Mendel's first law is stated briefly. The first and second laws of G. Mendel

Mendel's laws - these are the principles of transmission of hereditary characteristics from parent organisms to their descendants, resulting from experiments Gregor Mendel . These principles served as the basis for classical genetics and were subsequently explained as a consequence of the molecular mechanisms of heredity. Although three laws are usually described in Russian-language textbooks, the “first law” was not discovered by Mendel. Of particular importance among the patterns discovered by Mendel is the “hypothesis of gamete purity.”

Mendel's laws

Law of Uniformity of First Generation Hybrids

Mendel called the manifestation of the trait of only one of the parents in hybrids as dominance.

When crossing two homozygous organisms belonging to different pure lines and differing from each other in one pair of alternative manifestations of the trait, the entire first generation of hybrids (F1) will be uniform and will carry the manifestation of the trait of one of the parents

This law is also known as the "law of trait dominance." Its formulation is based on the conceptclean line relative to the characteristic under study - in modern language this means homozygosity individuals for this trait. Mendel formulated the purity of a character as the absence of manifestations of opposite characters in all descendants in several generations of a given individual during self-pollination.

When crossing pure lines peas with purple flowers and peas with white flowers, Mendel noticed that the descendants of the plants that emerged were all with purple flowers, there was not a single white one among them. Mendel repeated the experiment more than once and used other signs. If he crossed peas with yellow and green seeds, all the offspring would have yellow seeds. If he crossed peas with smooth and wrinkled seeds, the offspring would have smooth seeds. The offspring from tall and short plants were tall. So, hybrids of the first generation are always uniform in this characteristic and acquire the characteristic of one of the parents. This sign (stronger, dominant), always suppressed the other ( recessive).

Law of character splitting

Definition

The law of splitting, or the second law Mendel: when two heterozygous descendants of the first generation are crossed with each other, in the second generation a split in a certain numerical ratio is observed: by phenotype 3:1, by genotype 1:2:1.

By crossing organisms of two pure lines, differing in the manifestations of one studied trait, for which they are responsible alleles one gene is calledmonohybrid cross .

A phenomenon in which crossing heterozygous individuals leads to the formation of offspring, some of which carry a dominant trait, and some - a recessive one, called splitting. Consequently, segregation is the distribution of dominant and recessive traits among the offspring in a certain numerical ratio. The recessive trait does not disappear in the first generation hybrids, but is only suppressed and appears in the second hybrid generation.

Explanation

Law of gamete purity: each gamete contains only one allele from a pair of alleles of a given gene of the parent individual.

Normally, the gamete is always pure from the second gene of the allelic pair. This fact, which could not be firmly established in Mendel's time, is also called the gamete purity hypothesis. This hypothesis was later confirmed by cytological observations. Of all the laws of inheritance established by Mendel, this “Law” is the most general in nature (it is fulfilled under the widest range of conditions).

Purity hypothesis gametes . Mendel suggested that during the formation of hybrids, hereditary factors are not mixed, but remain unchanged. The hybrid has both factors - dominant and recessive, but the manifestation of the trait is determined by the dominanthereditary factor , the recessive is suppressed. Communication between generationssexual reproduction carried out through reproductive cells - gametes . Therefore, it must be assumed that each gamete carries only one factor from a pair. Then at fertilization the fusion of two gametes, each of which carries a recessive hereditary factor, will lead to the formation of an organism with a recessive trait, manifested phenotypically . The fusion of gametes, each of which carries a dominant factor, or two gametes, one of which contains a dominant and the other a recessive factor, will lead to the development of an organism with a dominant trait. Thus, the appearance in the second generation of a recessive trait of one of the parents can only occur under two conditions: 1) if in hybrids the hereditary factors remain unchanged; 2) if the germ cells contain only one hereditary factor from allelic couples. Mendel explained the splitting of offspring when crossing heterozygous individuals by the fact that the gametes are genetically pure, that is, they carry only one gene from an allelic pair. The hypothesis (now called the law) of gamete purity can be formulated as follows: during the formation of germ cells, only one allele from a pair of alleles of a given gene enters each gamete.

It is known that in every cell body in most cases there is exactly the same diploid set of chromosomes. Two homologous chromosomes usually each contain one allele of a given gene. Genetically “pure” gametes are formed as follows:

The diagram shows the meiosis of a cell with a diploid set of 2n=4 (two pairs of homologous chromosomes). Paternal and maternal chromosomes are indicated by different colors.

During the formation of gametes in a hybrid, homologous chromosomes end up in different cells during the first meiotic division. The fusion of male and female gametes results in a zygote with a diploid set of chromosomes. In this case, the zygote receives half of the chromosomes from the paternal body, and half from the maternal one. For a given pair of chromosomes (and a given pair of alleles), two types of gametes are formed. During fertilization, gametes carrying the same or different alleles encounter each other by chance. By virtue of statistical probability with a sufficiently large number of gametes in the offspring 25% genotypes will be homozygous dominant, 50% - heterozygous, 25% - homozygous recessive, that is, the ratio 1AA:2Aa:1aa is established (segregation by genotype 1:2:1). Accordingly, according to the phenotype, the offspring of the second generation during a monohybrid cross are distributed in a ratio of 3:1 (3/4 individuals with a dominant trait, 1/4 individuals with a recessive trait). Thus, in a monohybrid cross cytological the basis for the splitting of characters is the divergence of homologous chromosomes and the formation of haploid germ cells in meiosis

