README.Rmd

---
output: github_document
---

<!-- README.md is generated from README.Rmd. Please edit that file -->

[![Travis build status](https://travis-ci.org/kylebittinger/abdiv.svg?branch=master)](https://travis-ci.org/kylebittinger/abdiv)

```{r, echo = FALSE, message=FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  fig.path = "tools/readme/",
  dpi=300
)
devtools::load_all()
```

# abdiv

This package re-implements measures of ecological diversity from several other
software packages, including `vegan`, `scikit-bio`, `Mothur`, and `GUniFrac`.

## Installation

You can install `abdiv` from github with:

```{r gh-installation, eval = FALSE}
# install.packages("devtools")
devtools::install_github("kylebittinger/abdiv")
```

## Alpha diversity

Let's say we've surveyed a field and counted the number of plants in each of
two sites.  We've found five species in total, and we'd like to summarize
the diversity of the two sampling sites.  The diversity within each site is
called α-diversity.

Here are the number of plants for each species at site 1 and site 2,
represented as vectors.

```{r}
site1 <- c(2, 5, 16, 0, 1)
site2 <- c(0, 0, 8, 8, 8)
```

The two sites have about the same number of total plants, but the distribution
of species is much different.  More than half the plants in site 1 belong to a
single species, whereas the plants in site 2 are almost evenly distributed
across three different species.  To get started, let's look at a few ways to
quantify the α-diversity for each sample.

Richness measures the total number of species in each sample.

```{r}
richness(site1)
richness(site2)
```

The Shannon index measures both the number of species and the evenness of the
relative abundance values. Site 2 has fewer species, but each species has the
same relative abundance, so the Shannon index is higher.

```{r}
shannon(site1)
shannon(site2)
```

Let's summarize the diversity of site 1 and site 2 using all the functions
available in this library.  The full set of within-sample diversity functions
is available as a character vector in `alpha_diversities`. The term
"α-diversity" means the diversity within a single sample.

```{r alpha-diversity, message=FALSE}
library(tidyverse)
tibble(Site = rep(c("Site 1", "Site 2"), each=5), Counts = c(site1, site2)) |>
  group_by(Site) |>
  summarize_at(vars(Counts), alpha_diversities) |>
  pivot_longer(-Site, names_to = "Measure") |>
  ggplot(aes(x=Measure, y=value, color=Site)) +
  geom_point() +
  scale_color_manual(values=c("#E64B35", "#4DBBD5")) +
  coord_flip() +
  theme_bw()
```

We can see that site 1 is regarded as more diverse by some measures; it has the
most species. For other measures, site 2 is regarded as more diverse; it has
the most even distribution of species.

In our documentation, you can find more info on each α-diversity
function.

## Beta diversity

Having assessed the diversity within each sample, we can next ask about the
number of shared species between sites.  If species are shared, how similar is
the distribution across species? There are many ways to quantify the
between-sample diversity or β-diversity.

You can think about β-diversity as either the similarity or dissimilarity
between sites.  The functions in `abdiv` are written in terms of
dissimilarity: similar sites will have values close to zero, and highly
dissimilar sites will have values close to the maximum.  This way of thinking
goes along with our intuition about diversity: sites with greater
dissimilarity will exhibit increased diversity if we consider both sites
together.

Let's look at some examples. The Jaccard distance counts the fraction of
species present in only one site. The answer is 3 out of 5, or 0.6.

```{r}
jaccard(site1, site2)
```

The Bray-Curtis dissimilarity adds up the absolute differences between species
counts, then divides by the total counts. For our two sites, that's
(2 + 5 + 8 + 8 + 7) / 48, or 0.625.

```{r}
bray_curtis(site1, site2)
```

Again, we'll use a vector called `beta_diversities` to compute every dissimilarity
measure in the library.

```{r beta-diversity, warning=FALSE}
tibble(Measure = beta_diversities) |>
  group_by(Measure) |>
  mutate(value = get(Measure)(site1, site2)) |>
  ggplot(aes(x=Measure, y=value)) +
  geom_point(color="#4DBBD5") +
  scale_y_log10() +
  coord_flip() +
  theme_bw()
```

The dissimilarities are generally positive, and they have a range of scales.
Some dissimilarity measures range from 0 to 1, while others can go up
indefinitely.

As before, you can find more info on each β-diversity function in our
documentation.

