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Lessons from Mendel
When Mendel crossed his pea plants, he discovered several interesting things. When he bred certain plants with two different traits together -- for example, one with round seeds, and one with wrinkled seeds -- they would only produce offspring with one of the traits, such as round seeds. However, if he then bred two plants from that generation together, a few of the resultant offspring would display the seemingly lost trait again -- in this case, wrinkled seeds. After many trials, he found that these second-generation plants displayed the original traits in a ratio of about 3:1.
Heterozygotes and Homozygotes
Today, we call the plants of Mendel's first generation homozygotes (he called them "true-breeding"), which means they carry two copies of the same gene. In the example above, the gene that was being tracked was the gene for seed shape. Each plant carries two copies of a gene, one inherited from each of its parents. Because the original plants each had the same two copies of a gene, the first generation of offspring inherited two different genes for the same trait, which we now call "heterozygotes."
Dominant and Recessive Traits
While it may seem that the wrinkled seed trait was lost in the first generation of offspring, its reappearance in the second generation indicates that it is still held in the genetic material of the pea plants somehow. When an organism inherits genes for two different traits, one of these traits is often dominant and the other recessive. In this case, smooth seeds are the dominant trait -- even if a plant has genes for both wrinkled and smooth seeds, it will have smooth seeds. The smooth seed trait is its phenotype.
Typical Ratios
Because organisms that are homozygous for a dominant trait, and heterozygous for both possible traits, all display the same phenotype, in a "dihybrid cross" (breeding two heterozygous organisms together), three out of every four of the offspring, on average, will display the dominant trait. Only one out of four will display the recessive trait, since the organism must be homozygous with the recessive gene in order to display the trait. Thus, a dihybrid cross has a phenotypic ratio of 3:1. Other crosses have different phenotypic ratios; for example, a homozygous recessive and heterozygous cross will yield a phenotypic ratio of 1:1. Thus, phenotypic ratios of offspring can be used to determine the genetic status of parents.