Mendel's Laws of Inheritance & Monohybrid/Dihybrid Crosses - Tenth Grade Science
Heredity is the biological mechanism by which physical, physiological, and biochemical traits are transmitted from parents to their offspring across successive generations, maintaining species continuity while generating genetic variation. For centuries, the prevailing scientific hypothesis was the blending theory of inheritance, which posited that maternal and paternal fluids permanently mixed in the offspring like paints, diluting rare traits over time. In the mid-nineteenth century, an Austrian Augustinian monk named Gregor Johann Mendel overturned this model through hybridization experiments conducted on garden pea plants (Pisum sativum) between 1856 and 1863. Mendel demonstrated that inheritance is particulate: traits are governed by discrete, physical hereditary units—now known as genes—that remain distinct and unblended through generations. In this chapter, you will investigate Mendel's experimental methodology and his selection of garden peas, analyze monohybrid crosses and the Laws of Dominance and Segregation, examine dihybrid crosses and the Law of Independent Assortment, construct Punnett square matrices, and evaluate the chromosomal basis of inheritance.
Mendel's Experimental System: Why the Garden Pea?
Mendel's experimental success was driven by his selection of Pisum sativum (the common garden pea) as his model organism and his quantitative statistical record-keeping.
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| ADVANTAGES OF PISUM SATIVUM IN GENETICS |
+-----------------------------------+-----------------------------------------------+
| Biological Feature | Experimental Advantage |
+-----------------------------------+-----------------------------------------------+
| Well-defined Contrasting Traits | Seven distinct, observable binary phenotypes |
| | with no intermediate shades (e.g., Tall/Dwarf)|
| Bisexual Floral Architecture | Enclosed keeled petals naturally enforce |
| | strict self-pollination (Autogamy). |
| Ease of Artificial Hybridization | Anthers easily removed (emasculation) to |
| | permit controlled cross-pollination. |
| Short Life Cycle | Annual plant matures in months, yielding |
| | multiple generations in a single year. |
| High Fecundity (Seed Yield) | A single cross produces hundreds of seeds, |
| | providing statistical sample sizes. |
+-----------------------------------+-----------------------------------------------+
The Seven Pairs of Contrasting Traits
Mendel selected seven discrete morphological characters, each possessing two contrasting alternative character states (phenotypes):
+-----------------------+-----------------------+-----------------------+
| Character | Dominant Phenotype | Recessive Phenotype |
+-----------------------+-----------------------+-----------------------+
| 1. Stem Height | Tall (T) | Dwarf (t) |
| 2. Flower Color | Violet / Purple (W) | White (w) |
| 3. Flower Position | Axial (A) | Terminal (a) |
| 4. Pod Shape | Inflated / Full (I) | Constricted (i) |
| 5. Pod Color | Green (G) | Yellow (g) |
| 6. Seed Shape | Round (R) | Wrinkled (r) |
| 7. Seed Color | Yellow (Y) | Green (y) |
+-----------------------+-----------------------+-----------------------+
Pure-Breeding Lines and Controlled Cross-Pollination
Mendel began his investigations by self-pollinating his pea plants over several generations until he established true-breeding (pure-breeding) homozygous lines: plants that consistently produced progeny with identical traits generation after generation.
To perform cross-pollination between two contrasting true-breeding lines: Emasculation: He opened an immature floral bud of the designated female parent and removed the anthers with fine forceps before they could dehisce, preventing self-pollination. Bagging: The emasculated flower was enclosed in a paper or butter-paper bag to prevent accidental contamination by stray airborne pollen. Cross-Pollination: When the stigma matured, pollen from the designated male parent was brushed onto the receptive stigma, and the flower was re-bagged until seeds matured.
Monohybrid Inheritance: Segregation and Dominance
A monohybrid cross is a genetic hybridization between two parent organisms that differ in only one specific contrasting character (such as stem height).
