---
title: "Simulating communities with mobsim"
author: "Felix May"
date: "`r Sys.Date()`"
output:
 rmarkdown::html_vignette:
    number_sections: yes
    toc: yes
vignette: >
  %\VignetteIndexEntry{Simulating communities}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

# Biodiversity components

Biodiversity in any sampling area depends on three components:

1. The total number of individuals (total abundance)
2. The relative abundances of species
3. The spatial distribution of species

`mobsim` provides functions to simulate communities and thereby control for all 
these components. This vignette first shows how to simulate non-spatial
species abundance distributions (SADs) and second, how to simulate spatially-
explicit community data with `mobsim`.

# Simulating species abundance distributions

For this purpose `mobsim` provides the function `sim_sad`, which is a wrapper
around the function `rsad` from the package [sads](https://CRAN.R-project.org/package=sads).
In contrast to `rsad`, `sim_sad` allows simulating communities with user-defined
number of species *and* user-defined total number of individuals.

Here is an example for the simulation of an SAD using a log-normal model.

```{r}
library(mobsim)

abund1 <- sim_sad(s_pool = 100, n_sim = 1000, sad_type = "lnorm",
                  sad_coef = list("meanlog" = 5, "sdlog" = 0.5))
head(abund1)
summary(abund1)
```

`sim_sad` first simulates a *relative* species abundance distribution according
to the chosen SAD model and then samples the requested number of individuals 
according to this relative abundance distribution. Because of the use of a relative abundance
distribution as intermediate step, in the log-normal model the mean abundance 
is defined by the simulated number of individuals (`n_sim`) divided by the number 
of species (`s_pool`). Therefore, for the log-normal model `sim_sad` offers 
also a simpler parameterization that just specifies the coefficient of 
variation (`cv_abund`) of the log-normal SAD.

```{r}
abund2 <- sim_sad(s_pool = 100, n_sim = 1000, sad_type = "lnorm",
                  sad_coef = list("cv_abund" = 2))
summary(abund2)
```

Obviously, the simulated community includes less species than the user-defined 
value of `s_pool = 100`. This is a consequence of the stochastic sampling from the
relative abundance distribution. When some species have very low relative abundances,
they might not be sampled into the simulated community. However, `sim_sad` offers 
the option `fix_s_sim = TRUE`, which results in the user-defined value of species 
in the simulation. This is implemented by adding very rare species to the community,
while removing individuals from the common species. Please note that the constraint
`fix_s_sim = TRUE` might result in deviations from the underlying theoretical
SAD model.


```{r}
abund2a <- sim_sad(s_pool = 100, n_sim = 1000, sad_type = "lnorm",
                  sad_coef = list("cv_abund" = 2), fix_s_sim = T)
summary(abund2a)
```

The function `sim_sad` inherits all SAD models provided by `sads::rsad`.
For a complete list see `?sim_sad`. Here, we show an example of how to simulate
a log-series SAD. It has to be noted that for some SAD models the species richness
is not a direct parameter, but emerges from the other parameters. This is also true
for the log-series model. Therefore, the parameter `s_pool` is set to `NULL`.

```{r}
abund3 <- sim_sad(s_pool = NULL, n_sim = 10000, sad_type = "ls",
                  sad_coef = list("N" = 1e5, "alpha" = 20))
head(abund3)
```

Of course the simulated number of species can be easily evaluated

```{r}
length(abund3)
summary(abund3)
```

# Simulate spatial distributions

With `mobsim` random and aggregated species distributions can be simulated.
This can be done in two ways. Either, simulated coordinates of individuals 
can be added to an observed or simulated species abundance distributions, or
species abundances and distributions can be simulated simultaneously with
just one function call.