Law of independent inheritance of characteristics

Definition

Law of independent inheritance(Mendel’s third law) - when crossing two homozygous individuals that differ from each other in two (or more) pairs of alternative traits, genes and their corresponding traits are inherited independently of each other and are combined in all possible combinations (as in monohybrid crossing). When plants differing in several characters, such as white and purple flowers and yellow or green peas, were crossed, the inheritance of each character followed the first two laws and in the offspring they were combined in such a way as if their inheritance occurred independently of each other. The first generation after crossing had a dominant phenotype for all traits. In the second generation, a splitting of phenotypes was observed according to the formula 9:3:3:1, that is, 9:16 were with purple flowers and yellow peas, 3:16 were with white flowers and yellow peas, 3:16 were with purple flowers and green peas, 1 :16 with white flowers and green peas.

Explanation

Mendel came across characters whose genes were in different pairs of homologous chromosomes peas During meiosis, homologous chromosomes of different pairs are randomly combined in gametes. If the paternal chromosome of the first pair gets into the gamete, then with equal probability both the paternal and maternal chromosomes of the second pair can get into this gamete. Therefore, traits whose genes are located in different pairs of homologous chromosomes are combined independently of each other. (It later turned out that of the seven pairs of characters studied by Mendel in the pea, which has a diploid number of chromosomes 2n=14, the genes responsible for one of the pairs of characters were located on the same chromosome. However, Mendel did not discover a violation of the law of independent inheritance, since as linkage between these genes was not observed due to the large distance between them).

Basic provisions of Mendel's theory of heredity

In modern interpretation, these provisions are as follows:

• Discrete (separate, non-mixable) hereditary factors - genes are responsible for hereditary traits (the term “gene” was proposed in 1909 by V. Johannsen)
• Each diploid organism contains a pair of alleles of a given gene responsible for a given trait; one of them is received from the father, the other from the mother.
• Hereditary factors are transmitted to descendants through germ cells. When gametes are formed, each of them contains only one allele from each pair (the gametes are “pure” in the sense that they do not contain the second allele).

Conditions for the fulfillment of Mendel's laws

According to Mendel's laws, only monogenic traits are inherited. If more than one gene is responsible for a phenotypic trait (and the absolute majority of such traits), it has a more complex pattern of inheritance.

Conditions for fulfilling the law of segregation during monohybrid crossing

Splitting 3:1 by phenotype and 1:2:1 by genotype is performed approximately and only under the following conditions:

1. A large number of crosses (large number of offspring) are studied.
2. Gametes containing alleles A and a are formed in equal numbers (have equal viability).
3. There is no selective fertilization: gametes containing any allele fuse with each other with equal probability.
4. Zygotes (embryos) with different genotypes are equally viable.

Conditions for the implementation of the law of independent inheritance

1. All conditions necessary for the fulfillment of the law of splitting.
2. The location of the genes responsible for the traits being studied is in different pairs of chromosomes (unlinked).

Conditions for fulfilling the law of gamete purity

1. The normal course of meiosis. As a result of chromosome nondisjunction, both homologous chromosomes from a pair can end up in one gamete. In this case, the gamete will carry a pair of alleles of all genes that are contained in a given pair of chromosomes.

Lesson Plan #18

1 Educational:

2 Developmental:

During the classes:

I Organizational moment

II Main part

1 Checking homework

.

What is genotype, phenotype?

♂ ,♀ ?

2 Explanation of new material

D) What is gamete purity?

III Lesson summary

IV Homework

1 Notebook entries

Lesson No. 18

Subject:

MONOHYBRID CROSSING

hybridization, hybrid, and a separate individual - hybrid.

dominance.

In the offspring obtained from crossing first-generation hybrids, the phenomenon of splitting is observed: a quarter of individuals from second-generation hybrids carry a recessive trait, three quarters - a dominant one.

When two descendants of the first generation are crossed with each other (two heterozygous individuals), in the second generation a splitting is observed in a certain numerical ratio: by phenotype 3:1, by genotype 1:2:1

(25% - homozygous dominant, 50% - heterozygous, 25% - homozygous recessive)

Law of gamete purity

What is the cause of splitting? Why do individuals arise in the first, second and subsequent generations that, as a result of crossing, produce offspring with dominant and recessive traits?

From 1854, for eight years, Mendel conducted experiments on crossing pea plants. He discovered that as a result of crossing different varieties of peas with each other, the first generation hybrids have the same phenotype, and in the second generation hybrids, the characteristics are split in certain proportions. To explain this phenomenon, Mendel made a number of assumptions, which were called the “gamete purity hypothesis”, or the “gamete purity law”.

Communication between generations during sexual reproduction occurs through germ cells (gametes). Obviously, gametes carry material hereditary factors - genes that determine the development of a particular trait.

