---
title: "Analysis of biodiversity patterns"
author: "Felix May"
date: "`r Sys.Date()`"
output: 
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    number_sections: yes
    toc: yes
vignette: >
  %\VignetteIndexEntry{Analysis of biodiversity patterns}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

This introduction shows the list of biodiversity patterns that can be derived
using `mobsim`. In this vignette the patterns are evaluated on a simulated
data set, but of course the same patterns can be also derived from real data.

# Simulate and explore data

First, we generate community data by simulating 1,000 individuals from 30 species
with a cluster size of `sigma = 0.01` and one cluster per species (`mother_points = 1`).
For more information on the simulation of communities see the vignette **Simulating
communities with `mobsim`**.

```{r}
library(mobsim)
sim_dat1 <- sim_thomas_community(s_pool = 30,  n_sim = 1000, sad_type = "lnorm",
                                 sad_coef = list("meanlog" = 2, "sdlog" = 1),
                                 sigma = 0.1, mother_points = 1)
```

Then we explore the generated community object. In the plot each dot represents one individual and the colour indicates the species
identity.

```{r, fig.width = 5, fig.height = 5}
plot(sim_dat1)
summary(sim_dat1)
str(sim_dat1)
```

# Non-spatial patterns

## Species abundance distribution (SAD)

A fundamental non-spatial pattern of a community is the abundance distribution,
i.e. the distribution of commonness and rarity in a community. The abundance
distribution can be extracted from a community object using the function 
`communtiy_to_sad()`

```{r}
abund1 <- community_to_sad(sim_dat1)
```

A standard plot in community ecology is the *rank-abundance plot*, where the 
abundance of each species is plotted vs. its rank from highest to lowest abundance.
As a standard log-scaling is used for the abundance axis in this plot.

```{r, fig.width = 5, fig.height = 5}
plot(abund1, method = "rank")
```

Of course the abundance distribution can be also visualized as a histogram. 
By tradition for the binning of species abundances logarithms with base 2 are used,
following the suggestion of Preston (1948).
This means the first abundance class includes species with just one individual,
the second class with two individuals, the third class with 3-4, the fourth with
5-8 etc. These abundance classes are called "octaves".


```{r, fig.width = 5, fig.height = 5}
plot(abund1, method = "octave")
```

## Rarefaction curve

Another important biodiversity pattern is the *rarefaction curve*, which estimates
how the number of observed species increases with sample size of individuals.
The rarefaction curve assumes that individuals are sampled randomly and
independently (Gotelli & Colwell 2001). The rarefaction curve only depends on 
the abundance distribution of species.

```{r, fig.width = 5, fig.height = 5}
rare1 <- spec_sample_curve(sim_dat1, method = "rarefaction")
str(rare1)
plot(rare1)
```

# Spatial patterns

The main strengths of `mobsim` are the simulation and analysis of *spatial* 
biodiversity patterns. In the following all functions for spatial pattern
evaluation included in `mobsim` are introduced.

## Species-accumulation curve

Closely related to the *rarefaction curve* is the *spatial species accumulation curve*.
In contrast to the rarefaction curve for the derivation of the species accumulation
curve individuals are not sampled randomly, but starting from a focal individual
always the closest neighbour individual is sampled and the
number of encountered species is counted. The resulting curve is derived as the 
average of the curves for each focal individual. The species accumulation curve
is influenced by the abundance distribution, but also by the spatial distribution of 
individuals and species. Therefore the species accumulation curves requires 
individual's positions in addition to species abundances.

Due to the close relationship of the accumulation and rarefaction curves they are
calculated and plotted with the same function.

It is comprehensive to plot the rarefaction and the species accumulation curve
together. The difference between the two curves indicates aggregation or 
overdispersion of conspecific individuals.

```{r, fig.width = 5, fig.height = 5}
spec_curves1 <- spec_sample_curve(sim_dat1, method = c("accumulation", "rarefaction"))
plot(spec_curves1)
```

## Diversity-area relationships

The most well-known spatial biodiversity pattern is the *species-area relationship* 
(SAR). In `mobsim` the function `divar` (diversity-area relationships) calculates
the species richness in randomly located subplots (quadrats or rectangles) of 
different sizes. However, the function `divar` calculates additional indices,
including the Shannon and Simpson diversity indices for each subplot, as well
as the number of endemic species, which are the species that *only* occur within, 
but not outside the subplot. See `?div_rect` for detailed information on 
the diversity indices.

For the Shannon and Simpson diversity indices also the corresponding *Effective
Number of Species (ENS)* is calculated (Jost 2006). This measure corresponds
to the species number in a community of *equally abundant species*, which results
in the same Shannon and Simpson indices as the observed community (with unequal
abundances).

The endemics-area relationship (EAR) has been suggested as important tool to
investigate the consequences of habitat loss for biodiversity (He & Hubbell 2011,
Keil et al. 2015). For the evaluation of the diversity-area relationships a vector
with subplot sizes measured as proportion of the total community size has to be defined.

```{r}
subplot_size <- c(0.01, 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 
                   0.6, 0.7, 0.8, 0.9, 0.95, 0.99, 1)
divar1 <- divar(sim_dat1, prop_area = subplot_size)
head(divar1)
```


```{r, fig.width = 5, fig.height = 5}
plot(divar1)
```

## Distance decay of community similarity

The last spatial pattern provided by `mobsim` is the *distance decay of
community similarity*, which quantifies how quickly the similarity in species
composition between two subplots decreases with the distance between two subplots.
The function `dist_decay` distributes non-overlapping subplots with user-defined size
and number in the community and calculates all pairwise similarities. 

The function `dist_decay` makes use of the function `vegdist` from the package
[vegan](https://cran.r-project.org/package=vegan). Therefore you can consult 
`?vegdist` for a list of available similarity indices.

Here is a demonstration how the distance decay can be estimated and visualized

```{r,fig.width=5, fig.height=5}
dd1 <- dist_decay(sim_dat1, prop_area = 0.01, n_samples = 20, method = "bray")
head(dd1)

plot(dd1)
```


# References

1. F. W. Preston 1948. The Commonness, and Rarity, of Species. Ecology 29:254-283.

2. Gotelli & Colwell 2001. Quantifying biodiversity: procedures and pitfalls in 
the measurement and comparison of species richness. Ecology Letters 4: 379–391.

3. He & Hubbell 2001. Species-area relationships always overestimate extinction
rates from habitat loss. Nature 473:368–371

4. Jost 2006. Entropy and diversity. Oikos, 113:363–375.

5. Keil et al. 2015. On the decline of biodiversity due to area loss. 
Nature communications 6.

6. Morlon et al. 2008. A general framework for the distance–decay of similarity in ecological communities.
Ecology Letters 9:904–917.
