The Hardy-Weinberg Theorem: Teddy Grahams, Monsters, and Mold
Introduction: Charles Darwin’s unique contribution to biology was not that he “discovered evolution” but, rather, that he proposed a mechanism for evolutionary change- natural selection, the differential survival and reproduction of individuals in a population. In On the Origin of Species, published in 1859, Darwin described natural selection and provided abundant evidence in support of evolution, the change in populations over time. However, at the turn of the century, geneticists and naturalists still disagreed about the role of selection and the importance of small variations in natural populations. How could these variations provide a selective advantage that would result in evolutionary change?
Ayala (1982) defines evolution as “changes in the genetic constitution of populations.” A population is defined as a group of organisms of the same species that occur in the same area and interbreed or share a common gene pool: all the alleles at all gene loci of all individuals in the population. The population is considered to be the basic unit of evolution. Populations evolve, not individuals. In 1908, English mathematician G.H. Hardy and German physician W. Weinberg independently developed models of population genetics that showed that the process of heredity by itself did not affect the genetic structure of a population.
The Hardy-Weinberg theorem states that the:
*frequencies of alleles in the population will remain the same regardless of the starting frequencies.
Furthermore, the equilibrium genotypic frequencies will be established after one generation of random mating. In this scheme, if A and a are alleles for a particular gene locus and each diploid individual has two such loci, then p can be designated as the frequency of the A allele and q as the frequency of the a allele. Thus, in a population of 100 individuals (reach with two loci) in which 40% of the alleles are A, p would be 0.40. The rest of the alleles (60%) would be a, and q would equal 0.60 (i.e., p+q = 1.0). These are referred to as allele frequencies. The frequency of the possible diploid combinations of these alleles (AA, Aa, and aa) is expressed as:
p2 + 2pq + q2 = 1
This theorem is valid only if certain conditions are met:
***The population is very large. (The effect of chance on changes in allele frequencies is hereby greatly reduced).
***Matings are random. (Individuals show no mating preference for a particular phenotype).
***There are no net changes in the gene pool due to mutation. (Mutation from A to a equals mutation from a to A.)
***There is no migration of individuals into and out of the population.
***There is no selection; all genotypes are equal in reproductive success.
Purpose: To study the Hardy Weinberg theorem using Teddy Bear Grahams.
Welcome to the land of Teddy Grahams. These bears are a peaceful, herbivorous species that has long enjoyed life without a predator. Their population size remains around 12 bears. The number of caves in which to hibernate limits them. The bears live in a habitat with lots of shrubs. There are two general behaviors of teddy grahams. Type A bears run around with their hands up. This was an adaptation for preventing the growth of a deadly mold under their armpits. Type B bears, much more rare than type A bears, run around with their hands down. For the past few hundred years, the mold has no longer been a problem, so neither type of behavior is better than the other, therefore this variation is neutral. The hands-down behavior is a genetic trait caused by a dominant gene H. Therefore, hands-down bears are either HH or Hh. Hands-up bears are hh. Recently, a terrible thing has occurred. A new monster thing has emerged. The predator has developed a taste for teddy grahams. The hands-up bears are easy to see, with their hands rising high above the shrubs and bushes. Therefore they make easy prey for the predator. The hands-down bears, however, are nicely hidden and quite safe from the predator. Fortunately, the swamp thing can only manage to eat four bears a year.
Question: What do you predict will happen to the population of the bears, and
When the predator first arrives, there are 12 bears: 11 hands-up and only one hands-down. The hands-down is heterozygous (Hh).
A. Get about 20 bears. Count out 11 hands-up bears and 1 hands-down bear. This will be your first generation.
B. The predator eats 4 bears a year. So remove four of the bears (put them back with the rest of your bear supply.) REMEMBER: The predator can only catch hands-up bears.
1. Using the equation for Hardy-Weinberg equilibrium, calculate the frequencies of both the dominant and recessive alleles and the genotypes that are represented in the population.
Example: If 5 of 10 bears are happy, then 10 out of 20 alleles would be happy alleles.
Therefore the q2 number would be 0.5. You must then determine the q number by taking the square of 0.5.
2. Now, go hunting! Eat 4 hands-up bears.
3. Once you have consumed the bears obtain a new generation from your den (the box). You should only remove 7 additional bears from the den for a total of 15 bears.
4. Repeat the procedures again, be sure to record the number of each type of bear and the total population.
Materials: Teddy Bear Grahams, worksheet.
1. Describe what is happening to the genotype and allele frequencies in the population of Teddy Grahams?
2. What would you expect to happen if you continued the selection process for additional generations?
3. How would the frequencies change if you were to now select for the hands-up bears (like if the mold came back)?
4. In your opinion, why doesn’t the recessive allele disappear from the population? How is it protected?
5. List the three conditions necessary for natural selection to occur.
6. Describe how this model met each of the three conditions.
7. Did natural selection occur? What is your evidence?