Let us turn to the diagram on which the results are written in symbols:

The gene responsible for the dominant yellow color of seeds will be denoted by a capital letter, for example A ; the gene responsible for the recessive green color - in small letter A . Let us denote the connection of gametes carrying genes A and a with a multiplication sign: A X A=Ah. As can be seen, the resulting heterozygous form (F1) has both Aa genes. The gamete purity hypothesis states that in a hybrid (heterozygous) individual the gamete cells are pure, i.e. they have one gene from a given pair. This means that the Aa hybrid will produce equal numbers of gametes with the A gene and with the a gene. What combinations are possible between them? Obviously, four combinations are equally probable:

♂ ♀	A	A
A	AA	Ahh
A	aA	ahh

As a result of 4 combinations, the combinations AA, 2Aa and aa will be obtained. The first three will produce individuals with a dominant trait, the fourth will produce individuals with a recessive trait. The hypothesis of gamete purity explains the cause of splitting and the numerical relationships observed during this process. At the same time, the reasons for the differences in relation to the further splitting of individuals with dominant traits in subsequent generations of hybrids are also clear. Individuals with dominant traits are heterogeneous in their hereditary nature. One of the three (AA) will produce gametes of only one type (A) and will not split during self-pollination or crossing with its own kind. The other two (Aa) will produce gametes of 2 varieties; their offspring will undergo splitting in the same numerical ratios as the second generation hybrids. The hypothesis of gamete purity establishes that the law of splitting is the result of a random combination of gametes carrying different genes (Aa ). Whether a gamete carrying the A gene will unite with another gamete carrying the A or a gene, given equal viability of the gametes and their equal number, is equally likely.

Given the random nature of the connection of gametes, the overall result turns out to be statistically natural.

Thus, it was found that the splitting of traits in the offspring of hybrid plants is the result of the presence of two genes in them - A and a, responsible for the development of one trait, for example, seed color.

Mendel proposed that hereditary factors do not mix during the formation of hybrids, but remain unchanged. In the body of an F1 hybrid from crossing parents distinguished by alternative characteristics, both factors are present - a dominant gene and a recessive one, but the recessive gene is suppressed. The connection between generations during sexual reproduction is carried out through germ cells - gametes. Therefore, it must be assumed that each gamete carries only one factor from a pair. Then, during fertilization, the fusion of two gametes, each of which carries a recessive gene, leads to the formation of an organism with a recessive trait that manifests itself phenotypically. The fusion of gametes carrying a dominant gene, or two gametes, one of which contains a dominant and the other a recessive gene, will lead to the development of an organism with a dominant trait.

Thus, the appearance in the second generation (F 2) of a recessive trait of one of the parents (P) can only occur if two conditions are met: 1) if in hybrids the hereditary factors remain unchanged, 2) if the germ cells contain only one hereditary factor from an allelic pair. Mendel explained the splitting of characters in the offspring when crossing heterozygous individuals by the fact that gametes are genetically pure, i.e. carry only one gene from an allelic pair.

The law of gamete frequency can be formulated as follows: When germ cells are formed, only one gene from an allelic pair enters each gamete.

Why and how does this happen? It is known that every cell of the body has exactly the same diploid set of chromosomes. Two homologous chromosomes contain two identical allelic genes. Two varieties of gametes are formed according to a given allelic pair. During fertilization, gametes carrying the same or different alleles encounter each other by chance. Due to statistical probability, with a sufficiently large number of gametes in the offspring, 25% of the genotypes will be homozygous dominant, 50% will be heterozygous, 25% will be homozygous recessive, i.e. the ratio is established: 1AA:2Aa:1aa. Accordingly, according to the phenotype, the offspring of the second generation during a monohybrid cross are distributed in the ratio of 3/4 individuals with a dominant trait,/4 individuals with a recessive trait (3:1).

Thus, the cytological basis for the splitting of characteristics in offspring during monohybrid crossing is the divergence of homologous chromosomes and the formation of haploid germ cells in meiosis.

Analysis cross

The hybridological method of studying heredity developed by Mendel makes it possible to establish whether an organism that has a dominant phenotype for the gene (or genes under study) is homozygous or heterozygous. To do this, an individual with an unknown genotype is crossed with an organism homozygous for the recessive alley(s) and having a recessive phenotype.

If the dominant individual is homozygous, then the offspring from such a cross will be uniform and splitting will not occur (AAhaa = Aa). If the dominant individual is heterozygous, then splitting will occur in a 1:1 ratio according to the phenotype (Aa x aa = Aa, aa). This result of crossing is direct evidence of the formation at one of the parents of two varieties of gametes, i.e. its heterozygosity.

In dihybrid crossing, the splitting for each trait occurs independently of the other trait. Dihybrid crossing is two independently occurring monohybrid crosses, the results of which seem to overlap each other.

When crossing two homozygous individuals that differ from each other in two or more pairs of alternative traits, the genes and their corresponding traits are inherited independently of each other and are combined in all possible combinations.

The analysis of splitting is based on Mendel’s laws and in more complex cases - when individuals differ in three, four or more pairs of characteristics.

Lesson Plan #18

TOPIC: Monohybrid and dihybrid crossing. Mendel's laws

1 Educational:

To develop knowledge about monohybrid crossing, Mendel’s first law

Show the role of Mendel's research in understanding the essence of inheritance of traits

Expand the formulation of the law of splitting, Mendel’s second law

Reveal the essence of the gamete purity hypothesis

To develop knowledge about dihybrid crossing as a method of studying heredity

Use the example of di- and polyhybrid crossing to reveal the manifestation of Mendel’s third law

2 Developmental:

Develop memory, expand horizons

To promote the development of the skill of using genetic symbols when solving genetic problems

During the classes:

I Organizational moment

1 Introducing students to the topic and purpose of the lesson

2 Students are given a number of tasks that must be completed during the lesson:

Know the formulations of Mendel's laws

Understand the patterns of inheritance of traits established by Mendel

Understand the essence of the gamete purity hypothesis

Understand the essence of dihybrid crossing

II Main part

1 Checking homework

What does genetics study? What problems does genetics solve?

