Mendel's laws

    In Mendel's experiments, when pea varieties with yellow and green seeds were crossed, all the offspring (i.e., first-generation hybrids) turned out to have yellow seeds. It didn't matter which seed (yellow or green) the mother (parent) plants grew from. This means that both parents are equally capable of passing on their traits to their offspring.
       

    Similar results were found in experiments that took other traits into account. For example, when plants with smooth and wrinkled seeds were crossed, all the offspring had smooth seeds. When plants with purple and white flowers were crossed, all hybrids had only purple flower petals, etc.
      

    This pattern was called Mendel's first law, or the law of uniformity of first-generation hybrids. The state (allele) of a trait that manifests itself in the first generation is called dominant; the state (allele) that does not manifest itself in the first generation of hybrids is called recessive.
G. Mendel proposed to designate the "makings" of traits (in modern terminology, genes) with letters of the Latin alphabet. The states belonging to the same pair of traits are denoted by the same letter, but the dominant allele is capitalized and the recessive allele is lowercase.

Mendel's second law.

    When heterozygous hybrids of the first generation are crossed with each other (self-pollination or consanguineous crossing), individuals with both dominant and recessive trait states appear in the second generation, i.e., there is a splitting that occurs in certain respects. For example, in Mendel's experiments, out of 929 plants of the second generation, 705 had purple flowers and 224 had white flowers. In an experiment that took into account the color of the seeds, out of 8023 pea seeds obtained in the second generation, there were 6022 yellow and 2001 green seeds, and out of 7324 seeds for which the shape of the seed was taken into account, there were 5474 smooth and 1850 wrinkled seeds. Summarizing the actual material, Mendel concluded that in the second generation, 75% of individuals have a dominant state of the trait, and 25% have a recessive state (3:1 split). This pattern is called Mendel's second law, or the law of splitting.
       
    According to this law, and using modern terminology, the following conclusions can be drawn: a) gene alleles, being in the heterozygous state, do not change each other's structure; b) when gametes mature, hybrids produce approximately the same number of gametes with dominant and recessive alleles; c) during fertilization, male and female gametes carrying dominant and recessive alleles are freely combined.
    

    When crossing two heterozygotes (Aa), each of which produces two types of gametes (half with the dominant allele - A, half with the recessive allele - a), four possible combinations should be expected.   An egg with the A allele can be fertilized with the same probability by both a sperm with the A allele and a sperm with the a allele; and an egg with the a allele can be fertilized by a sperm with either the A allele or the a allele.
   
    In appearance (phenotype), AA and AA individuals do not differ, so the cleavage is 3:1. By genotype, individuals are distributed in the ratio IAA:2AA:aa. It is clear that if offspring are obtained from each group of individuals of the second generation only by self-pollination, then the first (AA) and last (aa) groups (they are homozygous) will give only uniform offspring (without cleavage), and heterozygous (Aa) forms will give cleavage in a ratio of 3:1.
        

    Thus, the second Mendel's law, or the law of cleavage, is formulated as follows: when two first-generation hybrids are crossed, analyzed for one alternative pair of trait states, the offspring will have a 3:1 split in phenotype and a 1:2:1 split in genotype.

Mendel's third law, or the law of independent inheritance of traits.

    When studying the cleavage in hybrid crosses, Mendel noticed the following circumstance. When crossing plants with yellow smooth (AABB) and green wrinkled (aabb) seeds, new combinations of traits appeared in the second generation: yellow wrinkled (aabb) and green smooth (aabb), which were not found in the original forms. From this observation, Mendel concluded that the cleavage for each trait occurs independently of the other trait. In this example, the shape of the seeds was inherited independently of their color. This pattern is called Mendel's third law, or the law of independent gene distribution.
        

    Mendel's third law is formulated as follows: when homozygous individuals differing in two (or more) traits are crossed, independent inheritance and combination of trait states are observed in the second generation if the genes that determine them are located in different pairs of chromosomes. This is possible because during meiosis, the distribution (combination) of chromosomes in germ cells during their maturation is independent and can lead to the appearance of offspring with a combination of traits different from the parental and ancestral individuals.
   

    To record crosses, special lattices are often used, which were proposed by the English geneticist Pennet (Pennet lattice). They are convenient to use when analyzing polyhybrid crosses. The principle of constructing the lattice is that the gametes of the father's individual are recorded horizontally from the top, the gametes of the mother's individual are recorded vertically from the left, and the probable genotypes of the offspring are recorded at the intersections.