Methods to partition data for evaluation

ENMeval provides several ways to partition occurrence and background localities into bins for training and validation (or, evaluation and calibration). Users should carefully consider the objectives of their study and the influence of spatial bias when deciding on a method of data partitioning.

These functions are used internally to partition data during a call of ENMevaluate but can also be used independently to generate data partitions. For user-specified partitions, users can simply define groups of occurrence records and background points directly with ENMevaluate.

The get.block method partitions occurrence localities by finding the latitude and/or longitude lines that divide the occurrence localities into four groups of (insofar as possible) equal numbers. The order and nature of the divisions can be controlled with the "orientation" parameter. The default is "lat_lon", which divides first by a latitudinal line, then second by longitudinal lines. This method is based on the spatial partitioning technique described in Radosavljevic & Anderson (2014), where the "lon_lon" option was used. Background localities are assigned to each of the four groups based on their position with respect to these lines. While the get.block method results in (approximately) equal division of occurrence localities among four groups, the number of background localities (and, consequently, environmental and geographic space) in each group depends on the distribution of occurrence localities across the study area.

The get.checkerboard1 and get.checkerboard2 methods are variants of a checkerboard approach to partition occurrence localities. These methods use the dismo::gridSample function of the dismo package (Hijmans et al. 2011) to partition records according to checkerboard grids across the study extent. The spatial grain of these grids is determined by resampling (or aggregating) the original environmental input grids based on the user-defined aggregation factor (e.g., an aggregation factor of 2 results in a checkerboard with grid cells four times as large in area as the original input grids). The get.checkerboard1 method partitions data into two groups according to a single checkerboard pattern, and the get.checkerboard2 method partitions data into four groups according to two nested checkerboard grids. In contrast to the get.block method, both the get.checkerboard1 and get.checkerboard2 methods subdivide geographic space equally but do not ensure a balanced number of occurrence localities in each group. The two get.checkerboard methods give warnings (and potentially errors) if zero points (occurrence or background) fall in any of the expected bins.

The get.jackknife method is a special case of k-fold cross validation where the number of bins (k) is equal to the number of occurrence localities (n) in the dataset. It is suggested for occurrence datasets of relatively small sample size (generally < 25 localities) (Pearson et al. 2007; Shcheglovitova and Anderson 2013).

The get.randomkfold method partitions occurrence localities randomly into a user-specified number of (k) bins. This is equivalent to the method of k-fold cross validation currently provided by Maxent.

Users can also define custom partitions for occurrence and background data in the call to `ENMevaluate` with the "user.grp" parameter.

Usage

get.block(occs, bg, orientation = "lat_lon")

get.checkerboard1(occs, envs, bg, aggregation.factor, gridSampleN = 10000)

get.checkerboard2(occs, envs, bg, aggregation.factor, gridSampleN = 10000)

get.jackknife(occs, bg)

get.randomkfold(occs, bg, kfolds)

Arguments

occs: matrix / data frame: longitude and latitude (in that order) of occurrence localities
bg: matrix / data frame: longitude and latitude (in that order) of background localities
orientation: character vector: the order of spatial partitioning for the get.block method; the first direction bisects the points into two groups, and the second direction bisects each of these further into two groups each, resulting in four groups; options are "lat_lon" (default), "lon_lat", "lon_lon", and "lat_lat"
envs: RasterStack: environmental predictor variables
aggregation.factor: numeric vector: the aggregation scale for the get.checkerboard1 and get.checkerboard2 methods; if a single number is given and get.checkerboard2 partitioning method is used, the single value is used for both scales of aggregation
gridSampleN: numeric: the number of points sampled from the input raster using gridSample() by the checkerboard partitioning functions
kfolds: numeric: number of random k-folds for get.randomkfold method

Value

A named list of two items:

$occs.grp: A vector of bin designation for occurrence localities in the same order they were provided.
$bg.grp: A vector of bin designation for background localities in the same order they were provided.

Note

The checkerboard1 and checkerboard2 methods are designed to partition occurrence localities into two and four evaluation bins, respectively. They may give fewer bins, however, depending on where the occurrence localities fall with respect to the grid cells (e.g., all records happen to fall in the "black" squares). A warning is given if the number of bins is < 4 for the checkerboard2 method, and an error is given if all localities fall into a single evaluation bin.

