In michaelfrancenelson/rmd.utils:
# source(here::here("formatting", "functions", "rmd_functions.R"))
# source(here::here("rmd_tools", "find_file.R"))
require(rmd.utils)
dat_dispersal = read.csv(find_file("salamander_dispersal.csv"))
exp_fun = function(x, a, b) { return(a * exp(-b * x))}
Question 01: Exponential plots
cat(readLines(here::here("formatting", "css", "styles.css")))
Instructions:
- Complete the template R code to build your exponential function. Make sure you read the note about parameter
b in the lab instructions.
- To gain visual intuition, try using
curve() to plot your function.
- Try out different values of the two parameters as well as plotting over different ranges of x-values.
- Try plotting two or more curves with slightly different parameter values on the same plot
- You may need to try out different ranges of x-values in your plot windows to make sure you are focusing on the interesting parts of the curves.
- Try different line colors, widths, and textures.
An example exploratory plotting exercise:
png("lab_05_q1.png", width = 1200, height = 800, res = 200)
curve(exp_fun(x, 1.9, 0.1), add = FALSE, from = 0, to = 50, ann = FALSE, axes = FALSE, ylab = "f(x)"); box()
curve(exp_fun(x, 1.2, 0.1), add = TRUE, from = 0, to = 100, col = 2)
curve(exp_fun(x, 1.2, 0.3), add = TRUE, from = 0, to = 100, col = 3, lty = 2, lwd = 3)
curve(exp_fun(x, 1.5, 0.03), add = TRUE, from = 0, to = 100, col = 4, lwd = 2)
curve(exp_fun(x, 1.75, 0.003), add = TRUE, from = 0, to = 100, col = 66, lwd = 3, lty = 4)
dev.off()
knitr::include_graphics(find_file("lab_05_q1.png"))
### Questions
- Q1 (2 pts.) Paste the R code you used to create `exp_fun()`
- Q2 (3 pts.) Create a single plot containing 4 curves with these parameter values:
- curve 1: a = 1.9, b = 0.1, line color = black, line texture = solid
- curve 2: a = 1.9, b = 0.3, line color = black, line texture = dotted
- curve 3: a = 1.2, b = 0.2, line color = red, line texture = solid
- curve 4: a = 1.2, b = 0.4, line color = red, line texture = dotted
Solution
exp_fun = function(x, a, b)
{
return(a * exp(-b * x))
}
# curve(exp_fun(x, 1.9, 0.1), add = FALSE, from = 0, to = 30, ann = FALSE, axes = FALSE); box()
curve(exp_fun(x, 1.9, 0.1), add = FALSE, from = 0, to = 30, ylab = "f(x)")
curve(exp_fun(x, 1.9, 0.3), add = TRUE, from = 0, to = 100, col = 1, lty = 2)
curve(exp_fun(x, 1.2, 0.2), add = TRUE, from = 0, to = 100, col = 2, lty = 1)
curve(exp_fun(x, 1.2, 0.4), add = TRUE, from = 0, to = 100, col = 2, lty = 2)
Meta-information
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# source(here::here("formatting", "functions", "rmd_functions.R"))
# source(here::here("rmd_tools", "find_file.R"))
require(rmd.utils)
dat_dispersal = read.csv(find_file("salamander_dispersal.csv"))
exp_fun = function(x, a, b) { return(a * exp(-b * x))}
Question 02: Exponential parameters
cat(readLines(here::here("formatting", "css", "styles.css")))
Consider the plot you made with the 4 exponential curves.
Observe how the curves vary as you change the two parameters' values.
### Questions
- Q1 (2 pts.) Qualitatively describe what happens to the curve as you vary parameter `a`
- Q2 (2 pts.) Qualitatively describe what happens to the curve as you vary parameter `b`
Solution
- Parameter
a sets the y-intercept.
- Parameter
b sets the [initial] steepness of the decay.
- Students may notice that a also affects the steepness of the decay.
exp_fun = function(x, a, b)
{
return(a * exp(-b * x))
}
curve(exp_fun(x, 1.9, 0.1), add = FALSE, from = 0, to = 30, col = 1, ylab = "f(x)")
curve(exp_fun(x, 1.9, 0.3), add = TRUE, from = 0, to = 100, col = 1, lty = 2)
curve(exp_fun(x, 1.2, 0.2), add = TRUE, from = 0, to = 100, col = 2, lty = 1)
curve(exp_fun(x, 1.2, 0.4), add = TRUE, from = 0, to = 100, col = 2, lty = 2)
curve(exp_fun(x, 0.9, 0.4), add = TRUE, from = 0, to = 100, col = 3, lty = 2)
Meta-information
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# source(here::here("formatting", "functions", "rmd_functions.R"))
# source(here::here("rmd_tools", "find_file.R"))
# dat_dispersal = read.csv(find_file("salamander_dispersal.csv"))
require(rmd.utils)
exp_fun = function(x, a, b) { return(a * exp(-b * x))}
ricker_fun = function(x, a, b) { return(a * x * exp(-b * x))}
# exp_fun = function(x, a, b) { return(a * exp(-b * x))}
Question 03: Ricker plots
cat(readLines(here::here("formatting", "css", "styles.css")))
Instructions:
- To gain visual intuition, try using
curve() to plot the Ricker function.
