusted for error). For example, one of the most severe autosomal recessive human diseases - cystic fibrosis, occurs with a frequency of 1: 2500. Since all cases of manifestation are due to the homozygous recessive allele, then:
q 2 = 0,0004; q= 0,02;
p= 1 – q= 1–0,02 = 0,98.
Frequency of heterozygotes (2 pq) = 2? 0.98? 0.02 = 0.039 (about 4%).
We see that almost 4% of people (not a few) are carriers of the gene cystic fibrosis. This shows how big number recessive pathogenic genes is in a latent state.
In multiple allelism, genotype frequencies are determined by squaring a polynomial of allele frequencies. For example, there are three alleles: a 1, a 2, and 3.
Their frequencies are respectively: p, q, r. Then p+ q+ r= 1.
To calculate genotype frequencies:
(p+ q+ r) 2 = p 2 + q 2 + r 2 + 2pq+ 2pr+ 2rq,
where p 2 – genotype frequency a 1 a 1; q 2 – genotype frequency a 2 a 2 ; r 2 – genotype frequency a 3 a 3 ; 2 pq– genotype frequency a 1 a 2 ; 2 pr– genotype frequency a 1 a 3 ; 2 rq– genotype frequency a 2 a 3 .
It should be noted that the sum of genotype frequencies, as the sum of allele frequencies, will always be equal to 1, i.e. ( p+ q) 2 = (p+ q+ r) 2 = =… = 1. Genotype frequencies remain unchanged in subsequent generations.
If the number of alleles of one locus is denoted k, then the number of possible genotypes ( N) can be calculated using a special formula:
AT strictly the Hardy-Weinberg law is applicable only for an ideal population, i.e., a sufficiently large population in which free crossing takes place and external factors do not act. Only under these conditions is the population in equilibrium. Such ideal conditions never occur in nature. Let us consider in more detail two limitations of the application of the Hardy-Weinberg law regarding free crossing and the action of external factors.
In population genetics, two types of crosses are distinguished:
1. Panmixia - free crossing: the probability of forming a marriage pair does not depend on the genotype of the partners. With regard to whole genotypes, panmixia is almost never observed in nature, but it is quite applicable to individual loci.
2. Assortativeness - selective crossing: the genotype affects the choice of a marriage partner, i.e. individuals with certain genotypes mate more often than with random probability. Selective crossing does not change gene frequencies, but it does change genotype frequencies. One of the extreme varieties of assortativity is purposeful inbreeding- crossbreeding between related individuals. In relation to a person, assortativeness will be considered in the section of psychogenetics.
Deviation from the Hardy-Weinberg equality indicates that some external factor. To analyze changes in gene frequencies, complex and rather cumbersome systems of equations have now been developed. This is due to the presence of variable factors that affect the result. We will consider the varieties of evolutionary factors a little lower, but for now we note that in any sufficiently large population, the deviations will be very small, so the Hardy-Weinberg law allows us to carry out the most important calculations and is the basis of population genetics. But these deviations become significant when we begin to consider the process on an evolutionary time scale. The dynamics of the gene pool of populations represents evolution at the genetic level.
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POPULATION GENETICS(Late Latin populatio, from Latin populus people, population; genetics) - a section of genetics devoted to the study of patterns of variability and heredity at the population level.
As an independent section of the P. city, it was formed at the beginning of the 20th century. In 1903, Johannsen (W. L. Johannsen) published the work "On Inheritance in Populations and Pure Lines". In 1908, G. H. Hardy and W. Weinberg gave a mathematical justification for the ratio of alleles in a population (see Population, population genetics). In 1926, S. S. Chetverikov showed that the genotypic evolution of populations is determined by the accumulation of mutations (see Mutation) and natural selection (see), in 1929 he also published the results of the first experimental study on the genetics of natural populations. In 1931 - 1932 N. P. Dubinin, D. D. Romashov and S. Wright formulated the theory of genetically automatic processes (the theory of gene drift). The result of all these studies was the establishment of four main factors that determine the patterns of variability and heredity in populations: 1) mutations of genes and chromosomes (see Mutation); 2) selection, which ensures the differential reproduction of individuals within a population; 3) genetic drift, which leads to changes in the concentration of alleles under conditions of isolation (see Isolates); 4) migration (mixing) of populations, leading to the alignment of the concentration of alleles (see Variability, Heredity).
