sim4 {DImodels} | R Documentation |

The `sim4`

dataset was simulated. There is a covariate treatment and six species that vary in proportions (`p1 - p6`

). It is assumed that species 1 and 2 come from functional group 1, species 3 and 4 from functional group 2 and species 5 and 6 from functional group 3. The response was simulated assuming that there were species identity effects, separate pairwise interaction effects and a covariate effect.

`data(sim4)`

A data frame with 141 observations on the following nine variables:

`richness`

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

`treatment`

A covariate taking values 50, 150 or 250.

`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.

`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 `sim4`

was simulated with:

identity effects for the six species with values = 25, 16, 18, 20, 10, 12

a covariate effect = 0.03

all 15 pairwise interaction effects with values: 30, 27, 20, 15, 10, 9, 14, 18, 36, 17, 26, 32, 9, 21, 16 (for pairs of species 1-2, 1-3, 1-4, 1-5, 1-6, 2-3, 2-4, ... , 5-6 respectively).

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 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 sim4 dataset
## Simulate dataset sim4 with 6 species, three functional groups and three levels of a covariate
## The species 1-2 are FG1, species 3-4 are FG2 and species 5-6 are FG3.
## Assume ID effects and the full pairwise interaction model, with a covariate.
## Set up proportions
data("design_b")
sim4a <- design_b
# Replicate the design for three values of a covariate
sim4b <- sim4a[rep(seq_len(nrow(sim4a)), times = 3), ]
sim4c <- data.frame(treatment = rep(c(50, 150, 250), each = 47))
sim4 <- data.frame(richness = sim4b[,1], sim4c, sim4b[,2:7])
row.names(sim4) <- NULL
## To simulate the response, first create a matrix of predictors that includes p1-p6, the treatment
## and all pairwise interaction variables
X <- model.matrix(~ p1 + p2 + p3 + p4 + p5 + p6 + treatment + (p1 + p2 + p3 + p4 + p5 + p6)^2 -1,
data = sim4)
## Create a vector of 'known' parameter values for simulating the response.
## The first six are the p1-p6 parameters, and the second set of one is the treatment parameter
## and the third set of 15 are the interaction parameters.
sim4_coeff <- c(25,16,18,20,10,12, 0.03, 30,27,20,15,10,9,14,18,36,17,26,32,9,21,16)
## Create response and add normally distributed error
sim4$response <- as.numeric(X %*% sim4_coeff)
set.seed(34261)
r <- rnorm(n = 141, mean = 0, sd = 2)
sim4$response <- round(sim4$response + r, digits = 3)
###########################
## Analyse the sim4 dataset
## Load the sim4 data
data(sim4)
## View the first few entries
head(sim4)
## Explore the variables in sim4
str(sim4)
## Check characteristics of sim4
hist(sim4$response)
summary(sim4$response)
plot(sim4$richness, sim4$response)
plot(sim4$richness[sim4$treatment==50], sim4$response[sim4$treatment==50], ylim=c(0,40))
plot(sim4$richness[sim4$treatment==150], sim4$response[sim4$treatment==150], ylim=c(0,40))
plot(sim4$richness[sim4$treatment==250], sim4$response[sim4$treatment==250], ylim=c(0,40))
plot(sim4$p1, sim4$response)
plot(sim4$p2, sim4$response)
plot(sim4$p3, sim4$response)
plot(sim4$p4, sim4$response)
plot(sim4$p5, sim4$response)
plot(sim4$p6, sim4$response)
## What model fits best? Selection using F-test
auto1 <- autoDI(y = "response", prop = 3:8, treat = "treatment",
FG = c("FG1","FG1","FG2","FG2","FG3","FG3"), data = sim4, selection = "Ftest")
summary(auto1)
## Ignore functional groups (will replace FG model with ADD model in Step 1 selection)
auto2 <- autoDI(y = "response", prop = 3:8, treat = "treatment", data = sim4, selection = "Ftest")
summary(auto2)
## Fit the functional group model using DI and the FG tag
m1 <- DI(y = "response", prop = 3:8, treat = "treatment",
FG = c("FG1","FG1","FG2","FG2","FG3","FG3"), DImodel = FG, data = sim4)
summary(m1)
## Fit the additive species model using DI and the ADD tag
m2 <- DI(y = "response", prop = 3:8, treat = "treatment", DImodel = ADD, data = sim4)
summary(m2)
## Fit the full pairwise model using DI and the FULL tag
m3 <- DI(y = "response", prop = 3:8, treat = "treatment", DImodel = FULL, data = sim4)
summary(m3)
plot(m3)
## Check goodness-of-fit using a half-normal plot with a simulated envelope
library(hnp)
hnp(m3)
## Create the functional group and additive species interaction variables,
## and store in a new data frame called sim4a
newlist <- DI_data(prop = 3:8, FG = c("FG1","FG1","FG2","FG2","FG3","FG3"),
data = sim4, what = c("FG", "ADD"))
sim4a <- data.frame(sim4, newlist$FG, newlist$ADD)
## Fit the functional group model using DI and custom_formula (equivalent to m1)
m4 <- DI(custom_formula = response ~ 0 + p1 + p2 + p3 + p4 + p5 + p6 + bfg_FG1_FG2
+ bfg_FG1_FG3 + bfg_FG2_FG3 + wfg_FG1 + wfg_FG2 + wfg_FG3 + treatment, data = sim4a)
summary(m4)
## Fit the additive species model using DI and custom_formula (equivalent to m2)
m5 <- DI(custom_formula = response ~ 0 + p1 + p2 + p3 + p4 + p5 + p6 + p1_add
+ p2_add + p3_add + p4_add + p5_add + p6_add + treatment, data = sim4a)
summary(m5)
## Fit the full pairwise model using DI and custom_formula (equivalent to m3)
m6 <- DI(custom_formula = response ~ 0 + p1 + p2 + p3 + p4 + p5 + p6
+ (p1 + p2 + p3 + p4 + p5 + p6)^2 + treatment, data = sim4a)
summary(m6)
```

[Package *DImodels* version 1.3 Index]