How to Use Hardy-Weinberg to Find Gene Frequencies in a Wild Population

Ken Nicholson

One of the remarkable features of the Princeton University campus is the presence of both black and gray squirrels. First time visitors to the campus are quick to notice the distinctive black hair coat on some of the normally gray squirrels. Professor Henry S. Horn states in the introduction to his Field Biology 407 Exercise, 'Squirrels on Campus,' that little is known concerning the population genetics of this squirrel population.

Dr. Horn states that both the black and gray squirrels are members of the same species, the Eastern gray squirrel (Sciurus carolinensis), and are simply different color morphs, one more melanistic than the other. He reports that he has observed matings between the two morphs, and found mixed litters, with both gray and black offspring.

He further states that the clean classification of the morphs, together with the presence of both in a single litter, suggests that a single tightly linked gene complex is responsible for the squirrels' coat color. Dr. Horn suggests that in many other such systems the darker morph is dominant, and this activity will proceed based on that tentative hypothesis.

It was reported as early as 1665 that black and gray squirrels were found in wild populations in the New York and New Jersey area, and presently they range as far north as the limit of the deciduous nut-bearing forests. Why the black morph seems so much more common on the Princeton University campus is not known.

In December of 1986, Dr. Horn's class observed a total of 158 squirrels on the Princeton University campus, with 25, or 16% of them with the black morph. Seven months later, in July, 1987, the percent black increased to 26% when another class reported 25 black individuals out of 95 observed on one day.

On July 19, 1994, five members of the Woodrow Wilson National Fellowship Foundation High School Biology Institute simultaneously walked five east-west transects across the Princeton University campus. They counted all squirrels that they observed and noted the fur color of each animal. The observations were taken at approximately 6 P.M. Of the 52 squirrels observed on this afternoon, 9 were the black morph, or 17% of the total.

These three rather informal surveys of the Princeton University squirrels leads to the conclusion that the black morph and the gray morph have been in a state of equilibrium over the past few years, with the black squirrels averaging about 20% of the total population. The Hardy-Weinberg Principle applies where a natural population is not affected by selective pressures or migration into or out of the area, and where the traits to be studied are determined by dominant and recessive genes. Assuming that the Princeton squirrels fit these criteria, and that the gene for the black morph is an autosomal dominant gene, and its allele is the recessive gray gene, we can apply the Hardy-Weinberg formula to determine the gene frequencies within the population. Also assume that if all the squirrels on the campus could be counted, the percentage of black squirrels would be 20%, and 80% would be gray.

The gene frequency of a population in Hardy-Weinberg Equilibrium is many times written as follows:

pp : 2pq : qq

where p = the frequency of the dominant allele, and q = the frequency of the recessive allele. It follows that p + q = 100% of all the genes in the gene pool.

For this population, qq = 0.80. Therefore q = the square root of 0.80, = 0.89, or 89% of the genes in this small gene pool. Therefore the frequency of the dominant allele must be 11% of the total genes for fur color. In other words, squirrels which are homozygous for the dominant gene make up about 1% (0.11 x 0.11) of the total population.

While 19% (2pq = 2 x 0.11 x 0.89) are the heterozygotes, and 80% are the homozygous recessive individuals!

Many students erroneously assume that the dominant allele will most assuredly be the most frequent phenotype. Mr. G.H. Hardy himself wrote to correct this misconception in Science, vol. 28, 1908, when he stated that 'there is not the slightest foundation for the idea that a dominant character should show a tendency to spread over a whole population, or that a recessive should tend to die out.' The squirrel population of the Princeton University campus is a good case to illustrate that the dominant allele is not always the most frequent in a wild population. If the aforementioned assumptions are in fact true!!!!

Lab: Hardy-Weinberg Problems Tutorial

Hardy-Weinberg Equilibrium Introduction

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