Unless specified otherwise, homework assignments should be emailed to the instructor as knitted R Markdown document with minimal (if any) code. Print the markdown to a pdf, and provide the .Rmd file as well.
For this assignment, we recommend using whatever dataset(s) you hope to use for your final project. If you don't have access to these yet, you can work with a Movebank dataset of your choice.
Your assignment is to make a “pretty” (static) map with your movement data and at least one additional spatial variable of some kind (e.g., raster of environmental data, vector data of roads or barriers or habitat, etc…). You can make this map using any R package you want as long as you can make a “pretty” map with it but we recommend trying one of the packages introduced in class (e.g., ggspatial, basemaps…). Your map should include at minimum, a background map of some kind (could just be a polygon of land, could be a basemap (e.g., an OSM basemap from ggspatial or basemaps), labeled X/Y axes, a legend, and of course, your data (movement data, additional spatial data). If you are feeling fancy/brave, try to add a north arrow and scale bar!
Remember to make sure that all your layers have the same CRS, GCS or PCS, and spatial extent… don't hesitate to email Nicki for help (barbour\@esf.edu). And if you need help finding spatial data for your project, Elie likely has some layers he can send you.
Pick a movement data set of your choice with multiple individuals (but no more than 20). Ideally, a dataset that you plan to investigate yourself. Alternatively, work with some subset of the Ya Ha Tinda elk dataset on Movebank, following the instructions in Chapter: Movement Data in R.
a) Create a table that reports for each individual (i) the number of locations, (ii) the start, end time and duration of the monitoring, (iii) the median, mean and standard deviation of the duty cycle (i.e. the duration between subsequent observations).
b) Report the following statistics:
1. The mean, standard deviation, median, range, and interquartile range (25% and 75% quantiles) of the number of locations per individual;
2. The median, mean, and standard deviation of the location frequency (aka "duty cycle") over all the individuals.
Produce the following plots:
For each location, compute the step-length preceding that location, the time interval of that step, and the movement rate.
Produce a box-plot of the movement rate across all individuals against month of year, i.e. not just “Jan-Feb” and “July-August” like in the example, but for each month.
Can you detect any patterns? Discuss.
Extrmely valuable extra credit: Fit some smoother (e.g. a GAM model or a LOESS smoother) to those movement rates across the year.
a. Provide a brief summary of the data - what is it, where did it come from, b. Load the data, convert the coordinates to complex numbers, plot the data (with a fixed aspect ratio) c. Report some basic stats: how many observations are there; what is the sampling rate (aka duty cycle); what is the total extent in the east-west direction and north-south direction? d. Compute the step lengths (\(S\)), report the mean, standard deviation, and draw a histogram, e. Compute the absolute orientations of the steps (\(\Phi\)), report the mean (\(\widehat{\mu} = \overline{\Phi}\)), the mean cosine (\(\widehat{\rho} = \overline{\cos(\Phi - \widehat{\mu})}\)), and draw a histogram and rose diagram of the angles. f. Perform the steps above for turning angles (\(\Theta\)).\ g. What do you think the statistic \(\widehat{\rho}\) tells you?
There are several amazing and underappreciated base R functions. For example, outer, which takes TWO vectors and ONE function (that takes two arguments) and applies that functon to every combination of the two vectors. For example, here's a multiplication table (to 5's):
a <- 1:5
b <- 1:5
outer(a,b,"*")
Another very useful function is apply, which lets you apply a function across rows or columns of a matrix. So, for example, here's the sum of the rows of this table:
apply(outer(a,b,"*"), 1, sum)
I emailed you a file, AmericanBeech.csv which contains the coordinates of American beech trees (Fagus grandifola) measured at SUNY-ESF's Adirondack Research Station in 1985, 2000 and 2009 (data courtesy of M. Dovciak).
(a) Load those data, convert the coordinates to complex numbers, and plot.
(b) Use outer and apply to compute the distance from each tree to it's nearest neighbor,
© Report the mean nearest neighbor distance, the inter-quartile intervals, and plot a histogram. Describe
Note: (b) is a bit tricky, but when you get it, it's very elegant (in my opinion). Just as a hint, you will need to create a new function that takes two locations, and computes the distance between them. Here's a template:
getD <- function(Z1, Z1){
...
return(distance)
}
your goals for this class and - if possible - an idea for a final project.