## Phylogenetic diversity and UniFrac

A phylogenetic tree can be incorporated into diversity measures to add
information about the evolutionary history of species. One of the first
measures in this area was Faith's phylogenetic diversity. Here, we take an
example from Figure 1 in Faith and Richards (PMID 24832524) to show how
phylogenetic diversity works. The tree is included as `faith_tree`:

```{r message=FALSE, fig.width=3, fig.height=2, dpi=100, fig.align="center"}
library(ggtree)
ggtree(faith_tree, ladderize = F) +
  geom_tiplab()
```

If all the species are present, the value of Faith's phylogenetic diversity
(PD) is the sum of the branch lengths. Here, we expect the total branch length
to be 5 + 4 + 2 + 4 + 1 + 20 + 5 + 1 + 3 = 45, adding from top to bottom.^[The
answer here is slightly different than that in the paper. See `faith_tree`
documentation for further explanation.]

Here is how you would calculate Faith's PD:

```{r}
faith_pd(c(1, 1, 1, 1, 1), faith_tree)
```

If species "a" is missing, we expect Faith's PD to be reduced by 5, the length
of the branch leading to species "a".

```{r}
faith_pd(c(0, 1, 1, 1, 1), faith_tree)
```

The practice of using phylogenetic information in diversity has been especially
popular in microbial ecology, where bacteria are surveyed using the 16S rRNA
marker gene. In addition to serving as a fingerprint for bacteria, the gene
sequence can be used to build a phylogenetic tree.

In this area, the UniFrac distance is widely used to measure β-diversity
between bacterial communities. We'll reproduce an example from the UniFrac
paper by Lozupone and Knight (PMID 16332807), which describes the unweighted
UniFrac distance. The tree from Figure 1 is available as `lozupone_tree`.

In the example from Figure 1A, we've measured two bacterial communities, where
the species detected in each are labeled with circles and squares. The
communities have no species in common.

```{r, fig.width=3.5, fig.height=2.5, dpi=100, fig.align="center"}
ggtree(lozupone_tree, ladderize = F) %<+%
  lozupone_panel_a +
  geom_tippoint(aes(shape=SampleID), x=2.6, size=3) +
  scale_shape_manual(values = c(1, 15)) +
  scale_x_continuous(limits=c(0, 2.8))
```

The circle and square communities are all mixed up on the phylogenetic tree. The
unweighted UniFrac distance is the fraction of the total branch length where the
branch leads to a circle or square, but not both. Here, we would only count the
branches leading to the tips of the tree. The length of these branches, added
together, is about half the total length for all branches in the tree.

```{r}
a_circle <- c(1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1)
a_square <- c(0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0)
unweighted_unifrac(a_circle, a_square, lozupone_tree)
```

We can increase the UniFrac distance if we rearrange the communities so that
all the circles are in the upper part of the tree and all the squares are in
the lower part. In the paper, this is shown in Figure 1B.

```{r, fig.width=3.5, fig.height=2.5, dpi=100, fig.align="center"}
ggtree(lozupone_tree, ladderize = F) %<+%
  lozupone_panel_b +
  geom_tippoint(aes(shape=SampleID), x=2.6, size=3) +
  scale_shape_manual(values = c(1, 15)) +
  scale_x_continuous(limits=c(0, 2.8))
```

With this arrangement, the species in each community are phylogenetically
very different.  Except for the root, each branch of the tree leads uniquely
to a species present in square or circle, and never to a species present in
both. Therefore, the UniFrac distance is close to 1.

```{r}
b_circle <- c(1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0)
b_square <- c(0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1)
unweighted_unifrac(b_circle, b_square, lozupone_tree)
```

## Practical use

Now that we've introduced you to the functions in this package, we should
probably tell you how to use them in your work.  Your data are likely to be
in one of two formats: a long-format data frame, or a matrix of counts. We'll
tackle the long format first.