- Try out different values of the two parameters as well as plotting over different ranges of x-values.
- Try plotting two or more curves with slightly different parameter values on the same plot
- You may need to try out different ranges of x-values in your plot windows to make sure you are focusing on the interesting parts of the curves.
- Try different line colors, widths, and textures.
An example exploratory plotting exercise:
# png("lab_05_q3.png", width = 1200, height = 800, res = 200)
curve(ricker_fun(x, 25.1, .5), add = FALSE, from = 0, to = 10, ann = FALSE, ylab = "f(x)", ylim = c(0, 30)); box()
curve(ricker_fun(x, 20.2, .3), add = TRUE, col = 2)
curve(ricker_fun(x, 49.2, .66), add = TRUE, col = 3, lty = 2, lwd = 3)
curve(ricker_fun(x, 10.5, 0.8), add = TRUE, col = 4, lwd = 2)
# dev.off()
knitr::include_graphics(find_file("lab_05_q3.png"))
### Questions
- Q1 (4 pts.) Create a single plot containing 6 Ricker curves with these parameter values:
- curve 1: a = 25, b = 0.1, line color = black, line texture = solid
- curve 2: a = 20, b = 0.2, line color = black, line texture = dotted
- curve 3: a = 10, b = 0.2, line color = black, line texture = dotted
- curve 4: a = 75, b = 0.3, line color = red, line texture = solid
- curve 5: a = 50, b = 0.3, line color = red, line texture = dotted
- curve 6: a = 40, b = 0.3, line color = red, line texture = dotted
Solution
curve(ricker_fun(x, 25, 0.1), add = FALSE, from = 0, to = 50, ylab = "f(x)")
curve(ricker_fun(x, 20, 0.1), add = TRUE, col = 1, lty = 2)
curve(ricker_fun(x, 10, 0.1), add = TRUE, col = 1, lty = 2)
curve(ricker_fun(x, 75, 0.3), add = TRUE, col = 2, lty = 1)
curve(ricker_fun(x, 50, 0.3), add = TRUE, col = 2, lty = 2)
curve(ricker_fun(x, 40, 0.3), add = TRUE, col = 2, lty = 2)
Meta-information
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require(rmd.utils)
ricker_fun = function(x, a, b) { return(a * x * exp(-b * x))}
Question 04: Ricker params
cat(readLines(here::here("formatting", "css", "styles.css")))
Instructions:
- To gain visual intuition, try using
curve() to plot the Ricker function.
- Try out different values of the two parameters as well as plotting over different ranges of x-values.
- Try plotting two or more curves with slightly different parameter values on the same plot
- You may need to try out different ranges of x-values in your plot windows to make sure you are focusing on the interesting parts of the curves.
- Try different line colors, widths, and textures.
An example exploratory plotting exercise:
curve(ricker_fun(x, 25.1, .5), add = FALSE, from = 0, to = 10, ann = FALSE, ylab = "f(x)", ylim = c(0, 30)); box()
curve(ricker_fun(x, 20.2, .3), add = TRUE, col = 2)
curve(ricker_fun(x, 49.2, .66), add = TRUE, col = 3, lty = 2, lwd = 3)
curve(ricker_fun(x, 10.5, 0.8), add = TRUE, col = 4, lwd = 2)
# curve(ricker_fun(x, 1.75, 0.003), add = TRUE, from = 0, to = 100, col = 66, lwd = 3, lty = 4)
### Questions
- Q1 (2 pts.) Qualitatively describe how the `a` parameter influences the curve shape.
- Q2 (2 pts.) Qualitatively describe how the `b` parameter influences the curve shape.
NOTE: make sure you choose an appropriate range of x-values in your plot.