Individuals divided into populations retain the possibility of interbreeding with another individual of this species, which ensures its integrity. A strong influence on the genetic structure of the population is exerted by random deviations in the composition of alleles (see), which occur in a small group of individuals when they populate new places. Mayer (E. Mayer) called this phenomenon the "principle of the founders." Migrations of individuals from one population to another lead to the leveling of genetic differences between populations; isolation, on the contrary, promotes their genetic differentiation. The distribution of many alleles in humans is due to the mixing of populations. For example, in the United States, the exchange of genes, which over the past two centuries has occurred predominantly from whites to blacks, led to the fact that by the second half of the 20th century. Negroes already have approx. 30% white human genes.
Discovery by N.P. Dubinin in 1931-1934. of recessive lethal mutations in Drosophila populations laid the foundation for the study of the genetic load of populations. This load is made up of lethal, semi-legal and sublethal changes and can be segregational, i.e. manifested by the “splitting out” of less adapted homozygotes in the presence of selection in favor of heterozygotes in the population, or it can be mutational, i.e. manifested in populations by mutations that reduce fitness of individuals carrying these mutations. There is a so-called drift load is a random increase in the concentrations of alleles in an isolated population. A particular result of such a load is an increase in the proportion of homozygous individuals during inbreeding (see) - the so-called. inbred cargo or inbred depression.
The amount of genetic load is determined by the diversity of mutations present in the population. The increase in the concentration of mutations is restrained by selection, so each recessive mutation is included in the gene pool of the population at a low level. However, the total number of recessive mutations is so high that each person carries, for example, 3-4 lethal mutations.
Bibliography: Dubinin N. P. Evolution of populations and radiation, M., 1966; Levontin R.K. Genetic foundations of evolution, trans. from English, M., 1978; JI and Ch. Introduction to population genetics, per. from English, M., 1978, bibliography; Mettler L. Yu. and Gregg T. G. Genetics of populations and evolution, trans. from English, M., 1972; P about to and c to and y P. F. Introduction to statistical genetics, Minsk, 1978; Chetverikov S. S. On some moments of the evolutionary process from the point of view modern genetics, in the book: Classics of Sov. genetics, ed. H. M. Zhukovsky, p. 133, L., 1968; Sheppard F. M. Natural selection and heredity, trans. from English, M., 1970; Crow J. F. a. K i m u g and M. An introduction to population genetics theory, N. Y., 1970; Dobzhansky Th. Genetics of the evolutionary process, N. Y., 1970; Ford E. B. Ecological genetics, L., 1971.
Tasks:
- Describe the main methods of studying human genetics.
- To study the genetic basis of the structure and evolution of populations.
Methods for studying human genetics
Each major stage in the development of genetics was associated with the use of certain objects for genetic research. The theory of the gene and the main patterns of inheritance of traits were established in experiments with peas, the Drosophila fly was used to substantiate the chromosome theory of heredity, and viruses and bacteria were used to establish molecular genetics. Currently, the main object of genetic research is the human being.
Rice. one. Conventions adopted in the preparation of pedigrees:
1 - man; 2 - woman; 3 - gender not clear; 4 - the owner of the trait under study; 5 - heterozygous carrier of the studied recessive gene; 6 - marriage; 7 - marriage of a man with two women; 8 - related marriage; 9 - parents, children and the order of their birth; 10 - fraternal twins; 11 - identical twins.
For genetic research, a person is a very inconvenient object, since a person has: a large number of chromosomes, experimental crossing is impossible, puberty comes late, a small number of offspring in each family, it is impossible to equalize living conditions for offspring.