First, we'll arrange the data from the plant survey example in long format.
We'll also add a third site to help with the demonstration.

```{r}
site3 <- c(15, 1, 4, 2, 2)
plants <- tibble(
  Site = rep(c("Site 1", "Site 2", "Site 3"), each = 5),
  Species = rep(letters[1:5], times = 3),
  Counts = c(site1, site2, site3)
)
plants
```

If we want to compute α-diversity, we can group by `Site` and create a new
column with the answer.  The α-diversity functions take the number of
counts for each species as an argument.

```{r}
plants |>
  group_by(Site) |>
  summarize(Richness = richness(Counts))
```

If you want to cover more than one α-diversity measure, you can use
`across()`.

```{r}
plants |>
  group_by(Site) |>
  summarise(across(Counts, list(shannon = shannon, invsimpson = invsimpson)))
```

The old school way to compute α-diversity is to arrange your data in a
matrix format, with rows representing different sites or "observations", and
columns representing species.  This is how you would do it with the `vegan`
package, for example. Here is our data in matrix format:

```{r}
plants_matrix <- matrix(
  c(site1, site2, site3), nrow=3, byrow=TRUE,
  dimnames = list(c("Site 1", "Site 2", "Site 3"), letters[1:5]))
plants_matrix
```

In matrix format, we can use the `apply()` function from base R to get the
diversity for each site.

```{r}
apply(plants_matrix, 1, shannon)
```

Here is the same example using `vegan`.

```{r}
vegan::diversity(plants_matrix)
```

The long format is friendlier to workflows using functions in the `tidyverse`,
but the matrix format has some advantages.  The matrix format ensures that every
sample has a valid count value for every species considered; the matrix
contains values of zeros for species not observed.  This quality is not
critically important for alpha-diversity measures, but it is important for
computing β-diversity.

For β-diversity, we recommend proceeding via the matrix format. If your data
is in long format, the `usedist` package has a function to convert to a
numeric matrix.^[Full disclosure: `usedist` and `abdiv` are authored by
the same person.]

```{r}
usedist::pivot_to_matrix(plants, Site, Species, Counts)
```

To create a distance matrix between samples, we can employ the `dist_make()`
function from `usedist`.

```{r}
usedist::dist_make(plants_matrix, bray_curtis)
```

## Practical use - phylogenetic diversity

One practical issue with phylogenetic diversity is to make sure that
the order of the species in your vectors matches the order of the tree. If
your vector is not named, and you're sure that the order matches, you can use
the phylogenetic diversity functions as above. To take the example from Faith's
phylogenetic diversity, let's say we had a vector representing 10 counts of
species "d" and 12 of species "e".

```{r}
faith_pd(c(0, 0, 0, 10, 12), faith_tree)
```

If your vector is named, the names will be automatically used to match the
vector with the tree. Missing names are filled in with zero counts.

```{r}
faith_pd(c(d=10, e=12), faith_tree)
```

If your vector is not named, or if you're not totally sure that the order of
species in your vector matches the order of species in the tree, you can pass
in the species labels for your vector as an additional argument.

```{r}
faith_pd(c(10, 12), faith_tree, c("d", "e"))
```

This last approach is useful for a `tidyverse` workflow, where the vectors are
not named and the species labels are found in a separate column.  Here is an
example for data in long format, where the species labels are in the column, 
"Species":

```{r}
plants |>
  group_by(Site) |>
  summarize(FaithPD = faith_pd(Counts, faith_tree, Species))
```

The rules are the same for phylogenetic β-diversity functions. The `dist_make()`
function from `usedist` will pass along additional keyword arguments to the
distance function, so you can give the tree and species labels to `dist_make()`.
Here's an example from the plants matrix.

```{r}
usedist::dist_make(plants_matrix, unweighted_unifrac, faith_tree)
```

Now, we'll re-order the species in the data matrix to see how things work.

```{r}
species_reorder <- c("d", "e", "a", "b", "c")
plants_matrix_reorder <- plants_matrix[,species_reorder]
plants_matrix_reorder
```

The column names of the matrix are automatically added to vectors extracted
from the matrix, so we get the same result as before.

```{r}
usedist::dist_make(plants_matrix_reorder, unweighted_unifrac, faith_tree)
```

If the column names are missing, first of all, you're probably in trouble. But
if you do have the species labels stored in a separate vector, you can pass
them along to the distance function. Let's remove the column names from our
matrix to check this out.

```{r}
plants_matrix_reorder_nonames <- plants_matrix_reorder
colnames(plants_matrix_reorder_nonames) <- NULL
plants_matrix_reorder_nonames
```

Now, we can pass the species labels to `dist_make()` and verify that we get
the correct answer.

```{r}
usedist::dist_make(
  plants_matrix_reorder_nonames, unweighted_unifrac, faith_tree,
  species_reorder)
```

## Support

Please don't hesitate to reach out via email or file an issue
if you need support when using this library.

## Footnotes