You can also find this homework posted online: http://rpubs.com/mistymcphee/599069
You do not have to use R for this homework. If you use R for some but not all, knit your document into Word and then type the rest directly into that document before printing it.
If you do use R, please put your .rmd file in your Google folder.
No matter how you do this - show me the equation you are using, define your variables, and show ALL of your work!
You can discuss with classmates, but you must do the work on your own.
For doing part or all in R, there are functions and shortcuts for a lot of this. Every type of math (except multiplying vectors) has been used or at least presented in previous homeworks. If you want to play with more efficient ways to calculate things, please ask.
Be sure to show me which equation(s) you are using to answer a given question! In the text BEFORE (not in!) the chunk of code, type out the basic equation and define your variables.
You can discuss with classmates, but you must do the work on your own.
Please proofread before turning it in!
As always:
Copy each question into your document and make sure your answers are clearly outlined and labeled.
If you use R, double space between paragraphs so that lines don’t run into each other.
Include a 0 before the decimal point in a number less than 1.
I will deduct points for typos - especially incorrect use of “data”.
You are working on wolverine populations on the Kenai Peninsula in Alaska. Wolverines are solitary and territorial animals who eat anything from small eggs to large ungulates.
Given an estimated r of 0.003 and carrying capacity of 2075, what is the wolverine abundance when recruitment to the population is greatest?
What is the rate of change of the population at this point?
What does this say about the increase in wolverines per year when recruitment is highest?
You are responsible for a study measuring demography, life history, and population growth in a population of African spurred tortoises. You set up a field site in Senegal and you tag 44 female tortoises. Because tortoises have such a long life span, you monitor the population every 5 years. You find that 38 were alive at the next sampling period, 29 the next, 18 the next, 11 the next, and 0 the next. During the first 5-year period, an average of 4 female offspring were produced and survived per female, 8 in the second, 3 in the third, 1 in the fourth, and 0 in the fifth.
Given this:
Develop a life table with the following parameters:
| x | nx | lx | mx | lxmx | xlxmx | qx | dx |
|---|---|---|---|---|---|---|---|
Below the table, provide the definition and equation (if appropriate) for each.
Plot a survivorship curve and a mortality curve from your table.
What is the generation time, net reproductive rate, and intrinsic rate of increase for the tortoises?
If you took 18 pairs and established a new breeding population elsewhere, what would the female population size be after 50 years? (Hint: if you get an insanely large number, rethink your time units.)
Plot the change in population size over time (for 50 years) starting with 18 females.
What does this information suggest about the status of the African spurred tortoise population?
You are working on conservation of the endangered Karner blue butterfly in Wisconsin, where the largest remaining population is found. This butterfly produces two broods of young each year, a spring brood and a summer brood. Larvae emerge in April that were laid the previous fall. Near the end of May, the larvae pupate and adults emerge in late May or early June. The butterfly then mates and lays eggs. The second brood of butterflies emerge mid-July to early August. Their eggs overwinter to hatch again in April.*
* background info factual but data are made up
You want to project population growth as a function of the life stages for the butterfly (egg, larvae, pupae, adult). I give you the following matrix:
| egg | larvae | pupae | adult | |
|---|---|---|---|---|
| egg | 0.00 | 0.000 | 0.00 | 292.00 |
| larvae | 0.73 | 0.000 | 0.00 | 0.00 |
| pupae | 0.00 | 0.098 | 0.00 | 0.00 |
| adult | 0.00 | 0.000 | 0.23 | 0.72 |
What do the following values tell you?
a2,1
a3,3
a1,4
If the spring abundances of the different age classes are as follows: egg = 1981, larvae = 1309, pupae = 459, adult = 202, how many adults do you predict for the fall?
If you use R to answer this, I want you to tell me how to do the calculations by hand, but you can use the code:
matrix %*% vector
to multiply your matrix by a vector. You’ll need to replace the words “matrix” and “vector” with whatever names you gave your matrix and vector when you created them.
What is a stable stage distribution?
λSSD and SSD itself are independent of the initial age distribution of a population. So what does the initial age distribution of animals across stages influence?