17 Homework: Ant Community Ecology and Invasive Fire Ants

17.1 Required Reading

This homework will prepare you to analyze the data from the Ant lab. You should read over that the material to properly understand the data you’ll be working with here. You should be familiar with the materials in Chapters 4, 5, 6, and 7.2. I will also use code from Chapter 8 to reshape the data, although fully understanding it is not necessary for this exercise.

17.2 Objectives (and what’s due)

There are four primary questions in this lab, along with the associated results you’ll be submitting:

What are the habitat preferences of Solenopsis invicta?
- Submit: Three contingency tables (one per contrast) showing the contrast vs. Fire Ant presence/absence; cell contents should be the number of baits that meet he conditions. With each table, submit a chi-square or Fisher’s exact test (as appropriate).
- Submit: A contingency table showing if the interaction of canopy openness & disturbance affect fire ant presence, along with a relevant statistical test.
How do different habitat characteristics affect the ant community?
- Submit: The Jaccard index of similarity for each contrast.
- Submit: The Shannon diversity for each contrast.
- Submit: A Species accumulation curb comparing sampling effort and estimated species richness for each contrast.
- Submit: A rank abundance curve comparing species evenness for each contrast.

17.3 Getting started

You’ll need to download F21_ant_data.csv and put it in your data directory.

# MRR Lab Analysis
#### Setup ####
# Load packages & data
library(tidyverse) 
# install.packages("vegan") # uncomment if necessary
library(vegan) 
theme_set(theme_classic()) # Removes gridlines from ggplot

raw_ant_data = read_csv("data/F21_ant_data.csv")

17.3.1 Contrasts

Most of these analyses will focus on ecological contrasts. There are four contrasts we’re interested in with this lab:

Open (canopy cover 0 or 1) vs. Closed (canopy cover 2 or 3) canopies.
Sparse (0/1) vs. dense (2/3) ground cover.
Low vs. high disturbance
Habitat types (Quarry vs. River Terrace vs. Old Pasture). This column isn’t present in the homework data (so you don’t need to do it now), but it will be included in the data you collect.

17.3.2 The data

The columns of this data frame that are:

Acre: Acre ID.
Site: Site number, 1-16 per acre.
Fire_ants_present: “Y” or “N” for fire ant presence at site.
GPS_easting, GPS_northing: Location of site; ignore.
Phorids_present: Ignore this.
Canopy_cover, Ground_cover: Canopy or ground cover at site, from 0 (none) to 3 (full), as per heterogeneity lab.
Disturbance: “high” or “low” disturbance at site.
Field_Notes: Notes from the field data collection
Name: Student Name; ignore.
Total_ants: Total number of ants caught at site.
Solenopsis invicta, and a large number of other species-names: Number of that species present at the site. Note that these columns have spaces in their names, so to use them, you need to surround them with back-ticks (`, on the ~ key).
Other species: Other species present; you can generally ignore this.

We’ll need to re-define some our columns to fit the above contrasts; you can use the if_else() function inside mutate to do this.


wide_ant_data = raw_ant_data |> 
  # Remove unnecessary columns
  select(-GPS_easting, -GPS_northing, -Phorids_present, -Field_Notes, -Name, -Total_ants, -`Other species`) |> 
  mutate(
    Canopy_cover = if_else(Canopy_cover %in% c(0, 1), "Open", "Closed"), # see ?if_else() for details
    Ground_cover = # define as sparse vs. dense
  )

We’re also going to transform the data into a long format using pivot_longer (8.2).

# Get a list of species columns
ant_species = wide_ant_data |> 
  # Remove the non-species columns
  select(-Acre, -Site, -Fire_ants_present, -Canopy_cover, -Ground_cover, -Disturbance) |> 
  names() # get the column names

# Convert all of the species columns to "Species" and "N"
tidy_ant_data = wide_ant_data |> 
  pivot_longer(cols = all_of(ant_species), # all_of() selects columns based on a character vector; it also works in select()
               names_to = "Species", # Put the column name in a "Species" column
               values_to = "N") |> # Cell values are counts, so make that an N column
  # replace the underscores in species names with a space:
  filter(N > 0) # Remove species that aren't present

17.4 S. invicta habitat preference

For all four contrasts (three in the homework), create a contingency table out of the contrast and Fire_ants_present. Run a chi-squared or Fisher’s exact test (7.2.2) on each table.

