Background
This is a guest post written by Joseph Mack
This post, written by Joseph Mack, explores the working of the unified
interpolation/extrapolation tools described in Colwell et al. 2012 Journal of
Plant Ecology “Models and estimators linking individual-based and sample-based
rarefaction, extrapolation and comparison of assemblages” doi:
10.1093/jpe/rtr044. Joseph shared this tutorial with the Fall 2021 Biodiversity
Measurement seminar.
Joseph’s tutorial
First, we must import a sample presence-absence dataset.
spp_incidence <- read.csv("data/ann_incidence.csv", row.names = 1)
The equations used in this analysis are derived from a Bernoulli Product model.
Under this model, species \(i\) has probability theta of occurring. What is the
probability that species \(i\) is not present in a given site?
Do we know this probability for each species in our dataset?
To proceed, we must determine how many species (Sobs
) and sites (sites
) are
in the data set (Sobs
)?
sites <- length(spp_incidence)
Sobs <- nrow(spp_incidence)
sites
## [1] 18
Sobs
## [1] 12
The equation below can be found on pg. 6 of Colwell et al. 2012. It calculates
the incidence-based frequency of a given species.
#What is the incidence-based frequency (Yi) of Sp1?
Ysp1 = sum(as.numeric(spp_incidence["sp1",]))
Ysp1
## [1] NA
#What about the other species?
spp_names = rownames(spp_incidence)
Yi <- c(1:12)
for (i in 1:12) {
Yi[i] <- sum(spp_incidence[i,])
}
The code below creates a table of incidence frequencies (the row sums of our
data set), which will be used to calculate Qk
.
incidence_freqs <- data.frame(cbind(Yi, spp_names))
Next, we must determine how many ‘unique’ species are in the dataset. In other
words, how many species occur in only one site? This requires us to calculate
Qk
, the incidence frequency count and an essential statistic for sample-based
extrapolation.
Q <- function(k) {
out = 0
for (i in 1:length(incidence_freqs$Yi)) {
if (incidence_freqs$Yi[i] == k) {
out = out + 1
}
}
return(out)
}
#How many species are found in only 1 site? 4 sites? 9 of the sites? All the sites?
Q(1)
## [1] 3
Q(4)
## [1] 1
Q(9)
## [1] 0
Q(18)
## [1] 1
Below is a function to interpolate/rarefy the sample dataset (equation 17 in
Colewll et al.). It computes the number of species we would recover if we
sampled from x
fewer sites (x < sites
).
Ssample_rare <- function(x) {
for (i in 1:Sobs) {
out <- (choose((sites - as.numeric(incidence_freqs$Yi[i])), x))/
choose(sites, x)
}
return(Sobs - sum(out))
}
#How many species would we recover if we sampled from only 1 site? 5 sites? 9 sites?
Ssample_rare(1)
## [1] 11.05556
Ssample_rare(5)
## [1] 11.27778
Ssample_rare(9)
## [1] 11.5
The values for Ssample_rare
don’t look right. This rarefaction function is
broken! Can you figure out why? Hint: what is [i]
doing in the code below?
The rarefaction code below works! Why?
Ssample_rare <- function(x) {
out = c()
for (i in 1:Sobs) {
out[i] <- (choose((sites - as.numeric(incidence_freqs$Yi[i])), x))/choose(sites, x)
}
return(Sobs - sum(out))
}
#NOW, how many species would we recover if we sampled from only 1 site? 5 sites? 9 sites?
Ssample_rare(1)
## [1] 4.611111
Ssample_rare(5)
## [1] 7.977708
Ssample_rare(9)
## [1] 9.748416
#These values make more sense!
Now that we have a means to interpolate our data, we can make a rarefaction plot.
diversity_r = sapply(1:18, Ssample_rare) # This outputs a vector of Ssample_rare
# outputs for 1 to 18 sampling sites.
plot(1:18
, diversity_r
, type = "l"
, ylab = "Number of Species"
, xlab = "Number of Sites")
![plot of chunk first rarefaction plot](data:image/png;base64,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)
Next, we can work on extrapolating the dataset (Ssample(sites + s))
using
equations 18 and 21 from Colwell et al. 2012. This addresses how many species we
would find if we sampled s
additional sites.
To do this, we first need to estimate Q(0)
: the number of species absent from
our samples.
#Because Q(2) > 0 for our data set, we can use the following equation based on the Chao2 estimator:
Q0 = ((sites-1)/sites)*((Q(1)^2)/(2*Q(2)))
Q0
## [1] 1.416667
With a value for Q0
, we can implement the authors’ equation for extrapolation
as a function of s
additional samples:
Ssample_extr <- function(s) {
out <- Sobs + (Q0*(1 - (1 - (Q(1)/(Q(1) + (sites*Q0))))^s))
return(out)
}
#How many species would we recover if we sampled 2 extra sites? 50 extra sites?
