3. We are using beads to simulate alleles. In this process, we develop and test

Question

3. We are using beads to simulate alleles. In this process, we develop and test three models. In the first model, we examine one gene with a dominant and a recessive allele, each occurring at equal frequencies. In subsequent models, allele frequencies are altered to reflect different mechanisms at play. For each model, describe (a) main parameters of interest (i.e. allelic frequencies, population size, etc) (b) what you expect to observe over multiple generations, and (c) why you expect this result given how the model was set up or inherent assumptions. Part (a) for the 1st model has been provided as an example. {{5 pts}}

Model #/ allelic freq or population size

Expectation over generations of allele frequency/ratio (brief)

Explanation (brief)

Model 1/ e.g. Equal allelic frequencies

Model 2/

Model 3/

Explanation / Answer

Hardy and Weinberg mathematically proved that in a population, all dominant and recessive alleles comprise all alleles for that gene.

This was mathematically represented as p+ q = 1.0

Where,

p = frequency of dominant alleles

q = frequency of recessive alleles.

Model 1:

Assume the population size is 1000. The individuals with AA genotype are 400 (0.4%), the individuals with Aa genotype are 200 (0.2%) and the individuals with aa genotype are 400. (0.4%)

Now, the frequency of alleles in this population is,

Frequency of A allele =

Population of AA + 1/2 (population of Aa)/ Total population = 400+100/ 1000 = 0.5

The frequency of A allele = 0.5

Frequency of a allele =

Population of aa + 1/2 (population of Aa)/ Total population = 400+100/ 1000 = 0.5

The frequency of a allele = 0.5                                   

This population is in Hardy's Weinberg equilibrium because A+a (or p+q) = 1.

In the next generation,

the frequency of AA individuals = AA = 0.5*0.5 = 0.25 (250/1000)

the frequency of aa individuals = AA = 0.5*0.5 = 0.25 (250/1000)

the frequency of Aa individuals = AA = 2* 0.5*0.5 = 0.5 (500/1000)

Now, let us calculate the allele frequencies. The frequency of A allele =

Population of AA + 1/2 (population of Aa)/ Total population = 250+500/ 1000 = 0.5

The frequency of A allele = 0.5

The frequency of a allele = Population of aa + 1/2 (population of Aa)/ Total population = 250+500/ 1000 = 0.5

The frequency of a allele = 0.5

The allele frequencies are not changed in the next generation because the population reached Hardy's Weinberg equilibrium. If we calculate the allele frequencies, the genotypic frequencies may change but the allele frequencies remain unchanged because the population is in Hardy's Weinberg equilibrium.

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