## Evolution Homework - Genetic Variation

1. The problem statement, all variables and given/known data

2. About 1 in 200 Amish are homozygous recessive for Ellis-van Crevald syndrome, which causes short stature, extra fingers and toes, and several other characters.

A) What % of Amish people are likely to be heterozygote carriers for the disorder?

B) If the proportion of heterozygotes in North America is generally around 2%, what 1 likely factor could result in a greater proportion of carriers amongst the Amish? (hint, consider that the Amish began as a group of ~30 individuals)

3. Consider the fruit fly that has a gene with two alleles, one for red (normal) eyes and another for mutant (white) eyes. In albinos, the lack of melanin (pigmentation) in the eyes can result in vision problems. An ecologist is interested in knowing if there may be a possible disadvantage of the mutant white-eyes with respect to their ability to detect and avoid predators. A very large population of fruit flies around a 500 acre plantation has been around for many years. Five years ago, researchers found that the allele for red eyes was found in 90% of the population and white eyes 10% of the population.

A) What proportion of homozygote and heterozygotes would you expect to find if there is no natural selection acting against white flies?

B) What would be the % of homozygote recessives if researchers found 84.5% homozygote dominant (red eyes) and 15.0% heterozygotes in recent samples? What would these genotype frequencies imply about any potential natural selection?

C) A small farmer growing similar foods on a nearby farm with a similar ecosystem surrounding it has reported a larger proportion of white eyed flies (36% of all the flies he finds are white eyed). What are the expected proportions of the % homozygote dominant and heterozygotes?

D) Give two reasonable explanations for how white eyed flies may have become more abundant in the farm described in C (incorporating the knowledge from the results in B)?

2. Relevant equations

I figure a good bunch of them are just proportions based on the information provided by the prompts. I utilized the Hardy-Weinberg Principle (H-WP for efficiency) to calculate allele frequencies:

p2 + q2 + 2pq = 1

3. The attempt at a solution

2. A) Using the given information that 1 in 200 Amish people are homozygous recessive for the disorder, I can find all the allele frequencies. To begin, I converted the given information into a decimal:

q2 = 1 $\div$ 200 = 0.005
q = $\sqrt{0.005}$ = 0.070711
p = 1 - q = 1 - 0.070711 = 0.929289
2pq = 2 $\times$ 0.929289 $\times$ 0.070711 = 0.131422

Therefore approximately 1% of Amish people are likely to be heterozygote carriers of the disorder.

3. A) Another problem to apply the H-WP to with 90% and 10% being the given values.

p = 90% = 0.9
q = 10% = 0.1
2pq = 2 $\times$ 0.9 $\times$ 0.1 = 0.18

So 18 % of the population is heterozygote. To obtain the homozygote values, I just squared the percentages given, as squaring them results in their respective allele frequencies.

p2 = 0.81
q2 = 0.01

The sum of those two values should be the homozygote frequency, and so we have 82 homozgotes to every 18 heterozygotes. This could be reduced to 41 to 9.

3. B) The percentage should be the difference between the two given percentages, so the percentage of homozygous recessives would be 0.5%. And this genotype frequency would suggest that natural selection is in great favor of the red eye allele.

3. C) Pretty much the same procedure as part A, only with a different value. I'll skip to my results:

q = 0.36
p = 0.64; p2 $\approx$ 0.41
2pq = 0.4608 $\approx$ 0.46

Therefore there are 41 homozygote dominants to 46 heterozygotes

3. D) I stated natural selection was in favor of the red-eyed flies, and since this environment is similar to the previous one, I don't see why the environment would suddenly be in favor of the white-eyed allele. My guesses here are that genetic drift and genetic flow are responsible for the different allele frequencies observed here. I mention these events because they both result in the reduction of genetic differences over a period of time (according to my textbook).

Hopefully I formatted this correctly ( I'm new with this), and hopefully, this isn't really long a read. I just want some confirmation on my answers here (especially on the last question). Any assistance would greatly be appreciated!
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