However, despite these difficulties, human genetics is well understood. This was made possible through the use of a variety of research methods.
genealogical method. The use of this method is possible only in the case when direct relatives are known - the ancestors of the owner of the hereditary trait (proband) on the maternal and paternal lines in a series of generations or the proband's descendants are also in several generations. When compiling pedigrees in genetics, a certain system of notation is used (Fig. 1). After compiling the pedigree, its analysis is carried out in order to establish the nature of the inheritance of the trait under study.
Thanks to the genealogical method, it has been established that in humans all types of inheritance of traits known to other organisms are observed, and the types of inheritance of some specific traits have been determined. So, according to the autosomal dominant type, polydactyly (an increased number of fingers) (Fig. 2), the ability to roll the tongue into a tube (Fig. 3), brachydactyly (short-fingered, due to the absence of two phalanges on the fingers), freckles, early baldness, fused fingers are inherited. , cleft lip, cleft palate, eye cataracts, bone fragility and many others. Albinism, red hair, susceptibility to polio, diabetes mellitus, congenital deafness, and other traits are inherited as autosomal recessive.
Rice. 2. Pedigree for polydactyly (autosomal dominant inheritance).
Rice. 3. Dominant trait - the ability to roll the tongue into a tube (1) and its recessive allele - the absence of this ability (2).
A number of traits are inherited sex-linked: X-linked inheritance - hemophilia, color blindness; Y-linked - hypertrichosis (increased hairiness of the auricle), membranes between the fingers. There are a number of genes located in homologous regions of the X and Y chromosomes, such as general color blindness.
The meaning of the method is not limited by establishing the type of trait inheritance. The use of the genealogical method showed that in a related marriage, compared with an unrelated one, the likelihood of deformities, stillbirths, and early mortality in the offspring increases significantly. In related marriages, recessive genes often go into a homozygous state, as a result, certain anomalies develop. A striking example of this is the inheritance of hemophilia in the royal houses of Europe.
twin method. Children born at the same time are called twins. They are monozygotic (identical) and dizygotic (fraternal) (Fig. 4).
Rice. 4. Formation of monozygotic (1) and dizygotic (2) twins.
In gametes and zygotes, only sex chromosomes are conditionally designated, as well as chromosomes carrying the dark hair gene (black) and the light hair gene (white).
Monozygotic twins develop from one zygote, which at the stage of crushing was divided into two (or more) parts. Therefore, such twins are genetically identical and always of the same sex. Monozygotic twins are characterized by a high degree of similarity (concordance) in many ways.
Dizygotic twins develop from eggs that are simultaneously ovulated and fertilized by different spermatozoa.
Therefore, they are hereditarily different and can be either the same or different sex. Unlike monozygotic twins, dizygotic twins are often characterized by discordance - dissimilarity in many ways. Data on the concordance of twins for some signs are given in the table.
Concordance of some human traits
As can be seen from the table, the degree of corondancy of monozygotic twins for all the above characteristics is significantly higher than that of dizygotic twins, but it is not absolute. As a rule, the discordance of identical twins occurs as a result of intrauterine development disorders of one of them or under the influence of the external environment, if it was different.
Thanks to the twin method, a person's hereditary predisposition to a number of diseases was clarified: schizophrenia, mental retardation, epilepsy, diabetes and others. Observations on identical twins provide material for elucidating the role of heredity and environment in the development of traits. And under external environment understand not only the physical factors of the environment, but also social conditions.
Cytogenetic method based on the study of human chromosomes in normal and pathological conditions. Normally, a human karyotype includes 46 chromosomes - 22 pairs of autosomes and two sex chromosomes. The use of this method made it possible to identify a group of diseases associated either with a change in the number of chromosomes or with changes in their structure. Such diseases are called chromosomal. These include: Klinefelter syndrome, Shereshevsky-Turner syndrome, trisomy X, Down syndrome, Patau syndrome, Edwards syndrome and others.
Patients with Klinefelter's syndrome(47, XXY) always men. They are characterized by underdevelopment of the sex glands, degeneration of the seminiferous tubules, often mental retardation, high growth (due to disproportionately long legs).
