Dihybrid Crosses and Independent Assortment

• A dihybrid cross is a cross between two different lines/genes that differ in two observed traits
• Mendel's principle of independent assortment states that the alleles of each gene assort independently
• Dihybrid crosses show the likelihood of certain traits appearing together in offspring

Dihybrid Cross Phenotypic Ratio

• A typical dihybrid cross (both parents heterozygous for both traits) results in a phenotypic ratio of 9:3:3:1 in the offspring
• 9 represents both dominant traits
• 3 represents dominant for the first trait, recessive for the second trait
• Another 3 represents recessive for the first trait, dominant for the second trait
• 1 represents both recessive traits

Example of a Dihybrid Cross

• In pea plants, genes for seed color and shape assort independently
• Yellow (Y) is dominant to green (y), and round (R) is dominant to wrinkled (r)
• Cross involves plants heterozygous for both traits (YyRr)

Set up a Punnett Square

• List all possible allele combinations that each parent can contribute
• A YyRr plant produces four types of gametes: YR, Yr, yR, and yr
• Set up a 4x4 Punnett square

Fill in the Punnett Square

• Combine the alleles from each parent to fill in the cells of the Punnett square
• Each cell represents a possible genotype of the offspring

Determine the Phenotypes

• Determine the phenotypes from the genotypes
• YR, Yr, yR, and yr represent the traits

Count the Offspring

• Count the number of offspring with each phenotype
• There will be 9 offspring with yellow, round seeds (Y_R_)
• There will be 3 offspring with yellow, wrinkled seeds (Y_rr)
• There will be 3 offspring with green, round seeds (yyR_)
• There will be 1 offspring with green, wrinkled seeds (yyrr)

Dihybrid Cross Genotypic Ratio

• The genotypic ratio from a dihybrid cross is more complex than the phenotypic ratio
• For a self-cross of a dihybrid organism (AaBb x AaBb) the genotypic ratio is 1:2:1:2:4:2:1:2:1
• 1 AABB
• 2 AABb
• 1 AAbb
• 2 AaBB
• 4 AaBb
• 2 Aabb
• 1 aaBB
• 2 aaBb
• 1 aabb
• The ratio represents different combinations of homozygous and heterozygous alleles for the two genes

Independent Assortment

• The 9:3:3:1 phenotypic ratio results from independent assortment
• Independent assortment occurs when the alleles of different genes sort independently of one another during gamete formation
• This occurs during meiosis I, where homologous chromosomes and their genes are randomly distributed into gametes

Linkage

• If genes are located near each other on the same chromosome, they are linked and do not assort independently
• Linked genes tend to be inherited together, so the phenotypic ratio deviates from 9:3:3:1

Chi-Square Analysis

• Chi-square test: A statistical test used to determine if the observed results of a cross align with the expected results
• Used to test the hypothesis that two genes assort independently
• Formulate a null hypothesis: There is no significant difference between observed and expected ratios
• Calculate the chi-square statistic (χ2) using the formula: χ2 = Σ [(Observed - Expected)^2 / Expected]
• Determine the degrees of freedom (df)
• df = (number of phenotypes - 1)
• For a dihybrid cross, df = (4 - 1) = 3
• Compare the calculated χ2 value to a critical value from a chi-square distribution table
• If the calculated χ2 value is less than the critical value, you fail to reject the null hypothesis
• Results observed are consistent with independent assortment
• If the calculated χ2 value is greater than the critical value, reject the null hypothesis
• Observed results are not consistent with independent assortment, potentially indicating linkage or another factor affecting inheritance

Applications of Dihybrid Crosses

• Dihybrid crosses predict the likelihood of inheriting specific combinations of traits
• Important in agriculture for breeding plants and animals with desirable traits
• Aids understanding of the genetic basis of complex traits and diseases

Limitations of Dihybrid Crosses

• Dihybrid crosses assume that the genes assort independently
• If genes are linked, then the results will not follow the expected 9:3:3:1 ratio
• These crosses only consider two genes at a time; many traits are influenced by multiple genes interacting in complex ways.

Explanation of dihybrid crosses, where two genes are observed. Mendel's principle of independent assortment is highlighted; alleles of each gene assort independently. The phenotypic ratio of 9:3:3:1 is thoroughly explained using the example of pea plants and their seed color and shape.