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| MENDELIAN MONOHYBRID CROSS (STEM HEIGHT) |
+-----------------------------------------------------------------------------------+
| |
| P-Generation: Homozygous Tall (TT) x Homozygous Dwarf (tt) |
| Gametes: (T) (t) |
| \ / |
| F1-Generation: Heterozygous Tall (Tt) |
| (100% Phenotypically Tall) |
| |
| Selfing F1 x F1: (Tt) x (Tt) |
| F1 Gametes: (T) and (t) x (T) and (t) |
| |
| F2-PUNNETT SQUARE: |
| +-------------------+-------------------+ |
| | T (1/2) | t (1/2) | |
| +------------------------+-------------------+-------------------+ |
| | T (1/2) | TT (Tall) | Tt (Tall) | |
| +------------------------+-------------------+-------------------+ |
| | t (1/2) | Tt (Tall) | tt (Dwarf) | |
| +------------------------+-------------------+-------------------+ |
| |
| F2 PHENOTYPIC RATIO: 3 Tall : 1 Dwarf (3:1 Ratio) |
| F2 GENOTYPIC RATIO: 1 TT : 2 Tt : 1 tt (1:2:1 Ratio) |
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The Monohybrid Cross Protocol
Mendel crossed a pure-breeding tall pea plant ($TT$) with a pure-breeding dwarf pea plant ($tt$): The F1 Generation (First Filial Generation): Every offspring plant in the F1 generation was tall. None were dwarf, and none were of intermediate height. The dwarf phenotype appeared to have vanished completely. The F2 Generation (Second Filial Generation): Mendel allowed the F1 tall plants to undergo self-pollination. In the resulting F2 generation, the dwarf phenotype reappeared in viable, healthy plants. Statistical Counting: Across 1,064 F2 offspring, Mendel counted 787 tall plants and 277 dwarf plants, establishing an empirical ratio of $2.84:1$, which approximates the integer ratio of $3:1$.
Formulating the Law of Dominance
From these results, Mendel formulated the Law of Dominance:
Characters are controlled by discrete physical units called factors (now called genes). In a diploid organism, these factors occur in pairs (alleles). In a dissimilar pair of factors (heterozygous condition, $Tt$), one factor masks or suppresses the expression of the other. The expressed factor is designated as dominant (the tall allele, $T$), while the unexpressed, masked factor is designated as recessive (the dwarf allele, $t$). The recessive trait is expressed only when the organism is homozygous for that factor ($tt$).
Formulating the Law of Segregation (Purity of Gametes)
To explain why the dwarf trait reappeared unaltered in the F2 generation, Mendel formulated the Law of Segregation:
The two alleles of a gene pair in a diploid organism do not blend or contaminate one another; they remain distinct throughout the life of the individual. During the formation of gametes (meiosis), the two alleles of a gene pair separate (segregate) from each other so that each gamete receives only one allele of the pair. Consequently, gametes are always pure for a particular trait, carrying either the dominant allele or the recessive allele, never both.
When male and female gametes fuse randomly at fertilization, the allelic pairs are restored: Homozygous dominant ($TT$, $25\%$ of F2): Phenotypically tall. Heterozygous ($Tt$, $50\%$ of F2): Phenotypically tall due to dominance. Homozygous recessive ($tt$, $25\%$ of F2): Phenotypically dwarf.
This yields the phenotypic ratio of $3\text{ Tall} : 1\text{ Dwarf}$ and the genotypic ratio of $1\text{ }TT : 2\text{ }Tt : 1\text{ }tt$.
Dihybrid Inheritance: The Law of Independent Assortment
A dihybrid cross is a genetic hybridization between two parent organisms that differ simultaneously in two distinct, independent contrasting characters.
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| MENDELIAN DIHYBRID CROSS (SEED SHAPE & COLOR) |
+-----------------------------------------------------------------------------------+
| |
| P-Generation: Round Yellow Seed (RRYY) x Wrinkled Green Seed (rryy) |
| P-Gametes: (RY) (ry) |
| \ / |
| F1-Generation: Heterozygous Round Yellow (RrYy) |
| (100% Round Yellow Phenotype) |
| |
| F1 Gamete Types: Four equal classes: RY, Ry, rY, ry (1:1:1:1) |
| |
| F2-PUNNETT SQUARE MATRIX (16 Possible Zygotic Combinations): |
| +-------+--------------------+--------------------+--------------------+--------+
| | | RY (1/4) | Ry (1/4) | rY (1/4) | ry (1/4|
| +-------+--------------------+--------------------+--------------------+--------+
| |RY(1/4)| RRYY (Rnd, Ylw) | RRYy (Rnd, Ylw) | RrYY (Rnd, Ylw) | RrYy...|
| |Ry(1/4)| RRYy (Rnd, Ylw) | RRyy (Rnd, Grn) | RrYy (Rnd, Ylw) | Rryy...|
| |rY(1/4)| RrYY (Rnd, Ylw) | RrYy (Rnd, Ylw) | rrYY (Wrk, Ylw) | rrYy...|
| |ry(1/4)| RrYy (Rnd, Ylw) | Rryy (Rnd, Grn) | rrYy (Wrk, Ylw) | rryy...|
| +-------+--------------------+--------------------+--------------------+--------+
| |
| F2 PHENOTYPIC DISTRIBUTION: |
| - Round, Yellow (Both Dominant): 9 / 16 (Parental phenotype) |
| - Round, Green (Dominant / Recessive): 3 / 16 (Recombinant phenotype) |
| - Wrinkled, Yellow (Recessive / Dominant): 3 / 16 (Recombinant phenotype) |
| - Wrinkled, Green (Both Recessive): 1 / 16 (Parental phenotype) |
| |
| Classic Dihybrid Phenotypic Ratio = 9 : 3 : 3 : 1 |
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The Dihybrid Protocol: Seed Shape and Seed Color
Mendel crossed a pure-breeding pea plant bearing round, yellow seeds ($RRYY$) with a pure-breeding plant bearing wrinkled, green seeds ($rryy$): Round seed shape ($R$) is dominant over wrinkled ($r$). Yellow seed color ($Y$) is dominant over green ($y$).
