Different ways of expressing frequency calculation,
Expressed allele frequency in fractions of a unit
Or a genotype in a population
1. In the study population 84 people 84: 420 = 0.2
out of 420 had a dominant trait.
2. In one of the populations, the occurrence is 15: 100 = 0.15
people with Rh-positive blood
(recessive trait) is 15%.
3. The incidence of patients suffering from 10 -4 = 1: 10000 = 0.0001
phenylketonuria, equal to 10 -4.
4. In European populations 0.02: 1000 = 0.00002
prevalence of achondroplasia
is 0.02 per 1000 newborns.
5. Alkaptonuria occurs with a frequency of 1: 100,000 = 0.00001
6. The studied trait is characterized by 0.09: 0.3 = 0.3
incomplete penetrance equal to
30%, and occurs in a population with
frequency 0.09.
Genotype frequency is the proportion of individuals in the population with a given genotype among all individuals in the population.
Allele frequency- the proportion of a particular allele among all alleles of the studied gene in the population.
Pair of alternative alleles Possible genotypes
traits gene
Albinism a (q) aa (q2)
Absence of albinism A (R) BUT _(p 2 + 2pq): AA (p 2) or Ah (2pq)
The frequency of homozygotes for a recessive trait in the population:
q 2 \u003d 1: 20,000 \u003d 0.00005
The frequency of the recessive allele in the population:
The frequency of the dominant allele in the population:
p \u003d 1 - q \u003d 1 - 0.07 \u003d 0.93
The frequency of heterozygotes in the population:
2pq \u003d 2 * 0.07 * 0.93 \u003d 0.1302 (13%)
Answer: The frequency of heterozygotes in the population is 13%.
1. One of the forms of fructosuria (weakening of the absorption of fructose and its increased content in the sword) manifests itself subclinically. Metabolic defects are reduced with the exclusion of fructose from food. The disease is inherited in an autosomal recessive manner and occurs with a frequency of 7:1000000 (VP Efroimson, 1968). Determine the frequency of heterozygotes in the population.
2. Congenital hip dislocation is dominantly inherited, the average penetrance of the gene is 25%. The disease occurs with a frequency of 0.06% (V.P. Efroimson, 1968). Determine the number of homozygous individuals for the recessive gene.
3. In one panmictic population, the allele frequency b is 0.1, and in the other, it is 0.9. Which population has more heterozygotes?
4. Tay-Sachs disease, caused by an autosomal recessive gene, is incurable; people suffering from this disease die in childhood. In one of the large populations, the birth rate of sick children is 1:5000. How many healthy people will live in a population of 400,000 people?
5. Cystic fibrosis of the pancreas (cystic fibrosis) affects individuals with a recessive homozygous phenotype and occurs in a population with a frequency of 1 in 2000. Calculate the frequency of the cystic fibrosis gene in a population of 1,000,000 people.
6. In the population, there are three genotypes for the eye color gene in the ratio: 9/16AA, 6/16Aa and 1/16aa. Brown eye color is an autosomal dominant trait with constant penetrance. Is this population in a state of genetic equilibrium?
7. Aniridia is inherited as a dominant autosomal trait and occurs with a frequency of 1:10,000 (V.P. Efroimson). Determine the genetic structure of the population.
8. Gengington's chorea is inherited as an autosomal dominant trait with a penetrance of 82.5%. There are 4 patients per 100 thousand people in the population. Determine the percentage of people carrying this disease in the population.
9. The population frequency of craniofacial dysostosis is 1:25,000. This trait is inherited in an autosomal dominant manner with a penetrance of 50%. How many people in the population will be carriers of this gene.
10. 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.
11. From the following diseases, indicate those whose population size can be calculated using the Hardy-Weinberg law: Patau's syndrome, Jacob's syndrome, phenylketonuria, polydactyly, sickle cell anemia, cat's cry syndrome, hypertrichosis, color blindness.
12. Tuberous sclerosis (epiloia) is inherited as an autosomal dominant trait. According to Penrose (1972), this disease occurs with a frequency of 1: 600,000. One of the symptoms of this disease, fundus phacoma (retinal tumors), is found in 80% of all homozygotes and in 20% of presumably heterozygous individuals who have no other clinical symptoms. . Determine the frequency of occurrence of the dominant gene (solution of the problem at the request of the student).
Belyaev's famous long-term experiment to breed domesticated (and also aggressive) foxes continues and gains momentum. Researchers are tapping into all the possibilities that today's research technologies provide. In 2018, several articles were published with the results of sequencing fox genomic DNA and RNA from their brain tissues. It was possible to identify many genes involved in changes and subjected to positive selection in different lines. Among them were genes related to hormonal regulation, differentiation of neural crest cells, the formation of intercellular contacts and synaptic signaling in the brain, as well as immunity genes.
The experiment on the domestication of foxes, which was started in 1959 by Dmitry Konstantinovich Belyaev and Lyudmila Nikolaevna Trut at the fur farm of the Novosibirsk Academic City of the Siberian Branch of the USSR Academy of Sciences, is widely known today not only among biologists, but also among the non-professional public. Many popular articles have been written about him and his intermediate results (see links at the end of the text).
The experiment began with the formation of a sample of silver-black foxes taken on a farm (the foxes were raised there for skins for fur coats, etc.). The idea was to replicate on foxes the same domestication process that wolves went through in the past to give rise to domestic dogs. To this end, among the offspring of silver-black foxes, they began to select fox cubs that demonstrated loyalty and friendliness towards humans.
For the selection, a methodology was selected that made it possible to determine the extent to which each fox is characterized by the manifestation of fear of a person or curiosity towards a person. This simple technique consists in analyzing the behavior of foxes (at the age of about 6 months) for the following situations:
1) the experimenter stands near the closed cage, not trying to attract the attention of the animal;
2) the experimenter opens the cell door, stands nearby, but does not initiate communication;
3) the experimenter stretches out his hand and tries to touch different parts of the animal's body;
4) the experimenter closes the cage door and stands quietly near the cage.
Test videos are then analyzed to evaluate the animal's behavior against a range of trait criteria (see R. M. Nelson et al., 2016. Genetics of Interactive Behavior in Silver Foxes ( Vulpes vulpes)).
From the least shy fox cubs, the next generation offspring were obtained, and then the testing and selection procedure was repeated again. Already in the fifth generation, individual individuals began to appear that showed an attraction to communicate with a person, comparable to that of dogs. Over time, there were more and more of these, the sign of "good nature" intensified. Now all the foxes of this line show such dog-like loyal and playful behavior (including even barking and "protection" of the owner) that some of them are sold as pets.
What was surprising about this experiment was not only the astonishingly rapid response to behavioral selection, but also the concomitant changes that began to appear in the phenotype of the foxes that were selected. These changes concerned signs that, at first glance, were not related to behavior in any way: white and red spots began to appear on the skin, foxes became more variable in terms of metric characteristics (shortening of the length of the muzzle and paws was observed in some animals), in some animals the tail began to twist, and disturbances appeared. bite, delayed hardening of the ear cartilage, changes in the color of the iris of the eyes. Moreover, foxes began to experience disruptions in the seasonality of reproductive behavior, an important trait for wild foxes that guarantees the appearance of puppies in the most favorable season of the year.
Taking into account the increase in variability in terms of phenotype traits under experimental conditions, Belyaev introduced the concept of “destabilizing selection” - as opposed to the more typical “stabilizing selection” for the natural evolutionary process (this term was introduced in the first half of the 20th century by I. I. Shmalgauzen), which, on the contrary makes the phenotype more stable. Belyaev admitted that the increase in variability observed in this experiment could also occur in the process of domestication of wolves, and that this could give a good start to the formation of all that variety of breeds among dogs, which cannot but be surprising, given that they all originate from from one common ancestor - the wolf, and this diversification of breeds began, apparently, no more than 15 thousand years ago.
