When Mendel considered two traits per cross (dihybrid, as opposed to single-trait-crosses, monohybrid), The resulting (F2) generation did not have 3:1 dominant:recessive phenotype ratios. The two traits, if considered to inherit independently, fit into the principle of segregation. Instead of 4 possible genotypes from a monohybrid cross, dihybrid crosses have as many as 16 possible genotypes.
Mendel realized the need to conduct his experiments on more complex situations. He performed experiments tracking two seed traits: shape and color. A cross concerning two traits is known as a dihybrid cross.
Crosses With Two Traits
Smooth seeds (S) are dominant over wrinkled (s) seeds.
Yellow seed color (Y) is dominant over green (g).
Again, meiosis helps us understand the behavior of alleles.
The inheritance of two traits on different chromosomes can be explained by meiosis.
Methods, Results, and Conclusions
Mendel started with true-breeding plants that had smooth, yellow seeds and crossed them with true-breeding plants having green, wrinkled seeds. All seeds in the F1 had smooth yellow seeds. The F2 plants self-fertilized, and produced four phenotypes:
315 smooth yellow
108 smooth green
101 wrinkled yellow
32 wrinkled green
Mendel analyzed each trait for separate inheritance as if the other trait were not present.The 3:1 ratio was seen separately and was in accordance with the Principle of Segregation. The segregation of S and s alleles must have happened independently of the segregation of Y and y alleles. The chance of any gamete having a Y is 1/2; the chance of any one gamete having a S is 1/2.The chance of a gamete having both Y and S is the product of their individual chances (or 1/2 X 1/2 = 1/4).
The chance of two gametes forming any given genotype is 1/4 X 1/4 (remember, the product of their individual chances). Thus, the Punnett Square has 16 boxes. Since there are more possible combinations to produce a smooth yellow phenotype (SSYY, SsYy, SsYY, and SSYy), that phenotype is more common in the F2.
From the results of the second experiment, Mendel formulated the Principle of Independent Assortment -- that when gametes are formed, alleles assort independently. If traits assort independent of each other during gamete formation, the results of the dihybrid cross can make sense. Since Mendel's time, scientists have discovered chromosomes and DNA. We now interpret the Principle of Independent Assortment as alleles of genes on different chromosomes are inherited independently during the formation of gametes. This was not known to Mendel.
Punnett squares deal only with probability of a genotype showing up in the next generation. Usually if enough offspring are produced, Mendelian ratios will also be produced.
Step 1 - definition of alleles and determination of dominance.
Step 2 - determination of alleles present in all different types of gametes.
Step 3 - construction of the square.
Step 4 - recombination of alleles into each small square.
Step 5 - Determination of Genotype and Phenotype ratios in the next generation.
Step 6 - Labeling of generations, for example P1, F1, etc.
While answering genetics problems, there are certain forms and protocols that will make unintelligible problems easier to do. The term "true-breeding strain" is a code word for homozygous. Dominant alleles are those that show up in the next generation in crosses between two different "true-breeding strains".
The key to any genetics problem is the recessive phenotype (more properly the phenotype that represents the recessive genotype). It is that organism whose genotype can be determined by examination of the phenotype. Usually homozygous dominant and heterozygous individuals have identical phenotypes (although their genotypes are different). This becomes even more important in dihybrid crosses.
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