Define heredity and variability.

What are the stages of the embryonic period?

Explain the terms: gene, dominant and recessive genes . - What kind of development is called direct?

What genes are called allelic? What is multiple allelism?

What is genotype, phenotype?

What is special about the hybridological method?

What does genetic symbolism mean: P, F1, F2, ♂ ,♀ ?

2 Explanation of new material

Monohybrid crossing; Mendel's first law

Mendel's second law; gamete frequency law

The essence of dihybrid crossing; Mendel's third law

3 Consolidating new material

A) Formulate Mendel’s 1st law.

B) Which cross is called monohybrid?

B) Formulate Mendel’s second law

D) What is gamete purity?

D) What rules and patterns appear during dihybrid crossing?

E) How is Mendel's third law formulated?

III Lesson summary

IV Homework

1 Notebook entries

2 Textbook by V.B. Zakharov, S.T. Mamontov “Biology” (pp. 266-277)

3 Textbook by Yu.I. Polyansky “General Biology” (pp. 210-217)

Lesson No. 18

Subject: “Monohybrid and dihybrid crossing. Mendel's laws."

1. Monohybrid crossing. The rule of uniformity of first generation hybrids is the first law of heredity established by G. Mendel.

2. Mendel's second law is the law of splitting. Gamete purity hypothesis

3. Dihybrid and polyhybrid crossing. Mendel's third law is the law of independent combination of characteristics.

MONOHYBRID CROSSING

To illustrate Mendel's first law, let us recall his experiments on monohybrid crossing of pea plants. The crossing of two organisms is called hybridization, the offspring from crossing two individuals with different heredity is called hybrid, and a separate individual - hybrid.

Monohybrid is the crossing of two organisms that differ from each other in one pair of alternative (mutually exclusive) characteristics.

For example, when crossing peas with yellow seeds (dominant trait) and green seeds (recessive trait), all hybrids will have yellow seeds. The same picture is observed when crossing plants with smooth and wrinkled seeds; all first generation offspring will have smooth seed shapes. Consequently, in the first generation hybrid, only one of each pair of alternative characters appears. The second sign seems to disappear and does not appear. Mendel called the predominance of the trait of one of the parents in a hybrid dominance. By phenotype, all hybrids have yellow seeds, and by genotype they are heterozygous (Aa). Thus, the entire generation is uniform.

Mendel's first law is the law of dominance.

The law of uniformity of the first generation of hybrids, or Mendel's first law- is also called the law of dominance, since all individuals of the first generation have the same manifestation of the trait. It can be formulated as follows: when crossing two organisms belonging to different pure lines (two homozygous organisms), differing from each other in one pair of alternative traits, the entire first generation of hybrids (F 1) will be uniform and will carry the trait of one of the parents.

This pattern will be observed in all cases when crossing two organisms belonging to two pure lines, when the phenomenon of complete dominance of a trait occurs (i.e., one trait completely suppresses the development of the other).

Czech explorer Gregor Mendel(1822-1884) considered founder of genetics, since he was the first, even before this science took shape, to formulate the basic laws of inheritance. Many scientists before Mendel, including the outstanding German hybridizer of the 18th century. I. Kelreuter noted that when crossing plants belonging to different varieties, great variability is observed in the hybrid offspring. However, no one was able to explain the complex splitting and, moreover, reduce it to precise formulas due to the lack of a scientific method of hybridological analysis.

It was thanks to the development of the hybridological method that Mendel managed to avoid the difficulties that had confused earlier researchers. G. Mendel reported on the results of his work in 1865 at a meeting of the Society of Natural Scientists in Brünn. The work itself, entitled “Experiments on Plant Hybrids,” was later published in the “Proceedings” of this society, but did not receive proper assessment from contemporaries and remained forgotten for 35 years.

As a monk, G. Mendel conducted his classical experiments on crossing different varieties of peas in the monastery garden in Brünn. He selected 22 pea varieties that had clear alternative differences in seven characteristics: seeds yellow and green, smooth and wrinkled, flowers red and white, plants tall and short, etc. An important condition of the hybridological method was the mandatory use of pure, i.e., as parents. forms that do not split according to the studied characteristics.

A successful choice of object played a major role in the success of Mendel's research. Peas are self-pollinators. To obtain first-generation hybrids, Mendel castrated the flowers of the mother plant (removed the anthers) and artificially pollinated the pistils with the pollen of the male parent. When obtaining second-generation hybrids, this procedure was no longer necessary: ​​he simply left the F 1 hybrids to self-pollinate, which made the experiment less labor-intensive. Pea plants reproduced exclusively sexually, so that no deviations could distort the results of the experiment. And finally, in peas, Mendel discovered a sufficient number of pairs of brightly contrasting (alternative) and easily distinguishable pairs of characters for analysis.