It should be added that some time after the start of the experiment (namely, since 1970), a second line of foxes was added. On the contrary, they were selected for maximum aggressiveness and distrust of people. Despite the fact that the behavior of foxes in response to selection changed accordingly, some of the external phenotypic characters in this line began to converge with the corresponding characters in the line of good-natured foxes, although not so noticeably. At the same time, a control line of foxes is also conducted in parallel, in which no selection is made - and in this line no special deviations from the original phenotype of farm silver-black foxes are noted. Parallel management of three lines allows for comparative analyzes, crossbreeding experiments aimed at searching for genetic loci associated with changes. The population of each line is constantly maintained at a level of about 200 individuals. The organization of the experiment implies taking measures to avoid excessive inbreeding between animals (this could lead to distortion of the results due to increased effects of genetic drift and reduced offspring viability).
There are quite a few explanations for concomitant changes in traits that are not directly related to behavior. For example:
1) Effects of selection of linked polymorphisms (this mechanism is also called genetic hitchhiking, see Genetic hitchhiking).
2) Pleiotropic effect of selected genes. In particular, there are genes that regulate the state of chromatin (working or not working) using DNA methylation or histone modification - such genes can change the work of a large number of other genes. A similar effect is expected for genes involved in alternative splicing or intracellular signaling.
3) Adaptive compromises, which are expressed in the fact that direct selection in some traits indirectly creates a new selection vector for other traits that are functionally related to the first ones in ontogenesis.
4) The random appearance and persistence of new traits due to the increasing role of genetic drift (for example, due to the relatively small size of populations). However, this explanation hardly has much weight here - after all, no significant changes were observed in the control line.
5) An increase in the overall frequency of mutations, due, for example, to fixation under the influence of ongoing selection of a mutation that reduces the accuracy of DNA replication or repair, cannot be excluded.
Belyaev offered his original explanation for the observed phenomenon. His hypothesis was that intense selection for behavior perpetuated multiple mutations that change the balance of hormones in the body. It is widely known that hormones play a huge role in determining temperament and emotional state in both humans and animals. These mutations probably have a pleiotropic effect, affecting, among other things, the provision of morphogenesis processes in the course of individual development. For example, the thyroid hormone system has a wide range of influence. It is possible that these mutations disable the mechanisms that normally ensure the stability (canalization) of morphogenesis, leading to the effect of destabilizing the phenotype. This hypothesis is supported by the weak heritability of some of the listed phenotypic abnormalities. Puppies from one pair of foxes are obtained outwardly, and in character, very heterogeneous.
The hypothesis suggests that mutations fixed during selection affect those genes that control the maturation of neural crest cells in vertebrates (see: "The fourth germ layer" of vertebrates originated in lower chordates, "Elements", 02/04/2015). These cells, being differentiated, firstly, participate in the formation of the adrenal cortex, where hormones such as adrenaline are produced, which, in particular, affect the triggering and implementation of fear reactions in animals. Secondly, the neural crest also produces ear cartilage cells and some bones of the skull, including jaw cells, pigment cells in animal skin, iris cells, sensory cells of the inner ear. It is logical that the same mutations in the genes that control the development of neural crest cells can have a complex effect on all these traits. In this case, it is assumed that mutations lead to inhibition of the differentiation or migration of neural crest cells and their lack in those tissues where they should eventually work. Getting into different combinations when crossing selected foxes, these mutations give rise to the observed diversity of phenotypes.
The genetic basis for the observed behavioral changes in foxes has been confirmed through embryo transfer or pup swapping experiments between females of different strains ("evil" and "good") - such exchanges do not eliminate differences in behavior developed during selection (AV Kukekova et al., 2008. Measurement of segregating behaviors in experimental silver fox pedigrees). And in recent work, scientists have identified a large number of genetic loci associated with 98 behavioral traits and showed that these associations are complicated by epistatic influences that depend on the combinatorics of allelic variants (HM Rando et al., 2018. Construction of Red Fox Chromosomal Fragments from the Short-Read Genome Assembly).
There is something remarkable in this whole story: the experiment was started when the technology molecular research were still very primitive. It was impossible to make a full-fledged test of certain hypotheses. But the experiment, thanks to Lyudmila Nikolaevna Trut and other employees of the Institute of Cytology and Genetics of the Siberian Branch of the Russian Academy of Sciences, continued even after the death of Belyaev in 1985 and continues to this day. Throughout all these years, the experiment has borne fruit in the form of regular publications, which invariably attract the attention of not only Russian but also foreign specialists working in the field of genetics, developmental biology, and evolutionary biology. With the advent of new sequencing technologies, which are becoming more efficient and accessible every year, scientists have been able to investigate the molecular genetic basis of the observed phenotypic changes in animals. And this, of course, was done. The expansion of the study was also facilitated by the cooperation established since 2011 with foreign laboratories.
During 2018, as part of this study, three articles were published in leading scientific journals. The results presented in these works will be discussed below.
Tatiana Romanovskaya
3. POPULATION GENETICS.
HARDY-WEINBERG LAW
population- this is a set of individuals of the same species, occupying a certain area for a long time, freely interbreeding with each other and relatively isolated from other individuals of the species.
The main pattern that allows you to explore genetic structure big populations, was established in 1908 independently by the English mathematician G. Hardy and the German physician W. Weinberg.
Hardy-Weinberg law: in an ideal population, the ratio of frequencies of genes and genotypes–constant from generation to generation.
signs ideal population: population size big, exists panmixia(no restrictions to the free choice of a partner), no mutations on this basis, does not work natural selection, absent inflow And outflow of genes.
First position The Hardy-Weinberg law states: sum of allele frequencies one gene in a given population equal to one. This is written as follows:
p+ q = 1 ,
where p– dominant allele frequency BUT,q- recessive allele frequency but. Both quantities are usually expressed in fractions of a unit, less often in percentages (then p+q = 100 %).
Second position Hardy-Weinberg law: sum of genotype frequencies one gene per population equal to one. The formula for calculating genotype frequencies is as follows:
p 2 + 2 pq + q 2 = 1 ,
where p 2– the frequency of homozygous individuals for the dominant allele (genotype AA), 2pq- frequency of heterozygotes (genotype BUTa), q 2 – the frequency of homozygous individuals for the recessive allele (genotype aa).
The derivation of this formula is: equilibrium population female and male individuals have the same frequencies as the A allele ( p), and allele a ( q). As a result of crossing female gametes ♀( p+q) with male ♂( p+q) and genotype frequencies are determined: ( p+q) (p+q) = p 2 + 2pq +q 2 .
Third position law: in an equilibrium population allele frequencies And genotype frequencies are preserved in a number of generations.
TASKS
3.1. In a population obeying the Hardy-Weinberg law, allele frequencies BUT And but respectively, are 0.8 and 0.2. Determine the frequencies of homozygotes and heterozygotes for these genes in the first generation.
Solution. Genotype frequencies are calculated using the Hardy-Weinberg equation:
p 2 + 2pq +q 2 = 1,
where p is the frequency of the dominant gene, and q is the frequency of the recessive gene.
In this problem, the allele frequency BUT is 0.8, and the allele frequency but equals 0.2. Substituting these numerical values into the Hardy-Weinberg equation, we obtain the following expression:
0.82 + 2 × 0.8 × 0.2 + 0.22 = 1 or 0.64 + 0.32 + 0.04 = 1
It follows from the equation that 0.64 is the frequency of the dominant homozygous genotype ( AA), and 0.04 is the frequency of the recessive homozygous genotype ( aa). 0.32 – frequency of heterozygous genotype ( Ah).
3.2. In a fox population, there are 10 white individuals per 1000 red foxes. Determine the percentage of red homozygous, red heterozygous and white foxes in this population.
Solution.
According to the equation:
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Thus, there are 81% of red homozygous foxes in the population, 18% of red heterozygous foxes, and 1% of white foxes.
3.3. The brown-eyed allele is dominant over blue-eyed. In a population, both alleles occur with equal probability.
Father and mother are brown-eyed. What is the probability that their child will be blue-eyed?
