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

# Introduction

Biodiversity in any sampled area depends on three components

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

Changes of each component result in specific signatures with respect to the change
of non-spatial and spatial biodiversity patterns (see vignette *Analysis of biodiversity patterns*).
Therefore, biodiversity patterns can be assessed to investigate the scale-dependent 
effects of biodiversity drivers, e.g. habitat loss, climate change etc. on the 
three biodiversity components.

In this vignette we simulate independent variations of each of the three components
and demonstrate how rarefaction and species-accumulation curves can be applied to 
diagnose changes in biodiversity components.

For this purpose we first simulate a reference community. We assume a random
distribution of species in sapce, so we can use the function `sim_poisson_community`:

```{r, fig.width = 5, fig.height = 5}
library(mobsim)

S0 <- 100
N0 <- 1000
cv0 <- 0.5

sim_ref <- sim_poisson_community(s_pool = S0, n_sim = N0, sad_type = "lnorm",
                                 sad_coef = list("cv_abund" = cv0), fix_s_sim = TRUE)
plot(sim_ref)
```

# Change in total number of individuals

First we vary the total number of individuals. For this purpose we simulate a second 
community with just half of the individuals.

```{r}
sim_lower_N <-  sim_poisson_community(s_pool = S0, n_sim = N0/2, sad_type = "lnorm",
                                      sad_coef = list("cv_abund" = cv0))
```

Then we evaluate the rarefaction and species-accumulation curve for both communities

```{r,  fig.width = 7, fig.height = 3.5}
curve_ref    <- spec_sample_curve(sim_ref)
curve_lower_N <- spec_sample_curve(sim_lower_N)

oldpar <- par(mfrow = c(1,2))
plot(spec_rarefied ~ n, data = curve_ref, type = "l", main = "Rarefaction curve",
     xlab = "No. of individuals", ylab = "No. of species" )
lines(spec_rarefied ~ n, data = curve_lower_N, col = "red")

plot(spec_accum ~ n, data = curve_ref, type = "l", main = "Species accumulation curve",
     xlab = "No. of individuals", ylab = "No. of species" )
lines(spec_accum ~ n, data = curve_lower_N, col = "red")
par(oldpar)
```

Due to the stochasticity of simulations the curves of the reference and the changed
community slightly differ, but on average random losses of individuals are indicated
by overlapping curves, which end at different numbers of individuals.

# Change in the abundance distribution 

The second simulated change represents a reduction of the evenness of the species
abundance distribution, i.e. there are more very rare and more very common
species than in the reference community. In `mobsim` there is the argument
`cv_abund` in the simulation functions, which is the coefficient of variation (cv)
of species abundances. The higher the cv the lower the evenness and vice versa.
We also use the argument `fix_s_local= TRUE` to simulate a community with exactly S0
species.

```{r, fig.width = 7, fig.height = 3.5}
sim_uneven <-  sim_poisson_community(s_pool = S0, n_sim = N0, sad_type = "lnorm",
                                     sad_coef = list("cv_abund" = cv0*4),
                                     fix_s_sim = TRUE)
curve_uneven <- spec_sample_curve(sim_uneven)

oldpar <- par(mfrow = c(1,2))
plot(spec_rarefied ~ n, data = curve_ref, type = "l", main = "Rarefaction curve",
     xlab = "No. of individuals", ylab = "No. of species" )
lines(spec_rarefied ~ n, data = curve_uneven, col = "red")

plot(spec_accum ~ n, data = curve_ref, type = "l", main = "Species accumulation curve",
     xlab = "No. of individuals", ylab = "No. of species" )
lines(spec_accum ~ n, data = curve_uneven, col = "red")
par(oldpar)
```

As we see changes in the abundance distributions without changes in total species
richness are indicated by changing slopes and shapes of the curves.


# Change in spatial distributions

Finally we change the spatial patterns of species, by simulating clumping of 
conspecific individuals using a Thomas process model instead of a Poisson

```{r, fig.width = 7, fig.height = 3.5}
sim_clumped <-  sim_thomas_community(s_pool = S0, n_sim = N0, sad_type = "lnorm",
                                     sad_coef = list("cv_abund" = cv0),
                                     fix_s_sim = TRUE,
                                     sigma = 0.05)

oldpar <- par(mfrow = c(1,2))
plot(sim_ref)
plot(sim_clumped)
par(oldpar)
```

As before we compare the rarefaction and accumulation curves:

```{r, fig.width = 7, fig.height = 3.5}
curve_clumped<- spec_sample_curve(sim_clumped)

oldpar <- par(mfrow = c(1,2))
plot(spec_rarefied ~ n, data = curve_ref, type = "l", main = "Rarefaction curve",
     xlab = "No. of individuals", ylab = "No. of species" )
lines(spec_rarefied ~ n, data = curve_clumped, col = "red")

plot(spec_accum ~ n, data = curve_ref, type = "l", main = "Species accumulation curve",
     xlab = "No. of individuals", ylab = "No. of species" )
lines(spec_accum ~ n, data = curve_clumped, col = "red")
par(oldpar)

```

When there is only a change in spatial distribution the rarefaction curve does not 
change, because it only depends on species abundances, but not on spatial distributions
(see vignette *Analysis of biodiversity patterns*). In contrast, the species-accumulation
curves indicates higher intraspecific clumping (also called aggregation) by a lower
slope and lower expected species richness for the same number of sampled individuals.


