sim3 {DImodels} | R Documentation |

The `sim3`

dataset was simulated. There are two treatments and nine species that vary in proportions (`p1 - p9`

). It is assumed that species 1 to 5 come from functional group 1, species 6 and 7 from functional group 2 and species 8 and 9 from functional group 3. The response was simulated assuming that there were species identity effects and functional group specific interaction effects.

`data(sim3)`

A data frame with 412 observations on the following 13 variables:

`community`

A numeric vector identifying each unique community, i.e., two rows with the same community value also share the same set of p1 to p9 values.

`richness`

A numeric vector identifying the number of species in the initial composition.

`treatment`

A factor with levels

`A`

or`B`

.`p1`

A numeric vector indicating the initial proportion of species 1.

`p2`

A numeric vector indicating the initial proportion of species 2.

`p3`

A numeric vector indicating the initial proportion of species 3.

`p4`

A numeric vector indicating the initial proportion of species 4.

`p5`

A numeric vector indicating the initial proportion of species 5.

`p6`

A numeric vector indicating the initial proportion of species 6.

`p7`

A numeric vector indicating the initial proportion of species 7.

`p8`

A numeric vector indicating the initial proportion of species 8.

`p9`

A numeric vector indicating the initial proportion of species 9.

`response`

A numeric vector giving the simulated response variable.

**What are Diversity-Interactions (DI) models?**

Diversity-Interactions (DI) models (Kirwan et al 2009) are a set of tools for analysing and interpreting data from experiments that explore the effects of species diversity on community-level responses. We strongly recommend that users read the short introduction to Diversity-Interactions models (available at: `DImodels`

). Further information on Diversity-Interactions models is also available in Kirwan et al 2009 and Connolly et al 2013.

**Parameter values for the simulation**

DI models take the general form of:

`y = Identities + Interactions + Structures + \epsilon`

where *y* is a community-level response, the *Identities* are the effects of species identities and enter the model as individual species proportions at the beginning of the time period, the *Interactions* are the interactions among the species proportions, while *Structures* include other experimental structures such as blocks, treatments or density.

The dataset `sim3`

was simulated with:

identity effects for the nine species with values = 10, 9, 8, 7, 11, 6, 5, 8, 9

treatment effects = 3, 0

functional group specific interact effects; assume functional groups are labelled FG1, FG2 and FG3, then the interaction parameter values are: between FG1 and FG2 = 4, between FG1 and FG3 = 9, between FG2 and FG3 = 3, within FG1 = 2, within FG2 = 3 and within FG3 = 1

theta = 1 (where

`\theta`

is a non-linear parameter included as a power on each`pipj`

product within interaction variables, see Connolly et al 2013 for details)-
`\epsilon`

assumed normally distributed with mean 0 and standard deviation 1.2.

Connolly J, T Bell, T Bolger, C Brophy, T Carnus, JA Finn, L Kirwan, F Isbell, J Levine, A Lüscher, V Picasso, C Roscher, MT Sebastia, M Suter and A Weigelt (2013) An improved model to predict the effects of changing biodiversity levels on ecosystem function. Journal of Ecology, 101, 344-355.