Solution. If both alleles are equally common in a population, then it has 1/4 dominant homozygotes, 1/2 heterozygotes (both brown-eyed) and 1/4 recessive homozygotes (blue-eyed). Thus, if a person is brown-eyed, then two against one, that this is a heterozygote. So, the probability of being heterozygous is 2/3. The probability of passing the blue-eyed allele to offspring is 0 if the organism is homozygous, and 1/2 if it is heterozygous. The overall probability that a given brown-eyed parent will pass on the blue-eye allele to offspring is 2/3 x 1/2, i.e. 1/3. In order for a child to be blue-eyed, it must receive an allele for blue eyes from each parent. This will happen with a probability of 1/3x1/3=1/9.
3.4. Cystic fibrosis of the pancreas affects individuals with a recessive homozygous phenotype and occurs in the population with a frequency of 1 in 2000. Calculate the carrier frequency.
Solution. Carriers are heterozygotes. Genotype frequencies are calculated using the Hardy-Weinberg equation:
p 2 + 2pq +q 2 = 1,
where p 2 - frequency of dominant homozygous genotype, 2 pq is the frequency of the heterozygous genotype and q 2 - the frequency of the recessive homozygous genotype.
Cystic fibrosis of the pancreas affects individuals with a recessive homozygous phenotype; Consequently, q 2 = 1 in 2000, or 1/2000 = 0.0005. From here
Insofar as, p+q = 1, p= 1 – q = 1 – 0,0224 = 0,9776.
Thus, the frequency of the heterozygous phenotype (2 pq) \u003d 2 × (0.9776) × (0.0224) \u003d 0.044 \u003d 1 in 23 » 5%, i.e., carriers of the recessive gene for pancreatic cystic fibrosis make up about 5% of the population.
3.5. When examining the population of the city N (100,000 people), 5 albinos were found. Determine the frequency of occurrence of heterozygous carriers of the albinism gene.
Solution. Since albinos are recessive homozygotes ( aa), then, according to the Hardy-Weinberg law: 
recessive gene frequency, p+q = 1, from here, p= 1 – q; The frequency of heterozygotes is 2 pq. 
Therefore, every 70th inhabitant of city N is a heterozygous carrier of the albinism gene.
3.6. In a population of 5,000 people, 64% are able to roll their tongue into a tube (dominant gene R), and 36% do not have this ability (recessive gene r). Calculate Gene Frequencies R And r and genotypes RR, Rr And rr in the population.
Solution. The frequency of occurrence of persons with genotypes RR And Rr equal to 0.64, and homozygotes rr(q 2) = 0.36. Based on this, the gene frequency r is equal to . And since p+q= 1, then p = 1 – q= 0.4, i.e. allele frequency R(p) is 0.4. If p= 0.4, then p 2 = 0.16. This means that the frequency of occurrence of individuals with the genotype RR is 16%.
So, the frequency of occurrence of genes R And r 0.4 and 0.6. Genotype Frequencies RR, Rr And rr are, respectively, 0.16, 0.48 and 0.36.
3.7. There are three albinism genotypes in the population but in ratio: 9/16 AA, 6/16 Ah and 1/16 aa. Is this population in a state of genetic equilibrium?
Solution. It is known that the population consists of 9/16 AA, 6/16 Ah and 1/16 aa genotypes. Does such a ratio correspond to the equilibrium in the population, expressed by the Hardy-Weinberg formula?
After converting the numbers, it becomes clear that the population according to the given trait is in equilibrium: (3/4)2 AA: 2×3/4×1/4 Ah: (1/4)2 aa. From here
3.8. Diabetes mellitus occurs in the population with a frequency of 1 in 200. Calculate the frequency of carrier heterozygotes.
3.9. Sickle cell anemia occurs in the human population with a frequency of 1: 700. Calculate the frequency of heterozygotes.
3.10. Share of individuals aa in a large population is 0.49. What fraction of the population is heterozygous for the gene BUT?
3.11. In the Drosophila population, the allele frequency b(black body color) is 0.1. Set the frequency of gray and black flies in the population and the number of homozygous and heterozygous individuals.
3.12. Does the following ratio of homozygotes and heterozygotes in the population correspond to the Hardy-Weinberg formula: 4096 AA : 4608 Ah : 1296 aa?
3.13. In one population, 70% of people are able to taste the bitter taste of phenylthiourea (PTU), and 30% do not distinguish its taste. The ability to taste FTM is determined by a dominant gene T. Determine the allele frequency T And t and genotypes TT, Tt And tt in this population.
3.14. Share of individuals AA in a large panmictic population is 0.09. What fraction of the population is heterozygous for the gene BUT?
3.15. Albinism in rye is inherited as an autosomal recessive trait. There are 84,000 plants in the surveyed area. Among them, 210 albinos were found.
Determine the frequency of the albinism gene in rye.
3.16.* In shorthorn cattle, the red color does not completely dominate the white color. Hybrids from crossing red with white have a roan suit. There are 4,169 reds, 3,780 roans and 756 whites registered in the shorthorn area.
Determine the frequency of genes for red and white color of cattle in the area.
3.17.* A single grain of wheat, heterozygous for a certain gene, accidentally fell on a deserted island BUT. It sprang up and gave rise to a series of generations that reproduced by self-pollination. What will be the proportion of heterozygous plants among representatives of the second, third, fourth, ..., nth generations, if the trait controlled by the gene under consideration does not affect the survival of plants and their ability to produce offspring under these conditions?
3.18.* Snyder examined 3643 people for the ability to taste phenylthiourea and found that 70.2% of them are "tasting" and 29.8% are "not tasting" this taste.
(a) What is the proportion of “non-sentient” children in “sentient” to “sentient” marriages?
b) What is the proportion of "not tasting" children in marriages "tasting" and "not tasting" phenylthiourea?
Lesson 1. Microevolution. Hardy–Weinberg law
I. Checking homework on the topic “Population structure of the species. Geographical variability within the range of the species"
Card work
1. On both sides Ural Range south of Yekaterinburg, hare hares live in the steppes. Although their habitats are separated by mountain forests, hares are outwardly indistinguishable, and when they meet (south of the Urals) they give fertile offspring. Determine what forms of existence of the species make up these hares?
2. The following types of fish live in two lakes that do not communicate with each other: crucian carp, roach, bream, ide, pike perch. Determine how many populations of fish live in the first lake? How many fish populations live in the second lake? How many species of fish live in two lakes? How many fish populations live in two lakes?
3. The unit of evolution is the population, not the individual. But the reason for the variability of the gene pool of a population is considered to be a change in the genotypes of individuals. Explain why.
1) the population structure of the species;
2) geographical variability within the range of the species and its causes; characteristics of the morphological criterion of the species;
3) clines and subspecies;
4) hybrid zones and geographic isolates.
II. Learning new material
1. The concept of micro- and macroevolution.
Evolution that goes below the level of the species (subspecies, populations) and ends with speciation is called microevolution (the evolution of populations under the influence of natural selection).
Microevolutionary phenomena and processes often take place in a relatively short period of time and therefore are available for direct observation.
Evolution at the level of systematic units above the species, proceeding for millions of years and inaccessible to direct study, is called macroevolution.
We do not directly see the processes of macroevolution, but we can observe their results: modern organisms and fossil remains of previously living creatures.
The terms "microevolution" and "macroevolution" were introduced into biology by the Russian geneticist Yu.A. Filippchenko in 1927
These two processes are one, macroevolution is a continuation of microevolution. By examining the driving forces of microevolution, one can explain 1 and macroevolution. At the lessons we study microevolutionary processes.
2. Introduction to population genetics.
At the junction of classical Darwinism and genetics, a whole trend was born - population genetics, which studies evolutionary processes in populations.
The fact is that in the 20s. 20th century between genetics and evolutionary theory Darwin disagreed. Opinions have been expressed that genetics has canceled the supposedly outdated Darwinism.
