This vignette will show how to
visualize the var-covariance matrix of random terms for
communityPGLMM models.
Main function
The main function to use is phyr::pglmm_plot_re()
(alias: phyr::pglmm_plot_ranef(),
phyr::communityPGLMM.show.re(),
phyr::communityPGLMM.plot.re()). Here are the arguments of
this function:
args(phyr::pglmm_plot_re)
## function (formula = NULL, data = NULL, family = "gaussian", sp.var = "sp",
## site.var = "site", tree = NULL, tree_site = NULL, repulsion = FALSE,
## x = NULL, show.image = TRUE, show.sim.image = FALSE, random.effects = NULL,
## add.tree.sp = TRUE, add.tree.site = FALSE, cov_ranef = NULL,
## tree.panel.space = 0.5, title.space = 5, tree.size = 3, ...)
## NULL
Some brief explanation of arguments:
x: a model with class communityPGLMM, if it is
specified, then all other argument before x will be ignored.show.image (TRUE or FALSE):
whether to plot the var-cov matrix of random terms?show.sim.image (TRUE or
FALSE): whether to plot simulated site by species matrix
for all random terms?add.tree.sp (TRUE or FALSE):
when show.sim.image = TRUE, whether to add a phylogeny of
species at the top of each matrix plot?add.tree.site (TRUE or
FALSE): when show.sim.image = TRUE, whether to
add a phylogeny of sites at the right of each matrix plot? This can be
useful for bipartite problems (e.g. pollinators (species) and plants
(sites)).tree.size (default is 3): the height of the phylogenies
to plot, unit is number of lines.
This function will return a hidden list, which includes all the
var-cov matrices of random terms, simulated site by species matrices,
individual plots, and all plots in one figure for both var-cov matrices
and simulated ones. Therefore, we can extract specific plots and then
update them or generate new figure with
gridExtra::grid.arrange(). This is because all generated
plots are based on lattice package and are all
grid object. Therefore, we can also use
gridExtra::arrangeGrob() to put multiple plots in one
figure and then use ggplot2::ggsave() to save it as
external file (e.g. PDF). Of course, pdf() and
dev.off() will also work.
Simulate data
Now, let’s show how to use this function to help us understanding
better the random terms.
library(ape)
library(phyr)
suppressPackageStartupMessages(library(dplyr))
set.seed(12345)
nspp <- 7
nsite <- 5
# Simulate a phylogeny that has a lot of phylogenetic signal (power = 1.3)
phy <- compute.brlen(rtree(n = nspp), method = "Grafen", power = 1.3)
# Simulate species means
sd.sp <- 1
mean.sp <- rTraitCont(phy, model = "BM", sigma = sd.sp^2)
Y.sp <- rep(mean.sp, times = nsite)
# Phylogenetically correlated response of species to env
sd.trait <- 1
trait <- rTraitCont(phy, model = "BM", sigma = sd.trait)
trait <- rep(trait, times = nsite)
# Simulate site means
sd.site <- 1
mean.site <- rnorm(nsite, sd = sd.site)
Y.site <- rep(mean.site, each = nspp)
# Site-specific environmental variation
sd.env <- 1
env <- rnorm(nsite, sd = sd.env)
# Generate covariance matrix for phylogenetic attraction
sd.attract <- 1
Vphy <- vcv(phy)
Vphy <- Vphy / (det(Vphy) ^ (1 / nspp))
V.attract <- kronecker(diag(nrow = nsite, ncol = nsite), Vphy)
Y.attract <- array(t(mvtnorm::rmvnorm(n = 1, sigma = sd.attract ^ 2 * V.attract)))
# Residual errors
sd.e <- 1
Y.e <- rnorm(nspp * nsite, sd = sd.e)
# Construct the dataset
d <- data.frame(sp = rep(phy$tip.label, times = nsite),
site = rep(1:nsite, each = nspp),
env = rep(env, each = nspp))
# Simulate abundance data
d$Y <- Y.sp + Y.attract + trait * d$env + Y.e
head(d)
## sp site env Y
## 1 t4 1 -1.060266 -1.3475684
## 2 t2 1 -1.060266 1.2422030
## 3 t5 1 -1.060266 -1.2711509
## 4 t3 1 -1.060266 1.8940820
## 5 t6 1 -1.060266 1.5771805
## 6 t7 1 -1.060266 0.3308875
# fit a model
mod_1 = pglmm(Y ~ 1 + env + (1|sp__) + (1|site) + (env|sp__) + (1|sp__@site),
data = d, cov_ranef = list(sp = phy))