Solution
curve(ricker_fun(x, 25, 0.1), add = FALSE, from = 0, to = 50, ylab = "f(x)")
curve(ricker_fun(x, 20, 0.1), add = TRUE, col = 1, lty = 2)
curve(ricker_fun(x, 10, 0.1), add = TRUE, col = 1, lty = 2)
curve(ricker_fun(x, 75, 0.3), add = TRUE, col = 2, lty = 1)
curve(ricker_fun(x, 50, 0.3), add = TRUE, col = 2, lty = 2)
curve(ricker_fun(x, 40, 0.3), add = TRUE, col = 2, lty = 2)
Meta-information
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require(rmd.utils)
dat_dispersal = read.csv(find_file("salamander_dispersal.csv"))
Question 05: salamander data scatterplot
cat(readLines(here::here("formatting", "css", "styles.css")))
Instructions:
- Read the salamander dispersal data into a
data.frame called dat_dispersal.
- Create a scatterplot of distance class and dispersal rate of first time breeding salamanders.
### Questions
- Q1 (1 pts.) Upload an image file with your scatterplot. Make sure it has appropriate axis labels and title.
- Q2 (2 pts.) Describe, in nontechnical language, what is shown on the x-axis
- Q3 (2 pts.) Describe, in nontechnical language, what is shown on the y-axis
Solution
dat_dispersal
plot(dat_dispersal$dist.class, dat_dispersal$disp.rate.ftb, xlab = "distance class", ylab = "standardized dispersal rate", main = "Marbled Salamander - first time breeders")
Meta-information
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require(rmd.utils)
dat_dispersal = read.csv(find_file("salamander_dispersal.csv"))
# Calculates the value of x for a linear function, given the coordinates
# of a known point (x1, y1) and the slope of the line.
line_point_slope = function(x, x1, y1, slope)
{
get_y_intercept =
function(x1, y1, slope)
return(-(x1 * slope) + y1)
linear =
function(x, yint, slope)
return(yint + x * slope)
return(linear(x, get_y_intercept(x1, y1, slope), slope))
}
Question 06: salamander linear model
cat(readLines(here::here("formatting", "css", "styles.css")))
Recall the function we have used to visually estimate linear model parameters:
# Calculates the value of x for a linear function, given the coordinates
# of a known point (x1, y1) and the slope of the line.
line_point_slope = function(x, x1, y1, slope)
{
get_y_intercept =
function(x1, y1, slope)
return(-(x1 * slope) + y1)
linear =
function(x, yint, slope)
return(yint + x * slope)
return(linear(x, get_y_intercept(x1, y1, slope), slope))
}
Instructions:
- Using the scatterplot of the dispersal data, visually fit a linear mode
### Questions
- Q1 (2 pts.) Upload an image file with your scatterplot and fitted line. Make sure it has appropriate axis labels and title.
Solution
line_point_slope = function(x, x1, y1, slope)
{
get_y_intercept =
function(x1, y1, slope)
return(-(x1 * slope) + y1)
linear =
function(x, yint, slope)
return(yint + x * slope)
return(linear(x, get_y_intercept(x1, y1, slope), slope))
}
For example:
plot(dat_dispersal$dist.class, dat_dispersal$disp.rate.ftb, xlab = "distance class", ylab = "standardized dispersal rate", main = "Marbled Salamander - first time breeders")
curve(line_point_slope(x, 1400, 0.1, -0.0001), add = TRUE)
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require(rmd.utils)
dat_dispersal = read.csv(find_file("salamander_dispersal.csv"))
exp_fun = function(x, a, b) { return(a * exp(-b * x))}
Question 07: salamander exponential model
cat(readLines(here::here("formatting", "css", "styles.css")))
Instructions:
- Using the scatterplot of the dispersal data, visually fit an model
### Questions
- Q1 (4 pts.) Upload an image file with your scatterplot and fitted curve. Make sure it has appropriate axis labels and title.
Solution
exp_fun = function(x, a, b) { return(a * exp(-b * x))}
plot(dat_dispersal$dist.class, dat_dispersal$disp.rate.ftb, xlab = "distance class", ylab = "standardized dispersal rate",
main = "Marbled Salamander - first time breeders\nExponential model")
curve(exp_fun(x, 0.75, 0.003), add = TRUE)
Meta-information
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require(rmd.utils)
dat_dispersal = read.csv(find_file("salamander_dispersal.csv"))
exp_fun = function(x, a, b) { return(a * exp(-b * x))}
ricker_fun = function(x, a, b) { return(a * x * exp(-b * x))}
Question 08: salamander ricker model
cat(readLines(here::here("formatting", "css", "styles.css")))
Instructions:
- Using the scatterplot of the dispersal data, visually fit a ricker curve model.
### Questions
- Q1 (4 pts.) Upload an image file with your scatterplot and fitted curve. Make sure it has appropriate axis labels and title.