Be sure to remove any NA columns from the data using filter() and is.na() (6.3) before making your tables.

To make the interaction chi-square test, use mutate() and the paste() function to define a new column that combines Canopy_cover and Disturbance (remove NA’s first). Use this new column to create a contingency table with Fire_ants_present and run the appropriate statistical text.

For information on the paste() function, enter ?paste in the console.

17.5 Jaccard similarity

Jaccard similarity is a measure of how similar the species composition is between a pair of communities (or between two levels of a contrast). To calculate the Jaccard similarity of two communities, you need to divide the number of shared species by the total number of species. This can be done with a combination of the intersect(), union(), and length() functions.

# Let's say these are the species in our two communities:
com_a = LETTERS[1:5]
com_b = LETTERS[3:8]

# Species in common:
intersect(com_a, com_b)
## [1] "C" "D" "E"

# Species present in either:
union(com_a, com_b)
## [1] "A" "B" "C" "D" "E" "F" "G" "H"

# Total number of species present:
length(union(com_a, com_b))
## [1] 8

# Jaccard similarity:
length(intersect(com_a, com_b)) / 
length(union(com_a, com_b))
## [1] 0.375

Since you’ll be doing this for several groups, it’s a good idea to write a function that will do this for us. For a background on functions, please see this chapter in R for Data Science. To use the function, first run the code that defines it:


jaccard_similarity = function(com_1, com_2, na.rm = FALSE) {
  # com_1 and com_2 are the arguments of the function,
  # they should be the names of species in different communities
  # Remove missing values from the two communities if na.rm == TRUE
  # 
  if(isTRUE(na.rm)) {
    com_1 = na.omit(com_1)
    com_2 = na.omit(com_2)
  }
  
  # Create local variables for the intersection and union;
  common_spp = intersect(com_1, com_2) 
  total_spp = union(com_1, com_2) 
  # these variables are created while the function runs & destroyed when it ends
  # The last value of the function is its output (a.k.a., return value)
  length(common_spp) / length(total_spp) # return this
}

# Here's an example of running the function
jaccard_similarity(com_1 = com_a, com_2 = com_b)
## [1] 0.375
# This is the same thing:
jaccard_similarity(com_a, com_b)
## [1] 0.375

How would this work for our data? Filter the data for each level of the contrast and pull out the species column. Then run the function.

# Contrast: Disturbance
disturb_low = tidy_ant_data |> 
  # Subset the data to get the "community" you want
  filter(Disturbance == "low") |> 
  # Get the list of species as a vector
  pull(Species) # pull() is like $ but works with pipes
disturb_hi = #  fill this in for hight disturbance
  
jaccard_similarity(disturb_low, disturb_hi)

For habitat (in the final assignment), you’ll need to make 3 pairwise similarity comparisons (Q vs. R, Q vs. P, P vs. R).

17.6 Shannon Index & Diversity

Let’s make a function that calculates the Shannon index of a community:


shannon_diversity = function(species, count) {
  # species: vector of species names; 
  # count: how many of each species are present
  
  # Create p, a vector of relative frequencies
  p = tibble(species, count) |> 
    # Merge duplicate species 
    group_by(species) |> 
    summarize(count = sum(count)) |> 
    ungroup() |> 
    # Remove zeroes
    filter(count > 0) |> 
    # Convert to frequencies
    mutate(p = count / sum(count)) |> 
    # Extract column p
    pull(p) 
  if(length(p) < 2) return(0) # one or 0 species has an H of 0
  # Return value:
  exp( -sum(p * log(p)) ) # exponential of shannon index
}

# Calculate the shannon diversity
shannon_diversity(LETTERS[1:5], # Species names, A : E
                 c(100, 5, 30, 22, 140)) # Species counts
## [1] 3.367463

