How many possible genotypes and phenotypes are there for a single gene trait that shows dominance in any given population?

Dd x dd>> dd, dD, so two here.

Dd x Dd>> DD, Dd, dd so three here.
DD x dd>> dD one
DD x Dd>> DD, Dd, dd three there.
so three genotypes. Two phenotypes, dd, and Dx

To determine the number of possible genotypes and phenotypes for a single gene trait that shows dominance in a population, we need to understand a few concepts and apply basic principles of genetics.

First, let's define some terms:
- Genotype: This refers to the specific combination of alleles (versions of a gene) an individual possesses for a particular trait. In our case, we are considering a single gene trait, so there are two possible alleles involved: dominant allele (usually represented by a capital letter) and recessive allele (usually represented by a lowercase letter).
- Phenotype: This refers to the physical or observable characteristics resulting from the expression of a particular genotype. The phenotype depends on the dominant or recessive nature of the alleles.

For a single gene trait that shows dominance, there are three possible combinations of alleles:
1. Two dominant alleles (DD): In this case, the dominant trait will be expressed, and the individual will have the corresponding dominant phenotype.
2. One dominant and one recessive allele (Dd): The dominant allele will be expressed, and the individual will have the dominant phenotype.
3. Two recessive alleles (dd): In this case, the recessive trait will be expressed, and the individual will have the corresponding recessive phenotype.

Therefore, there are three possible genotypes (DD, Dd, and dd) and two possible phenotypes (dominant and recessive) for a single gene trait that shows dominance.

It's important to note that the population size can influence the frequencies of each genotype and phenotype. If you have information about the frequency of different genotypes in a population, you could also calculate the probability of a certain phenotype being expressed.