Shereshevsky-Turner syndrome(45, X0) is observed in women. It manifests itself in slowing down puberty, underdevelopment of the gonads, amenorrhea (absence of menstruation), infertility. Women with Shereshevsky-Turner syndrome are small in stature, the body is disproportionate - the upper body is more developed, the shoulders are wide, the pelvis is narrow - the lower limbs are shortened, the neck is short with folds, the "Mongoloid" incision of the eyes and a number of other signs.
Down syndrome- one of the most common chromosomal diseases. It develops as a result of trisomy on chromosome 21 (47, 21,21,21). The disease is easily diagnosed, as it has a number of characteristic features: shortened limbs, small skull, flat, wide nose bridge, narrow palpebral fissures with an oblique incision, the presence of a fold of the upper eyelid, mental retardation. Violations of the structure of internal organs are often observed.
Chromosomal diseases arise as a result of changes in the chromosomes themselves. Thus, a deletion of the 5th chromosome leads to the development of the "cat's cry" syndrome. In children with this syndrome, the structure of the larynx is disturbed, and in early childhood they have a kind of "meowing" voice timbre. In addition, there is a retardation of psychomotor development and dementia. Deletion of chromosome 21 leads to the appearance of one of the forms of leukemia.
Most often, chromosomal diseases are the result of mutations that have occurred in the germ cells of one of the parents.
Biochemical method allows you to detect metabolic disorders caused by changes in genes and, as a result, changes in the activity of various enzymes. Hereditary metabolic diseases are divided into diseases of carbohydrate metabolism (diabetes mellitus), metabolism of amino acids, lipids, minerals, etc.
Phenylketonuria refers to diseases of amino acid metabolism. The conversion of the essential amino acid phenylalanine to tyrosine is blocked, while phenylalanine is converted to phenylpyruvic acid, which is excreted in the urine. The disease leads to the rapid development of dementia in children. Early diagnosis and diet can stop the development of the disease.
human genetics is one of the fastest growing branches of science. She is theoretical basis medicine, reveals the biological basis of hereditary diseases. Knowing the genetic nature of diseases allows you to make an accurate diagnosis in time and carry out the necessary treatment.
Population genetics
A population is a collection of individuals of the same species long time living in a certain territory, freely interbreeding with each other, having a common origin, a certain genetic structure and, to one degree or another, isolated from other such populations of individuals of a given species. A population is not only a unit of a species, a form of its existence, but also a unit of evolution. Microevolutionary processes culminating in speciation are based on genetic transformations in populations.
The study of the genetic structure and dynamics of populations deals with a special branch of genetics - population genetics.
From a genetic point of view, a population is an open system, while a species is a closed system. In a general form, the process of speciation is reduced to the transformation of genetically open system in genetically closed.
Each population has a certain gene pool and genetic structure. The gene pool of a population is the totality of the genotypes of all individuals in a population. The genetic structure of a population is understood as the ratio of different genotypes and alleles in it.
One of the basic concepts of population genetics is the frequency of the genotype and the frequency of the allele. Under the frequency of the genotype (or allele) understand its share, related to the total number of genotypes (or alleles) in the population. The frequency of the genotype, or allele, is expressed either as a percentage or as a fraction of one (if the total number of genotypes or alleles of the population is taken as 100% or 1). So, if a gene has two allelic forms and the proportion of the recessive allele a is 3/4 (or 75%), then the proportion of the dominant allele A will be 1/4 (or 25%) total number alleles of a given gene in a population.
The method of reproduction has a great influence on the genetic structure of populations. For example, populations of self-pollinating and cross-pollinating plants differ significantly from each other.
The first study of the genetic structure of a population was undertaken by W. Johannsen in 1903. Populations of self-pollinating plants were chosen as objects of study. Investigating for several generations the mass of seeds in beans, he found that the population of self-pollinators consists of genotypically heterogeneous groups, the so-called pure lines, represented by homozygous individuals. Moreover, from generation to generation in such a population, an equal ratio of homozygous dominant and homozygous recessive genotypes is preserved. Their frequency in each generation increases, while the frequency of heterozygous genotypes will decrease. Thus, in populations of self-pollinating plants, the process of homozygotization, or decomposition into lines with different genotypes, is observed.