Ssample_extr(2)
## [1] 12.28255
Ssample_extr(50)
## [1] 13.41122
#Make an extrapolation plot for 72 additional sites.
diversity_e = sapply(1:72, Ssample_extr) #This outputs a vector of Ssample_extr
# outputs for 1 to 50 additional sampling sites.
plot(1:72
, diversity_e
, type = "l"
, lty = 2
, ylab = "Number of species"
, xlab = "Number of Additional Sites")
![plot of chunk extrapolation function](data:image/png;base64,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)
Now, we can combine the rarefaction and extrapolation plots into a single plot:
library(ggplot2)
combined_diversity = c(diversity_r, diversity_e) #Combining the vectors of
# rarefied and extrapolated species counts, for 1 - 90 sites.
combined_diversity
## [1] 4.611111 5.882353 6.713235 7.391830 7.977708 8.494344 8.955505 9.371041 9.748416 10.093263 10.409754 10.700927
## [13] 10.968954 11.215359 11.441176 11.647059 11.833333 12.000000 12.149123 12.282548 12.401929 12.508744 12.604315 12.689825
## [25] 12.766335 12.834791 12.896041 12.950844 12.999878 13.043750 13.083005 13.118127 13.149552 13.177669 13.202827 13.225337
## [37] 13.245477 13.263497 13.279620 13.294046 13.306953 13.318502 13.328835 13.338081 13.346353 13.353754 13.360377 13.366302
## [49] 13.371603 13.376347 13.380591 13.384389 13.387786 13.390826 13.393546 13.395980 13.398158 13.400106 13.401849 13.403409
## [61] 13.404804 13.406053 13.407170 13.408170 13.409064 13.409865 13.410581 13.411221 13.411794 13.412307 13.412766 13.413177
## [73] 13.413544 13.413873 13.414167 13.414430 13.414665 13.414876 13.415065 13.415233 13.415384 13.415519 13.415640 13.415748
## [85] 13.415845 13.415931 13.416009 13.416078 13.416140 13.416195
sampling_sites = 1:90 #vector for 18 rarefied sites + 72 additional extrapolated
# sites
sampling_sites
## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
## [43] 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84
## [85] 85 86 87 88 89 90
diversity_est <-
data.frame(cbind(combined_diversity, sampling_sites))
sac_plot = ggplot(
data = subset(diversity_est, sampling_sites <= 18),
aes(x = sampling_sites, y = combined_diversity)
) +
geom_line(size = 0.75) +
geom_line(
data = subset(diversity_est, sampling_sites >= 18),
aes(x = sampling_sites, y = combined_diversity),
lty = 2,
size = 0.75
) +
geom_point(aes(x = 18, y = 12), size = 3, pch = 16) +
xlab("Number of Sampling Sites") +
ylab("Number of Species") +
ggtitle("Species Accumulation Curve") +
theme(plot.title = element_text(size = 8.5))
sac_plot
![plot of chunk print SAC plot](data:image/png;base64,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)
What does the point represent in this plot? The dotted line? The solid line? Is
our data set a good approximation for the total number of species in the region
sampled?
It is possible to obtain a 95% confidence interval about the species
accumulation curve. However, the variance estimators provided by Colwell et al.
2012 are difficult to understand. As an alternative, we can employ
non-parametric bootstrapping to get 95% confidence intervals about the curve.
The code below is not explicitly described in Colwell et al. 2012, but it
employs the same estimators we used above.
Below is a function for getting bootstrap replicates of our rarefaction and
extrapolation estimates.
Ssample_boot <- function(x, s) {
# First, we need to build matrices and vectors to hold our boot-strapped data replicates.
boot_data <- matrix(nrow = 12, ncol = 18)
Yi_boot <- c(1:12)
for (i in 1:12) {
# The line below creates a replicate dataset from our original spp_incidence dataset,
# with replacement.
boot_data[i, ] <- rbind(as.numeric(sample(spp_incidence[i, ]
, size = 18
, replace = TRUE)))
#The for loop below calculates the incidence frequencies from the replicated dataset.
for (j in 1:12) {
Yi_boot[j] <- sum(boot_data[j,])
}
}
# Below is the equation for rarefaction that we implemented earlier, where x is
# a sample smaller than sites.
out_rare = c()
for (i in 1:Sobs) {
out_rare[i] <- choose(sites - Yi_boot[i], x)/choose(sites, x)
}
#This calculates a value of Q2 for the replicate data set.
Q2 = sum(Yi_boot == 2)
#This calculates a value of Q1 for replicate data set.
