Notations in genetic problems
Standard symbols are used for the correct recording of crosses. The letter P (parentes) designates parent organisms, G (gametae) denotes gametes, i.e., sex cells whose fusion forms a zygote. Descendants (hybrids) are denoted by the letter F with a numerical index: F1 — the first generation, F2 — the second, and so on.
The female organism is traditionally denoted by the symbol ♀ (mirror of Venus), and the male by ♂ (shield and spear of Mars). When writing a cross, the female individual is placed on the left, and the gametes of each parent are positioned directly beneath them (often enclosed in circles to avoid confusion).
Descendant segregation is analyzed in two ways:
- By genotype — by the allele combination (letter notation).
- By phenotype — by the external expression of traits (color, shape, size).
Alleles and zygote types
Each trait is encoded by a pair of alleles. The uppercase letter denotes the dominant trait (expressed in the phenotype), and the lowercase letter denotes the recessive trait (suppressed in the presence of the dominant one).
- Homozygote — an organism with identical alleles: AA or aa.
- Heterozygote — with different alleles: Aa; the dominant trait is expressed in the phenotype.
- Dihomozygote — a homozygote for two pairs of genes: AABB or aabb.
- Diheterozygote — a heterozygote for two pairs of genes: AaBb.
Pure lines are homozygous organisms that do not show segregation upon self-pollination.
Mendel's first law — the law of uniformity
When crossing two homozygous individuals belonging to pure lines and differing in a single pair of alternative traits, the entire first generation of hybrids (F1) is uniform in both genotype and phenotype.
Example: crossing pea plants with purple flowers (AA) and white flowers (aa) yields only purple-flowered plants of the Aa genotype in F1. Similar results were obtained when crossing plants with yellow and green seeds, as well as with smooth and wrinkled seed shapes. This makes it possible to identify which trait is dominant.
Sample problem. The black coat gene (A) in cattle is dominant over the red coat gene (a). Crossing a black homozygous bull (AA) with red cows (aa) yields all offspring of the Aa genotype with a black coat.
Mendel's second law — the law of segregation
When two heterozygous offspring of the first generation (Aa × Aa) are crossed, trait segregation is observed in the second generation. Heterozygotes form two types of gametes (A and a) in equal proportions.
F2 results:
- Segregation by genotype: 1 AA : 2 Aa : 1 aa.
- Segregation by phenotype: 3 (dominant trait) : 1 (recessive).
Sample problem. Parents with normal hearing had a deaf child. Since deafness is a recessive trait (a) and the parents have normal hearing, both are heterozygotes (Aa). A 3:1 segregation is expected in the offspring: three children with normal hearing (1 AA + 2 Aa) to one deaf child (aa).
Mendel's third law — the law of independent assortment
When crossing individuals differing in two or more pairs of traits, the genes of each pair are inherited independently of one another and combine in all possible combinations. F1 hybrids are uniform, while F2 exhibits phenotypic segregation in a 9 : 3 : 3 : 1 ratio.
The diheterozygote AaBb forms four types of gametes: AB, Ab, aB, ab. Crossing two diheterozygotes yields 16 combinations, which are conveniently depicted using a Punnett square — a table where female gametes are written in the rows, male gametes in the columns, and the genotypes of the offspring at the intersections.
Sample problem. In beans, yellow pod color (A) is dominant over green (a), and black seed color (B) is dominant over white (b). Upon self-pollination of a diheterozygous AaBb plant, the offspring segregate as 9 (yellow pods, black seeds) : 3 (yellow, white) : 3 (green, black) : 1 (green, white). The probability of plants with green pods and white seeds is 1/16.
Conditions for Mendel's laws to hold
The inheritance patterns described by Mendel hold true under a number of conditions:
- The genes under study must be located in different pairs of homologous chromosomes (for the third law).
- Alleles exhibit complete dominance.
- All types of gametes are formed in equal amounts and are equally viable.
- All descendant genotypes have equal survival rates.
- A sufficiently large number of offspring is analyzed for statistical manifestation of segregation.
Key points
- P — parents, G — gametes, F — offspring; ♀ is placed first when recording a cross.
- A homozygote produces one type of gamete, a heterozygote produces two, and a diheterozygote produces four.
- Mendel's first law: F1 from crossing pure lines is uniform.
- Second law: in F2, the phenotypic segregation is 3:1 and the genotypic segregation is 1:2:1.
- Third law: in a dihybrid cross, F2 segregates in a 9:3:3:1 ratio.
- A Punnett square is used to analyze dihybrid and more complex crosses.
- The dominant trait masks the recessive one; the recessive trait appears only in the homozygous state.
- Mendel's laws are valid under independent gene inheritance and complete dominance.