Kirwan L, J Connolly, JA Finn, C Brophy, A Lüscher, D Nyfeler and MT Sebastia (2009) Diversity-interaction modelling - estimating contributions of species identities and interactions to ecosystem function. Ecology, 90, 2032-2038.

```
####################################
## Code to simulate the sim3 dataset
## Simulate dataset sim3 with 9 species, three functional groups and two levels of a treatment.
## The species 1-5 are FG1, species 6-7 are FG2 and species 8-9 are FG3.
## Assume ID effects and the FG interaction model, with a treatment (factor with two levels).
## Set up proportions
data("design_a")
sim3a <- design_a
# Replicate the design over two treatments
sim3b <- sim3a[rep(seq_len(nrow(sim3a)), each = 2), ]
sim3c <- data.frame(treatment = factor(rep(c("A","B"), times = 206)))
sim3 <- data.frame(sim3b[,1:2], sim3c, sim3b[,3:11])
row.names(sim3) <- NULL
## Create the functional group interaction variables
FG_matrix <- DI_data(prop = 4:12, FG = c("FG1","FG1","FG1","FG1","FG1","FG2","FG2","FG3","FG3"),
data = sim3, what = "FG")
sim3 <- data.frame(sim3, FG_matrix)
## To simulate the response, first create a matrix of predictors that includes p1-p9, the treatment
## and the interaction variables.
X <- model.matrix(~ p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9 + treatment
+ bfg_FG1_FG2 + bfg_FG1_FG3 + bfg_FG2_FG3
+ wfg_FG1 + wfg_FG2 + wfg_FG3 -1, data=sim3)
## Create a vector of 'known' parameter values for simulating the response.
## The first nine are the p1-p9 parameters, and the second set of two are the treatment effects
## and the third set of six are the interaction parameters.
sim3_coeff <- c(10,9,8,7,11, 6,5, 8,9, 3,0, 4,9,3, 2,3,1)
## Create response and add normally distributed error
sim3$response <- as.numeric(X %*% sim3_coeff)
set.seed(1657914)
r <- rnorm(n = 412, mean = 0, sd = 1.2)
sim3$response <- round(sim3$response + r, digits = 3)
sim3[,13:18] <- NULL
###########################
## Analyse the sim3 dataset
## Load the sim3 data
data(sim3)
## View the first few entries
head(sim3)
## Explore the variables in sim3
str(sim3)
## Check characteristics of sim3
hist(sim3$response)
summary(sim3$response)
plot(sim3$richness, sim3$response)
plot(sim3$p1, sim3$response)
plot(sim3$p2, sim3$response)
plot(sim3$p3, sim3$response)
plot(sim3$p4, sim3$response)
plot(sim3$p5, sim3$response)
plot(sim3$p6, sim3$response)
plot(sim3$p7, sim3$response)
plot(sim3$p8, sim3$response)
plot(sim3$p9, sim3$response)
## What model fits best? Selection using F-test in autoDI
auto1 <- autoDI(y = "response", prop = 4:12, treat = "treatment",
FG = c("FG1","FG1","FG1","FG1","FG1","FG2","FG2","FG3","FG3"), data = sim3,
selection = "Ftest")
summary(auto1)
## Fit the functional group model, with treatment, using DI and the FG tag
m1 <- DI(y = "response", prop = 4:12,
FG = c("FG1","FG1","FG1","FG1","FG1","FG2","FG2","FG3","FG3"), treat = "treatment",
DImodel = "FG", data = sim3)
summary(m1)
plot(m1)
## Check goodness-of-fit using a half-normal plot with a simulated envelope
library(hnp)
hnp(m1)
## Create the functional group interactions and store them in a new dataset
FG_matrix <- DI_data(prop = 4:12, FG = c("FG1","FG1","FG1","FG1","FG1","FG2","FG2","FG3","FG3"),
data = sim3, what = "FG")
sim3a <- data.frame(sim3, FG_matrix)
## Test if the FG interaction variables interact with treatment using 'extra_formula'
m2 <- DI(y = "response", prop = 4:12,
FG = c("FG1","FG1","FG1","FG1","FG1","FG2","FG2","FG3","FG3"),
treat = "treatment", DImodel = "FG", extra_formula = ~ bfg_FG1_FG2:treatment
+ bfg_FG1_FG3:treatment + bfg_FG2_FG3:treatment + wfg_FG1:treatment + wfg_FG2:treatment
+ wfg_FG3:treatment, data = sim3a)
summary(m2)
## Fit the functional group model using DI and custom_formula
## Set up a dummy variable for treatment first (required).
sim3a$treatmentA <- as.numeric(sim3a$treatment=="A")
m3 <- DI(y = "response", custom_formula = response ~ 0 + p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8
+ p9 + treatmentA + bfg_FG1_FG2 + bfg_FG1_FG3 + bfg_FG2_FG3 + wfg_FG1 + wfg_FG2
+ wfg_FG3, data = sim3a)
summary(m3)
```

[Package *DImodels* version 1.3 Index]