diversity.rmd

---
title: Diversity calculation
author: Masatoshi Katabuchi
date: "2020/11/2 (updated: `r Sys.Date()`)"
output:
#rmdformats::material
  html_document:
    fig_caption: yes
    theme: spacelab #readable #sandstone #spacelab #flatly
    highlight: pygments #tango #kate
    toc: TRUE
    toc_depth: 2
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---

```{r global_options, include=FALSE}
knitr::opts_chunk$set(echo=TRUE,
                      warning=FALSE,
                      cache=FALSE,
                      message=FALSE)

htmltools::tagList(rmarkdown::html_dependency_font_awesome())
```

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Course materials for 2020-11-2 AFEC at XTBG.

# Prerequisites

Did you install `picante` and `FD`?

```{r, eval = F}
install.packages("picante")
install.packages("FD")
```

It's better if you have those packages too.

```{r, eval = F}
install.packages("tidyverse")
install.packages("rmarkdown")
install.packages("DT")
```

Load pacakges.
```{r}
library(picante)
library(FD)
library(tidyverse)
library(rmarkdown)
```


# Data

## Community

```{r}

samp <- read_csv("./gr3/group_3.csv")

DT::datatable(samp)

samp_mat <- as.matrix(samp[, -1])
rownames(samp_mat) <- samp$Sample_code

samp_mat

```


## Phylogeny


```{r, fig.height = 20}
phylo <- read.tree("/dummy_tree.newick")
plot(phylo)
```



## Traits

| Abbreviation | Trait                                      | Unit              |
| ------------ | ------------------------------------------ | ----------------- |
| LMA          | Leaf mass per area                         | g m^-2^           |
| LL           | Leaf lifespans (longevity)                 | months            |
| Amass        | Maximum photosynthetic rates per unit mass | nnoml g^-1^ s^-^1 |
| Rmass        | Dark resperation rates per unit mass       | nnoml g^-1^ s^-^1 |
| Nmass        | Leaf nitrogen per unit mass                | %                 |
| Pmass        | Leaf phosphorus per unit mass              | %                 |
| WD           | Wood density                               | g cm^-3^          |
| SM           | Seed dry mass                              | mg                |

```{r}

trait <- read_csv("./data/dummy_trait.csv") 

# trait <- read.csv("./data/dummy_trait.csv") is fine too.

DT::datatable(trait)
```

## Check the histograms of trait values first

```{r}

trait_long <- trait %>%
  gather(trait, val, 2:9)

ggplot(trait_long, aes(x = val)) +
  geom_histogram(position = "identity") +
  facet_wrap(~ trait, scale = "free")

```


Probably we can do log-transformation for all the traits except for WD.

```{r}

trait2 <- trait %>%
  mutate(logLMA = log(LMA),
         logLL = log(LL),
         logAmass = log(Amass),
         logRmass = log(Rmass),
         logNmass = log(Nmass),
         logPmass = log(Pmass),
         logSM = log(SM)) %>%
  dplyr::select(sp, logLMA, logLL, logAmass, logRmass, logNmass, logPmass, WD, logSM)

DT::datatable(trait2)

```

```{r}

trait2 %>%
  gather(trait, val, 2:9) %>%
  ggplot(., aes(x = val)) +
  geom_histogram(position = "identity") +
  facet_wrap(~ trait, scale = "free")

```

# Fisrt-order metrics (without phylogeny or traits)

## Species richness, Beta diversity metrics

Skip

## Nonmetric Multidimensional Scaling (NMDS)

```{r}

res_mds <- metaMDS(samp_mat)

plot(res_mds)

```

We can use the function ordiplot and orditorp to add text to the plot in place of points to make some more sence.

```{r}

ordiplot(res_mds, type = "n")
orditorp(res_mds,display="species",col="red",air=0.01)
orditorp(res_mds,display="sites",cex=1.25,air=0.01)

