Punnett squares Knowledge-Based Study

Study notes

1. Foundations of Inheritance

   In Mendelian genetics, traits are controlled by discrete units of inheritance known as genes. A gene can exist in alternative forms called alleles. An organism carries two alleles for each autosomal gene—one inherited from each parent.

   Key terminology includes:

   • Dominant Allele: An allele that is fully expressed whenever present, typically represented by an uppercase letter (for example, B).
   • Recessive Allele: An allele that is masked in the presence of a dominant allele and only expressed when two copies are present, represented by a lowercase letter (for example, b).
   • Homozygous: Having two identical alleles for a particular gene (such as BB or bb).
   • Heterozygous: Having two different alleles for a particular gene (such as Bb).
   • Genotype: The genetic makeup or combination of alleles in an organism.
   • Phenotype: The observable physical or physiological traits of an organism resulting from its genotype and environmental influences.

   According to Gregor Mendel's Law of Segregation, during meiosis (gamete formation), the two alleles for each gene segregate from each other so that each gamete carries only one allele for each gene.

   Setting Up a Monohybrid Cross

   A Punnett square is a visual grid designed by Reginald Punnett used to predict the possible genotypes and phenotypes of offspring from a particular genetic cross. A monohybrid cross examines the inheritance of a single characteristic.

   Step-by-Step Procedure

   1. Identify Parental Genotypes: Determine the genetic makeup of both parents. For example, consider a cross between two heterozygous purple-flowered pea plants (Pp × Pp), where purple (P) is dominant to white (p).
   2. Determine Possible Gametes: By segregation, each parent produces gametes containing either the P allele or the p allele with equal probability (50% P, 50% p).
   3. Set Up the Grid: Draw a 2 × 2 grid. Write the gametes from one parent across the top and the gametes from the second parent along the left side.
   4. Fill the Cells: Combine the corresponding row and column alleles inside each box to represent possible fertilization events.

   In this cross, the four resulting boxes contain: PP, Pp, Pp, and pp.

   Interpreting the Results

   Each box within a Punnett square represents an equally likely outcome. Because fertilization is a random process, each box represents a 25% (or 1/4) probability for each fertilization event.

   Analyzing the Pp × Pp Cross

   • Genotypic Ratio: Counting the combinations yields 1 PP : 2 Pp : 1 pp. In terms of percentages, this corresponds to 25% homozygous dominant, 50% heterozygous, and 25% homozygous recessive.
   • Phenotypic Ratio: Because both PP and Pp display the dominant purple flower phenotype, 3 out of 4 offspring are expected to have purple flowers, while 1 out of 4 (pp) will have white flowers. The phenotypic ratio is therefore 3 purple : 1 white.

   Important Note on Probability: These ratios describe mathematical probabilities, not exact guarantees in small sample sizes. Each offspring represents an independent event.

   The Testcross

   To determine the unknown genotype of an individual showing a dominant phenotype (which could be either homozygous dominant or heterozygous), geneticists perform a testcross by breeding that individual with a known homozygous recessive individual (pp). If any offspring display the recessive phenotype, the parent with the dominant phenotype must be heterozygous.

   Tracking Two Traits Simultaneously

   A dihybrid cross analyzes the inheritance of two distinct traits located on different chromosome pairs. Mendel formulated the Law of Independent Assortment, which states that alleles of two or more different genes sort into gametes independently of one another.

   Determining Gametes for Two Genes

   Consider two traits: seed shape (Round R dominant to wrinkled r) and seed color (Yellow Y dominant to green y). For a dihybrid heterozygous individual with the genotype RrYy:

   • Apply the product rule across both gene pairs: R can pair with Y or y, and r can pair with Y or y.
   • The four possible gamete types produced in equal proportions (25% each) are: RY, Ry, rY, and ry.

   The 4 × 4 Grid

   When two dihybrid heterozygotes are crossed (RrYy × RrYy), a 4 × 4 grid with 16 squares is required. Combining the gametes produces the classic Mendelian phenotypic ratio:

   • 9/16 Round, Yellow (dominant for both traits)
   • 3/16 Round, green (dominant for first, recessive for second)
   • 3/16 wrinkled, Yellow (recessive for first, dominant for second)
   • 1/16 wrinkled, green (recessive for both traits)

   This characteristic 9 : 3 : 3 : 1 ratio confirms the independent assortment of unlinked genes.