In the F1 generation, all offspring were heterozygous round yellow ($RrYy$).
When the F1 plants were self-pollinated ($RrYy \times RrYy$), four distinct phenotypic classes emerged in the F2 generation in a characteristic $9:3:3:1$ ratio: 9 Round, Yellow (parental phenotype) 3 Round, Green (new recombinant phenotype) 3 Wrinkled, Yellow (new recombinant phenotype) 1 Wrinkled, Green (parental phenotype)
The emergence of the recombinant phenotypes—Round Green and Wrinkled Yellow—proved that seed shape and seed color are inherited independently.
Formulating the Law of Independent Assortment
From his dihybrid results, Mendel formulated the Law of Independent Assortment:
When two pairs of traits are combined in a hybrid, the segregation of alleles of one gene pair during gamete formation is completely independent of the segregation of alleles of the other gene pair.
The alleles for seed shape ($R$ and $r$) segregate into gametes in a $1:1$ ratio, independently of how the alleles for seed color ($Y$ and $y$) segregate. This independent assortment generates four types of gametes in equal proportions: $25\%\text{ }RY, \quad 25\%\text{ }Ry, \quad 25\%\text{ }rY, \quad 25\%\text{ }ry$
Random fertilization among these four male and female gamete types generates the 16 combinations visualized in a $4 \times 4$ Punnett square.
Modern genetics has clarified that Mendel's Law of Independent Assortment holds true when the genes governing the traits reside on non-homologous chromosomes, or far apart on the same chromosome. Genes located close together on the same chromosome exhibit genetic linkage, deviating from independent assortment.
Molecular and Chromosomal Basis of Mendelian Genetics
In 1902, Walter Sutton and Theodor Boveri formulated the Chromosomal Theory of Inheritance, demonstrating that chromosomes provide the physical vehicle for Mendel's hereditary factors.
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| PARALLELISM BETWEEN GENES AND CHROMOSOMES |
+-----------------------------------+-----------------------------------------------+
| Mendelian Factors (Genes) | Chromosomes in Meiosis |
+-----------------------------------+-----------------------------------------------+
| Occur in pairs in somatic cells | Occur in homologous pairs in diploid cells |
| Segregate equally into gametes | Homologous chromosomes segregate during |
| during gametogenesis | Anaphase I of meiosis |
| Assort independently into gametes | Non-homologous chromosome pairs align and |
| during reproduction | assort independently at Metaphase I |
| Restored to pairs upon syngamy | Diploid chromosome number restored at syngamy |
+-----------------------------------+-----------------------------------------------+
From Factors to DNA and Enzymes
At the molecular level: A gene is a functional segment of deoxyribonucleic acid (DNA) that encodes the amino acid sequence of a specific protein or enzyme. The dominant tall allele ($T$) encodes a functional enzyme (gibberellin 3-$\beta$-hydroxylase) that catalyzes the synthesis of the plant hormone gibberellin, which drives internodal stem elongation. The recessive dwarf allele ($t$) contains a single nucleotide substitution mutation that alters an amino acid in the enzyme's catalytic site, rendering the enzyme inactive. Without functional gibberellin, stem internodes fail to elongate, resulting in a dwarf plant.
Heterozygous plants ($Tt$) are tall because a single copy of the dominant allele produces sufficient active enzyme to synthesize adequate gibberellin, explaining why the recessive trait is masked.
Chapter Exercises
Exercise 1: In garden peas, axial flower position ($A$) is dominant over terminal flower position ($a$), and tall stem height ($T$) is dominant over dwarf height ($t$). A heterozygous tall plant with axial flowers is cross-pollinated with a dwarf plant bearing terminal flowers. Determine the genotypes of both parents, write down the gamete types each parent produces, construct a Punnett square, and state the expected phenotypic and genotypic ratios of the offspring.
