Question

The genome of a diploid species has 10 genes. In a population of this species, if each gene has two unique alleles, then the number of possible unique genotypes in this population is ______ (Answer in integer)

Hint:

Work out how many genotype combinations are possible at a single gene locus with two alleles, then multiply that count across all the genes since they assort independently.

Answer 1

Correct Answer: 59049

Step 1: Work out the genotypes possible at one gene.
The species is diploid, so every individual carries two copies of each gene, one from each parent. If a gene has two unique alleles, call them \(A\) and \(a\), then a single individual's genotype at that gene can be \(AA\), \(Aa\), or \(aa\). That gives \[ 3 \] possible genotypes at each single gene.

Step 2: Treat the 10 genes as independent choices.
The genome has \(10\) genes in total. Since each gene has its own two alleles and its genotype at that gene does not restrict the genotype at any other gene, the overall genotype of an individual is built by picking one of the \(3\) options at gene 1, one of \(3\) options at gene 2, and so on through all \(10\) genes.

Step 3: Multiply the choices across all genes.
By the basic counting principle, the total number of unique whole-genome genotypes is \[ 3\times3\times3\times\cdots\times3\ (10\ \text{times})=3^{10} \]

Step 4: Evaluate the power.
\[ 3^{10}=(3^5)^2=243^2=59049 \]

Step 5: Final answer.
The number of possible unique genotypes in the population is \[ \boxed{59049} \]