Population Genetics Exercise
Every generation sexually reproducing organisms mix their genetic materials. Such shared genetic material of a population is called a gene pool and all of the organisms contributing to a gene pool are called a Mendelian population. Gene pools have continuity through time---unlike individuals which are added or removed by births and deaths. One can calculate the frequency of alleles in the gene pool and if the Hardy-Weinberg Principle is true, then after one generation of random mating both the genotypic frequencies and the allelic frequencies will not change from one generation to the next. Remember Hardy-Weinberg assumes the following:
- Organism is diploid
- Reproduction is sexual
- Generations are nonoverlapping
- Mating is random
- Population size is very large
- Migration is negligible
- Mutation can be ignored
- Natural selection does not affect these alleles
With Hardy-Weinberg Equilibrium there will be an equilibrium of genotypes according to : (p + q)(p + q) = p2 + 2pq + q2 = 1
- p is the frequency of allele A
- q is the frequency of allele a
- (p + q) = 1
- p2 is the frequency of AA
- 2pq is the frequency of Aa
- q2 is the frequency of aa
Changes in the allelic frequencies in a gene pool constitute evolution and the ability of an individual to contribute to the gene pool of the next generation is a measure of fitness.
Fruit Flies
In the lab we have two types of fruit flies, Drosophila melanogaster, wildtype and vestigial or short-winged flies. The vestigial mutants have a mutation on the second chromosome which results in a lack of development of the wings. This mutation is recessive so both copies of the chromosome must carry the mutation for the phenotype to be vestigial.
The life cycle of Drosophila takes approximately two weeks at room temperature. Females lay eggs which hatch after 24 h. The larvae grow for about 5 to 7 days and then encapsulate themselves in a puparium within which they undergo a 5 day-long metamorphosis and then emerge as an adult fly. The females first mate about 8 hours after emergence (note their wings are wet and shrived immediately after emergence). They store sperm for approximately two weeks and after mating the female is significantly less receptive to males due to proteins transferred in the male’s seminal fluids. These proteins also result in elevated egg-laying rates. Females will however mate more than once and often their sperm storage reservoirs contain the sperm of more than one male. The sperm storage reservoirs are sacs and the sperm deposited last is used first. The mating of Drosophila involves the male orienting its body to the female and ‘singing’ by extending a wing and vibrating it rapidly. As a result of the involvement of the wings in mating, male flies with vestigial wings might be expected to be less successful in mating than wildtype males.
Experiment
Using the fly population cages in the laboratory, we are going to setup a series of fly cultures comprised of mixtures of vestigial and wildtype flies. We will not be using virgin females so we will assume that all the females with which we initiate the cultures have already mated and contain sperm of males of the same genotype as themselves. Every two weeks we will remove a sample of the population and count the flies according to phenotype and sex and record the data in the lab spreadsheet. Your responsibility is to propose what you expect to see at termination of these cultures in April and why. You can estimate the changes you might expect to see using a population modeling package called Populus which is on the computers in the laboratory and is available for free download from
What you need to decide is to what degree you expect wildtype males to be successful in mating versus vestigial males and whether you think the vestigial flies are as viable as wildtype flies. (Hint: vestigial flies have much lower amounts of stored glycogen at one week of age than wildtype flies.) These determine your choice of waa in Populus.
Populus
To run Populus click on the shortcut to Populus on your desktop, click on ‘Model’, click on ‘Mendelian Genetics’, click on ‘Drift and Selection’. A box will appear with values for population size, initial allelic frequency (p), number of generations, wAA, wAa, and waa. The relative fitness of the vestigial phenotype is represented by waa. Since this is a recessive trait, a simplifying assumption would be that the fitness of both the homozygote and the heterozygote genotypes is the same. Choose what values you want and then click on view to see the resulting graph.
You may also wish to look at what happens using another part of Populus which will display the changes in p2, 2pq and q2. To do this click on ‘Model’, click on ‘Natural Selection’, click on ‘Selection on a Diallelic Autosomal Locus’, click on ‘Genotypic frequency vs t’ under ‘Plot Options’ and after altering the fitness (w) values to your preferences and the ‘Initial Conditions’ then click on ‘View’ to see the results of your choices.