```

# Phylogenetic metrics

## Branch length based metric

### PD 

```{r}

res_pd <- pd(samp_mat, phylo)

res_pd

rownames(res_pd) %>% 
  str_split("_") 

rownames(res_pd) %>% 
  str_split("_") %>%
  sapply(., "[[", 1)


rownames(res_pd) %>% 
  str_split("_") %>%
  sapply(., "[[", 1) %>%
  tibble(forest = .) %>%
  mutate(pd = res_pd$PD)


rownames(res_pd) %>% 
  str_split("_") %>%
  sapply(., "[[", 1) %>%
  tibble(forest = .) %>%
  mutate(pd = res_pd$PD) %>%
  ggplot(., aes(x = forest, y = pd)) +
    geom_boxplot()



```


You can always see the help.

```{r, eval = F}
?pd
```


## Distance based metric 

`cophenetic()` creates distance matrices based on phylogenetic trees. Let's see the first 5 species.

```{r}
cophenetic(phylo)[1:5, 1:5]
```


### MPD

$MPD = \frac{1}{n} \Sigma^n_i \Sigma^n_j \delta_{i,j} \; i \neq j$, where
$\delta_{i, j}$ is the pairwised distance between species *i* and *j*

```{r}

res_mpd <- mpd(samp_mat, cophenetic(phylo))

res_mpd

```

The above vector shows MPD for each site.

### MNTD

$MNTD = \frac{1}{n} \Sigma^n_i min \delta_{i,j} \; i \neq j$, where $min \delta_{i, j}$ is the minimum distance between species *i* and all other species in the community.

```{r}

res_mntd <- mntd(samp_mat, cophenetic(phylo))

res_mntd

```



# Functional metrics

## Community weighted means (CWM)

$$
CWM_i = \frac{\sum_{j=1}^n a_{ij} \times t_{j}}{\sum_{j=1}^n a_{ij}}
$$

```{r}
tmp <- trait2 %>%
  filter(sp %in% colnames(samp_mat)) 

tmp

(ab <- apply(samp_mat, 1, sum))
# inner product
(CWS <- samp_mat %*% as.matrix(tmp[,-1]))
```
```{r}
(CWM <- CWS / ab)
```

## Distance based metrics

### Prepare a trait distance matrix

We have a `data.fame` of traits. First we need to prepare a trait matrix, then a distance matrix based on trait values.

```{r}

trait_mat0 <- as.matrix(trait2[, -1])
rownames(trait_mat0) <- trait2$sp

```

Let's see a subset of the trait matrix

```{r}
trait_mat0[1:5, 1:5]
```

Then, we will make trait distance matrix based on the Euclidean distance. There are
other distance measures, for example [Gower's Distance](https://www.rdocumentation.org/packages/gower/versions/0.2.1/topics/gower_dist), but we focus on the Euclidean distance today.

Before calulating distance, we need to make sure unit change in ditances have
same for different traits. We will scale trait values so that then have mean = 0
and SD = 1. (e.g., $(X_i - \mu) / \sigma$)

```{r}
trait_mat <- scale(trait_mat0)

par(mfrow = c(2, 2))
hist(trait_mat0[, "logLMA"])
hist(trait_mat[, "logLMA"])
hist(trait_mat0[, "WD"])
hist(trait_mat[, "WD"])
par(mfrow = c(1, 1))

```

Now we can make a trait distance matirx. 

```{r}
trait_dm <- as.matrix(dist(trait_mat))

```

Let's see the first 5 species.


```{r}
trait_dm[1:5, 1:5]
```

### MPD

```{r}
mpd(samp_mat, trait_dm)

ses.mpd(samp_mat, trait_dm)

```



### MNTD

```{r}
mntd(samp_mat, trait_dm)
```

## Branch length based metric

### FD

We will make a functional dendrogram using clustring methods. We use [UPGMA](https://en.wikipedia.org/wiki/UPGMA) in
this example.

```{r, fig.width = 15, fig.height = 15}

t_clust <- hclust(dist(trait_mat), method = "average")

plot(t_clust)

```


### More functional diversity metrics

```{r, eval = TRUE}

res_fd <- dbFD(trait_mat[colnames(samp_mat), ], samp_mat)

res_fd

```


# Computing Environment

```{r}
devtools::session_info()
```