Mendel began his analysis with the simplest type of crossing - monohybrid, in which the parent individuals differ in one pair of traits. The first pattern of inheritance discovered by Mendel was that all first-generation hybrids had the same phenotype and inherited the trait of one of the parents. Mendel called this trait dominant. An alternative trait of the other parent, which did not appear in hybrids, was called recessive. The discovered pattern was named I of Mendel's law, or the law of uniformity of hybrids of the 1st generation. During the analysis of the second generation, a second pattern was established: the splitting of hybrids into two phenotypic classes (with a dominant trait and with a recessive trait) in certain numerical ratios. By counting the number of individuals in each phenotypic class, Mendel established that splitting in a monohybrid cross corresponds to the formula 3: 1 (three plants with a dominant trait, one with a recessive trait). This pattern is called Mendel's II law, or law of segregation. Open patterns emerged in the analysis of all seven pairs of characteristics, on the basis of which the author came to the conclusion about their universality. When self-pollinating F 2 hybrids, Mendel obtained the following results. Plants with white flowers produced offspring with only white flowers. Plants with red flowers behaved differently. Only a third of them gave uniform offspring with red flowers. The offspring of the rest were split in the ratio of red and white colors in a ratio of 3: 1.

Below is a diagram of the inheritance of pea flower color, illustrating Mendel's I and II laws.

In an attempt to explain the cytological basis of open patterns, Mendel formulated the idea of ​​discrete hereditary inclinations contained in gametes and determining the development of paired alternative characters. Each gamete carries one hereditary deposit, i.e. is “pure”. After fertilization, the zygote receives two hereditary deposits (one from the mother, the other from the father), which do not mix and later, when gametes are formed by the hybrid, they also end up in different gametes. This hypothesis of Mendel was called the rule of “purity of gametes.” The combination of hereditary inclinations in the zygote determines what character the hybrid will have. Mendel denoted the inclination that determines the development of a dominant trait with a capital letter ( A), and recessive is capitalized ( A). Combination AA And Ahh in the zygote determines the development of a dominant trait in the hybrid. A recessive trait appears only when combined ahh.

In 1902, V. Betson proposed to designate the phenomenon of paired characters by the term “allelomorphism”, and the characters themselves, accordingly, “allelomorphic”. According to his proposal, organisms containing the same hereditary inclinations began to be called homozygous, and those containing different inclinations - heterozygous. Later, the term “allelomorphism” was replaced by the shorter term “allelism” (Johansen, 1926), and the hereditary inclinations (genes) responsible for the development of alternative traits were called “allelic”.

Hybridological analysis involves reciprocal crossing of parental forms, i.e. using the same individual first as the maternal parent (forward crossing) and then as the paternal parent (backcrossing). If both crosses produce the same results, corresponding to Mendel’s laws, then this indicates that the analyzed trait is determined by an autosomal gene. Otherwise, the trait is linked to sex, due to the localization of the gene on the sex chromosome.

Letter designations: P - parental individual, F - hybrid individual, ♀ and ♂ - female or male individual (or gamete),
capital letter (A) is a dominant hereditary disposition (gene), lowercase letter (a) is a recessive gene.

Among the second generation hybrids with yellow seed color there are both dominant homozygotes and heterozygotes. To determine the specific genotype of a hybrid, Mendel proposed crossing the hybrid with a homozygous recessive form. It is called analyzing. When crossing a heterozygote ( Ahh) with the analyzer line (aa), splitting is observed both by genotype and phenotype in a 1: 1 ratio.

If one of the parents is a homozygous recessive form, then the analyzing cross simultaneously becomes a backcross - a return crossing of the hybrid with the parent form. The offspring from such a cross are designated Fb.

The patterns Mendel discovered in his analysis of monohybrid crosses also appeared in dihybrid crosses in which the parents differed in two pairs of alternative traits (for example, yellow and green seed color, smooth and wrinkled shape). However, the number of phenotypic classes in F 2 doubled, and the phenotypic splitting formula was 9: 3: 3: 1 (for 9 individuals with two dominant traits, three individuals each with one dominant and one recessive trait, and one individual with two recessive traits ).

To facilitate the analysis of splitting in F 2, the English geneticist R. Punnett proposed a graphical representation of it in the form of a lattice, which began to be called after his name ( Punnett grid). On the left, vertically, it contains the female gametes of the F1 hybrid, and on the right - the male ones. The inner squares of the lattice contain the combinations of genes that arise when they merge, and the phenotype corresponding to each genotype. If the gametes are placed in a lattice in the sequence shown in the diagram, then in the lattice you can notice the order in the arrangement of genotypes: all homozygotes are located along one diagonal, and heterozygotes for two genes (diheterozygotes) are located along the other. All other cells are occupied by monoheterozygotes (heterozygotes for one gene).

The cleavage in F 2 can be represented using phenotypic radicals, i.e. indicating not the entire genotype, but only the genes that determine the phenotype. This entry looks like this:

The dashes in the radicals mean that the second allelic genes can be either dominant or recessive, and the phenotype will be the same.

Dihybrid crossing scheme
(Punnet grid)

	AB	Ab	aB	ab
AB	AABB yellow Ch.	AABb yellow Ch.	AaBB yellow Ch.	AaBb yellow Ch.
Ab	AABb yellow Ch.	AAbb yellow wrinkle	AaBb yellow Ch.	Aabb yellow wrinkle
aB	AaBB yellow Ch.	AaBb yellow Ch.	aaBB green Ch.	aaBb green Ch.
ab	AaBb yellow Ch.	Aabb yellow wrinkle	aaBb green Ch.	aabb green wrinkle

The total number of F2 genotypes in the Punnett lattice is 16, but there are 9 different ones, since some genotypes are repeated. The frequency of different genotypes is described by the rule:

In an F2 dihybrid cross, all homozygotes occur once, monoheterozygotes occur twice, and diheterozygotes occur four times. The Punnett grid contains 4 homozygotes, 8 monoheterozygotes and 4 diheterozygotes.