Most plants and animals in populations reproduce sexually through free interbreeding, which ensures the equiprobable occurrence of gametes. The equiprobable occurrence of gametes in free crossing is called panmixia, and such a population is called panmictic.
Hardy-Weinberg law
In 1908, the English mathematician G. Hardy and the German physician N. Weinberg independently formulated the law governing the distribution of homozygotes and heterozygotes in a panmictic population and expressed it in the form of an algebraic formula.
The frequency of occurrence of gametes with the dominant allele A is denoted by p, and the frequency of occurrence of gametes with the recessive allele a is denoted by q. The frequencies of these alleles in the population are expressed by the formula p + q = 1 (or 100%). Since the occurrence of gametes is equiprobable in a panmictic population, it is also possible to determine the frequencies of genotypes.
Hardy and Weinberg, summing up the data on the frequency of genotypes resulting from the equiprobable occurrence of gametes, derived the formula for the frequency of genotypes in a panmictic population:
p 2 + 2pq + q 2 = 1.
AA + 2Aa + aa = 1
Using these formulas, it is possible to calculate the frequencies of alleles and genotypes in a particular panmictic population. However, this law is subject to the following conditions: an unlimitedly large population, all individuals can freely interbreed with each other, all genotypes are equally viable, fertile and not subject to selection, forward and reverse mutations occur with the same frequency or so rarely that they can be neglected, there is no outflow or inflow of new genotypes into the population .
In real populations, these conditions cannot be met, so the law is valid only for an ideal population. Despite this, the Hardy-Weinberg law is the basis for the analysis of some genetic phenomena occurring in natural populations. For example, if it is known that phenylketonuria occurs at a frequency of 1:10,000 and is inherited in an autosomal recessive manner, the frequency of occurrence of heterozygotes and homozygotes for a dominant trait can be calculated. Patients with phenylketonuria have the genotype q2(aa) = 0.0001. Hence q = 0.01. p = 1 - 0.01 = 0.99. The frequency of occurrence of heterozygotes is 2pq, equal to 2 x 0.99 x 0.01 0.02, or about 2%. The frequency of occurrence of homozygotes for dominant and recessive traits: AA = p2 = 0.992 98%, aa = 0.01%.
Changes in the balance of genotypes and alleles in a panmictic population occur under the influence of constantly acting factors, which include: the mutation process, population waves, isolation, natural selection, gene drift, and others.
It is thanks to these phenomena that an elementary evolutionary phenomenon arises - a change in the genetic composition of a population, which is the initial stage of the process of speciation.
Literature.
1. Green N., Stout W., Taylor D. Biology. - M.: world, 1990. - V.1-3.
2. Goncharov O.V. Pimenov A.V. Biology. Part 1, Cytology, genetics, selection: A guide for applicants to universities. - Saratov: Boarding Lyceum at SSAU im. N.I. Vavilova, 2001.
3. Yarygin V.N. Biology for entering universities. - M.: Higher school, 2006.
population genetics
Population genetics studies the patterns of distribution of genes and genotypes in populations. The establishment of these patterns has both scientific and practical value in various branches of biology, such as ecology and ecological genetics, biogeography, breeding, etc. In medical practice, it is also often necessary to establish the quantitative ratios of 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 nonequilibrium. 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 (AA
) + 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 a special selection of pairs for any individual characteristics, contribute to:
Large population;
Lack of outflow or inflow of genes into it due to the migration of individuals;
No pressure of mutations that change the frequency of any allele of a given gene or lead to the emergence of new alleles;
The absence of natural selection, which may result in unequal viability or unequal fecundity of individuals with different genotypes.
