In a population of lizards, the allele that causes red eyes (R) is dominant, while the allele that causes green eyes is recessive (r). If 72% of the lizards have red eyes, what is the frequency of the dominant allele?

The answer is 0.47 or 47%.

Let's first distinguish some terms and their frequencies.
R - the dominant allele that causes red eyes
r - the recessive allele that causes green eyes

Since R is dominant over r, lizards with at least one dominant R allele will have red eyes. Therefore, the genotypes and the phenotypes are as following:
genotypes - phenotypes
RR - the lizards with red eyes
Rr - the lizards with red eyes
rr - the lizards with green eyes

Now, we will use some Hardy-Weinberg equations:
p + q = 1
p² + 2pq + q² = 1

where:
p - the frequency of dominant allele R
q - the frequency of recessive allele r
p² - the frequency of lizards with genotype RR
2pq - the frequency of lizards with genotype Rr
q² - the frequency of lizards with genotype rr

We are interested in the frequency p of the dominant R allele.
So, we have the frequency (72%) of the lizards that have red eyes. However, lizards with genotypes RR and Rr will have red eyes. Since their frequencies are p² and 2pq, respectively, we have:
p² and 2pq = 72% = 72/100 = 0.72

Now, use this in the equation p² + 2pq + q² = 1:
0.72 + q² = 1
q² = 1 - 0.72 = 0.28

From here, we will calculate q and later p using the formula p + q = 1:
q² = 0.28
q = √0.28 = 0.53

p + q = 1
p + 0.53 = 1
p = 1 - 0.53
p = 0.47