Solution
ricker_fun = function(x, a, b) { return(a * x * exp(-b * x))}
For example:
plot(dat_dispersal$dist.class, dat_dispersal$disp.rate.ftb, xlab = "distance class", ylab = "standardized dispersal rate",
main = "Marbled Salamander - first time breeders\nRicker model")
curve(ricker_fun(x, 0.007, 1/200), add = TRUE)
Meta-information
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require(rmd.utils)
dat_dispersal = read.csv(find_file("salamander_dispersal.csv"))
# Calculates the value of x for a linear function, given the coordinates
# of a known point (x1, y1) and the slope of the line.
line_point_slope = function(x, x1, y1, slope)
{
get_y_intercept =
function(x1, y1, slope)
return(-(x1 * slope) + y1)
linear =
function(x, yint, slope)
return(yint + x * slope)
return(linear(x, get_y_intercept(x1, y1, slope), slope))
}
Question 09: salamander linear model residuals
cat(readLines(here::here("formatting", "css", "styles.css")))
Recall the function we have used to visually estimate linear model parameters:
# Calculates the value of x for a linear function, given the coordinates
# of a known point (x1, y1) and the slope of the line.
line_point_slope = function(x, x1, y1, slope)
{
get_y_intercept =
function(x1, y1, slope)
return(-(x1 * slope) + y1)
linear =
function(x, yint, slope)
return(yint + x * slope)
return(linear(x, get_y_intercept(x1, y1, slope), slope))
}
Instructions:
- Using the parameters you chose for your linear fit, calculate the residuals and store them in a vector
resids_linear.
### Questions
- Q1 (3 pts.) Paste the code you used to create `resids_linear`.
- Q1 (1 pts.) Upload an image file with a histogram of the residuals of your linear model.
Solution
line_point_slope = function(x, x1, y1, slope)
{
get_y_intercept =
function(x1, y1, slope)
return(-(x1 * slope) + y1)
linear =
function(x, yint, slope)
return(yint + x * slope)
return(linear(x, get_y_intercept(x1, y1, slope), slope))
}
For example:
param_x1 = 1400
param_y1 = 0.1
param_slope = -0.0001
plot(dat_dispersal$dist.class, dat_dispersal$disp.rate.ftb, xlab = "distance class", ylab = "standardized dispersal rate", main = "Marbled Salamander - first time breeders\nLinear model")
curve(line_point_slope(x, param_x1, param_y1, param_slope), add = TRUE)
resids_linear =
line_point_slope(dat_dispersal$dist.class, param_x1, param_y1, param_slope) - dat_dispersal$disp.rate.ftb
hist(resids_linear, main = "residuals: linear model")
Meta-information
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require(rmd.utils)
dat_dispersal = read.csv(find_file("salamander_dispersal.csv"))
exp_fun = function(x, a, b) { return(a * exp(-b * x))}
Question 10: salamander exponential model residuals
cat(readLines(here::here("formatting", "css", "styles.css")))
Instructions:
- Using the parameters you chose for your exponential fit, calculate the residuals and store them in a vector
resids_exp.
### Questions
- Q1 (4 pts.) Upload an image file with a histogram of the residuals of your exponential model.
Solution
exp_fun = function(x, a, b) { return(a * exp(-b * x))}
plot(dat_dispersal$dist.class,
dat_dispersal$disp.rate.ftb,
xlab = "distance class", ylab = "standardized dispersal rate",
main = "Marbled Salamander - first time breeders\nExponential model")
exp_a = 0.75
exp_b = 0.003
curve(exp_fun(x, exp_a, exp_b), add = TRUE)
resids_exp = exp_fun(dat_dispersal$dist.class, exp_a, exp_b) - dat_dispersal$disp.rate.ftb
hist(resids_exp)
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require(rmd.utils)
dat_dispersal = read.csv(find_file("salamander_dispersal.csv"))
exp_fun = function(x, a, b) { return(a * exp(-b * x))}
ricker_fun = function(x, a, b) { return(a * x * exp(-b * x))}
Question 11: salamander ricker model residuals
cat(readLines(here::here("formatting", "css", "styles.css")))
Instructions:
-
Using the parameters you chose for your Ricker curve fit, calculate the residuals and store them in a vector resids_ricker.
-
Using the scatterplot of the dispersal data, visually fit a ricker curve model.
### Questions
- Q1 (4 pts.) Upload an image file with a histogram of the residuals of your Ricker curve model.
Solution
ricker_fun = function(x, a, b) { return(a * x * exp(-b * x))}
For example:
plot(
dat_dispersal$dist.class, dat_dispersal$disp.rate.ftb,
xlab = "distance class", ylab = "standardized dispersal rate",
main = "Marbled Salamander - first time breeders\nRicker model")
rick_a = 0.007
rick_b = 1/200
resids_ricker = ricker_fun(dat_dispersal$dist.class, rick_a, rick_b) - dat_dispersal$disp.rate.ftb
hist(resids_ricker)
curve(ricker_fun(x, rick_a, rick_b), add = TRUE)
Meta-information
extitle: salamander ricker model
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exextra[essay_attachmentsrequired,logical]: TRUE
expoints: 4
michaelfrancenelson/rmd.utils documentation built on Dec. 21, 2021, 5:57 p.m.