Segregation by genotype corresponds to the following formula:

1AABB: 2AABBb: 1AAbb: 2AaBB: 4AaBBb: 2Aabb: 1aaBB: 2aaBBb: 1aabb.

Abbreviated as 1:2:1:2:4:2:1:2:1.

Among the F 2 hybrids, only two genotypes repeat the genotypes of the parental forms: AABB And aabb; in the rest, recombination of parental genes occurred. It led to the emergence of two new phenotypic classes: yellow wrinkled seeds and green smooth ones.

Having analyzed the results of dihybrid crossing for each pair of characters separately, Mendel established the third pattern: the independent nature of inheritance of different pairs of characters ( Mendel's III law). Independence is expressed in the fact that splitting for each pair of characteristics corresponds to the monohybrid crossing formula 3: 1. Thus, a dihybrid crossing can be represented as two simultaneously occurring monohybrid ones.

As was established later, the independent type of inheritance is due to the localization of genes in different pairs of homologous chromosomes. The cytological basis of Mendelian segregation is the behavior of chromosomes during cell division and the subsequent fusion of gametes during fertilization. In prophase I of the reduction division of meiosis, homologous chromosomes conjugate, and then in anaphase I they diverge to different poles, due to which allelic genes cannot enter the same gamete. When they diverge, non-homologous chromosomes freely combine with each other and move to the poles in different combinations. This determines the genetic heterogeneity of germ cells, and after their fusion during the process of fertilization, the genetic heterogeneity of zygotes, and as a consequence, the genotypic and phenotypic diversity of the offspring.

Independent inheritance of different pairs of traits makes it easy to calculate segregation formulas in di- and polyhybrid crosses, since they are based on simple monohybrid cross formulas. When calculating, the law of probability is used (the probability of the occurrence of two or more phenomena at the same time is equal to the product of their probabilities). A dihybrid cross can be decomposed into two, and a trihybrid cross into three independent monohybrid crosses, in each of which the probability of the manifestation of two different traits in F 2 is equal to 3: 1. Therefore, the formula for splitting the phenotype in F 2 dihybrid cross will be:

(3: 1) 2 = 9: 3: 3: 1,

trihybrid (3: 1) 3 = 27: 9: 9: 9: 3: 3: 3: 1, etc.

The number of phenotypes in an F2 polyhybrid cross is equal to 2 n, where n is the number of pairs of characteristics in which the parent individuals differ.

Formulas for calculating other characteristics of hybrids are presented in Table 1.

Table 1. Quantitative patterns of segregation in hybrid offspring
for various types of crossings

Quantitative characteristics	Type of crossing
	monohybrid	dihybrid	polyhybrid
Number of gamete types formed by hybrid F 1	2	2 2	2n
Number of gamete combinations during the formation of F 2	4	4 2	4n
Number of phenotypes F 2	2	2 2	2n
Number of genotypes F 2	3	3 2	3
Phenotype splitting in F 2	3: 1	(3: 1) 2	(3:1)n
Segregation by genotype in F 2	1: 2: 1	(1: 2: 1) 2	(1:2:1)n

The manifestation of the patterns of inheritance discovered by Mendel is possible only under certain conditions (independent of the experimenter). They are:

1. Equally probable formation by hybridomas of all varieties of gametes.
2. All possible combinations of gametes during the process of fertilization.
3. Equal viability of all varieties of zygotes.

If these conditions are not met, then the nature of segregation in the hybrid offspring changes.

The first condition may be violated due to the non-viability of one or another type of gamete, possibly due to various reasons, for example, the negative effect of another gene manifested at the gametic level.

The second condition is violated in the case of selective fertilization, in which there is a preferential fusion of certain types of gametes. Moreover, a gamete with the same gene can behave differently during the process of fertilization, depending on whether it is female or male.

The third condition is usually violated if the dominant gene has a lethal effect in the homozygous state. In this case, in F 2 monohybrid crossing as a result of the death of dominant homozygotes AA instead of a 3:1 split, a 2:1 split is observed. Examples of such genes are: the gene for platinum fur color in foxes, the gene for gray coat color in Shirazi sheep. (More details in the next lecture.)

The reason for deviation from Mendelian segregation formulas can also be incomplete manifestation of the trait. The degree of manifestation of the action of genes in the phenotype is denoted by the term expressivity. For some genes it is unstable and highly dependent on external conditions. An example is the recessive gene for black body color in Drosophila (mutation ebony), the expressivity of which depends on temperature, as a result of which individuals heterozygous for this gene can have a dark color.

Mendel's discovery of the laws of inheritance was more than three decades ahead of the development of genetics. The work “Experience with Plant Hybrids” published by the author was not understood and appreciated by his contemporaries, including Charles Darwin. The main reason for this is that at the time of the publication of Mendel’s work, chromosomes had not yet been discovered and the process of cell division, which, as mentioned above, constituted the cytological basis of Mendelian patterns, had not yet been described. In addition, Mendel himself doubted the universality of the patterns he discovered when, on the advice of K. Nägeli, he began to check the results obtained on another object - the hawkweed. Not knowing that the hawksbill reproduces parthenogenetically and, therefore, it is impossible to obtain hybrids from it, Mendel was completely discouraged by the results of the experiments, which did not fit into the framework of his laws. Under the influence of failure, he abandoned his research.

