Population genetic analysis with tidypopgen
In tidypopgen: Tidy Population Genetics

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
set.seed(123)

An example workflow with real data

We will explore the genetic structure of Anolis punctatus in South America, using data from Prates et al 2018. We downloaded the vcf file of the genotypes from "https://github.com/ivanprates/2018_Anolis_EcolEvol/blob/master/data/VCFtools_SNMF_punctatus_t70_s10_n46/punctatus_t70_s10_n46_filtered.recode.vcf?raw=true" and compressed it to a vcf.gz file.

We read in the data from the compressed vcf with:

library(tidypopgen)
vcf_path <-
  system.file("/extdata/anolis/punctatus_t70_s10_n46_filtered.recode.vcf.gz",
    package = "tidypopgen"
  )
anole_gt <-
  gen_tibble(vcf_path, quiet = TRUE, backingfile = tempfile("anolis_"))

Now let's inspect our gen_tibble:

anole_gt

We can see that we have 46 individuals, from 3249 loci. Note that we don't have any information on population from the vcf. That information can be found from another csv file. We will have add the population information manually. Let's start by reading the file:

pops_path <- system.file("/extdata/anolis/punctatus_n46_meta.csv",
  package = "tidypopgen"
)
pops <- read.csv(pops_path)
pops

We can now attempt to join the tables. We recommend using a left_join to do so, rather than cbind or bind_cols, as the latter functions assume that the two tables are in the same order. In this case, we do not want to bring over the wrong data due to mismatched ordering.

anole_gt <- anole_gt %>% left_join(pops, by = "id")

Let us check that we have been successful:

anole_gt %>% glimpse()

Map

Lets begin by visualising our samples geographically. We have latitudes and longitudes in our tibble; we can transform them into an sf geometry with the function gt_add_sf(). Once we have done that, our gen_tibble will act as an sf object, which can be plotted with ggplot2.

anole_gt <- gt_add_sf(anole_gt, c("longitude", "latitude"))
anole_gt

To visualise our samples, we can create a map of South America using the rnaturalearth package. We will use the ne_countries() function to get the countries in South America. We will then plot the map and add our samples using the geom_sf() function from ggplot2.

library(rnaturalearth)
library(ggplot2)

map <- ne_countries(
  continent = "South America",
  type = "map_units", scale = "medium"
)

ggplot() +
  geom_sf(data = map) +
  geom_sf(data = anole_gt$geometry) +
  coord_sf(
    xlim = c(-85, -30),
    ylim = c(-30, 15)
  ) +
  theme_minimal()

From our map we can see that we have samples from the coastal Atlantic Forest and the Amazonian Forest.

PCA

That was easy. The loci had already been filtered and cleaned, so we don't need to do any QC. Let us jump straight into analysis and run a PCA:

anole_pca <- anole_gt %>% gt_pca_partialSVD(k = 30)

OK, we jumped too quickly. There are missing data, and we need first to impute them:

anole_gt <- gt_impute_simple(anole_gt, method = "mode")

And now:

anole_pca <- anole_gt %>% gt_pca_partialSVD(k = 30)

Let us look at the object:

anole_pca

The print function (implicitly called when we type the name of the object) gives us information about the most important elements in the object (and the names of the elements in which they are stored).

We can extract those elements with the tidy function, which returns a tibble that can be easily used for further analysis, e.g.:

tidy(anole_pca, matrix = "eigenvalues")

We can return information on the eigenvalues, scores and loadings of the pca. There is also an autoplot method that allows to visualise those elements (type screeplot for eigenvalues, type scores for scores, and loadings for loadings:

autoplot(anole_pca, type = "screeplot")

To plot the sample in principal coordinates space, we can simply use:

autoplot(anole_pca, type = "scores")

autoplots are deliberately kept simple: they are just a way to quickly inspect the results. They generate ggplot2 objects, and so they can be further embellished with the usual ggplot2 grammar:

library(ggplot2)
autoplot(anole_pca, type = "scores") +
  aes(color = anole_gt$population) +
  labs(color = "population")

For more complex/publication ready plots, we will want to add the PC scores to the tibble, so that we can create a custom plot with ggplot2. We can easily add the data with the augment method:

anole_gt <- augment(anole_pca, data = anole_gt)

And now we can use ggplot2 directly to generate our plot:

anole_gt %>% ggplot(aes(.fittedPC1, .fittedPC2, color = population)) +
  geom_point() +
  labs(x = "PC1", y = "PC2", color = "Population")

We can see that the two population separate clearly in the PCA space, with individuals from the Atlantic Forest clustering closely together while Amazonian Forest individuals are spread across the first two principal components.