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# source(here::here("formatting", "functions", "rmd_functions.R")) # source(here::here("rmd_tools", "find_file.R")) require(rmd.utils) dat_dispersal = read.csv(find_file("salamander_dispersal.csv")) exp_fun = function(x, a, b) { return(a * exp(-b * x))}
Question 01: Exponential plots
cat(readLines(here::here("formatting", "css", "styles.css")))
Instructions:
- Complete the template R code to build your exponential function. Make sure you read the note about parameter
bin the lab instructions. - To gain visual intuition, try using
curve()to plot your function. - Try out different values of the two parameters as well as plotting over different ranges of x-values.
- Try plotting two or more curves with slightly different parameter values on the same plot
- You may need to try out different ranges of x-values in your plot windows to make sure you are focusing on the interesting parts of the curves.
- Try different line colors, widths, and textures.
An example exploratory plotting exercise:
png("lab_05_q1.png", width = 1200, height = 800, res = 200) curve(exp_fun(x, 1.9, 0.1), add = FALSE, from = 0, to = 50, ann = FALSE, axes = FALSE, ylab = "f(x)"); box() curve(exp_fun(x, 1.2, 0.1), add = TRUE, from = 0, to = 100, col = 2) curve(exp_fun(x, 1.2, 0.3), add = TRUE, from = 0, to = 100, col = 3, lty = 2, lwd = 3) curve(exp_fun(x, 1.5, 0.03), add = TRUE, from = 0, to = 100, col = 4, lwd = 2) curve(exp_fun(x, 1.75, 0.003), add = TRUE, from = 0, to = 100, col = 66, lwd = 3, lty = 4) dev.off()
knitr::include_graphics(find_file("lab_05_q1.png"))
### Questions
- Q1 (2 pts.) Paste the R code you used to create `exp_fun()`
- Q2 (3 pts.) Create a single plot containing 4 curves with these parameter values:
- curve 1: a = 1.9, b = 0.1, line color = black, line texture = solid
- curve 2: a = 1.9, b = 0.3, line color = black, line texture = dotted
- curve 3: a = 1.2, b = 0.2, line color = red, line texture = solid
- curve 4: a = 1.2, b = 0.4, line color = red, line texture = dotted
Solution
exp_fun = function(x, a, b) { return(a * exp(-b * x)) } # curve(exp_fun(x, 1.9, 0.1), add = FALSE, from = 0, to = 30, ann = FALSE, axes = FALSE); box() curve(exp_fun(x, 1.9, 0.1), add = FALSE, from = 0, to = 30, ylab = "f(x)") curve(exp_fun(x, 1.9, 0.3), add = TRUE, from = 0, to = 100, col = 1, lty = 2) curve(exp_fun(x, 1.2, 0.2), add = TRUE, from = 0, to = 100, col = 2, lty = 1) curve(exp_fun(x, 1.2, 0.4), add = TRUE, from = 0, to = 100, col = 2, lty = 2)
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# source(here::here("formatting", "functions", "rmd_functions.R")) # source(here::here("rmd_tools", "find_file.R")) require(rmd.utils) dat_dispersal = read.csv(find_file("salamander_dispersal.csv")) exp_fun = function(x, a, b) { return(a * exp(-b * x))}
Question 02: Exponential parameters
cat(readLines(here::here("formatting", "css", "styles.css")))
Consider the plot you made with the 4 exponential curves.
Observe how the curves vary as you change the two parameters' values.
### Questions
- Q1 (2 pts.) Qualitatively describe what happens to the curve as you vary parameter `a`
- Q2 (2 pts.) Qualitatively describe what happens to the curve as you vary parameter `b`
Solution
- Parameter
asets the y-intercept. - Parameter
bsets the [initial] steepness of the decay. - Students may notice that a also affects the steepness of the decay.