Recognition came to Mendel at the very beginning of the twentieth century, when in 1900 three researchers - G. de Vries, K. Correns and E. Cermak - independently published the results of their studies, reproducing Mendel's experiments, and confirmed the correctness of his conclusions . Since by this time mitosis, almost completely meiosis (its complete description was completed in 1905), as well as the process of fertilization, had been completely described, scientists were able to connect the behavior of Mendelian hereditary factors with the behavior of chromosomes during cell division. The rediscovery of Mendel's laws became the starting point for the development of genetics.

The first decade of the twentieth century. became the period of the triumphal march of Mendelism. The patterns discovered by Mendel were confirmed in the study of various characteristics in both plant and animal objects. The idea of ​​the universality of Mendel's laws arose. At the same time, facts began to accumulate that did not fit within the framework of these laws. But it was the hybridological method that made it possible to clarify the nature of these deviations and confirm the correctness of Mendel’s conclusions.

All pairs of characters that were used by Mendel were inherited according to the type of complete dominance. In this case, the recessive gene in the heterozygote has no effect, and the phenotype of the heterozygote is determined solely by the dominant gene. However, a large number of traits in plants and animals are inherited according to the type of incomplete dominance. In this case, the F 1 hybrid does not completely reproduce the trait of one or the other parent. The expression of the trait is intermediate, with a greater or lesser deviation in one direction or the other.

An example of incomplete dominance can be the intermediate pink color of flowers in night beauty hybrids obtained by crossing plants with a dominant red and recessive white color (see diagram).

Scheme of incomplete dominance in the inheritance of flower color in the night beauty

As can be seen from the diagram, the law of uniformity of first-generation hybrids applies in crossing. All hybrids have the same color - pink - as a result of incomplete dominance of the gene A. In the second generation, different genotypes have the same frequency as in Mendel’s experiment, and only the phenotypic segregation formula changes. It coincides with the formula for segregation by genotype - 1: 2: 1, since each genotype has its own characteristic. This circumstance facilitates the analysis, since there is no need for analytical crossing.

There is another type of behavior of allelic genes in a heterozygote. It is called codominance and is described in the study of the inheritance of blood groups in humans and a number of domestic animals. In this case, a hybrid whose genotype contains both allelic genes exhibits both alternative traits equally. Codominance is observed when inheriting blood groups of the A, B, 0 system in humans. People with a group AB(IV group) there are two different antigens in the blood, the synthesis of which is controlled by two allelic genes.

In his crossing experiments, Mendel used the hybridological method. Using this method, he studied inheritance for individual characters, and not for the entire complex, carried out an accurate quantitative accounting of the inheritance of each trait in a number of generations, and studied the character of the offspring of each hybrid separately . Mendel's first law is the law of uniformity of first generation hybrids. When crossing homozygous individuals that differ in one paraalternative (mutually exclusive) trait, all offspring in the first generation are uniform in both phenotype and genotype. Mendel carried out monohybrid crossings of pure pea lines that differed in one pair of alternative characters, for example, in the color of the peas (yellow and green). Peas with yellow seeds (dominant trait) were used as the mother plant, and peas with green seeds (recessive trait) were used as the father plant. As a result of meiosis, each plant produced one type of gamete. During meiosis, from each homologous pair of chromosomes, one chromosome with one of the allelic genes (A or a) went into gametes. As a result of fertilization, the pairing of homologous chromosomes was restored and hybrids were formed. All plants had only yellow seeds (by phenotype) and were heterozygous by genotype. The 1st generation hybrid Aa had one gene - A from one parent, and the second gene -a from the other parent and exhibited a dominant trait, hiding the recessive one. By genotype, all peas are heterozygous. The first generation is uniform and showed the trait of one of the parents. To record crosses, a special table is used, proposed by the English geneticist Punnett and called the Punnett grid. The gametes of the paternal individual are written out horizontally, and the gametes of the maternal individual vertically. At the intersections there are probable genotypes of the descendants. In the table, the number of cells depends on the number of gamete types produced by the individuals being crossed. Next, Mendel crossed hybrids with each other . Mendel's second law– the law of hybrid splitting. When hybrids of the 1st generation are crossed with each other, individuals with both dominant and recessive traits appear in the second generation, and splitting occurs according to the genotype in a ratio of 3:1 and 1:2:1 according to the genotype. As a result of crossing hybrids with each other, individuals were obtained with both dominant and recessive traits. Such splitting is possible with complete dominance.

