Please place your name in the upper-right corner.
Last week in lab you learned about some R basics. Please:
1.1. Name three data types in R.
1.2. Name the two types of data structures that are 2-dimensional and
note which has homogeneous data types and which heterogeneous.
We represent population change as \(\Delta N = N_{t} - N_{t-1}\). The units for
\(N\) are \([\text{individuals}]/[\text{area}]\) or,
alternatively written, \([\text{individuals}][\text{area}]^{-1}\).
Remember when you add or subtract units, they remain unchanged; i.e.,
the right-hand side equation in the first sentence has units of \([\text{individuals}][\text{area}]^{-1} -
[\text{individuals}][\text{area}]^{-1} =
[\text{individuals}][\text{area}]^{-1}\). When you multiply units
they square; e.g., the area of a rectangle has units of length squared
because it is a side (units in length) times another side (units in
length). With division, like speed (i.e., velocity), it’s distance units
of distance divided by time. Notice, too, that the units balance between
the left- and right-hand sides balance.
With all of that, the book reads that populations change \(\Delta N = bN_{t-1} - dN_{t-1}\). \(b\) is the per-capita birth rate and \(d\) is the per-capita death rate. Please
justify why \(b\) and \(d\) are called “per-capita” by finding the
units of \(b\) and \(d\) while remembering that the left- and
right-hand sides of the equation must balance.
If in year 2022, female white-footed mouse (Peromyscus
leucopus) density is 0.1 / ha here in Maine forests. Lifespans are
around 1 year for this species. If females produce 2 female pups per
year, how many female mice would we expect after 7 years? (No need to
recall an equation, just arithmetically trudge through.)
(So cute)
If in year 2022, female white-footed mouse (Peromyscus
leucopus) density is \(N_{2022}\)
/ ha here in Maine forests. Lifespans are around 1 year for this
species. If females produce \(\lambda\)
female pups per year, how many female mice would we expect after \(t\) years? (This is the same question as
above, but with parameter names instead of numbers.)
Please make 3 graphs below, based on the data your generated in question 3. Please make the first as a time series; i.e., a graph with time (years) on the horizontal axis and the variable (density) on the vertical axis. Second, plot change against density; i.e., from question 2, a graph with \(N_t\) on the horizontal axis and population change (\(\Delta N\)) on the vertical axis. Last, please plot the per-capita change against density; i.e., a graph with \(N_t\) on the horizontal axis and per-capita change (\(\Delta N/N_t\)) on the vertical axis.