## Random distributions

In spatial statistics for point patterns a random distribution of points in a
given area is called Poisson process. Accordingly, the function to add random 
coordinates to an existing species abundance distribution is called 
`sim_poisson_coords`. Here is an example of its application.


```{r}
abund1 <- c(20,10,10,5,5)
comm1 <- sim_poisson_coords(abund_vec = abund1, xrange = c(0,1), yrange = c(0,1))
```

The community object includes x and y coordinates, as well as the species
identity for every individual in the community. `mobsim` offers functions for
exploring and plotting the community objects.


```{r, fig.width = 3.5, fig.height = 4}
class(comm1)
summary(comm1)
plot(comm1)
```

As mentioned above, abundances and (random) spatial distributions can be also
simulated at the same time using `sim_poisson_community`, which essentially calls
`sim_sad` and `sim_poisson_coords` consecutively.

```{r, fig.width = 3.5, fig.height = 4}
comm2 <- sim_poisson_community(s_pool = 20, n_sim = 200,
                               sad_type = "lnorm",
                               sad_coef = list(cv_abund = 1))
plot(comm2)
```


## Aggregated positions

Aggregated, or clustered species distributions are simulated based on the
Thomas process, also known as Poisson cluster process, in `mobsim`
(Morlon et al. 2008, Wiegand & Moloney 2014). For each
species, the Thomas process first distributes a given number of mother points
in the landscape. Then, offspring points are distributed around the mother points
according to a bivariate Gaussian distance kernel, where the average displacement
between mother and offspring points is called `sigma`. The offspring points
constitute the final distribution of the species. 

By variations in the size of clusters (`sigma`), the number of 
clusters (`mother_points`), and the mean number of individuals per cluster 
(`cluster_points`) the Thomas process can generate a large range of different
species distributions with intraspecific aggregation.

It is important to note the each species distribution is simulated independently
from the other species. That means the Thomas process in `mobsim` cannot be
used to simulate spatial dependence between different species, i.e. interspecific
aggregation or segregation.


Here is one example for a community with intraspecific aggregation:

```{r, fig.width = 3.5, fig.height = 4}
comm3 <- sim_thomas_coords(abund_vec = abund1, sigma = 0.02)
plot(comm3)
```

First, we change the size of the clusters using the argument `sigma`.

```{r, fig.width = 7, fig.height = 4}
comm3a <- sim_thomas_coords(abund_vec = abund1, sigma = 0.05)
par(mfrow = c(1,2))
plot(comm3)
plot(comm3a)
```

Second, we change the number of clusters per species using the argument 
`mother_points`.

```{r, fig.width = 7, fig.height = 4}
comm3b <- sim_thomas_coords(abund_vec = abund1, sigma = 0.02, mother_points = 1)
par(mfrow = c(1,2))
plot(comm3)
plot(comm3b)
```
Third, we change the average number of points (i.e. individuals) per cluster using
the argument `cluster_points`.

```{r, fig.width = 7, fig.height = 4}
comm3c <- sim_thomas_coords(abund_vec = abund1, sigma = 0.02, cluster_points = 5)
par(mfrow = c(1,2))
plot(comm3)
plot(comm3c)
```

Each of these parameters can be either set to the same equal value for all species
as in the examples before, or individually for all species by providing a vector
with a length equal to the number of species. For example,
each species can has its specific number of clusters.

```{r, fig.width = 3.5, fig.height = 4}
comm4 <- sim_thomas_coords(abund_vec = abund1, sigma = 0.02,
                           mother_points = c(5,4,3,2,1))
plot(comm4)
```

Please note that there can be clusters with zero individuals, so the simulated
number of clusters does not necessarily match the parameter settings.

In analogy to random distributions, there is a function to simulate
abundances and aggregated distributions at the same time.

```{r, fig.width = 3.5, fig.height = 4}
comm5 <- sim_thomas_community(s_pool = 100, n_sim = 500, sad_type = "lnorm",
                              sad_coef = list(cv_abund = 1),sigma = 0.05)
plot(comm5)
```

# References

Morlon et al. 2008. A general framework for the distance-decay of similarity in ecological communities. Ecology Letters 11, 904-917.