It is also possible to inspect which loci contribute the most to a given component:

autoplot(anole_pca, type = "loadings")

By using information from the loci table, we could easily embellish the plot, for example colouring by chromosome or maf.

For more complex plots, we can augment the loci table with the loadings using augment_loci():

anole_gt_load <- augment_loci(anole_pca, data = anole_gt)

Explore population structure with DAPC

DAPC is a powerful tool to investigate population structure. It has the advantage of scaling well to very large datasets. It does not have the assumptions of STRUCTURE or ADMIXTURE (which also limits its power).

The first step is to determine the number of genetic clusters in the dataset. DAPC can be either used to test a a-priori hypothesis, or we can use the data to suggest the number of clusters. In this case, we did not have any strong expectations of structure in our study system, so we will let the data inform the number of possible genetic clusters. We will use a k-clustering algorithm applied to the principal components (allowing us to reduce the dimensions from the thousands of loci to just a few tens of components). We need to decide how many components to use; this decision is often made based on a plot of the cumulative explained variance of the components. Using tidy on the gt_pca object allows us easily obtain those quantities, and it is then trivial to plot them:

library(ggplot2)
tidy(anole_pca, matrix = "eigenvalues") %>%
  ggplot(mapping = aes(x = PC, y = cumulative)) +
  geom_point()

Note that, as we were working with a truncated SVD algorithm for our PCA, we can not easily phrase the eigenvalues in terms of proportion of total variance, so the cumulative y axis simply shows the cumulative sum of the eigenvalues. Ideally, we are looking for the point where the curve starts flattening. In this case, we can not see a very clear flattening, but by PC 10 the increase in explained variance has markedly decelerated. We can now find clusters based on those 10 PCs:

anole_clusters <- gt_cluster_pca(anole_pca, n_pca = 10)

As we did not define the k values to explore, the default 1 to 5 was used (we can change that by setting the k parameter to change the range). To choose an appropriate k, we plot the number of clusters against a measure of fit. BIC has been shown to be a very good metric under many scenarios:

autoplot(anole_clusters)

We are looking for the minimum value of BIC. There is no clear elbow (a minimum after which BIC increases with increasing k). However, we notice that there is a quick levelling off in the decrease in BIC at 3 clusters. Arguably, these are sufficient to capture the main structure. We can also use a number of algorithmic approaches (based on the original find.clusters() function in adegenet) to choose the best k value from this plot through gt_cluster_pca_best_k(). We will use the defaults (BIC with "diffNgroup", see the help page for gt_cluster_pca_best_k() for a description of the various options):

anole_clusters <- gt_cluster_pca_best_k(anole_clusters)

The algorithm confirms our choice. Note that this function simply adds an element $best_k to the gt_cluster_pca object:

anole_clusters$best_k

If we decided that we wanted to explore a different value, we could simply overwrite that number with anole_clusters$best_k<-5

In this case, we are happy with the option of 3 clusters, and we can run a DAPC:

anole_dapc <- gt_dapc(anole_clusters)

Note that gt_dapc() takes automatically the number of clusters from the anole_clusters object, but can change that behaviour by setting some of its parameters (see the help page for gt_dapc()). When we print the object, we are given information about the most important elements of the object and where to find them (as we saw for gt_pca):

anole_dapc

Again, these elements can be obtained with tidiers (with matrix equal to eigenvalues, scores,ld_loadings and loci_loadings):

tidy(anole_dapc, matrix = "eigenvalues")

And they can be visualised with autoplot:

autoplot(anole_dapc, type = "screeplot")

As for pca, there is a tidy method that can be used to extract information from gt_dapc objects. For example, if we want to create a bar plot of the eigenvalues (since we only have two), we could simply use:

tidy(anole_dapc, matrix = "eigenvalues") %>%
  ggplot(aes(x = LD, y = eigenvalue)) +
  geom_col()

We can plot the scores with:

autoplot(anole_dapc, type = "scores")

The DAPC plot shows the separation of individuals into 3 clusters.