Our domestic scientists were the first to understand the significance of relatively small associations of individuals into which a population of any kind breaks up - populations.
In 1926 S.S. Chetverikov (1880–1959) wrote his main work “On Some Moments of the Evolutionary Process from the Point of View modern genetics". Chetverikov proved that the expansion of knowledge about the nature of heredity, on the contrary, strengthened and developed Darwinism.
The publication of his work gave rise to a synthetic theory of evolution that combined genetics and the teachings of Darwin - evolutionary genetics.
Population genetics is primarily concerned with elucidating the mechanisms of microevolution.
3. Population and gene pool.
The main principle that unites individuals into one population is their ability to freely interbreed with each other - panmixia (from the Greek. pan- all and mixis- mixing). The possibility of interbreeding, the availability of a partner within a population must necessarily be higher than the possibility of meeting two individuals of the opposite sex from different populations.
Panmixia provides the possibility of a constant exchange of hereditary material. As a result, a single gene pool of the population is formed.
Gene pool (from Greek. genos- birth and lat. fund- base, stock) - a set of genes that individuals of a given population have (the term was introduced into biology in 1928 by A.S. Serebrovsky).
4. Frequency (concentration) of genes and genotypes.
The most important feature of a single gene pool is its internal heterogeneity. The gene pool of a population can be described either by gene frequencies or by genotype frequencies.
Suppose we are interested in some gene localized in the autosome, for example, gene A, which has two alleles - BUT And but. Suppose there are N individuals in the population that differ in this pair of alleles. There are three possible genotypes in a population - AA; Ah; aa. Let us introduce the following notation:
D is the number of homozygotes for the dominant allele ( AA);
P is the number of homozygotes for the recessive allele ( aa);
G is the number of heterozygotes ( Ah).
Total number of alleles BUT can be written as 2D + G, then the frequency of occurrence of the dominant allele BUT(denoted by the Latin letter "p") will be equal to:
p \u003d (2D + G) / N,
where N is the number of individuals.
The frequency of occurrence of the recessive allele is indicated by the letter "g". It can be determined based on the fact that the sum of allele frequencies is equal to one. Hence the frequency of the recessive allele:
g \u003d 1 - p.
Thus, we got acquainted with the formulas by which it is possible to calculate the frequencies of occurrence of alleles in the gene pool of a population. What are the frequencies of the three possible genotypes? This question is answered by the Hardy-Weinberg law.
5. The Hardy–Weinberg law on the equilibrium state of populations.
The law on the frequencies of occurrence of genotypes in the gene pool of a population was formulated independently by the English mathematician J. Hardy and the German geneticist G. Weinberg.
Suppose males and females in a population interbreed randomly.
The formation of individuals with genotypes AA due to the probability of obtaining an allele BUT from mother and allele BUT from the father, i.e.:
p x p \u003d p 2.
Similarly, the emergence of the genotype aa, whose frequency of occurrence is g 2 .
Genotype Ah can occur in two ways: the body receives the allele BUT from mother, allele but from the father or, conversely, the probability of both events is p x g, and the total probability of the occurrence of the genotype Ah is equal to 2рg.
Thus, the frequency of the three possible genotypes can be expressed by the equation:
(p + g) 2 \u003d p 2 + 2pg + g 2 \u003d 1,
where p is the allele frequency BUT; g - allele frequency but; g 2 - the frequency of occurrence of the genotype aa; p 2 - the frequency of occurrence of the genotype AA; pg - frequency of occurrence of the genotype Ah.
Thus, if the crossing is random, then the frequencies of the genotypes are associated with the frequencies of the alleles simple equation sum square. The above formula is called the Hardy–Weinberg equation.
Suppose that in the population p = 0.7 BUT, g = 0.3 but, then the frequencies of occurrence of genotypes will be equal to (0.7 + 0.3) 2 = 0.49 + 0.42 + 0.09 = 1.
Interestingly, in the next generation of gametes with the allele BUT will re-occur with a frequency of 0.7 (0.49 of AA+ 0.21 off Ah), but with the allele but- with a frequency of 0.3 (0.09 from aa+ 0.21 off Ah), i.e. the frequencies of genes and genotypes remain unchanged from generation to generation - this is the Hardy-Weinberg law.
6. Conditions for the fulfillment of the Hardy–Weinberg law.
The Hardy-Weinberg law is fully applicable to the “ideal population”, which is characterized by the following features:
- endlessly big sizes;
– unlimited panmixia;
– no mutations;
– absence of immigration of individuals from neighboring populations;
- Lack of natural selection.
None of these conditions is observed in natural populations, and therefore the Hardy–Weinberg law is also conditional. Nevertheless, it really reflects trends in the nature of the frequency distribution of certain alleles and genotypes.
III. Consolidation of knowledge - solving problems using the Hardy-Weinberg law
Solution
1) g 2 \u003d 1/400 (frequency of the homozygous genotype for the recessive allele);
2) recessive allele frequency but will be equal to:
g =, i.e. 1 part (one allele) out of 20;
3) the frequency of the dominant allele will be equal to: 20 - 1 = 19;
4) population composition: (р + g) 2 = р 2 + 2рg + g 2 .
(19 + 1) 2 = 19 2 AA+ 2 x 19 Ah+ 1 2 aa= 361 AA+ 38 Ah+ 1 aa.
Answer: 361 AA: 38 Ah: 1 aa.
2. In the population of outbred dogs of the city of Vladivostok, 245 short-legged animals and 24 with legs of normal length were found. Short-leggedness in dogs is a dominant trait ( BUT), normal leg length - recessive ( but). Determine the allele frequency BUT And but and genotypes AA, Ah And aa in this population.
Solution
1) The total number of dogs is 245 + 24 = 269.
The genotype of dogs with legs of normal length is aa, allele frequency but(in fractions of a unit) is denoted by the letter "g". Then the frequency of the genotype aa= g 2 .
g 2 \u003d 24/269 \u003d 0.09 2
Recessive allele frequency: 
BUT, i.e. R:
p \u003d 1 - g \u003d 1 - 0.3 \u003d 0.7
AA, i.e. p 2:
p 2 \u003d 0.72 \u003d 0.49
4) We determine the frequency of heterozygotes, that is, 2рg:
2рg \u003d 2 x 0.7 x 0.3 \u003d 0.42
5) Calculate the number of dogs of different genotypes:
determine the sum of the frequencies of dominant homozygotes and heterozygotes:
0,49 AA+ 0,42 Ah= 0,91;
AA:
245 individuals - 0.91
x individuals - 0.49,
x= 132 individuals;
determine the number of dogs with the genotype Ah:
245 individuals - 0.91
x individuals - 0.42,
x= 113 individuals
Answer: 132 AA: 113 Ah: 24 aa
3. In European populations, out of 20,000 people, one is an albino. Determine the genotypic structure of the population.
Solution
1) Find the frequency of recessive homozygotes (g 2) in fractions of a unit:
g 2 \u003d 1/20,000 \u003d 0.00005,
then the frequency of the recessive allele but will be:
2) Determine the frequency of the dominant allele BUT:
p \u003d 1 - 0.007 \u003d 0.993
3) Determine the frequency of the genotype AA, i.e. p 2:
p 2 \u003d 0.9932 \u003d 0.986
4) Determine the frequency of the genotype Ah, that is, 2рg:
2рg \u003d 2 x 0.993 x 0.007 \u003d 0.014
5) We paint the genotypic structure of the population of Europeans:
0,986 AA: 0,014 Ah: 0,00005 aa, or per 20,000 people:
19 720 AA: 280 Ah: 1 aa
Answer: 0,986 AA: 0,014 Ah: 0,00005 aa, or 19 720 AA: 280 Ah: 1 aa 3
IV. Homework
Study the paragraph of the textbook (introduction to population genetics, Hardy-Weinberg law) and the notes made in the class.