Wiegand and Moloney 2014. Handbook of Spatial Point-Pattern Analysis in Ecology. CRC Press


<!-- ```{r} -->
<!-- abund1 <-  -->
<!-- abund2 <- sim_sad(s_pool = 100, n_sim = 1000, sad_type = "lnorm", -->
<!--                 sad_coef = list("cv_abund" = 1.0)) -->
<!-- abund3 <- sim_sad(s_pool = 100, n_sim = 1000, sad_type = "lnorm", -->
<!--                 sad_coef = list("cv_abund" = 2.0)) -->
<!-- ``` -->

<!-- ```{r} -->
<!-- str(abund1) -->
<!-- ``` -->

<!-- With fixed local species richness -->

<!-- ```{r} -->
<!-- abund1a <- sim_sad(s_pool = 100, n_sim = 1000, sad_type = "lnorm", -->
<!--                 sad_coef = list("meanlog" = 2, "sdlog" = 0.5), fix_s_sim = T) -->
<!-- abund2a <- sim_sad(s_pool = 100, n_sim = 1000, sad_type = "lnorm", -->
<!--                 sad_coef = list("meanlog" = 2, "sdlog" = 1.0), fix_s_sim = T) -->
<!-- abund3a <- sim_sad(s_pool = 100, n_sim = 1000, sad_type = "lnorm", -->
<!--                 sad_coef = list("meanlog" = 2, "sdlog" = 2.0), fix_s_sim = T) -->
<!-- ``` -->

<!-- ```{r} -->
<!-- str(abund1a) -->
<!-- ``` -->

<!-- ### Plotting abundance distributions -->

<!-- #### Rank-abundance plots -->

<!-- ```{r, fig.width = 5, fig.height = 5} -->
<!-- plot(as.numeric(abund1), type="b", log="y", -->
<!--      xlab="Species rank", ylab="Species abundance", ylim = c(1, 200)) -->
<!-- lines(1:length(abund2), as.numeric(abund2), col = 2, type = "b") -->
<!-- lines(1:length(abund3), as.numeric(abund3), col = 3, type = "b") -->
<!-- ``` -->

<!-- **How would a perfectly even community look like?** -->

<!-- #### Species abundance distributions -->

<!-- **Normal histogram** -->

<!-- ```{r, fig.width = 8, fig.height = 8} -->
<!-- par(mfrow = c(2,2)) -->
<!-- hist(abund1, xlab = "Abundance", ylab = "No. of species") -->
<!-- hist(abund2, xlab = "Abundance", ylab = "No. of species") -->
<!-- hist(abund3, xlab = "Abundance", ylab = "No. of species") -->
<!-- ``` -->

<!-- **Preston binning method** -->

<!-- * First class: 1 individual -->
<!-- * Second class: 2 individuals -->
<!-- * Third class: 3-4 individuals -->
<!-- * Fourth class: 5-8 individuals -->

<!-- ```{r} -->
<!-- oct_max <- ceiling(log2(max(c(abund1, abund2, abund3)))) -->
<!-- sad1 <- sads::octav(as.numeric(abund1), oct = 0:oct_max) -->
<!-- sad2 <- sads::octav(as.numeric(abund2), oct = 0:oct_max) -->
<!-- sad3 <- sads::octav(as.numeric(abund3), oct = 0:oct_max) -->

<!-- sad1 -->
<!-- ``` -->

<!-- ```{r, fig.width = 5, fig.height = 5} -->
<!-- class_names <- c("1","2","3-4","5-8","9-16","17-32","33-64","64-128","128-256",">256") -->
<!-- class_names <- class_names[1:nrow(sad1)] -->
<!-- barplot(height = sad2$Freq, names.arg = class_names, -->
<!--         xlab = "Abundance class", ylab ="No. of species", col = 2) -->
<!-- ``` -->

<!-- ```{r, fig.width = 5, fig.height = 5} -->

<!-- abund_mat <- rbind(sad1$Freq, sad2$Freq, sad3$Freq) -->

<!-- barplot(height = abund_mat, names.arg = class_names, beside = T, -->
<!--         xlab = "Abundance class", ylab ="No. of species", col = 1:3) -->
<!-- ``` -->