Q1 = sum(Yi_boot == 1)
# We are using a different equation for Q0 here (Equation 22),
# to avoid dividing by 0 when Q2 is 0 in some of our replicates.
Q0_b = ((sites - 1)/sites) * (Q1 * ((Q1 - 1))/(2 * (Q2 + 1)))
# Below is just equation 18, with some special conditions to account for
# scenarios where the function divides by 0.
out_extr <- Q0_b * (1 - (exp((-s * Q1))/(Q1 + sites * (Q0_b))))
if (is.nan(out_extr) == TRUE) {
return(c(Sobs - sum(out_rare), Sobs))
} else {
return(c(Sobs - sum(out_rare), Sobs + out_extr))
}
}
The code below tests that the function is working. The first variable (x
)
specifies the sample size to be interpolated/rarefied, while the second variable
(s
) specifies the additional sites to be extrapolated. The output should be
different each time you run it.
Ssample_boot(1,2)
## [1] 4.388889 12.000000
The code below gets bootstrap replicates using replicate
and mapply
. How
many bootstrap replicates are we running?
var1 <- 1:18
var2 <- 1:90
boot_data <- replicate(100, mapply(Ssample_boot, var1, var2))
Now that we have our bootstrap replicates, we can set up an empty matrix to
store our bootstrap replicate data. Each column is a site (1 – 18 interpolated,
19 – 90 extrapolated), and each row is a bootstrapped replicate.
combined_boot_data <- matrix(ncol = 90, nrow = 100)
#The code below populates the matrix.
for (i in 1:100) {
combined_boot_data[i, 1:18] <- boot_data[, , i][1, 1:18]
}
for (i in 1:100) {
combined_boot_data[i, 19:90] <- boot_data[, , i][2, 19:90]
}
combined_boot_data <- data.frame(combined_boot_data)
Now that we have bootstrapped replicates for rarefaction and extrapolation, we
can estimate mean, 2.5% , and 97.5% quantiles for each site (1 – 18 rarefied, 19
- 90 extrapolated). These values can then be used to estimate a 95% confidence
interval centered about our sample data.
#This creates an empty vector to store the means of our bootstrapped data.
boot_means <- c()
#This estimates the average across 100 bootstrap replicates for each site (1 - 90).
for (i in 1:90) {
boot_means[i] = (sum(combined_boot_data[,i]))/100
}
#This creates an empty data frame to store the 2.5% and 97.5% quantiles of our bootstrapped data.
boot_quantiles <- matrix(nrow = 2, ncol = 90)
boot_quantiles <- data.frame(boot_quantiles)
# This computes the 2.5% and 97.5% quantiles of our data set,
# populating the data frame we created above.
for (i in 1:90) {
boot_quantiles[,i] <- unname(quantile(combined_boot_data[,i], probs = c(0.025, 0.975)))
}
CI_data <- rbind(combined_boot_data, boot_means, boot_quantiles)
With the average, 2.5%, and 97.5% quantiles, we can compute the lower and upper
confidence bounds for each rarefied and extrapolated site.
For each site, the lower confidence bound = sample data – (bootstrap average –
2.5% bootstrap quantile).
LCB <- c()
for (i in 1:90) {
LCB[i] <- combined_diversity[i] - (CI_data[101,i] - CI_data[102,i])
}
For each site, the upper confidence bound = sample data + (97.5% bootstrap
quantile – bootstrap average).
UCB <- c()
for (i in 1:90) {
UCB[i] <- combined_diversity[i] + (CI_data[103,i] - CI_data[101,i])
}
confidence_intervals <- data.frame(cbind(LCB,UCB))
With this, we can plot 95% confidence intervals about the species accumulation
curve using the LCB and UCB values calculated above. The block of code below is
mostly identical to the plotting section above. What did we change?
sampling_sites = 1:90 #18 sites + 72 additional sites
diversity_est <-
data.frame(cbind(combined_diversity, sampling_sites))
sac_plot = ggplot(
data = subset(diversity_est, sampling_sites <= 18),
aes(x = sampling_sites, y = combined_diversity)
) +
geom_ribbon(
confidence_intervals,
mapping = aes(ymin = LCB, ymax = UCB),
fill = "skyblue",
col = "blue"
) + #Use geom_ribbon to plot our upper and lower confidence intervals.
geom_line(size = 0.75) +
geom_line(
data = subset(diversity_est, sampling_sites >= 18),
aes(x = sampling_sites, y = combined_diversity),
lty = 2,
size = 0.75
) +
geom_point(aes(x = 18, y = 12), size = 3, pch = 16) +
xlab("Number of Sampling Sites") +
ylab("Number of Species") +
ggtitle("Species Accumulation Curve") +
theme(plot.title = element_text(size = 8.5))
sac_plot
![plot of chunk plot SAC with bounds](data:image/png;base64,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)