Question

You are studying a population of cactus and you discover that there are two spine lengths (short and long) that follow Mendelian inheritance patterns. Breeding data suggest that the long-spine allele (LS) is dominant to the short-spine allele (SS), and when you examine plants from your wild population you find 182 plants (out of 200) with the long-spine phenotype. Based on this, what would you expect to be the frequency of the SS allele?

1) 4.2
2) 9
3) 30
4) 50
5) 70

Answer 1

The frequency of the SS allele, which is recessive for short spines in a cactus population following Mendelian inheritance, is approximately 30%. This calculation is based on the observation that 18 out of 200 plants exhibit the short-spine phenotype and uses the Hardy-Weinberg principle.

Step-by-step explanation:

In a population of cacti with spine length being a trait that follows Mendelian inheritance patterns, if the long-spine allele (LS) is dominant to the short-spine allele (SS) and 182 out of 200 plants show the long-spine phenotype, we can use the Hardy-Weinberg principle to estimate the frequency of the SS allele. We start by finding the frequency of the short-spine phenotype (which must be homozygous recessive, SS) by subtracting the observed long-spine phenotypes from the total. Since only 18 plants exhibit the short-spine phenotype (200 - 182), we can calculate the frequency of the homozygous recessive genotype (q²) as 18/200 or 0.09.

Next, we solve for q (the frequency of the SS allele) by taking the square root of q², which results in approximately 0.3. To find the percentage, we multiply by 100, yielding 30%. Therefore, the frequency of the SS allele in the population is about 30%.

It's important to note that in a Mendelian 3:1 ratio from a heterozygous (Ss x Ss) cross, as you would expect from a dominant/recessive allele interaction, 25% of the offspring would be homozygous recessive. In this case, however, the wild population may not reflect a simple Punnett square ratio due to other evolutionary factors like selection, migration, or mutation. Nonetheless, in this example, the 30% frequency closely aligns with the expected Mendelian ratio.