Solve the problem: “In a sample of 84 thousand rye plants, 210 plants turned out to be albinos, since they have recessive genes rr are in the homozygous state. Determine Allele Frequencies R And r and the frequency of heterozygous plants bearing the trait of albinism."
Lesson 2. Elementary evolutionary factors. Hereditary variability and its role in evolution
I. Checking homework
Card work
1. In 1908, the English mathematician J. Hardy and the German geneticist G. Weinberg independently formulated a law, the essence of which is that from generation to generation with free crossing, the relative frequencies of genes in populations do not change. Why is the gene pool of natural populations subject to change?
2.
According to the Hardy–Weinberg law, in a large freely interbreeding population, the genotype frequencies AA,
Ah And aa p 2 , 2pg and g 2 are equal, respectively, where p and g are allele frequencies BUT And but, and p + g = 1.
Due to what phenomena can the frequency of heterozygotes in a real population exceed the theoretical value?
Oral knowledge test on:
1) population and gene pool;
2) the frequency of occurrence of genes in the gene pool of the population;
3) the relationship between the frequencies of genes and genotypes in the gene pool of a population. Hardy-Weinberg law.
Checking the solution of the problem given at home.
Solution
1) Determine the frequency of occurrence of the genotype rr:
g 2 \u003d 210/84,000 \u003d 0.0025.
p \u003d 1 - g \u003d 1 - 0.05 \u003d 0.95
4) Determine the frequency of occurrence of heterozygotes:
2рg \u003d 2 x 0.05 x 0.95 \u003d 0.095
Answer: R( R) = 0.95; g( r) = 0.05; frequency of occurrence of heterozygotes 0.095 (homozygotes RR: (0.95)2 = 0.9025; homozygotes rr– 0,0025)
Independent work (solving problems on the Hardy–Weinberg law)
1st option
1. Determine the probable number of heterozygotes in a group of rabbits, numbering 500 animals, if about 4% of albinos are split out in it (albinism is inherited as a recessive autosomal trait).
Solution
1) Determine the frequency of occurrence of homozygotes for the recessive allele:
g 2 \u003d 4/100 \u003d 0.04
2) Determine the frequency of occurrence of the recessive allele: 
3) Determine the frequency of occurrence of the dominant allele:
p \u003d 1 - 0.2 \u003d 0.8
4) Determine the frequency of occurrence of the heterozygous genotype:
2рg \u003d 2 x 0.2 x 0.8 \u003d 0.32, or 32%;
5) Determine the probable number of heterozygotes:
500 individuals - 100%
x individuals - 32%;
x= 160 individuals
Answer: 160 individuals - with a heterozygous genotype.
2. Calculate allele frequency M And m in the corresponding sample from the population: 180 MM and 20 mm.
Solution
1) Determine the frequency of occurrence of the allele M:
p \u003d (2D + G) / N \u003d (180 + 0) / 200 \u003d 0.9
2) Determine the frequency of occurrence of the allele m:
g \u003d 1 - p \u003d 1 - 0.9 \u003d 0.1.
Answer: R ( M) = 0.9; g( m) = 0,1
2nd option
1. Plants producing yellow and green beans have been observed in the garden pea population. Yellow color is dominant. The proportion of plants producing green beans is 81%. What is the frequency of homo- and heterozygous plants in this population?
Solution
1) Determine the frequency of occurrence of the recessive allele. It follows from the condition of the problem that gg 2 = 0.81, then:
2) Determine the frequency of occurrence of the dominant allele:
p \u003d 1 - g \u003d 1 - 0.9 \u003d 0.1
3) Determine the genotypic structure of the pea plant population:
(0,1 + 0,9)2 = 0,01 AA+ 0,18 Ah+ 0,81 aa
Answer: 1% aa: 18% Ah: 81% aa
2. Calculate allele frequency BUT And but in a population with a ratio of genotypes: 64 AA: 32 Ah: 4 aa.
Solution
1) From the condition of the problem, we can conclude about the genotypic structure of the population:
0,64 AA: 0,32 Ah: 0,04 aa, we determine the frequency of occurrence of the dominant allele:
p 2 = 0.64, then p == 0.8.
We determine the frequency of occurrence of the recessive allele:
g 2 = 0.04, then g = = 0.2
Answer: p = 0.8; g = 0.2
II. Learning new material
1. The concept of factors of evolution.
An ideal population, in which the Hardy–Weinberg law operates, is in a state of equilibrium. But in natural populations, the concentration of genes and genotypes is constantly changing under the influence of environmental factors, mutations, etc. As a result, populations change, i.e. evolve. Factors that cause the evolution of populations are called evolutionary. These include: the mutation process, population waves, isolation, the struggle for existence, natural selection, etc.
2. The role of mutations in evolution.
Evolution is manifested in a change in the characteristics and properties of individual species. These transformations of organisms must be based on some hereditary changes. As elementary hereditary changes, only mutations are known.
There are no signs and properties of an organism that would not be affected to some extent by mutations.
It is known that up to 1/4 of all Drosophila eggs laid in each generation contain certain mutations. And in snapdragons, 25% of all seeds carry mutant traits.
Of course, a few mutations that appear will not yet change the population. But, arising continuously, they will accumulate and spread in the gene pool. The rate at which mutations spread in a population depends on several factors:
– degree of dominance;
– impact on the viability of individuals;
– population size;
- the degree of isolation of the population.
If mutations are beneficial, then they are picked up by natural selection, and after 1-2 generations, the number of individuals possessing them will increase significantly. Therefore, mutations are the elementary evolutionary material with which natural selection "works".
The study of a large number of natural populations confirmed the conclusion of S.S. Chetverikov about their saturation with various mutations. In different populations, the frequencies of mutant genes are different. There are practically no two populations in which mutations would occur with the same frequency and would affect the same traits. Chetverikov wrote: “Populations are like a sponge, they absorb recessive mutations, while remaining phenotypically homogeneous. The existence of such a hidden reserve hereditary variability creates an opportunity for evolutionary transformations of populations under the influence of natural selection.
To be continued
1 The expression “you can try to explain” seems to be more correct. The categoricalness of statements in this very complex issue can cause students to protest internally and, as a result, push them to the other extreme. - Approx. ed.
3 In total, we have not 20,000, but 20,001 people: such an error is the result of rounding the results when the initial values differ by several orders of magnitude. But getting a more precise answer: AA 19,718, 281 Ah and 1 aa would require too laborious calculations.
For psychogenetics, the concepts and theories of population genetics are extremely important because individuals who carry out the transfer of genetic material from generation to generation are not isolated individuals; they reflect the features of the genetic structure of the population to which they belong.
Consider the following example. The already mentioned phenolketonuria (PKU) is an inborn error of metabolism that causes postnatal brain damage, leading, in the absence of necessary
* panmixia- random, independent of the genotype and phenotype of individuals, the formation of parental pairs (random crossing).
** Insulation- the existence of any barriers that violate panmixia; isolation is the main boundary separating neighboring populations in any group of organisms.
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dim intervention, to severe forms of mental retardation. The incidence of this disease varies from 1:2600 in Turkey to 1:11 9000 in Japan, indicating different frequencies of mutant alleles in different populations.
In 1985, a gene whose mutations cause the development of PKU (gene phe), was mapped; it turned out that it is localized on the short arm of the 12th chromosome. Studying the structure of this gene in healthy and PKU patients, scientists found 31 mutations in different parts of the gene Phe. The fact that the frequencies of occurrence and the nature of these mutations in different populations are different allows us to formulate hypotheses that most of them occurred independently of each other, at different points in time and, most likely, after the division of mankind into populations.
The results of population studies are of great practical importance. In Italy, for example, the frequency of occurrence of certain mutant alleles in the heterozygous state is quite high, so prenatal diagnosis of PKU is carried out there for timely medical intervention. In Asian populations, the frequency of occurrence of mutant alleles is 10–20 times lower than in European populations; therefore, prenatal screening is not a top priority in the countries of this region.