exp_fun = function(x, a, b) { return(a * exp(-b * x)) } curve(exp_fun(x, 1.9, 0.1), add = FALSE, from = 0, to = 30, col = 1, ylab = "f(x)") curve(exp_fun(x, 1.9, 0.3), add = TRUE, from = 0, to = 100, col = 1, lty = 2) curve(exp_fun(x, 1.2, 0.2), add = TRUE, from = 0, to = 100, col = 2, lty = 1) curve(exp_fun(x, 1.2, 0.4), add = TRUE, from = 0, to = 100, col = 2, lty = 2) curve(exp_fun(x, 0.9, 0.4), add = TRUE, from = 0, to = 100, col = 3, lty = 2)
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# source(here::here("formatting", "functions", "rmd_functions.R")) # source(here::here("rmd_tools", "find_file.R")) # dat_dispersal = read.csv(find_file("salamander_dispersal.csv")) require(rmd.utils) exp_fun = function(x, a, b) { return(a * exp(-b * x))} ricker_fun = function(x, a, b) { return(a * x * exp(-b * x))} # exp_fun = function(x, a, b) { return(a * exp(-b * x))}
Question 03: Ricker plots
cat(readLines(here::here("formatting", "css", "styles.css")))
Instructions:
- To gain visual intuition, try using
curve()to plot the Ricker function. - Try out different values of the two parameters as well as plotting over different ranges of x-values.
- Try plotting two or more curves with slightly different parameter values on the same plot
- You may need to try out different ranges of x-values in your plot windows to make sure you are focusing on the interesting parts of the curves.
- Try different line colors, widths, and textures.
An example exploratory plotting exercise:
# png("lab_05_q3.png", width = 1200, height = 800, res = 200) curve(ricker_fun(x, 25.1, .5), add = FALSE, from = 0, to = 10, ann = FALSE, ylab = "f(x)", ylim = c(0, 30)); box() curve(ricker_fun(x, 20.2, .3), add = TRUE, col = 2) curve(ricker_fun(x, 49.2, .66), add = TRUE, col = 3, lty = 2, lwd = 3) curve(ricker_fun(x, 10.5, 0.8), add = TRUE, col = 4, lwd = 2) # dev.off()
knitr::include_graphics(find_file("lab_05_q3.png"))
### Questions
- Q1 (4 pts.) Create a single plot containing 6 Ricker curves with these parameter values:
- curve 1: a = 25, b = 0.1, line color = black, line texture = solid
- curve 2: a = 20, b = 0.2, line color = black, line texture = dotted
- curve 3: a = 10, b = 0.2, line color = black, line texture = dotted
- curve 4: a = 75, b = 0.3, line color = red, line texture = solid
- curve 5: a = 50, b = 0.3, line color = red, line texture = dotted
- curve 6: a = 40, b = 0.3, line color = red, line texture = dotted
Solution
curve(ricker_fun(x, 25, 0.1), add = FALSE, from = 0, to = 50, ylab = "f(x)") curve(ricker_fun(x, 20, 0.1), add = TRUE, col = 1, lty = 2) curve(ricker_fun(x, 10, 0.1), add = TRUE, col = 1, lty = 2) curve(ricker_fun(x, 75, 0.3), add = TRUE, col = 2, lty = 1) curve(ricker_fun(x, 50, 0.3), add = TRUE, col = 2, lty = 2) curve(ricker_fun(x, 40, 0.3), add = TRUE, col = 2, lty = 2)
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require(rmd.utils) ricker_fun = function(x, a, b) { return(a * x * exp(-b * x))}
Question 04: Ricker params
cat(readLines(here::here("formatting", "css", "styles.css")))
Instructions:
- To gain visual intuition, try using
curve()to plot the Ricker function. - Try out different values of the two parameters as well as plotting over different ranges of x-values.
- Try plotting two or more curves with slightly different parameter values on the same plot
- You may need to try out different ranges of x-values in your plot windows to make sure you are focusing on the interesting parts of the curves.
- Try different line colors, widths, and textures.
An example exploratory plotting exercise:
curve(ricker_fun(x, 25.1, .5), add = FALSE, from = 0, to = 10, ann = FALSE, ylab = "f(x)", ylim = c(0, 30)); box() curve(ricker_fun(x, 20.2, .3), add = TRUE, col = 2) curve(ricker_fun(x, 49.2, .66), add = TRUE, col = 3, lty = 2, lwd = 3) curve(ricker_fun(x, 10.5, 0.8), add = TRUE, col = 4, lwd = 2) # curve(ricker_fun(x, 1.75, 0.003), add = TRUE, from = 0, to = 100, col = 66, lwd = 3, lty = 4)
### Questions
- Q1 (2 pts.) Qualitatively describe how the `a` parameter influences the curve shape.
- Q2 (2 pts.) Qualitatively describe how the `b` parameter influences the curve shape.
NOTE: make sure you choose an appropriate range of x-values in your plot.
