Having two of the same alleles for a trait

is called homozygosity. An individual who is homozygous for a particular trait will have two identical alleles, either both dominant or both recessive, for that trait. Homozygosity can lead to the expression of certain traits, such as in the case of having two dominant alleles resulting in a dominant phenotype, or in the case of having two recessive alleles resulting in a recessive phenotype.