We can inspect this assignment by DAPC with autoplot using the type components, ordering the samples by their original population labels:

autoplot(anole_dapc, type = "components", group = anole_gt$population)

Here we can see that DAPC splits the Amazonian Forest individuals into two clusters. Because of the very clear separation we observed when plotting the LD scores, no individual is modelled as a mixture: all assignments are with 100% probability to a single cluster.

Finally, we can explore which loci have the biggest impact on separating the clusters (either because of drift or selection):

autoplot(anole_dapc, "loadings")

There is no strong outlier, suggesting drift across many loci has created the signal picked up by DAPC.

Note that anole_dapc is of class gt_dapc, which is a subclass of dapc from adegenet. This means that functions written to work on dapc objects should work out of the box (the only exception is adegenet::predict.dapc, which does not work because the underlying pca object is different). For example, we can obtain the standard dapc plot with:

library(adegenet)
scatter(anole_dapc, posi.da = "bottomright")

We can also plot these results onto the map we created earlier.

anole_gt <- anole_gt %>% mutate(dapc = anole_dapc$grp)

ggplot() +
  geom_sf(data = map) +
  geom_sf(data = anole_gt$geometry, aes(color = anole_gt$dapc)) +
  coord_sf(
    xlim = c(-85, -30),
    ylim = c(-30, 15)
  ) +
  labs(color = "DAPC cluster") +
  theme_minimal()

Atlantic forest lizards form distinct geographic cluster, separate from the Amazonian lizards.

Clustering with ADMIXTURE

ADMIXTURE is a fast clustering algorithm which provides results similar to STRUCTURE. We can run it directly from tidypopgen using the gt_admixture function.

The output of gt_admixture is a gt_admix object. gt_admix objects are designed to make visualising data from different clustering algorithms swift and easy.

Lets begin by running gt_admixture. We can run K clusters from k=2 to k=6. We will use just one repeat, but ideally we should run multiple repetitions for each K:

anole_gt <- anole_gt %>% group_by(population)

anole_adm_original <- gt_admixture(
  x = anole_gt,
  k = 2:6,
  n_runs = 1,
  crossval = TRUE,
  seed = 1
)

anole_gt <- anole_gt %>% group_by(population)

anole_adm <- readRDS("a03_anole_adm.rds")

Note that within this vignette we are not running the gt_admixture function, as it requires the ADMIXTURE software to be installed on your machine and available in your PATH. Instead, we load the results from a previous run of ADMIXTURE. If you would prefer a native clustering algorithm, we recommend using the gt_snmf function, which is a wrapper for the snmf function from the LEA package. sNMF is a fast clustering algorithm which provides results similar to STRUCTURE and ADMIXTURE, and is available directly using the tidypopgen package. We can examine the suitability of our K values by plotting the cross-entropy values for each K value, which is contained in the cv element of the gt_admix object:

autoplot(anole_adm, type = "cv")

Here we can see that K = 3 is a sensible choice, as K = 3 represents the 'elbow' in the plot, where cross-entropy is at it's lowest.

We can quickly plot this data with autoplot by using the type barplot and selecting our chosen value of k:

autoplot(anole_adm,
  k = 3, run = 1, data = anole_gt, annotate_group = FALSE,
  type = "barplot"
)

This plot is fine, but it is messy, and not a very helpful visualisation if we want to understand how our populations are structured.

To re-order this plot, grouping individuals by population, we can use the annotate_group and arrange_by_group arguments in autoplot:

autoplot(anole_adm,
  type = "barplot", k = 3, run = 1, data = anole_gt,
  annotate_group = TRUE, arrange_by_group = TRUE
)

This plot is much better. Now the plot is labelled by population we can see that the individuals from each population are grouped together, with a few individuals showing mixed ancestry between populations.

However, for a more visually appealing plot, we can re-order the individuals within each population as follows:

autoplot(anole_adm,
  type = "barplot", k = 3, run = 1,
  data = anole_gt, annotate_group = TRUE, arrange_by_group = TRUE,
  arrange_by_indiv = TRUE, reorder_within_groups = TRUE
)

Now individuals are neatly ordered within each population.

