After understanding how the spatial null model algorithms work
(`vignette("spatial-null-models")`

), let’s see how to create
multiple null models and test for the effect size using
`SESraster()`

.

Standardized effect size (SES) is a measure of the magnitude of the
studied effect. It indicates the direction and the degree that the
effect departures from the null model. SESraster uses Cohen’s *d*
(Cohen 1988),
which is measured as the difference between the observed pattern and the
average of *n* randomized observations divided by the standard
deviation of the randomized observations \(SES
= (Obs-mean(Null))/sd(Null)\).

First, we will create some random species distributions using the
package `terra`

.

```
library(SESraster)
#> This is SESraster 0.7.1
#> If you use SESraster, please cite in your publications. See:
#> citation("SESraster")
library(terra)
#> terra 1.7.83
# creating random species distributions
f <- system.file("ex/elev.tif", package="terra")
r <- rast(f)
set.seed(510)
r <- rast(lapply(1:18,
function(i, r, mn, mx){
app(r, function(x, t){
sapply(x, function(x, t){
x<max(t) & x>min(t)
}, t = t)
}, t = sample(seq(mn, mx), 2))
}, r = r, mn = minmax(r)[1]+10, mx = minmax(r)[2]-10))
names(r) <- paste("sp", 1:nlyr(r))
plot(r)
```

With the distributions in hand, we can perform the spatial randomizations.

First we need a function that computes the desired metric. The function must work with spatial data. Just to exemplify, we are creating a function to compute the mean of presences and absences (1/0) within each cell. You probably wants to use a more ecologically meaningful function, but here is just an example of use.

Now, to compute SES, we will compute our desired metric by sending
our function `appmean()`

to `SESraster()`

through
`FUN`

argument. We also randomize the original data by
`species`

using the `bootspat_naive()`

algorithm
and passing the argument `random="species"`

through
`spat_alg_args`

.

```
ses.sp <- SESraster(r, FUN = appmean,
spat_alg = "bootspat_naive", spat_alg_args = list(random = "species"),
aleats = 5)
plot(ses.sp)
```

Compute metric and SES using `bootspat_naive()`

and
randomize by `site`

changing the argument to
`random="site"`

in `spat_alg_args`

.

```
ses.st <- SESraster(r, FUN = appmean,
spat_alg = "bootspat_naive", spat_alg_args = list(random = "site"),
aleats = 5)
plot(ses.st)
```

`FUN`

It is also possible to send arguments to the function that calculates
the desired metric (`FUN`

). It can be done by sending a list
of arguments through `FUN_args`

.

```
## let's create some missing values for layer/species 1
r2 <- r
set.seed(10)
cellsNA <- terra::spatSample(r2, 30, na.rm = TRUE, cells = TRUE, values = FALSE)
r2[cellsNA][1] <- NA
# plot(r)
set.seed(10)
sesNA <- SESraster(r2, FUN = appmean, FUN_args = list(na.rm = FALSE),
spat_alg = "bootspat_naive", spat_alg_args=list(random = "species"),
aleats = 5)
head(sesNA[cellsNA])
#> Observed.mean Null_Mean.mean Null_SD.mean SES.mean p_lower.mean p_upper.mean
#> 1 NA NA NA NA 0 0
#> 2 NA NA NA NA 0 0
#> 3 NA NA NA NA 0 0
#> 4 NA NA NA NA 0 0
#> 5 NA NA NA NA 0 0
#> 6 NA NA NA NA 0 0
plot(sesNA)
```

Notice that NAs can be ignored by the `appmean()`

function
by using `FUN_args = list(na.rm = TRUE)`

:

```
set.seed(10)
ses.woNA <- SESraster(r2, FUN = appmean, FUN_args = list(na.rm = TRUE),
spat_alg = "bootspat_naive", spat_alg_args=list(random = "species"),
aleats = 5)
head(ses.woNA[cellsNA])
#> Observed.mean Null_Mean.mean Null_SD.mean SES.mean p_lower.mean
#> 1 0.11764706 0.3882353 0.08921030 -3.0331502 1.0
#> 2 0.41176471 0.3882353 0.08921030 0.2637522 0.2
#> 3 0.41176471 0.4117647 0.09300817 0.0000000 0.4
#> 4 0.05882353 0.3647059 0.07669650 -3.9882179 1.0
#> 5 0.35294118 0.4000000 0.07669650 -0.6135720 0.6
#> 6 0.52941176 0.4941176 0.08921030 0.3956283 0.2
#> p_upper.mean
#> 1 0.0
#> 2 0.6
#> 3 0.4
#> 4 0.0
#> 5 0.2
#> 6 0.4
plot(ses.woNA)
```

In addition to the spatial randomizations, it is possible to create a
null model by randomizing a parameter (i.e. argument) of the metric
passed to FUN. This is useful, for example, to randomize a species trait
(e.g. branch length) that is used to compute the metric. In the example
below the function `appsv()`

uses the argument
`lyrv`

to compute the fictional metric. We also create some
fictional values for the trait.

```
## example with `Fa_alg`
appsv <- function(x, lyrv, na.rm = FALSE, ...){
sumw <- function(x, lyrv, na.rm, ...){
ifelse(all(is.na(x)), NA,
sum(x*lyrv, na.rm=na.rm, ...))
}
stats::setNames(terra::app(x, sumw, lyrv = lyrv, na.rm=na.rm, ...), "sumw")
}
set.seed(10)
trait <- sample(100:2000, nlyr(r))
trait
#> [1] 590 1772 1453 467 1583 538 1707 1561 1546 1634 1846 443 1394 242 1037
#> [16] 1578 1998 1029
```

In this exapmle, no spatial randomization will be performed, only
trait randomization. To select the *trait* to be randomized, pick
the desired argument of `FUN_args`

using
`Fa_sample`

and the name of the desired argument (here
“lyrv”). Then select a function, here “sample” is used. It is also
possible to send arguments to the function in `Fa_alg`

through `Fa_alg_args`

. It works in the same way that
arguments are sent to `FUN`

and `spat_alg`

through
`FUN_args`

and `spat_alg_args`

.

In this first
example it is performed a trait sampling **without**
replacement.

```
set.seed(10)
ses <- SESraster(r, FUN = appsv,
FUN_args = list(lyrv = trait, na.rm = TRUE),
Fa_sample = "lyrv",
Fa_alg = "sample", Fa_alg_args = list(replace = FALSE),
aleats = 5)
plot(ses)
```

In this second example it is performed a trait sampling
**with** replacement by passing `replace = TRUE`

through `Fa_alg_args`

.

```
set.seed(10)
ses <- SESraster(r, FUN = appsv,
FUN_args = list(lyrv = trait, na.rm = TRUE),
Fa_sample = "lyrv",
Fa_alg = "sample", Fa_alg_args = list(replace = TRUE),
aleats = 5)
plot(ses)
```

The `SESraster`

R package aims to simplify the
randomization of raster data and the calculation of standardized effect
sizes for spatial data. We hope it is useful to analize the vast amount
of raster data generated for the analysis of biogeographycal and
macroecological patterns.

Cohen, Jacob. 1988. *Statistical Power Analysis for the Behavioral
Sciences*. Academic Press.