HYPOTHESIS OF "PURITY" OF GAMETES

The law of splitting can be explained by the hypothesis of the “purity” of gametes. Mendel called the phenomenon of non-mixing of alleles and alternative characteristics in the gametes of a heterozygous organism (hybrid) the hypothesis of the “purity” of gametes. Two allelic genes are responsible for each trait. When hybrids (heterozygous individuals) are formed, allelic genes are not mixed, but remain unchanged. Hybrids - Aa - as a result of meiosis, form two types of gametes. Each gamete contains one of a pair of homologous chromosomes with a dominant allelic gene A or with a recessive allelic gene a. Gametes are pure from another allelic gene. During fertilization, male and female gametes carrying dominant and recessive alleles are freely combined. In this case, the homology of chromosomes and allelicity of genes are restored. As a result of the interaction of genes and fertilization, a recessive trait appeared (the green color of peas), the gene of which did not reveal its effect in the hybrid organism. Traits whose inheritance occurs according to the laws established by Mendel are called Mendelian. Simple Mendelian traits are discrete and controlled monogenically - i.e. one genome. In humans, a large number of traits are inherited according to Mendel's laws. Dominant traits include brown eye color, bradydactyly (short fingers), polydactyly (polydactyly, 6-7 fingers), myopia, and the ability to synthesize melanin. According to Mendel's laws, blood type and Rh factor are inherited according to the dominant type. Recessive traits include blue eyes, normal hand structure, the presence of 5 fingers, normal vision, albinism (inability to synthesize melanin)

Mendel's third law is the law of independent distribution of characteristics. This means that each gene of one allelic pair can appear in a gamete with any other gene from another allelic pair. For example, if an organism is heterozygous for two genes under study (AaBb), then it forms the following types of gametes: AB, Ab, aB, ab. That is, for example, gene A can be in the same gamete with both gene B and b. The same applies to other genes (their arbitrary combination with non-allelic genes).

Mendel's third law is already evident with dihybrid crossing(especially with trihybrid and polyhybrid), when pure lines differ in two studied characteristics. Mendel crossed a pea variety with yellow smooth seeds with a variety that had green wrinkled seeds and obtained exclusively yellow smooth seeds F 1 . Next, he grew F 1 plants from the seeds, allowed them to self-pollinate, and obtained F 2 seeds. And here he observed splitting: plants appeared with both green and wrinkled seeds. The most surprising thing was that among the second generation hybrids there were not only plants with smooth yellow and green wrinkled seeds. There were also yellow wrinkled and green smooth seeds, i.e., recombination of characters occurred, and combinations were obtained that were not found in the original parental forms.

Analyzing the quantitative ratio of different F2 seeds, Mendel discovered the following:

If we consider each trait separately, it was split in a ratio of 3:1, as in a monohybrid cross. That is, for every three yellow seeds there was one green one, and for every 3 smooth ones there was one wrinkled one.

Plants with new combinations of traits appeared.

The phenotypic ratio was 9:3:3:1, where for every nine yellow smooth pea seeds there were three yellow wrinkled, three green smooth and one green wrinkled.

Mendel's third law is well illustrated by the Punnett lattice. Here, the possible gametes of the parents (in this case, first-generation hybrids) are written in the row and column headings. The probability of producing each type of gamete is ¼. It is also equally likely that they will combine differently into one zygote.

We see that four phenotypes are formed, two of which did not previously exist. The ratio of phenotypes is 9: 3: 3: 1. The number of different genotypes and their ratio is more complex:

This results in 9 different genotypes. Their ratio is: 4: 2: 2: 2: 2: 1: 1: 1: 1. At the same time, heterozygotes are more common, and homozygotes are less common.

If we return to the fact that each trait is inherited independently, and a 3:1 split is observed for each, then we can calculate the probability of phenotypes for two traits of different alleles by multiplying the probability of manifestation of each allele (i.e., it is not necessary to use the Punnett lattice). Thus, the probability of smooth yellow seeds will be equal to ¾ × ¾ = 9/16, smooth green – ¾ × ¼ = 3/16, wrinkled yellow – ¼ × ¾ = 3/16, wrinkled green – ¼ × ¼ = 1/16. Thus, we get the same phenotypic ratio: 9:3:3:1.

Mendel's third law is explained by the independent divergence of homologous chromosomes of different pairs during the first division of meiosis. A chromosome containing gene A can, with equal probability, go into the same cell with both a chromosome containing gene B and a chromosome containing gene b. The chromosome with gene A is in no way linked to the chromosome with gene B, although they were both inherited from the same parent. We can say that as a result of meiosis, the chromosomes are mixed. The number of their different combinations is calculated by the formula 2 n, where n is the number of chromosomes of the haploid set. So, if a species has three pairs of chromosomes, then the number of different combinations of them will be 8 (2 3).

When the law of independent inheritance of characteristics does not apply

Mendel's third law, or the law of independent inheritance of traits, applies only to genes localized on different chromosomes or located on the same chromosome, but quite far from each other.

Basically, if genes are located on the same chromosome, then they are inherited together, that is, they exhibit linkage with each other, and the law of independent inheritance of traits no longer applies.

For example, if the genes responsible for the color and shape of pea seeds were on the same chromosome, then the first generation hybrids could form gametes of only two types (AB and ab), since during meiosis the parental chromosomes diverge independently of each other, but not individual genes. In this case, in the second generation there would be a 3:1 split (three yellow smooth to one green wrinkled).

However, it's not that simple. Due to the existence in nature of conjugation (bringing together) of chromosomes and crossing over (exchange of chromosome sections), genes located on homologous chromosomes also recombine. So, if a chromosome with the AB genes, during the process of crossing over, exchanges a section with the B gene with a homologous chromosome, whose section contains the b gene, then new gametes (Ab and, for example, aB) can be obtained. The percentage of such recombinant gametes will be less than if the genes were on different chromosomes. In this case, the probability of crossing over depends on the distance of genes on the chromosome: the further away, the greater the probability.