The action of any of the above factors can cause a genetic imbalance 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, a number of calculations can be made. So, for example, based on the known frequencies of phenotypes, the genotypes of which are known, it is possible to calculate the allele frequencies of the corresponding genes. Knowing the frequency of the 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 establish whether a given population with a certain ratio of genotype frequencies is genetically balanced. Thus, the analysis of populations from the standpoint of the main provisions of the Hardy-Weinberg law makes it possible 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, which reflects 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, there are approximately 16% of people who have Rh-negative blood (a recessive trait). Set 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 Ah: 6 aa?
3. Gout occurs in 2% of people and is caused by an autosomal dominant gene. In women, the gout gene does not appear; in men, its penetrance is 20% (V.P. Efroimson, 1968). Determine the genetic structure of the population for 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 (NP 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 Englishmen.
Homework:
1. In one of the panmictic populations, the allele frequency b is 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 population of the island descended from several people 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. Determine the percentage of people with brown and blue eyes in the first generation for this island population. Will this ratio of individuals by phenotype and the gene pool of the population change after several generations, provided that the population is panmictic in nature, and there were practically no mutations in eye color.
4. In the US, about 30% of the population feel the bitter taste of phenylthiocarbamide (PTC), 70% of people do not distinguish its taste. The ability to taste FTK is determined by a recessive gene. a. Determine the allele frequency BUT and a and genotypes AA, Ah and aa in this population.
5. There are three genotypes for the albinism gene in the population - a in ratio: 9/16 AA, 6/16 aa and 1/16 aa. Is this population in a state of genetic equilibrium?
6. Congenital hip dislocation is dominantly inherited, with an average penetrance of 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 problem 4 - Buryats and British. Compare.
The structure of the gene pool in a panmictic stationary population is described by the basic law of population genetics - Hardy-Weinberg law , which states that in an ideal population there is a constant ratio of the relative frequencies of alleles and genotypes, which is described by the equation:
(p A + q a)2 = p2 AA + 2∙p∙q Aa + q2 aa = 1
If the relative allele frequencies p and q and the total population size Ntotal are known, then the expected or estimated absolute frequency (that is, the number of individuals) of each genotype can be calculated. To do this, each term of the equation must be multiplied by Ntotal:
p2 AA Ntot + 2 p q Aa Ntot + q2 aa Ntot = Ntot
In this equation:
p2 AA Ntot is the expected absolute frequency (number) of dominant AA homozygotes
2 p q Aa Ntot is the expected absolute frequency (number) of Aa heterozygotes
q2 aa Ntot is the expected absolute frequency (number) of recessive homozygotes aa
Operation of the Hardy-Weinberg law with incomplete dominance
Let us consider the operation of the Hardy-Weinberg law with incomplete dominance using the example of the inheritance of coat color in foxes. It is known that the main influence on coat color in foxes is exerted by gene A, which exists in the form of two main alleles: A and a. Each possible genotype corresponds to a specific phenotype:
AA - red, Aa - gray-haired, aa - black-brown (or silver)
For many years (in Russia, since the 18th century), records of the skins handed over have been kept at fur procurement stations. Let's open a book of account of delivered fox skins at one of the procurement centers of the North-East of Russia and choose arbitrarily 100 successive entries. Count the number of skins with various colors. Suppose that the following results are obtained: red (AA) - 81 skins, gray hair (Aa) - 18 skins, black-brown (aa) - 1 skin.
Let us calculate the number (absolute frequency) of dominant alleles A, given that each fox is a diploid organism. Red foxes carry 2 A alleles, there are 81 individuals, in total 2A × 81 = 162A. Sivodushki carry 1 allele A each, there are 18 individuals, in total 1A × 18 = 18A. The total sum of dominant alleles NA \u003d 162 + 18 \u003d 180. Similarly, we calculate the number of recessive alleles a: in black-brown foxes 2a × 1 \u003d 2a, in gray foxes 1a × 18 \u003d 18a, total amount recessive alleles Na = 2 + 18 = 20.
