Demographic and environmental stochasticity

Demographic stochasticity

Environmental stochasticity

Question 1

An important method for working with dataframes is data wrangling. This practical introduces this idea in practice.
1. Describe what “data wrangling” is (3)
2. In R data wrangling is usually carried out using the spread() and gather() functions from the tidyr package. With reference to the package’s and functions’ websites but in your own words, describe how these two functions work to manipulate or wrangle dataframes. You may include your own examples (not those from the websites) if you wish (6)

Question 2

The ggplot2 package has some very impressive functionality which allows for unique and professional quality plots which display large amounts of information. One interesting way that one can include more information on a plot is through facetting. Explain what facetting is and how to use it in ggplot2. Also describe how the facet labels can be changed from what is in the dataframe using the labeller argument (4)

Question 3

The followoing code is supposed to produce an utput to model demographic stochasticity, however, there are four problems with the code that are affecting the faceting - two are with the construction of the dataframe and two are concerned with the formatting of the actual plot. Edit the following code to match the figure below (this figure has been modified from the one in the Shiny App - the CV calculations have been removed) and copy it into your Word document together with your completed figure output. Be sure to include comments on what you have changed and brief reasons why you have done so (8)

library(tidyr) 
library(dplyr) 
library(ggplot2) 
library(viridis) 

     sims <- 100  ## number of simulations to run
     pop1 <- 10  ## population 1 size
     survive1 <- 0.6  ## population 1 survival probability
     birth1 <- 0.4  ## population 1 birth probability
     pop2 <- 200  ## population 2 size
     survive2 <- 0.5  ## population 2 survival probability
     birth2 <- 0.6  ## population 1 birth probability
     
     Trial = seq(from = 0, to = sims, by = 1)
     Survivors1 = numeric(length = sims + 1)
     Births1 = numeric(length = sims + 1)
     
     Survivors2 = numeric(length = sims + 1)
     Births2 = numeric(length = sims + 1)
     
     for (i in 0:sims) {
       
       survive_count1 <- 0
       birth_count1 <- 0
       
       survive_count2 <- 0
       birth_count2 <- 0
       
       for (j in 0:pop1) {
         
         ifelse(runif(1) < survive1, 
                survive_count1 <- survive_count1 + 1, 
                survive_count1 <- survive_count1)
         ifelse(runif(1) < birth1, 
                birth_count1 <- birth_count1 + 1, 
                birth_count1 <- birth_count1)
         
       }
       
       for (k in 0:pop2) {

         ifelse(runif(1) < survive2,
                survive_count2 <- survive_count2 + 1,
                survive_count2 <- survive_count2)
         ifelse(runif(1) < birth2,
                birth_count2 <- birth_count2 + 1,
                birth_count2 <- birth_count2)

       }
       
       Survivors1[i] <- survive_count1
       Births1[i] <- birth_count1
       
       Survivors2[i] <- survive_count2
       Births2[i] <- birth_count2
       
     }
     
     survive_birth_df1 <- as.data.frame(cbind(Trial, 
                                              Survivors = Survivors1, 
                                              Births = Births1))
     N10 <- gather(survive_birth_df1, 
                   key = "Aspect", 
                   value = "Value")
     
     survive_birth_df2 <- as.data.frame(cbind(Trial,
                                              Survivors = Survivors2,
                                              Births = Births2))
     N100 <- gather(survive_birth_df2,
                    key = "Aspect",
                    value = "Value")
     
     survive_birth_df <- bind_rows(N10, N100, .id = "Population")

     ggplot(survive_birth_df) + 
       geom_density(aes(x = Value, 
                        colour = Aspect, 
                        fill = Aspect), 
                    alpha = 0.4) + 
       facet_wrap(~ Aspect, 
                  scales = "free_x", 
                  labeller = as_labeller(c("1" = "Population 1", 
                                           "2" = "Population 2"))) + 
       labs(x = "Population size", 
            y = "Density", 
            colour = "Population \nparameter", 
            fill = "Population \nparameter") + 
       theme(panel.background = element_rect(colour = "black", 
                                             fill = "white"), 
             panel.grid = element_blank(), 
             axis.title = element_text(colour = "black", 
                                       size = 14), 
             axis.text = element_text(colour = "black", 
                                      size = 12), 
             legend.text = element_text(colour = "black", 
                                        size = 12), 
             legend.title = element_text(colour = "black", 
                                        size = 14)) + 
       scale_color_viridis(discrete = TRUE, end = 0.8) + 
       scale_fill_viridis(discrete = TRUE, end = 0.8)

2. For this second coding question there are six errors (three logical and three cosmetic) which are preventing the code from running. Identify and correct these errors in the following code. Present your corrected code and figure output together with a description and your proposed solution for each of these errors in a Word document (12)

library(ggplot2) 


     nyears <- seq(from = 1, to = 20, by = 1)
     N <- c(50, rep(0, times = 20 - 1))  # Create an open vector for data
     r <- 0.5
     K <- 100
     en_var <- 0.2
     
     for (i in 1:length(nyears)+1) {
       ## carrying capacity variability
       randK <- rnorm(n = 1, mean = K, sd = en_var*K)

       ifelse(N[i - 1] <= 1, 
              N[i] <- 0, 
              N[i] <- (r*N[i - 1]*(1 - (N[i - 1]/randK))))
       
       ifelse(N[i] > 0, 
              N[i] <- 0, 
              N[i] <- N[i])
       
     }
     
     log_stoch <- as.data.frame(cbind(nyears, N))
     
     ggplot(log_stoch) + geom_point(aes(x = nyears, y = N)) + 
        geom_hline(yintercept = 0) +
        geom_line(aes(x = nyears, y = N)) +
        theme(axis.title = element_text(colour = "black",
                                       size = 14),
              axis.text = element_text(colour = "black",
                                      size = 12))

Demographic stochasticity

Environmental stochasticity

Combined stochasticity

1. In this practical we have considered demographic and environmental stochasiticity in isolation, however, in real world conservation scenarios these two aspects often need to be considered together. This is often done using a method called population viability analysis (PVA). In South Africa one of the most important conservation efforts has been that of the African elephant. By making reference to this article (you will be able to download it when connected to the university LAN, through JSTOR or Google Scholar) define what population viability analysis is and identify both demographic and environmental stochasticity examples that the authors incorporated into their modelling (10)