## Exercise 6: Basic programming in R

1. Create a function to calculate the area of a circle. Test the function by finding the area of a circle with a diameter of 3.4 cm. Can you use it on a vector of data?

# area of a circle
# the equation to calculate the area of a circle is pi * radius^2

circle.area <- function(d){
pi * (d/2)^2
}

# to use your new function

circle.area(10)
# [1] 78.53982

# to test on a vector of diameters
# first create a vector with diameters ranging from 0 to 50 in steps of 10

cir.diam <- seq(from = 0, to = 50, by = 10)

circle.area(cir.diam)
# [1]    0.00000   78.53982  314.15927  706.85835 1256.63706 1963.49541

1. Write a function to convert farenheit to centegrade (oC = (oF - 32) x 5/9). Get your function to print out your result in the following format: “Farenheit : value of oF is equivalent to value oC centigrade.”

far.cent <- function(a) {
val <- (a - 32) * 5/9
print(paste("Fahrenheit: ", round(a, digits = 3), "oF", sep = " "), quote = FALSE)  # round 3dp
print(paste("Centigrade: ", round(val, digits = 3), "oC", sep = " "), quote = FALSE)  # round 3dp
}

# alternative Fahrenheit to centigrade using cat function

far.cent2 <- function(a) {
val <- (a - 32) * 5/9  #calculation
cat("Fahrenheit: ", round(a, digits = 3), "oF", "\n")  # use cat function
cat("Centigrade: ", round(val, digits = 3), "oC", "\n")
}

1. Create a vector of normally distributed data, of length 100, mean 35 and standard deviation of 15. Write a function to calculate the mean, median, and range of the vector, print these values out with appropriate labels. Also get the function to plot a histogram (as a proportion) of the values and add a density curve.

# Create a vector of normally distributed data
# length 100, mean 35 and standard deviation of 29

vals <- rnorm(100, 35, 15)  # create some norm dist data mean 35, sd = 15

summary.fun <- function(dat){
mymean <- round(mean(dat), digits = 4)          # calc mean
mymedian <- round(median(dat), digits = 4)    # calc median
mymin <- round(min(dat), digits = 4)          # calc min
mymax <- round(max(dat), digits = 4)          # calc max
print(paste("mean:", mymean, sep = " "), quote = FALSE)     # print mean
print(paste("median:", mymedian, sep = " "), quote = FALSE)     # print median
print(paste("range:", "from:", mymin, "to", mymax, sep = " "), quote = FALSE)
dens <- density(dat)                          # estimate density curve
hist(dat, main = "",type = "l",freq = FALSE)  # plot histogram
lines(dens, lty = 1, col = "red")             # plot density curve
}

# use the function
summary.fun(vals)

1. Write a function to calculate the median value of a vector of numbers (yes I know there’s a median() function already but this is fun!). Be careful with vectors of an even sample size, as you will have to take the average of the two central numbers (hint: use modulo %%2 to determine whether the vector is an odd or an even size). Test your function on vectors with both odd and even sample sizes.

# calculate a median

ourmedian <- function(x){
n <- length(x)
if (n %% 2 == 1)      # odd numbers
sort(x)[(n + 1)/2]  # find the middle number by adding 1 to length and div 2
else {                # even numbers
middletwo <- sort(x)[(n/2) + 0:1]   #find the two middle numbers
mean(middletwo)
}
}

# use the function
mydat <- sample(1:50, size = 10, replace = TRUE )

# our function
ourmedian(mydat)

# R median function
median(mydat)

1. You are a population ecologist for the day and wish to investigate the properties of the Ricker model. The Ricker model is defined as:

$N_{t+1} = N_{t} exp\left[r\left(1- \frac{N_{t}}{K} \right) \right]$

1. (cont) Where Nt is the population size at time t, r is the population growth rate and K is the carrying capacity. Write a function to simulate this model so you can conveniently determine the effect of changing r and the initial population size N0. K is often set to 100 by default, but you want the option of being able to change this with your function. So, you will need a function with the following arguments; nzero which sets the initial population size, r which will determine the population growth rate, time which sets how long the simulation will run for and K which we will initially set to 100 by default.

# function to simulate Ricker model

Ricker.model <- function(nzero, r, time, K = 1) {
# sets initial parameters
N <- numeric(time + 1)  # creates a real vector of length time+1 to store values of Nt+1
N[1] <- nzero  # sets initial population size in first element of N
for (i in 1:time) {
# loops over time
N[i + 1] <- N[i] * exp(r * (1 - N[i]/K))
}
Time <- 0:time  # creates vector for x axis
plot(Time, N, type = "o", xlim = c(0, time), xlab = "Time", ylab = "Population size (N)", main = paste("r =",
r, sep = " "))  # plots     output
}

# To run play around with the different parameters, especially r
Ricker.model(nzero = 0.1, r = 1, time = 100)

End of Exercise 6