Solution
curve(ricker_fun(x, 25, 0.1), add = FALSE, from = 0, to = 50, ylab = "f(x)") curve(ricker_fun(x, 20, 0.1), add = TRUE, col = 1, lty = 2) curve(ricker_fun(x, 10, 0.1), add = TRUE, col = 1, lty = 2) curve(ricker_fun(x, 75, 0.3), add = TRUE, col = 2, lty = 1) curve(ricker_fun(x, 50, 0.3), add = TRUE, col = 2, lty = 2) curve(ricker_fun(x, 40, 0.3), add = TRUE, col = 2, lty = 2)
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require(rmd.utils) dat_dispersal = read.csv(find_file("salamander_dispersal.csv"))
Question 05: salamander data scatterplot
cat(readLines(here::here("formatting", "css", "styles.css")))
Instructions:
- Read the salamander dispersal data into a
data.framecalleddat_dispersal. - Create a scatterplot of distance class and dispersal rate of first time breeding salamanders.
### Questions
- Q1 (1 pts.) Upload an image file with your scatterplot. Make sure it has appropriate axis labels and title.
- Q2 (2 pts.) Describe, in nontechnical language, what is shown on the x-axis
- Q3 (2 pts.) Describe, in nontechnical language, what is shown on the y-axis
Solution
dat_dispersal plot(dat_dispersal$dist.class, dat_dispersal$disp.rate.ftb, xlab = "distance class", ylab = "standardized dispersal rate", main = "Marbled Salamander - first time breeders")
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require(rmd.utils) dat_dispersal = read.csv(find_file("salamander_dispersal.csv")) # Calculates the value of x for a linear function, given the coordinates # of a known point (x1, y1) and the slope of the line. line_point_slope = function(x, x1, y1, slope) { get_y_intercept = function(x1, y1, slope) return(-(x1 * slope) + y1) linear = function(x, yint, slope) return(yint + x * slope) return(linear(x, get_y_intercept(x1, y1, slope), slope)) }
Question 06: salamander linear model
cat(readLines(here::here("formatting", "css", "styles.css")))
Recall the function we have used to visually estimate linear model parameters:
# Calculates the value of x for a linear function, given the coordinates # of a known point (x1, y1) and the slope of the line. line_point_slope = function(x, x1, y1, slope) { get_y_intercept = function(x1, y1, slope) return(-(x1 * slope) + y1) linear = function(x, yint, slope) return(yint + x * slope) return(linear(x, get_y_intercept(x1, y1, slope), slope)) }
Instructions:
- Using the scatterplot of the dispersal data, visually fit a linear mode
### Questions
- Q1 (2 pts.) Upload an image file with your scatterplot and fitted line. Make sure it has appropriate axis labels and title.
Solution
line_point_slope = function(x, x1, y1, slope) { get_y_intercept = function(x1, y1, slope) return(-(x1 * slope) + y1) linear = function(x, yint, slope) return(yint + x * slope) return(linear(x, get_y_intercept(x1, y1, slope), slope)) }
For example:
plot(dat_dispersal$dist.class, dat_dispersal$disp.rate.ftb, xlab = "distance class", ylab = "standardized dispersal rate", main = "Marbled Salamander - first time breeders") curve(line_point_slope(x, 1400, 0.1, -0.0001), add = TRUE)
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require(rmd.utils) dat_dispersal = read.csv(find_file("salamander_dispersal.csv")) exp_fun = function(x, a, b) { return(a * exp(-b * x))}
Question 07: salamander exponential model
cat(readLines(here::here("formatting", "css", "styles.css")))
Instructions:
- Using the scatterplot of the dispersal data, visually fit an model
### Questions
- Q1 (4 pts.) Upload an image file with your scatterplot and fitted curve. Make sure it has appropriate axis labels and title.
Solution
exp_fun = function(x, a, b) { return(a * exp(-b * x))}
plot(dat_dispersal$dist.class, dat_dispersal$disp.rate.ftb, xlab = "distance class", ylab = "standardized dispersal rate", main = "Marbled Salamander - first time breeders\nExponential model") curve(exp_fun(x, 0.75, 0.003), add = TRUE)
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require(rmd.utils) dat_dispersal = read.csv(find_file("salamander_dispersal.csv")) exp_fun = function(x, a, b) { return(a * exp(-b * x))} ricker_fun = function(x, a, b) { return(a * x * exp(-b * x))}
Question 08: salamander ricker model
cat(readLines(here::here("formatting", "css", "styles.css")))
Instructions:
- Using the scatterplot of the dispersal data, visually fit a ricker curve model.
### Questions
- Q1 (4 pts.) Upload an image file with your scatterplot and fitted curve. Make sure it has appropriate axis labels and title.
