Genetics homework
You can also find this at: http://rpubs.com/mistymcphee/601031
- As always, show your all of your work, including your R code, if you have any.
Fixation
For this one, you can rercuit a family member or pair up with a friend or classmate.
Make sure each of you has a coin, with the “heads” side of the coin representing the “A1” allele and the “tails” side representing the “A2” allele. This means the frequency of each allele begins as 0.5 (p = q = 0.50).
Our coins have discrete generations, producing an offspring when two ‘parent’ coins are flipped at the same time. After having two offspring the parents die so that only their two offspring are available to reproduce next generation.
When flipped, if your two coin mates come up both A1 or both A2 then they produce a homozygous offspring, if they come up differently they produce a heterozygous offspring. Once an offspring becomes homozygous (A1,A1 or A2,A2), it can pass on only that allele to its offspring. A heterozygous individual will still get flipped to see which allele it passes on.
On the data sheet in the folder, fill in the first column (REPLICATE 1) until either one allele or the other becomes fixed (that is p = 1.0 or 0), or six generations have elapsed.
You’ve just performed one replicate of an outcome of genetic drift for two individuals. Now repeat 10 more times.
Answer the following:
How many times was the A1 allele lost (e.g., A1 = 0).
How many times was the A2 allele lost (e.g., A1 = 1.0).
If you had 1,000 coins as parents, what would you expect for the frequency of each allele after five generations? Why?
If you had 10 coins as parents, what would you expect for the frequency of each allele after 500 generations? Why?
Effective population size
As you’ve learned, the effective population size, Ne, is affected by several factors, notably the mating system, how skewed the sex ratio is, and how much the population varies over time. These factors are addressed in Box 9.2 of your text for a population of adders. For this exercise you will use the sorts of equations used in Box 9.2. We’ll work with a hypothetical deer population.
| Year | N females | N males | N total | Ne females | Ne males | Ne total |
|---|---|---|---|---|---|---|
| 2011 | 149 | 122 | 271 | 58 | 48 | |
| 2012 | 168 | 140 | 308 | 68 | 58 | |
| 2013 | 197 | 152 | 349 | 77 | 63 | |
| 2014 | 58 | 76 | 134 | 22 | 29 | |
| 2015 | 59 | 81 | 140 | 24 | 34 | |
| 2016 | 63 | 75 | 138 | 26 | 30 |
Use the appropriate equation from Box 9.2 to calculate, for each year, the overall effective population size, given the effective size of males and females.
Calculate the arithmetic mean of the adult abundance over time.
Calculate the harmonic mean of the Ne over time (see the equation in the box).
What is the ratio of Ne / N for this population?
As I talked about (quickly), Ne is a measure of how quickly a population is losing heterozygosity. In other words, if Ne = N, then the population is losing H at the expected rate. But if Ne < N, the population is losing H more quickly than you would expect for that N.
- What does this ratio tell you about the rate of heterozygosity loss in this population of deer?
Using the 2011 and 2016 data:
For both years, what is F after 1 generation?
…after 30 generations?
How do your F values differ? What does this difference tell you about the loss of H in the two populations (be explicit and thorough)?
Population Viability Analysis
The following graphs are from:
Bishop, J. M., Leslie, A. J., Bourquin, S. L., & O’Ryan, C. (2009). Reduced effective population size in an overexploited population of the Nile crocodile (Crocodylus niloticus). Biological Conservation, 142(10), 2335–2341.
In this study, the authors examine how unchecked hunting of the Nile crocodile in the mid to late 20th century has affected the population’s Ne. Using current census data they estimated the contemporary Ne / N ratio and, in light of quotas that permit the ongoing removal of adults, simulated the likely effects of genetic drift on extant levels of variation. The graph shows the simulated loss of genetic diversity over time for different starting Ne values (i.e., the different lines on the graphs) for (a) observed allelic diversity (A0), and (b) observed heterozygosity (H0). In each simulation starting Ne was kept constant over time.
Study them and tell me what you think the authors’ conclusions were.