Exercise 2: Contrast the genetic outcome of self-pollinating an F1 heterozygous tall pea plant ($Tt$) with that of performing a test cross (crossing the F1 tall plant with a homozygous recessive dwarf plant, $Tt \times tt$), providing phenotypic and genotypic ratios for both crosses.
Exercise 3: Explain the molecular mechanism by which a single recessive allele ($t$) causes a garden pea plant to be dwarf, explaining why a heterozygous plant ($Tt$) displays a normal tall phenotype.
Solutions and Explanations
Solution 1: The heterozygous tall plant with axial flowers has the genotype $TtAa$. The dwarf plant with terminal flowers is homozygous recessive for both traits, possessing the genotype $ttaa$. The heterozygous parent ($TtAa$) produces four distinct gamete types in equal proportions through independent assortment: $1/4\text{ }TA, 1/4\text{ }Ta, 1/4\text{ }tA,$ and $1/4\text{ }ta$. The homozygous recessive parent ($ttaa$) produces only one gamete type: $100\text{ percent }ta$. Constructing a Punnett square combining these gametes yields four equally probable offspring classes: First, $TA \times ta \rightarrow TtAa$ (Phenotype: Tall with Axial flowers); Second, $Ta \times ta \rightarrow Ttaa$ (Phenotype: Tall with Terminal flowers); Third, $tA \times ta \rightarrow ttAa$ (Phenotype: Dwarf with Axial flowers); Fourth, $ta \times ta \rightarrow ttaa$ (Phenotype: Dwarf with Terminal flowers). The expected phenotypic ratio is $1\text{ Tall Axial} : 1\text{ Tall Terminal} : 1\text{ Dwarf Axial} : 1\text{ Dwarf Terminal}$ (a $1:1:1:1$ ratio). The genotypic ratio is $1\text{ }TtAa : 1\text{ }Ttaa : 1\text{ }ttAa : 1\text{ }ttaa$.
Solution 2: Self-pollinating an F1 heterozygous tall pea plant ($Tt \times Tt$) involves crossing two parents that each produce two gamete types ($1/2\text{ }T$ and $1/2\text{ }t$). Random fertilization yields three genotypes: $1/4\text{ }TT, 1/2\text{ }Tt,$ and $1/4\text{ }tt$, establishing a genotypic ratio of $1\text{ }TT : 2\text{ }Tt : 1\text{ }tt$. Because $T$ is dominant over $t$, the $TT$ and $Tt$ plants are phenotypically tall, yielding a phenotypic ratio of $3\text{ Tall} : 1\text{ Dwarf}$ ($75\%$ tall, $25\%$ dwarf). In contrast, performing a test cross involves crossing the heterozygous tall plant ($Tt$) with a homozygous recessive dwarf tester ($tt$). The $Tt$ parent produces two gamete types ($1/2\text{ }T$ and $1/2\text{ }t$), while the $tt$ tester produces only $t$ gametes. Random combination yields two genotypes in equal proportions: $1/2\text{ }Tt$ and $1/2\text{ }tt$, establishing a genotypic ratio of $1\text{ }Tt : 1\text{ }tt$. The resulting phenotypic ratio is $1\text{ Tall} : 1\text{ Dwarf}$ ($50\%$ tall, $50\%$ dwarf). The test cross is used experimentally to determine whether an individual displaying a dominant phenotype is homozygous ($TT$) or heterozygous ($Tt$), because a homozygous dominant parent would produce $100\%$ tall offspring in a test cross.
Solution 3: At the molecular level, stem height in garden peas is regulated by the gene *Le* (standing for *length*), which encodes the metabolic enzyme gibberellin 3-$\beta$-hydroxylase. This enzyme catalyzes the conversion of inactive gibberellin precursor ($\text{GA}_{20}$) into biologically active gibberellin ($\text{GA}_1$), a plant hormone that promotes mitotic division and cell elongation in stem internodes. The dominant allele ($T$, or *Le*) possesses the standard wild-type nucleotide sequence, producing a functional enzyme that synthesizes normal levels of active gibberellin, resulting in tall stem growth. The recessive allele ($t$, or *le*) contains a single nucleotide substitution mutation (a missense mutation substituting a threonine amino acid for an alanine in the polypeptide chain), which disrupts the enzyme's catalytic site and reduces its enzymatic activity by over ninety-five percent. In a homozygous recessive dwarf plant ($tt$), both alleles encode non-functional enzymes; active gibberellin cannot be synthesized, internodes fail to elongate, and the plant remains dwarf. A heterozygous plant ($Tt$) displays a normal tall phenotype because a single copy of the dominant allele produces enough functional gibberellin 3-$\beta$-hydroxylase enzyme to synthesize adequate active gibberellin for normal internodal elongation.