lab10_competition.RmdIn this lab, you will explore how the relative strength of intra- vs. inter-specific competition influences the joint dynamics of two competing species.
Objectives
To complete this week’s homework assignment, you will follow along with the instructions below, entering code and answering questions in the .Rmd file for homework 9. From within Rstudio cloud:
Click on the WILD3810 link under spaces
Click the blue New project button at the top of the screen
Rename the project LastnameFirstname-HW10
Navigate to New file -> R Markdown -> From Template
Scroll down to find WILD3810-Homework10
In the Name box type LastnameFirstname-HW10
Click Ok
In this lab, we’ll imagine we have data on two competing frog species. The species inhabit the same breeding ponds and compete with each other for similar, though not totally overlapping, food resources. To start, we’ll assume the following parameters correspond to the two species in the pond where we are conducting our experiment:
| Parameter | Species 1 | Species 2 |
|---|---|---|
| K | 200.0 | 200.0 |
| r | 0.1 | 0.1 |
| a | 1.2 | 0.9 |
| 1 K = carrying capacity | ||
| 2 r = population growth rate | ||
| 3 a = relatives strength of inter-specific competition |
Remember from the lecture the Lotka-Voltera competition model (written in a slightly different format here):
\[\large \frac{dN_1}{dt} = r_AN_1\bigg(\frac{K_1 - [N_1 + a_{21} N_2]}{K_1}\bigg)\]
\[\large \frac{dN_2}{dt} = r_2N_2\bigg( \frac{K_2 - [N_2 + a_{12} N_1]}{K_2}\bigg)\]
So \(a_{12}\) is the effect that adding one individual of species 1 has on the growth rate of species 2 (inter-specific competition) and \(a_{21}\) is the effect that adding one individual of species 2 has on the growth rate of species 1.
Using the information above, answer question 2 on the homework assignment
In the chunk named ‘isocline’, create objects to store the carrying capacity, growth rate, and competitive ability of each species.
Be sure to change eval = FALSE to eval = TRUE on line 46 and then knit the document. Use the figure that is created by that chunk to answer questions 3a-3c
In the chunk named ‘experiment1’, set the initial abundances of each population to any value of your choosing. Change eval = FALSE to eval = TRUE in the chunk options and then knit the document to run the code.
Use the figure that is created by the experiment1 chunk to answer questions 4a-4b
Now imagine two species with slightly different competitive abilities:
| Parameter | Species 1 | Species 2 |
|---|---|---|
| K | 200.00 | 200.00 |
| r | 0.10 | 0.10 |
| a | 0.85 | 0.75 |
| 1 K = carrying capacity | ||
| 2 r = population growth rate | ||
| 3 a = relatives strength of inter-specific competition |
Using the information above, answer question 5 on the homework assignment
In the chunk named ‘isocline2’, create objects to store the carrying capacity, growth rate, and competitive ability of the new species.
Be sure to change eval = FALSE to eval = TRUE in the chunk options and then knit the document. Use the figure that is created by that chunk to answer question 6
In the chunk named ‘experiment2’, set the initial abundances of each population to any value of your choosing. Change eval = FALSE to eval = TRUE in the chunk options and then knit the document to run the code.
Use the figure that is created by the experiment2 chunk to answer question 7a
Now start with different initial conditions. In the chunk named ‘experiment3’, set the initial abundances of each population start in a different quadrant of the graph. Change eval = FALSE to eval = TRUE in the chunk options and then knit the document to run the code.
Use the figure that is created by the experiment3 chunk to answer question 7b
Finally, we’ll imagine a new pair of species with the following parameters:
| Parameter | Species 1 | Species 2 |
|---|---|---|
| K | 200.0 | 200.0 |
| r | 0.1 | 0.1 |
| a | 1.2 | 1.4 |
| 1 K = carrying capacity | ||
| 2 r = population growth rate | ||
| 3 a = relatives strength of inter-specific competition |
Using the information above, answer question 8 on the homework assignment
In the chunk named ‘isocline3’, create objects to store the carrying capacity, growth rate, and competitive ability of the new species.
Be sure to change eval = FALSE to eval = TRUE in the chunk options and then knit the document. Use the figure that is created by that chunk to answer question 9
In the chunk named ‘experiment4’, set the initial abundances of each population so that species 1 starts at a low abundance and species 2 starts at a high abundance (aim to start on the left hand side of regions A or B or within region C). Change eval = FALSE to eval = TRUE in the chunk options and then knit the document to run the code.
Use the figure that is created by the experiment4 chunk to answer question 10a
Now start with different initial conditions. In the chunk named ‘experiment5’, set the initial abundances of each population start in a different quadrant of the graph (aim to start on the right side with high abundance of species 1 and low abundance of species 2). Change eval = FALSE to eval = TRUE in the chunk options and then knit the document to run the code.
Use the figure that is created by the experiment5 chunk to answer question 10b
In the Files pane (bottom right), navigate to the LastnameFirstname_HW10.Rmd and LastnameFirstname_HW10.html files
Click on the square button next to each file to select them
Click on the More button
Click Export
Select the location on your computer where you want to save the .zip file
Decompress the .zip file
Log in to Canvas
Go to Homework 10 assignment page
Upload your files