Section 1. Practice problems

Evaluate the following:

  1. By hand: Evaluate \(f(x,y)=x^2-1+3xy\) at \(x=1\) and \(y = 0\)

  2. In the R Console: given \(G(t,z)=3.1(t-4.2)^2 + 0.06z\), find the value of \(G(1, 2.5)\) (you do NOT need to write a function - just do the calculation in R using R as a calculator)

Units:

  1. You are combining information from multiple sources to estimate the total annual oil spilled in a watershed, reported by different companies. The following are reported for the year:
  • Company A: 14.6 barrels spilled (with 9.3 barrels recovered)
  • Company B: 692 liters spilled (94% recovered)
  • Company C: 18.1 gallons spilled (0% recovered)

What is the total unrecovered amount of oil spilled into the watershed that year, in barrels. Use R & Google here for calculations.

Average slope

  1. By hand: If an urchin population in a study plot in 1990 is 432, and in 2004 is 801, what is the average rate of population increase? Find the slope, then write a statement about the average increase (including units).

Section 2: Projects and functions

  • Create a new Quarto project (named eds-212-day-1)

  • Add a new Quarto document in the project

  • Press ‘Render’ (save this in your project as fish-length-weight.qmd)

  • Delete everything below the first code chunk

  • Attach the tidyverse package

  • Play around with markdown cells in the Quarto doc. Try adding text with at least the following:

    • Headers of varying size
    • Italics
    • Bold
    • Superscripts / subscripts
    • Bulletpoints
    • An image (google how!)

  • Add a new code chunk (for R code)

  • Within the R code chunk, write a function to estimate fish standard weight, given parameters \(a\), \(b\), and fish length \(L\) as inputs. “Standard weight” is how much we expect a fish to weigh, give the species and fish length, and the nonlinear relationship is given by:

\[W=aL^b\]

where L is total fish length (centimeters), W is the expected fish weight (grams), and a and b are species-dependent parameter values.

  • Test out your function to find the mass (g) for a 60 cm fish of the following species (parameter estimates from Peyton et al. (2016)):

    • Milkfish: a = 0.0905, b = 2.52
    • Giant trevally: a = 0.0353, b = 3.05
    • Great barracuda: a = 0.0181, b = 3.27

Peyton, K. A., T. S. Sakihara, L. K. Nishiura, T. T. Shindo, T. E. Shimoda, S. Hau, A. Akiona, and K. Lorance. 2016. “Length–Weight Relationships for Common Juvenile Fishes and Prey Species in Hawaiian Estuaries.” Journal of Applied Ichthyology 32 (3): 499–502. https://doi.org/10.1111/jai.12957.

  • Make and store (as fish_length) sequence of size ranges from 0 to 200 cm, by increments of 1 cm

  • Estimate the weight for giant barracudas along that entire range (given the parameters above). Store the output as barracuda_weight

  • Bind the lengths and estimated barracuda weights into a single data frame using data.frame()

  • Create a ggplot graph of predicted length versus weight for giant barracuda

  • Update the graph axis labels and title

  • Render the .qmd. Make sure everything is saved.

  • Close your project. Reopen the project, and ensure that you can re-run the entire Quarto document (reproducibility check).

END Activity Session 1