References

Hijmans, R. J., Phillips, S., Leathwick, J. and Elith, J. (2011). dismo package for R. Available online at: https://cran.r-project.org/package=dismo.

Pearson, R. G., Raxworthy, C. J., Nakamura, M. and Peterson, A. T. (2007). Predicting species distributions from small numbers of occurrence records: a test case using cryptic geckos in Madagascar. Journal of Biogeography, 34: 102-117. doi:10.1111/j.1365-2699.2006.01594.x

Radosavljevic, A., & Anderson, R. P. (2014). Making better Maxent models of species distributions: complexity, overfitting and evaluation. Journal of Biogeography, 41: 629-643. doi:10.1111/jbi.12227

Shcheglovitova, M. and Anderson, R. P. (2013). Estimating optimal complexity for ecological niche models: a jackknife approach for species with small sample sizes. Ecological Modelling, 269: 9-17. doi:10.1016/j.ecolmodel.2013.08.011

Author

Robert Muscarella <bob.muscarella@gmail.com> and Jamie M. Kass <jkass@gc.cuny.edu>

Examples

require(raster)
#> Loading required package: raster
#> Loading required package: sp

set.seed(1)

### Create environmental extent (raster)
envs <- raster(matrix(nrow=25, ncol=25))

### Create occurrence localities
set.seed(1)
nocc <- 25
xocc <- rnorm(nocc, sd=0.25) + 0.5
yocc <- runif(nocc, 0, 1)
occs <- as.data.frame(cbind(xocc, yocc))

### Create background points
nbg <- 500
xbg <- runif(nbg, 0, 1)
ybg <- runif(nbg, 0, 1)
bg <- as.data.frame(cbind(xbg, ybg))

### Plot points on environmental raster
plot(envs)
points(bg)
points(occs, pch=21, bg=2)


### Block partitioning method (default orientation is "lat_lon"))
blk.latLon <- get.block(occs, bg)
plot(envs)
points(occs, pch=23, bg=blk.latLon$occs.grp)

plot(envs)
points(bg, pch=21, bg=blk.latLon$bg.grp)

# Can partition with other orientations
blk.latLat <- get.block(occs, bg, orientation = "lat_lat")
plot(envs)
points(occs, pch=23, bg=blk.latLat$occs.grp)

plot(envs)
points(bg, pch=21, bg=blk.latLat$bg.grp)


### Checkerboard1 partitioning method with aggregation factor of 4
chk1.ag4 <- get.checkerboard1(occs, envs, bg, aggregation.factor = 4)
plot(envs)
points(occs, pch=23, bg=chk1.ag4$occs.grp)

plot(envs)
points(bg, pch=21, bg=chk1.ag4$bg.grp)

# Higher aggregation factors result in bigger checkerboard blocks
chk1.ag8 <- get.checkerboard1(occs, envs, bg, aggregation.factor = 8)
plot(envs)
points(occs, pch=23, bg=chk1.ag8$occs.grp)

plot(envs)
points(bg, pch=21, bg=chk1.ag8$bg.grp)


### Checkerboard2 partitioning method with aggregation factors of 2, 2
chk2.ag2_2 <- get.checkerboard2(occs, envs, bg, c(2,2))
plot(envs)
points(occs, pch=23, bg=chk2.ag2_2$occs.grp)

plot(envs)
points(bg, pch=21, bg=chk2.ag2_2$bg.grp)

# Higher aggregation factors result in bigger checkerboard blocks,
# and can vary between hierarchical levels
chk2.ag4_6 <- get.checkerboard2(occs, envs, bg, c(4,6))
#> Warning: occurrence points fall in only 2 bins
plot(envs)
points(occs, pch=23, bg=chk2.ag4_6$occs.grp)

plot(envs)
points(bg, pch=21, bg=chk2.ag4_6$bg.grp)


### Random partitions with 4 folds
# Note that get.randomkkfold does not partition the background
krandom <- get.randomkfold(occs, bg, 4)
plot(envs)
points(occs, pch=23, bg=krandom$occs.grp)

plot(envs)
points(bg, pch=21, bg=krandom$bg.grp)


### k-1 jackknife partitions
# Note that get.jackknife does not partition the background
jack <- get.jackknife(occs, bg)
plot(envs)
points(occs, pch=23, bg=rainbow(length(jack$occs.grp)))

plot(envs)
points(bg, pch=21, bg=jack$bg.grp)