Thus, the genetic structure of populations is one of the most important factors determining the characteristics of the inheritance of various traits. The PKU example (as well as many other facts) shows that the specificity of the studied population should be taken into account when studying the mechanisms of inheritance of any human trait.
Human populations are like living organisms that subtly react to all changes in their internal state and are under the constant influence of external factors. We will begin our brief introduction to the basic concepts of population genetics with a certain simplification: we will, as it were, turn off for a while all the numerous external and internal factors that affect natural populations, and imagine a population at rest. Then we will "turn on" one factor after another, adding them to complex system, which determines the state of natural populations, and consider the nature of their specific influences. This will allow us to get an idea of the multidimensional reality of the existence of human populations.
RESTING POPULATIONS (HARDY-WEINBERG LAW)
At first glance, dominant inheritance, when two alleles meet, one suppresses the action of the other, should lead to the fact that the frequency of occurrence of dominant genes from generation to generation will increase. However, this does not happen; the observed pattern is explained by the Hardy-Weinberg law.
Let us imagine that we are playing a computer game, the program of which is written in such a way that there is no
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there is no element of chance, i.e. events develop in full accordance with the program. The point of the game is to create a population of diploid (that is, containing a double set of chromosomes) organisms, set the law of their crossing and see what happens to this population after several generations. Let us also imagine that the organisms we create are genetically extremely simple: each of them has only one gene (the gene BUT). To begin with, we determine that there are only two alternative forms of the gene in the population BUT- alleles a and a. Since we are dealing with diploid organisms, the genetic diversity of a population can be described by listing the following genotypes: ah, ah and Art. Let's determine the frequency of occurrence but how R, how about the frequency of occurrence q, and R And q are the same for both sexes. Now let's determine the nature of the crossing of the organisms we have created: we will establish that the probability of the formation of a marriage pair between individuals does not depend on their genetic structure, i.e. the frequency of crossing certain genes is proportional to the proportion in which these genotypes are represented in the population. Such a crossing is called random crossing. Let's start playing and recalculate the frequency of occurrence of the original genotypes (ah, ah and aa) in the daughter population. We will find that
where the letters in the bottom line, denoting alleles and genotypes, correspond to their frequencies located in the top line. Now let's play the game 10 times in a row and recalculate the frequency of occurrence of genotypes in the 10th generation. The result obtained will be confirmed: the frequencies of occurrence will be the same as in formula 5.1.
Let's repeat the game from the beginning, only now we define the conditions differently, namely: R And q are not equal in males and females. Having determined the frequencies of occurrence of the initial genotypes in the first generation of offspring, we will find that the found frequencies do not correspond to formula 5.1. Let's create another generation, recalculate the genotypes again and find that in the second generation the frequencies of occurrence of the original genotypes again correspond to this formula.
Let's repeat the game again, but now instead of two alternative
gene forms BUT set three - in, ai but, whose occurrence frequencies are, respectively, p, q And z and are approximately the same for males and females. Recalculating the frequency of occurrence of the original genotypes in the second generation, we find that
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Let's create a few more generations and recalculate again - the frequencies of occurrence of the original genotypes will not change.
So, let's sum up. Based on our research on a computer simulation game, we found that:
About the expected frequencies of the original genotypes in derived generations are described by squaring a polynomial that is the sum of allele frequencies in the population (in other words, genotype frequencies are related to gene frequencies by quadratic ratios);
□ genotype frequencies remain the same from generation to generation
generation;
□ in case of random crossing, the expected frequencies of the original
genotypes are achieved in one generation if allele frequencies
the lei of the two sexes are the same, and in two generations, if two
sexes in the first generation of frequency are different.
The dependencies reproduced by us were first described at the beginning of this century (1908) independently by the English mathematician G. Hardy and the German physician W. Weinberg. In their honor, this pattern was named the Hardy-Weinberg law (sometimes other terms are used: the Hardy-Weinberg equilibrium, the Hardy-Weinberg ratio).
This law describes the relationship between the frequencies of occurrence of alleles in the original population and the frequency of genotypes that include these alleles in the daughter population. It is one of the cornerstone principles of population genetics and is applied in the study of natural populations. If in a natural population the observed frequencies of occurrence of certain genes correspond to the frequencies theoretically expected on the basis of the Hardy-Weinberg law, then such a population is said to be in a state of Hardy-Weinberg equilibrium.
The Hardy-Weinberg law makes it possible to calculate the frequencies of genes and genotypes in situations where not all genotypes can be identified phenotypically as a result of the dominance of some alleles. As an example, let us again turn to the FKU. Let us assume that the frequency of occurrence of the PKU gene (ie, the frequency of occurrence of the mutant allele) in a certain population is q = 0.006. It follows from this that the frequency of occurrence of the normal allele is equal to p = 1 - 0.006 = 0.994. The frequencies of the genotypes of people who do not suffer from mental retardation as a result of PKU are p 2 = 0.994 2 = 0.988 for the genotype aa And 2pq=2-0.994-0.006 = 0.012 for genotype aa.
Now imagine that some dictator, who does not know the laws of population genetics, but is obsessed with the ideas of eugenics, decides to rid his people of mentally retarded individuals. Due to the fact that heterozygotes are phenotypically indistinguishable from homozygotes, the dictator's program should be based solely on the destruction or sterilization of recessive homozygotes.
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Zygote. However, as we have already determined, most mutant alleles are found not in homozygotes (qf 2 = 0.000036), but in heterozygotes (2pq= 0.012). Consequently, even the total sterilization of the mentally retarded will only lead to a slight decrease in the frequency of the mutant allele in the population: in the daughter generation, the frequency of mental retardation will be approximately the same as in the original generation. In order to significantly reduce the frequency of occurrence of the mutant allele, the dictator and his descendants would have to carry out this kind of selection or sterilization for many generations.
As already noted, the Hardy-Weinberg law has two components, one of which tells what happens in the population with the frequencies of alleles, and the other - with the frequencies of genotypes containing these genes in the transition from generation to generation. Recall that the Hardy-Weinberg equation does not take into account the impact of many internal and external factors that determine the state of the population at each step of its evolutionary development. The Hardy-Weinberg law is fulfilled when in the population: 1) there is no mutation process; 2) there is no selection pressure; 3) the population is infinitely large; 4) the population is isolated from other populations and panmixia* takes place in it. Usually, the processes that determine the state of a population are divided into two broad categories - those that affect the genetic profile of the population by changing the frequencies of genes in it (natural selection, mutation, random gene drift, migration), and those that affect the genetic profile of the population by changes in the frequency of occurrence of certain genotypes in it (assortative selection of married couples and inbreeding). What happens to the frequencies of alleles and genotypes under the condition of activation of processes that act as "Natural Violators" of the dormancy of populations?
EVOLVING POPULATIONS
Any description of natural phenomena - verbal, graphic or mathematical - is always a simplification. Sometimes such a description concentrates mainly on one, for some reason the most important, aspect of the phenomenon under consideration. Thus, we consider it convenient and graphically expressive to depict atoms in the form of miniature planetary systems, and DNA in the form
* There are some other conditions under which this law adequately describes the state of the population. They have been analyzed by F. Vogel and A. Motulski. For psychogenetic studies, the non-observance of condition 4 is especially important: the phenomenon of assortativeness is well known, i.e. non-random selection of married couples on psychological grounds; for example, the correlation between spouses on IQ scores reaches 0.3-0.4. In other words, there is no panmixia in this case. Similarly, the intensive migration of the population in our time removes the condition of isolation of populations.
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twisted stairs. There are also many similar simplifying models in population genetics. For example, genetic changes at the population level are usually analyzed within the framework of two main mathematical approaches - deterministic And stochastic. According to deterministic models, changes in allele frequencies in populations during the transition from generation to generation occur according to a certain pattern and can be predicted if: 1) the size of the population is unlimited; 2) the environment is unchanged in time or environmental changes occur according to certain laws. The existence of human populations does not fit within the framework of these conditions, so the deterministic model in its extreme form is an abstraction. In reality, allele frequencies in populations also change under the influence of random processes.