Solution
ricker_fun = function(x, a, b) { return(a * x * exp(-b * x))}
For example:
plot(dat_dispersal$dist.class, dat_dispersal$disp.rate.ftb, xlab = "distance class", ylab = "standardized dispersal rate", main = "Marbled Salamander - first time breeders\nRicker model") curve(ricker_fun(x, 0.007, 1/200), add = TRUE)
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require(rmd.utils) dat_dispersal = read.csv(find_file("salamander_dispersal.csv")) # Calculates the value of x for a linear function, given the coordinates # of a known point (x1, y1) and the slope of the line. line_point_slope = function(x, x1, y1, slope) { get_y_intercept = function(x1, y1, slope) return(-(x1 * slope) + y1) linear = function(x, yint, slope) return(yint + x * slope) return(linear(x, get_y_intercept(x1, y1, slope), slope)) }
Question 09: salamander linear model residuals
cat(readLines(here::here("formatting", "css", "styles.css")))
Recall the function we have used to visually estimate linear model parameters:
# Calculates the value of x for a linear function, given the coordinates # of a known point (x1, y1) and the slope of the line. line_point_slope = function(x, x1, y1, slope) { get_y_intercept = function(x1, y1, slope) return(-(x1 * slope) + y1) linear = function(x, yint, slope) return(yint + x * slope) return(linear(x, get_y_intercept(x1, y1, slope), slope)) }
Instructions:
- Using the parameters you chose for your linear fit, calculate the residuals and store them in a vector
resids_linear.
### Questions
- Q1 (3 pts.) Paste the code you used to create `resids_linear`.
- Q1 (1 pts.) Upload an image file with a histogram of the residuals of your linear model.
Solution
line_point_slope = function(x, x1, y1, slope) { get_y_intercept = function(x1, y1, slope) return(-(x1 * slope) + y1) linear = function(x, yint, slope) return(yint + x * slope) return(linear(x, get_y_intercept(x1, y1, slope), slope)) }
For example:
param_x1 = 1400 param_y1 = 0.1 param_slope = -0.0001 plot(dat_dispersal$dist.class, dat_dispersal$disp.rate.ftb, xlab = "distance class", ylab = "standardized dispersal rate", main = "Marbled Salamander - first time breeders\nLinear model") curve(line_point_slope(x, param_x1, param_y1, param_slope), add = TRUE) resids_linear = line_point_slope(dat_dispersal$dist.class, param_x1, param_y1, param_slope) - dat_dispersal$disp.rate.ftb hist(resids_linear, main = "residuals: linear model")
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require(rmd.utils) dat_dispersal = read.csv(find_file("salamander_dispersal.csv")) exp_fun = function(x, a, b) { return(a * exp(-b * x))}
Question 10: salamander exponential model residuals
cat(readLines(here::here("formatting", "css", "styles.css")))
Instructions:
- Using the parameters you chose for your exponential fit, calculate the residuals and store them in a vector
resids_exp.
### Questions
- Q1 (4 pts.) Upload an image file with a histogram of the residuals of your exponential model.
Solution
exp_fun = function(x, a, b) { return(a * exp(-b * x))} plot(dat_dispersal$dist.class, dat_dispersal$disp.rate.ftb, xlab = "distance class", ylab = "standardized dispersal rate", main = "Marbled Salamander - first time breeders\nExponential model") exp_a = 0.75 exp_b = 0.003 curve(exp_fun(x, exp_a, exp_b), add = TRUE) resids_exp = exp_fun(dat_dispersal$dist.class, exp_a, exp_b) - dat_dispersal$disp.rate.ftb hist(resids_exp)
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require(rmd.utils) dat_dispersal = read.csv(find_file("salamander_dispersal.csv")) exp_fun = function(x, a, b) { return(a * exp(-b * x))} ricker_fun = function(x, a, b) { return(a * x * exp(-b * x))}
Question 11: salamander ricker model residuals
cat(readLines(here::here("formatting", "css", "styles.css")))
Instructions:
-
Using the parameters you chose for your Ricker curve fit, calculate the residuals and store them in a vector
resids_ricker. -
Using the scatterplot of the dispersal data, visually fit a ricker curve model.
### Questions
- Q1 (4 pts.) Upload an image file with a histogram of the residuals of your Ricker curve model.
Solution
ricker_fun = function(x, a, b) { return(a * x * exp(-b * x))}
For example:
plot( dat_dispersal$dist.class, dat_dispersal$disp.rate.ftb, xlab = "distance class", ylab = "standardized dispersal rate", main = "Marbled Salamander - first time breeders\nRicker model") rick_a = 0.007 rick_b = 1/200 resids_ricker = ricker_fun(dat_dispersal$dist.class, rick_a, rick_b) - dat_dispersal$disp.rate.ftb hist(resids_ricker) curve(ricker_fun(x, rick_a, rick_b), add = TRUE)
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