The total number of all alleles of gene A = NA + Na = 180 + 20 = 200. We analyzed 100 individuals, each with 2 alleles, the total sum of alleles is 2 × 100 = 200. The number of alleles counted for each geno/phenotype and the number alleles calculated from the total number of individuals is in any case equal to 200, which means that the calculations were carried out correctly.
Let's find the relative frequency (or share) of allele A in relation to the total number of alleles:
pA = NA: (NA + Na) = 180: 200 = 0.9
Similarly, we find the relative frequency (or proportion) of the allele a:
qa = Na: (NA + Na) = 20: 200 = 0.1
The sum of the relative frequencies of alleles in a population is described by the relation:
рА + qa = 0.9 + 0.1 = 1
The above equation is a quantitative description of the allele pool of a given population and reflects its structure. Since individuals are presented randomly in the accounting book, and the sample of 100 individuals is large enough, the results obtained can be generalized (extrapolated) to the entire population.
Consider the change in the structure of the allele pool (that is, the frequencies of all alleles) and the gene pool (that is, the frequencies of all genotypes) of a given population during alternation of generations. All males and females give alleles A and a in a ratio of 0.9A: 0.1a.
This is the difference between population genetics and classical genetics. When considering Mendel's laws, the ratio 1A: 1a was initially set, since the parents were always homozygous: AA and aa.
To find the relative frequencies of genotypes, we compose the Punnett lattice. At the same time, we take into account that the probability of meeting alleles in a zygote is equal to the product of the probabilities of finding each allele.
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Female gametes |
Male gametes |
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sivodushki |
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sivodushki |
black-brown |
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Let's find the final relative and absolute frequencies of genotypes and phenotypes:
Comparing the result obtained with the initial state of the population, we see that the structure of the allele pool and the gene pool have not changed. Thus, in the considered population of foxes, the Hardy-Weinberg law is fulfilled with ideal accuracy.
Operation of the Hardy-Weinberg law under complete dominance
Consider the operation of the Hardy-Weinberg law with complete dominance using the example of inheritance of coat color in cats.
It is known that the black coat color in cats is determined by the aa genotype. In this case, the black color can be either continuous or partial. The genotypes AA and Aa determine the rest of the variety of color types, but black is completely absent.
Suppose that in one of the urban populations of cats on about. Sakhalin out of 100 examined animals, 36 animals had full or partial black coloration.
Direct calculation of the population allele pool structure in this case is impossible due to complete dominance: AA homozygotes and Aa heterozygotes are phenotypically indistinguishable. According to the Hardy-Weinberg equation, the frequency of black cats is q2 aa. Then the allele frequencies can be calculated:
q2aa = 36/100 = 0.36; qa = 0.36 –1/2 =0.6; pA = 1 – 0.6 = 0.4
Thus, the structure of the allele pool of this population is described by the ratio: р А + q a = 0.4 + 0.6 = 1. The frequency of the recessive allele was higher than the frequency of the dominant one.
Let's calculate the frequencies of genotypes:
p2 AA = 0.42 = 0.16; 2 pq Aa = 2 ´ 0.4 ´ 0.6 = 0.48; q2aa = 0.62 = 0.36
However, it is impossible to verify the correctness of the calculations in this case, since the actual frequencies of dominant homozygotes and heterozygotes are unknown.
3. Fulfillment of the Hardy–Weinberg law in natural populations. Practical significance of the Hardy–Weinberg law
In some cases (for example, in the case of complete dominance), when describing the structure of the gene pool of natural populations, one has to assume that they have the features of ideal populations.