The study of random processes requires the use of another mathematical approach - stochastic. According to stochastic model, the change in allele frequencies in populations occurs according to probabilistic laws, i.e. even if the initial conditions of the progenitor population are known, the allele frequencies in the daughter population definitely cannot be predicted. can only be predicted probabilities occurrence of certain alleles at a certain frequency.
Obviously, stochastic models are closer to reality and, from this point of view, are more adequate. However, mathematical operations are much easier to perform within the framework of deterministic models, moreover, in certain situations they still represent a fairly accurate approximation to real processes. Therefore, the population theory of natural selection, which we will consider below, is presented in the framework of a deterministic model.
2. FACTORS AFFECTING IA CHANGES IN ALLELE FREQUENCIES IN A POPULATION
As already mentioned, the Hardy-Weinberg law describes populations at rest. In this sense, it is similar to Newton's first law in mechanics, according to which any body retains a state of rest or uniform rectilinear motion until the forces acting on it change this state.
The Hardy-Weinberg law states that in the absence of perturbing processes, the frequencies of genes in a population do not change. However, in real life, genes are constantly under the influence of processes that change their frequencies. Without such processes, evolution simply would not occur. It is in this sense that the Hardy-Weinberg law is similar to Newton's first law - it sets the reference point against which the changes caused by evolutionary processes are analyzed. The latter include mutations, migrations and genetic drift.
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Mutations are the main source of genetic variation, but their frequency is extremely low. Mutation is an extremely slow process, so if mutation occurs on its own, and not in the context of the actions of others population factors(for example, genetic drift or migration), then evolution would proceed unimaginably slowly. Let's take an example.
Suppose there are two alleles of the same locus (i.e. two variants of the same gene) - but and a. Let us assume that as a result of the mutation but turns into a, and the frequency of this phenomenon is v per one gamete per generation. Let us also assume that at the initial moment of time (before the start of the mutation process), the allele frequency ce was equal to r 0 . Accordingly, in the next generation and alleles of the type but turn into alleles of type a, and the allele frequency but will be equal to p 1 \u003d p 0 - vp 0= p 0(1 -v). In the second generation, the proportion and remaining alleles but(the frequency of which in the population is now p x) mutates again into a, and the frequency but will be equal to p 2=p,(1 - v ) - p o (1-v) x (1 -v ) =p 0 (1 - v) 2 . After t generations, the allele frequency but will be equal to p o (1- v) t .
Since the value (1 - v ) < 1, it is obvious that over time the allele frequency but decreases. If this process continues indefinitely, then it tends to zero. Intuitively, this pattern is quite transparent: if in each generation some part of the alleles but turns into alleles a, then sooner or later from alleles of type but there will be nothing left - they will all turn into a alleles.
However, the question of how soon this will happen remains open - everything is determined by the value of and. Under natural conditions, it is extremely small and amounts to approximately 10~5. At this pace, in order to change the allele frequency but from 1 to 0.99, approximately 1000 generations will be required; in order to change its frequency from 0.50 to 0.49 - 2000 generations, and from 0.10 to 0.09 - 10,000 generations. In general, the lower the initial allele frequency, the longer it takes for it to decrease. (Let's translate generations into years: it is generally accepted that a person changes generations every 25 years.)
Analyzing this example, we made the assumption that the mutation process is one-way - but turns into a, but reverse movement (a to but) not happening. In fact, mutations can be both one-sided (a -> a) and two-sided (a --> a and a -> a), while mutations of the type a -*■ a are called direct, and mutations of the type a ~* a are called reverse. This circumstance, of course, somewhat complicates the calculation of the frequencies of occurrence of alleles in the population.
Note that allele frequencies in natural populations are usually not in a state of equilibrium between forward and back mutations. In particular, natural selection may favor
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favor one allele at the expense of another, in which case allele frequencies are determined by the interaction between mutations and selection. In addition, in the presence of a two-way mutation process (forward and reverse mutations), the change in allele frequencies occurs more slowly than in the case when mutations partially compensate for the decrease in the frequency of occurrence of the original wild allele (allele but). This once again confirms what was said above: in order for the mutations themselves to lead to any significant change in allele frequencies, an extremely long time is required.
MIGRATION
Migration called the process of moving individuals from one population to another and the subsequent crossing of representatives of these two populations. Migration provides "gene flow", i.e. a change in the genetic composition of a population due to the arrival of new genes. Migration does not affect the allele frequency in the species as a whole, however, in local populations, gene flow can significantly change the relative allele frequencies, provided that the initial allele frequencies are different for “old-timers” and “migrants”.
As an example, consider some local population A, whose members we will call old-timers, and population B, whose members we will call migrants. Let us assume that the proportion of the latter in the population is equal to \X, so that in the next generation, the offspring receives from old-timers a share of genes equal to (1 - q), and from migrants - a share equal to [x. Let's make one more assumption, assuming that in the population from which migration occurs, the average allele frequency but is R, and in a local population that accepts migrants, its initial frequency is equal to r 0 . Allele frequency but in the next (mixed) generation in the local population (recipient population) will be:
In other words, the new allele frequency is equal to the original allele frequency (p 0), multiplied by the share of old-timers (1 - R.) plus the proportion of aliens (u) multiplied by their allele frequency (/>). Applying elementary algebraic tricks and rearranging the terms of the equation, we find that the new allele frequency is equal to the original frequency (p 0) minus the proportion of newcomers M(u) multiplied by the difference in allele frequencies between old-timers and newcomers (p - P).
In one generation, the allele frequency but changes by the amount AR, calculated by the formula: AR -r x- p Q . Substituting into this equation the value obtained above pv we get: AR \u003d p 0 - m(p 0 - P) - p o \u003d ~ ~ \ * - (P 0 ~ P) - In other words, the greater the proportion of aliens in the population and the greater the difference in allele frequencies but among representatives of the population
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The ion into which individuals immigrate and the population from which they emigrate, the higher the rate of change in the frequency of this allele. Note that DP = 0 only when zero are equal to either c, those. no migration, or (r d - R), those. allele frequencies but match in both populations. Therefore, if migration does not stop and populations continue to mix, then the allele frequency in the recipient population will change until p 0 will not equal R, those. while the frequency of occurrence but will not be the same in both populations.
How does the difference in allele frequency in two neighboring populations change over time?
Let's say we observe migration over two generations. Then, after the second generation, the difference in allele frequencies but in both populations will be equal
and after / generations
This formula is extremely helpful. First, it allows you to calculate the allele frequency but in a local population (a population of old-timers) after t generations of migration at a known rate q (provided that the researcher knows the initial allele frequencies p o and p t). And secondly, knowing the original allele frequencies but in the population from which individuals migrate, and in the population to which they migrate, the final (post-migration) allele frequencies but in the recipient population and the duration of the migration process (/), it is possible to calculate the intensity of gene flow m.
The genetic footprint of migration. In the United States, offspring from mixed marriages between whites and blacks are usually attributed to the black population. Therefore, intermarriage can be seen as a flow of genes from a white population to a black one. The frequency of the I 0 allele, which controls the Rh factor of blood, is approximately P = 0.028. In African populations whose distant descendants are modern members of the black population of the United States, the frequency of this allele is p 0 = 0.630. The ancestors of the modern black population of the United States were taken out of Africa about 300 years ago (i.e., about 10-12 generations passed); for simplicity, let's assume that t = 10. The frequency of the allele I 0 of the modern black population of the United States is pt - 0,446.
Rewriting equation 5.5 in the form and substituting the values
corresponding values, we get (1 - q) "° \u003d 0.694, q \u003d 0.036. Thus, the flow of genes from the white population of the USA to the black went with an average intensity of 3.6% per generation. As a result, after 10 generations, the proportion of genes of African ancestors makes up approximately 60% of the total number of genes of the modern black population of the United States and about 30% of the genes (1 - 0.694 = 0.306) are inherited from whites.