## 'as(<matrix>, "dgTMatrix")' is deprecated.
## Use 'as(as(as(., "dMatrix"), "generalMatrix"), "TsparseMatrix")' instead.
## See help("Deprecated") and help("Matrix-deprecated").
summary(mod_1)
## Linear mixed model fit by restricted maximum likelihood
##
## Call:Y ~ 1 + env
##
## logLik AIC BIC
## -64.34 146.68 150.38
##
## Random effects:
## Variance Std.Dev
## 1|sp 2.085e-06 0.0014439
## 1|sp__ 4.218e-01 0.6494991
## 1|site 1.235e-07 0.0003515
## env|sp 1.209e-06 0.0010993
## env|sp__ 5.434e-01 0.7371383
## 1|sp__@site 1.375e-01 0.3707606
## residual 1.885e+00 1.3729463
##
## Fixed effects:
## Value Std.Error Zscore Pvalue
## (Intercept) 0.83092 0.63742 1.3036 0.1924
## env 0.75052 0.68819 1.0906 0.2755
Var-cov matrices of random terms
Plot var-cov matrices of all random terms in one figure
# plot var-cov matrices of random terms
mod1re = pglmm_plot_re(Y ~ 1 + env + (1|sp__) + (1|site) + (env|sp__) + (1|sp__@site),
data = d, cov_ranef = list(sp = phy), show.image = TRUE,
show.sim.image = FALSE)
In the above plot, we can see that some of the panels are black-white
but some have colors. This is because, by default, if a matrix has both
positive and negative values, then the function will use red-blue color
and will draw a key for that (use colorkey = FALSE to
suppress it). If a matrix does not have negative values, then the
function will use black/white color (use useAbs = FALSE to
use color instead, and use colorkey = FALSE to suppress key
if wanted). In both cases, value 0 will be white so that the structure
of the var-cov matrix can be easier to see.
# all use color with useAbs = FALSE
pglmm_plot_re(Y ~ 1 + env + (1|sp__) + (1|site) + (env|sp__) + (1|sp__@site),
data = d, cov_ranef = list(sp = phy), show.image = TRUE,
show.sim.image = FALSE, useAbs = FALSE)
For the above plot, notice that for 1|sp and
1|site, all values are either 1 or 0 even though we have a
range in the key. We can suppress the key with
colorkey = FALSE.
# suppress key with colorkey = FALSE
pglmm_plot_re(Y ~ 1 + env + (1|sp__) + (1|site) + (env|sp__) + (1|sp__@site),
data = d, cov_ranef = list(sp = phy), show.image = TRUE,
show.sim.image = FALSE, useAbs = FALSE, colorkey = FALSE)
We can also just use colorkey = FALSE and still use
black/white color for matrices that do not have negative values (without
setting useAbs).
# suppress colorkey, let the function decide whether use color or not
pglmm_plot_re(Y ~ 1 + env + (1|sp__) + (1|site) + (env|sp__) + (1|sp__@site),
data = d, cov_ranef = list(sp = phy), show.image = TRUE,
show.sim.image = FALSE, colorkey = FALSE)
To make all plots black or white, use useAbs = TRUE.
# all black and white
pglmm_plot_re(Y ~ 1 + env + (1|sp__) + (1|site) + (env|sp__) + (1|sp__@site),
data = d, cov_ranef = list(sp = phy), show.image = TRUE,
show.sim.image = FALSE, useAbs = TRUE)
Individual plots for var-cov matrices
Instead of plotting all var-cov matrices in one figure, we can also
select the ones we are interested and then work from there.
names(mod1re)
## [1] "vcv" "sim" "tree"
## [4] "plt_re_list" "plt_sim_list" "plt_re_all_in_one"
So, the data of var-cov matrices are saved as
mod1re$vcv, which is a list. We can use this list to plot
the random terms in other ways, using either the base R or ggplot2
package.
names(mod1re$vcv)
## [1] "1|sp" "1|sp__" "1|site" "env|sp" "env|sp__"
## [6] "1|sp__@site"
The individual plots are saved as mod1re$plt_re_list,
which is also a list.
names(mod1re$plt_re_list)
## [1] "1|sp" "1|sp__" "1|site" "env|sp" "env|sp__"
## [6] "1|sp__@site"
mod1re$plt_re_list[[6]]
The individual plots were generated using
Matrix::image(), which used
lattice::levelplot() as the back bone function.
Matrix::image(mod1re$vcv[[6]], xlab = "", ylab = "", sub = "", main = "1|sp__@site")
We can also pick the ones that we are interested in and put them in
one figure. For example, suppose that we are only interested in those
with phylogenetic relationships. That is, 1|sp__,
env|sp__, and 1|sp__@site.
gridExtra::grid.arrange(grobs = mod1re$plt_re_list[c(2, 5, 6)], nrow = 1)
To save this plot, we can wrap the above line of code within
pdf() and dev.off().
Simulated site by species matrix for random terms
For each random term, we can simulate some values for all data
points. We can reshape this long format into a site by species matrix.
By plotting this site by species matrix, we can see what does “closely
related species have similar abundance (within or across sites)”
mean.
Individual plots for simulated site by species matrix
names(mod1sim)
## [1] "vcv" "sim" "tree"
## [4] "plt_re_list" "plt_sim_list" "plt_sim_all_in_one"
The individual simulated matrices are saved as
mod1sim$sim and individual plots are saved as
mod1sim$plt_sim_list. We can use the same approach to
select our own plots as those of var-cov matrices.
We can control the space between the phylogeny and the matrix plot
with key.top argument in lattice::levelplot(),
which has a default value of 1 (line).
gridExtra::grid.arrange(grobs = mod1sim$plt_sim_list[c(2, 6)], nrow = 1)
gridExtra::grid.arrange(grobs = lapply(mod1sim$plt_sim_list[c(2, 6)],
update,
par.settings = list(layout.heights =
list(key.top = 0.3,
main = 5))),
nrow = 1)