Comparative characteristics of ideal and natural populations
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Ideal Population |
natural populations |
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1. The population size is infinitely large, and random elimination (death) of some individuals does not affect the structure of the population |
1. The population consists of a finite number of individuals |
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2. There is no sexual differentiation, female and male gametes are equivalent (for example, with homothallic isogamy in algae) |
2. Exist different types sexual differentiation, various ways playback and various systems crossbreeding |
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3. The presence of panmixia - free crossing; the existence of a gamete reservoir; the equiprobability of the meeting of gametes and the formation of zygotes, regardless of the genotype and age of the parents |
3. There is selectivity in the formation of marriage pairs, in the meeting of gametes and the formation of zygotes |
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4. There are no mutations in the population |
4 Mutations Always Happen |
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5. There is no natural selection in the population |
5. There is always differential reproduction of genotypes, including differential survival and differential success in reproduction. |
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6. The population is isolated from other populations of this species |
6. There are migrations - gene flow |
In most populations studied, deviations from these conditions usually do not affect the implementation of the Hardy-Weinberg law. It means that:
– the number of natural populations is quite large;
- female and male gametes are equivalent; males and females equally pass on their alleles to their offspring);
- most genes do not affect the formation of marriage pairs;
- Mutations are rare.
- natural selection does not have a noticeable effect on the frequency of most alleles;
populations are sufficiently isolated from each other.
If the Hardy-Weinberg law is not fulfilled, then by deviations from the calculated values it is possible to establish the effect of limited numbers, the difference between females and males in the transfer of alleles to descendants, the absence of free crossing, the presence of mutations, the effect of natural selection, the presence of migration links between populations.
In real research, there are always deviations of empirical or actual absolute frequencies (Nfact or Nph) from the calculated or theoretical ones (Ncalc, Ntheor or Nt). Therefore, the question arises: are these deviations regular or random, in other words, reliable or unreliable? To answer this question, you need to know the actual frequencies of dominant homozygotes and heterozygotes. Therefore, in population genetic studies, the identification of heterozygotes plays a very important role.
Practical significance of the Hardy–Weinberg law
1. In healthcare - allows you to assess the population risk of genetically determined diseases, since each population has its own allele pool and, accordingly, different frequencies of unfavorable alleles. Knowing the frequency of birth of children with hereditary diseases, it is possible to calculate the structure of the allele pool. At the same time, knowing the frequencies of unfavorable alleles, one can predict the risk of having a sick child.
Example 1 Albinism is known to be an autosomal recessive disease. It has been established that in most European populations the birth rate of albino children is 1 in 20 thousand newborns. Consequently,
q2aa = 1/20000 = 0.00005; qa = 0.00005–1/2 = 0.007; pA = 1 - 0.007 = 0.993 ≈ 1
Since pA ≈ 1 for rare diseases, the frequency of heterozygous carriers can be calculated using the formula 2 q. In this population, the frequency of heterozygous carriers of the albinism allele is 2 q Aa = 2 ´ 0.007 = 0.014, or approximately every seventieth member of the population.
Example 2 Suppose that in one of the populations, 1% of the population has a recessive allele that does not occur in the homozygous state (it can be assumed that this allele is lethal in the homozygous state). Then 2 q Aa = 0.01, therefore, qa = 0.01:2 = 0.005. Knowing the frequency of the recessive allele, it is possible to establish the frequency of death of homozygous embryos: q2aa = 0.0052 = 0.000025 (25 per million, or 1 per 40 thousand).
2. In selection - allows you to identify the genetic potential of the source material (natural populations, as well as varieties and breeds of folk selection), since different varieties and breeds are characterized by their own allele pools, which can be calculated using the Hardy-Weinberg law. If a high frequency of the desired allele is found in the source material, then the desired result can be expected to be obtained quickly during selection. If the frequency of the required allele is low, then it is necessary either to look for another source material, or to introduce the required allele from other populations (cultivars and breeds).
3. In ecology - allows you to identify the influence of a wide variety of factors on populations. The fact is that, while remaining phenotypically homogeneous, a population can significantly change its genetic structure under the influence of ionizing radiation, electromagnetic fields, and other unfavorable factors. Based on the deviations of the actual genotype frequencies from the calculated values, one can establish the effect of environmental factors. (In this case, the principle of the only difference must be strictly observed. Let the influence of the content be studied heavy metals in the soil on the genetic structure of populations of a particular plant species. Then two populations living in extremely similar conditions should be compared. The only difference in living conditions should be the different content of a certain metal in the soil).