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RANDOM GENE DRIFT
Any natural population is characterized by the fact that it has a finite (limited) the number of individuals included in it. This fact manifests itself in purely random, statistical fluctuations in the frequencies of genes and genotypes in the processes of formation of a sample of gametes from which the next generation is formed (since not every individual in a population produces offspring); association of gametes into zygotes; implementation of "social" processes (death of carriers of certain genotypes as a result of wars, disasters, deaths before reproductive age); the influence of mutational and migration processes and natural selection. Obviously, in large populations, the influence of such processes is much weaker than in small ones. Random, statistical fluctuations in the frequencies of genes and genotypes are called population waves. To denote the role of random factors in changing the frequencies of genes in a population, S. Wright introduced the concept of "gene drift" (random gene drift), and N.P. Dubinin and D.D. Romashov - the concept of "genetic-automatic processes". We will use the concept of "random genetic drift".
random genetic drift called a change in allele frequencies over a number of generations, which is the result of random causes, for example, a sharp reduction in population size as a result of war or famine. Suppose that in some population the frequencies of two alleles a and a are 0.3 and 0.7, respectively. Then in the next generation the allele frequency but may be greater or less than 0.3, simply as a result of the fact that in the set of zygotes from which the next generation is formed, its frequency, for some reason, turned out to be different from what was expected.
General rule random processes is as follows: the value of the standard deviation of gene frequencies in a population is always inversely related to the size of the sample - the larger the sample, the smaller the deviation. In the context of population genetics, this means that the smaller the number of interbreeding individuals in a population, the greater the variability in allele frequencies in the generations of the population. In small populations, the frequency of a single gene may occasionally be very high. So, in a small isolate (dunkers in Pennsylvania, USA, immigrants from Germany), the frequency of blood group genes AVO significantly higher than in the original population in Germany. And vice versa than more number of individuals involved in the creation of the next generation, the closer the theoretically expected allele frequency (in the parent generation) to the frequency observed in the next generation (in the offspring generation).
An important point is that the population size is determined not by the total number of individuals in the population, but by its so-called effective strength, which is determined by the number of interbreeding individuals that give rise to the next generation. Exactly these
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individuals (and not the entire population as a whole), becoming parents, make a gene contribution to the next generation.
If the population is not too small, then the changes in allele frequencies due to genetic drift that occur in one generation are also relatively small, but, having accumulated over a number of generations, they can become very significant. In the event that allele frequencies at a given locus are not affected by any other processes (mutations, migrations, or selection), evolution, determined by random gene drift, will eventually lead to the fixation of one of the alleles and the destruction of the other. In a population in which only genetic drift operates, the probability that a given allele will be fixed is equal to the initial frequency of its occurrence. In other words, if the allele of a gene BUT occurs in a population with a frequency of 0.1, then the probability that at some point in the development of the population this allele will become the only form of the gene in it BUT, is 0.1. Accordingly, the probability that at some point in the development of a population an allele occurring in it with a frequency of 0.9 is fixed is 0.9. However, fixation takes a long time to occur, since the average number of generations needed to fix an allele is about 4 times greater than the number of parents in each generation.
The extreme case of genetic drift is the process of the emergence of a new population, descended from just a few individuals. This phenomenon is known as founder effect(or "progenitor effect").
W. McKusick described the founder effect in the Mennonite sect (Pennsylvania, USA). In the mid-60s, this population isolate numbered 8,000 people, and almost all of them descended from three married couples who arrived in America before 1770. They were characterized by an unusually high frequency of a gene that causes a special form of dwarfism with polydactyly (presence of extra fingers) . This is such a rare pathology that by the time McKusick's book was published, no more than 50 such cases had been described in the entire medical literature; in the Mennonite isolate, 55 cases of this anomaly were found. Obviously, it happened by chance that one of the carriers of this rare gene became the "founder" of its increased frequency in Mennonites. But in those groups that live in other parts of the United States and originate from other ancestors, this anomaly was not found.
A random change in the frequencies of alleles, which are a kind of random gene drift, is a phenomenon that occurs if a population in the process of evolution passes through "bottleneck". When climatic or some other conditions for the existence of a population become unfavorable, its numbers are sharply reduced and there is a danger of its complete disappearance. If the situation changes in a favorable direction, then the population restores its size, however, as a result of gene drift at the time of passage through the “bottleneck” in it,
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allele frequencies change significantly, and then these changes persist throughout subsequent generations. So, at the first stages of human evolutionary development, many tribes repeatedly found themselves on the verge of complete extinction. Some of them disappeared, while others, having passed the stage of a sharp decline in numbers, grew - sometimes due to migrants from other tribes, and sometimes due to an increase in the birth rate. observed in modern world
differences in the frequencies of occurrence of the same alleles in different populations can be explained to a certain extent by the influence of different variants of the genetic drift process.
NATURAL SELECTION
Natural selection is a process of differential
reproduction of offspring by genetically different organisms in a population. In fact, this means that carriers of certain genetic variants (i.e. certain genotypes) are more likely to survive and reproduce than carriers of other variants (genotypes). Differential reproduction can be associated with the action of various factors, among which are mortality, fertility, fertility, mating success and the duration of the reproductive period, the survival of the offspring (sometimes called viability).
A measure of an individual's ability to survive and reproduce is fitness. However, since the size of a population is usually limited by the characteristics of the environment in which it exists, the evolutionary performance of an individual is determined not by absolute, but by relative fitness, i.e. its ability to survive and reproduce compared to carriers of other genotypes in a given population. In nature, the fitness of genotypes is not constant, but subject to change. Nevertheless, in mathematical models, the value of fitness is taken as a constant, which helps in the development of theories of population genetics. For example, one of the simplest models assumes that the fitness of an organism is completely determined by the structure of its genotype. In addition, when assessing fitness, it is assumed that all loci make independent contributions, i.e. each locus can be analyzed independently of the others.
stand out three main types of mutations: harmful, neutral and favorable. Most new mutations that appear in a population are harmful, as they reduce the fitness of their carriers. Selection usually works against such mutants, and after a while they disappear from the population. This type of selection is called negative(stabilizing). However, there are mutations, the appearance of which does not disrupt the functioning
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organism. The fitness of such mutants can be as high as the fitness of non-mutant alleles (original alleles) in the population. These mutations are neutral and natural selection remains indifferent to them without acting against them. (disruptive selection). Under the action of disruptive selection, polymorphism usually arises within a population - several distinctly different forms of a gene (see Chapter IV). The third type of mutants appears extremely rarely: such mutations can increase the fitness of the organism. In this case, selection may act so that the frequency of occurrence of mutant alleles may increase. This type of selection is called positive(driving) selection.
GENE SUBSTITUTION
The limiting case of population evolution is the complete disappearance of the original alleles from it. Gene substitution(complete replacement of one allele by another) is the process in which the mutant allele displaces the originally dominant "wild-type" allele. In other words, as a result of the action of various population processes (for example, the mutation process, random gene drift, selection), only mutant alleles are found in the population: the mutant allele appears in the population in the singular as a result of a single mutation, and then, after changing a sufficient number generations, its frequency reaches 100%, i.e. it is fixed in the population. The time it takes for an allele to reach 100% frequency is called fixation time. Obviously, not all mutant alleles reach 100% occurrence and are fixed in the population. Usually the opposite happens: most of the mutant alleles are eliminated within several generations. The probability that a given mutant allele will be fixed in a population is denoted by a value called fixation probability. New mutants constantly appear in populations, and one of the processes accompanying the mutation is the process of substituting genes in which the allele BUT replaced by a new allele B, which in turn is replaced by the allele IN etc. The dynamics of this process is described by the concept "speed of gene substitution processes", reflecting the number of substitutions and fixations per unit of time.
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