For more complex/publication ready plots, we can extract the specific K value and run that we are interested in plotting, and add this .Q matrix to our gen_tibble object, so that we can create a custom plot with ggplot2.

First we extract the q_matrix of interest using the get_q_matrix function:

q_mat <- get_q_matrix(anole_adm, k = 3, run = 1)

Then we can easily add the data with the augment method:

anole_gt_adm <- augment(q_mat, data = anole_gt)
head(anole_gt_adm)

Alternatively, we can convert our q matrix into tidy format, which is more suitable for plotting:

tidy_q <- tidy(q_mat, anole_gt)
head(tidy_q)

And now we can use ggplot2 directly to generate our custom plot:

tidy_q <- tidy_q %>%
  dplyr::group_by(id) %>%
  dplyr::mutate(dominant_q = max(percentage)) %>%
  dplyr::ungroup() %>%
  dplyr::arrange(group, dplyr::desc(dominant_q)) %>%
  dplyr::mutate(
    plot_order = dplyr::row_number(),
    id = factor(id, levels = unique(id))
  )

plt <- ggplot2::ggplot(tidy_q, ggplot2::aes(x = id, y = percentage, fill = q)) +
  ggplot2::geom_col(
    width = 1,
    position = ggplot2::position_stack(reverse = TRUE)
  ) +
  ggplot2::labs(
    y = "Population Structure for K = 3",
    title = "ADMIXTURE algorithm on A. punctatus"
  ) +
  theme_distruct() +
  scale_fill_distruct()

plt

In the Prates et al 2018 data, anolis lizards were assigned to three regions, described as Af, Eam, and Wam, acronyms which correspond to the Atlantic Forest, Eastern Amazonia, and Western Amazonia of Brazil. Our metadata also contains this assignment, in the column pop.

Lets say we wanted to change the grouping variable of our plot to match these regions. We can use the gt_admix_reorder_q function to reorder the Q matrix by a different grouping variable:

anole_adm <- gt_admix_reorder_q(anole_adm, group = anole_gt$pop)

And replot the data:

autoplot(anole_adm,
  type = "barplot", k = 3, run = 1,
  annotate_group = TRUE, arrange_by_group = TRUE,
  arrange_by_indiv = TRUE, reorder_within_groups = TRUE
)

And here we can see the clear distinction between the three regions, with a few individuals that have admixed ancestry.

Handling Q matrices

For clustering algorithms that operate outside the R environment, the function q_matrix() can take a path to a directory containing results from multiple runs of a clustering algorithm for multiple values of K, read the .Q files, and summarise them in a single q_matrix_list object.

In the analysis above, through gt_admxiture(), we ran 1 repetition for K values 2 to 6. Let us now collate the results from a standard run of ADMIXTURE for which we stored the files in a directory:

# reload the admxiture results (they were reordered above)
anole_adm <- readRDS("a03_anole_adm.rds")
runs <- c(1)
k_values <- c(2:6)
q_matrices <- list()
adm_dir <- file.path(tempdir(), "anolis_adm")
if (!dir.exists(adm_dir)) {
  dir.create(adm_dir)
}

for (x in k_values) {
  q_matrices[[x]] <- list()

  for (i in runs) {
    q_matrices[[x]][[i]] <- get_q_matrix(anole_adm, k = x, run = i)

    write.table(q_matrices[[x]][[i]],
      file = paste0(adm_dir, "/K", x, "run", i, ".Q"),
      col.names = FALSE, row.names = FALSE, quote = FALSE
    )
  }
}

adm_dir <- file.path(tempdir(), "anolis_adm")
list.files(adm_dir)

And read them back into our R environment using q_matrix_list:

q_list <- read_q_files(adm_dir)
summary(q_list)

q_matrix_list has read and summarised the .Q files from our analysis, and we can access a single matrix from the list by selecting the run number and K value of interest using get_q_matrix as before.

For example, if we would like to view the second run of K = 3:

head(get_q_matrix(q_list, k = 3, run = 1))

And, again, we can then autoplot any matrix by selecting from the q_matrix_list object:

autoplot(get_q_matrix(q_list, k = 3, run = 1),
  data = anole_gt,
  annotate_group = TRUE, arrange_by_group = TRUE,
  arrange_by_indiv = TRUE, reorder_within_groups = TRUE
)