A nullizygous organism carries two mutant alleles for the same gene. The mutant alleles are both complete loss-of-function or 'null' alleles, so homozygous null and nullizygous are synonymous. The mutant cell or organism is called a nullizygote.hen an organism is homozygous-dominant for a particular trait, the genotype is represented by a doubling of the symbol for that trait, such as PP. An individual that is homozygous-recessive for a particular trait carries two copies of the allele that codes for the recessive trait.