This function should work well with a grouped summarize function:

tidy_ant_data |> 
  group_by(Acre, Disturbance) |> # group by Acre & habitat
  summarize(shannon = shannon_diversity(Species, N)) 
## `summarise()` has grouped output by 'Acre'. You can override using the
## `.groups` argument.
## # A tibble: 24 × 3
## # Groups:   Acre [14]
##    Acre  Disturbance shannon
##    <chr> <chr>         <dbl>
##  1 A1    high           1.63
##  2 A1    low            2.03
##  3 A10   high           0   
##  4 A10   low            1.69
##  5 A11   high           1.21
##  6 A11   low            1.33
##  7 A14   high           2.79
##  8 A14   low            1.93
##  9 A15   high           1.24
## 10 A15   low            1.12
## # … with 14 more rows
## # ℹ Use `print(n = ...)` to see more rows

Make a figure out of this (a boxplot or a jitterplot).

17.7 Species Accumulation Curves

Species accumulation curves are calculated by the specaccum() function in vegan. This function requires a data set where each column is a species, each_row is a site, and each cell is a 1 (indicating presence) or 0 (indicating absence). Let’s create a function that will format the data for this:

# Create a function that converts a number to presence-absense
to_presence_absense = function(x) if_else(x <= 0 | is.na(x), 0, 1) # Recodes data as 0 if it's 0 or missing or 1 otherwise

# Format data for the species accumulation curve
format_sac_data = function(wide_data, ant_spp = ant_species) {
  # Takes a wide data format
  # ant_spp is the name of all ant species in the dataset; it's defined earlier
    wide_data |> 
      # Select only species columns
      select(all_of(ant_spp)) |> 
      # use to_presence_absense() on all columns
      mutate(across(everything(), to_presence_absense))
}

# Here's what the results looks like on open canopy data:
wide_ant_data |> 
  filter(Canopy_cover == "Open") |> 
  format_sac_data() |> 
  View()

Solenopsis invicta	Paratrechina terricola	Pheidole dentata	Pheidole floridana
1	0	0	0
0	0	0	1
0	0	1	0
0	0	1	0
0	0	1	0
0	0	1	0
0	1	0	1
1	0	0	0
0	0	1	0
0	0	1	0

From here, you can use it to calculate an SAC.

sac_open = wide_ant_data |> 
  filter(Canopy_cover == "Open") |> 
  format_sac_data() |> 
  specaccum(method = "random", permutations = 500)   # Use these argument options

Use print(sac_open) to look at the output. The results are basically a tidy data frame turned on its side: one row for the number of sites sampled, one for the estimated richness, and one for the error around the richness estimate. To plot this, we need to re-format the output.

sac_open_tidy = 
  tibble(
    sites = sac_open$sites,
    richness = sac_open$richness,
    se = sac_open$sd # the "SD" column is actually a standard error measure
  ) 
View(sac_open_tidy)

sites	richness	se
1	0.762	0.4623674
2	1.442	0.5961096
3	1.968	0.6927740
4	2.418	0.7800596
5	2.760	0.8578297
6	3.074	0.9023039
7	3.328	0.9044623
8	3.552	0.9279106
9	3.764	0.9391848
10	3.944	0.9668161

From this, it’s relatively simple to create the actual plot:

sac_open_plot = sac_open_tidy |> 
  # Define the confidence intervals based on mean richness & standard errors
  mutate(lower_ci = richness - se * 1.96,
         upper_ci = richness + se * 1.96) |> 
  ggplot() + aes(x = sites, y = richness) +
  geom_line(size = 1) + # line for richness
  # The lines below add in confidence intervals
  geom_line(aes(y = lower_ci), linetype = 2, alpha = .7) + 
  geom_line(aes(y = upper_ci), linetype = 2, alpha = .7) +
  # alpha adds a bit of transparency
  xlab("Sampling intensity (number of sites)") +
  ylab("Number of ant species")
sac_open_plot

Let’s combine these last few steps into a pair of functions, for re-use with different data sub-sets:

