A Mendelian trait is controlled by one gene and features a one-two-one genotype ratio and a three-one phenotype ratio. These ratios exist because these genes possess two alleles.
Mendelian traits exhibit what some call a simple inheritance. Of the gene's two alleles, one is dominant and one is recessive. Because of this, the phenotypes in a population obey strict numeric patterns. Three-quarters of offspring show the dominant trait, and one-quarter shows the recessive trait. The statistical relationship Mendel derived from his observation distinguishes these traits from other traits with more complex genetics. Traits controlled by more than one gene, more than two alleles, or that exhibit co-dominance or incomplete dominance do not follow this three-one ratio and are not Mendelian traits.
What puzzled Mendel and his contemporaries was the difficulty of creating pure-breeding lineages. This is not a problem when it comes to preserving the recessive trait, as breeding two (aa) parents always produces (aa) offspring. However, with the dominant trait, there is a two-in-three chance of accidentally breeding two hybrids (Aa). When this happens, one-quarter of the offspring inherit the recessive trait (aa). Even more confusing, these alleles continue to appear in offspring regardless of how distantly their lineage last featured an individual with that phenotype.