# Calculate the tidy SAC data
get_sac = function(wide_data) {
  # wide_data is data in the wide format, probably subset or filtered
  sac = format_sac_data(wide_data) |> # Convert to SAC format
    specaccum(method = "random", permutations = 500) # calculate SAC
  tibble( # Tidy output
    sites = sac$sites,
    richness = sac$richness,
    se = sac$sd
  ) |>   
    mutate(lower_ci = richness - se * 1.96,
           upper_ci = richness + se * 1.96)
}
# Make the plot
plot_sac = function(sac_data) {
  # sac_data is the output of get_sac()
  sac_data |> ggplot() + 
    aes(x = sites, y = richness) +
    geom_line(size = 1) + # line for richness
    # The lines below add in confidence intervals
    geom_line(aes(y = lower_ci), linetype = 2, alpha = .7) + 
    geom_line(aes(y = upper_ci), linetype = 2, alpha = .7) +
    # alpha adds a bit of transparency
    xlab("Sampling intensity (number of sites)") +
    ylab("Number of ant species")
}

From here, we easily try different combinations

wide_ant_data |> 
  filter(Canopy_cover == "Closed") |> 
  get_sac() |> 
  plot_sac()

When comparing multiple groups, it’s best to put them together in a single plot. The easiest way to do that is to calculate the SAC data, then combine the resulting data frames

# Create the SAC data frames for each group in your comparison
sac_cnpy_open = wide_ant_data |> 
    filter(Canopy_cover == "Open") |> 
    get_sac() |> 
    mutate(Canopy_cover = "Open") # Use the Mutate Add disturbance column to sac results
sac_cnpy_closed = wide_ant_data |> 
    filter(Canopy_cover == "Closed") |> 
    get_sac() |> 
    mutate(Canopy_cover = "Closed") # Add disturbance column back to sac results

sac_cnpy_combined = # Combine them into one data frame
  bind_rows(sac_cnpy_open, sac_cnpy_closed) # Note that bind_rows() can combine more than two data frames, if you're doing a 3+ part comparison

plot_sac(sac_cnpy_combined) + # Creates a standard SAC Plot
  aes(color=Canopy_cover) +    # Separates out the lines by color based on the Disturbance column
  scale_color_viridis_d()     # Make the colors look nice

Do this for all of your contrasts.

17.8 Rank Abundance Curves

This is really just an exercise in data manipulation: we want to get the total number of individuals of each species, then display them in decreasing frequency. You need to do a grouped summarize() on the tidy data so that there’s one row per species/contrast combination, with columns Species, N (which is the species-level sum of the already existing N column in tidy_ant_data), and whatever your contrast is. From here, sort the summary by contrast and descending N, group by the contrast, and use mutate() to make a new column species_rank = 1:n().

To make the plot itself, you can use this function; use aes() to separate your contrasts by color like you did with plot_sac() above.


plot_rank_abundance = function(summarized_data, right_margin = 2.8) {
  # Make the rank abundance plot
  # The right_margin argument is used to make sure that 
  # the angled axis labels don't go of the page
  # make it larger or smaller to suit your tastes
  ggplot(summarized_data, aes(x = species_rank, y = N)) +
    geom_line() + # Create a descending line
    scale_y_log10() + # puts y axis on log scale
    xlab("Species (In Rank Order)") + 
    scale_color_viridis_d()
}

Your resulting plot should look something like this:

## `summarise()` has grouped output by 'Disturbance'. You can override using the
## `.groups` argument.

Solenopsis invicta	Paratrechina terricola	Pheidole dentata	Pheidole floridana
1	0	0	0
0	0	0	1
0	0	1	0
0	0	1	0
0	0	1	0
0	0	1	0
0	1	0	1
1	0	0	0
0	0	1	0
0	0	1	0

Solenopsis invicta	Paratrechina terricola	Pheidole dentata	Pheidole floridana
1	0	0	0
0	0	0	1
0	0	1	0
0	0	1	0
0	0	1	0
0	0	1	0
0	1	0	1
1	0	0	0
0	0	1	0
0	0	1	0

Solenopsis invicta	Paratrechina terricola	Pheidole dentata	Pheidole floridana
1	0	0	0
0	0	0	1
0	0	1	0
0	0	1	0
0	0	1	0
0	0	1	0
0	1	0	1
1	0	0	0
0	0	1	0
0	0	1	0