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Ensembles of species distribution models

sdm_ensemble.Rd

sdm_ensemble() fits several algorithms to the same presence-background (or presence-absence) data, scores each with spatial block cross-validation, and combines them into one weighted ensemble, in the spirit of biomod2 (Thuiller et al. 2009) but without its dependencies and with fixes for common weaknesses:

  • Spatial cross-validation by default. Random folds put test points next to training points, so spatially autocorrelated data look better than they are (Roberts et al. 2017). Folds here are whole spatial blocks.

  • Comparable algorithms. Presence-background data are fitted with equal total weight for presences and background (Barbet-Massin et al. 2012) for GLM and GAM, Maxent uses its own infinitely-weighted formulation, and the random forest grows each tree on a balanced bootstrap (down-sampling; Valavi et al. 2021), so all four answer the same question on the same 0-1 scale.

  • Weights from transferable skill. Each algorithm is weighted by its cross-validated true skill statistic above min_tss; algorithms below it are left out rather than allowed to dilute the ensemble.

  • Standardised predictors. Every algorithm sees predictors rescaled to 0-1 on the training range, so results do not depend on units or on where zero lies.

  • Agreement as uncertainty. Predictions give the weighted mean and the weighted standard deviation across algorithms.

The random forest and Maxent are written in C++ and run on several cores.

Usage

sdm_ensemble(
  presence,
  data,
  coords = NULL,
  algorithms = c("maxent", "glm", "gam", "rf"),
  folds = 5,
  block_size = NULL,
  min_tss = 0.3,
  ntree = 500,
  mtry = NULL,
  seed = 1,
  ...
)

# S3 method for class 'tmr_sdm_ensemble'
predict(object, newdata, what = c("mean", "sd", "all"), ...)

Arguments

presence

0/1 vector: 1 for presences, 0 for background or absence.

data

Data frame of predictors (numeric, or factors for Maxent and the random forest).

coords

Optional two-column matrix or data frame of x and y coordinates for spatial blocks. Without it, folds are random.

algorithms

Any of "maxent", "glm", "gam", "rf".

folds

Number of cross-validation folds.

block_size

Side of the square spatial blocks, in the units of coords. By default a tenth of the larger side of the extent.

min_tss

Algorithms with a cross-validated TSS below this get no weight.

ntree, mtry

Random forest size and variables tried at each split (default: square root of the number of predictors).

seed

Random seed for the folds and the forest.

...

Passed on to sdm_maxent().

object

An ensemble from sdm_ensemble().

newdata

Data frame or SpatRaster of predictors.

what

"mean" (weighted ensemble), "sd" (weighted standard deviation across algorithms), "all" (every algorithm and both summaries).

Value

sdm_ensemble(): an object of class tmr_sdm_ensemble, with scores (a tibble of AUC, TSS and Boyce index per algorithm and fold), summary (mean scores and the ensemble weight of each algorithm) and the models fitted on all data. predict(): a numeric vector, data frame or SpatRaster.

References

Barbet-Massin M, Jiguet F, Albert CH, Thuiller W (2012) Selecting pseudo-absences for species distribution models: how, where and how many? Methods in Ecology and Evolution 3:327-338.

Hirzel AH, Le Lay G, Helfer V, Randin C, Guisan A (2006) Evaluating the ability of habitat suitability models to predict species presences. Ecological Modelling 199:142-152.

Roberts DR et al. (2017) Cross-validation strategies for data with temporal, spatial, hierarchical, or phylogenetic structure. Ecography 40:913-929.

Thuiller W, Lafourcade B, Engler R, Araujo MB (2009) BIOMOD: a platform for ensemble forecasting of species distributions. Ecography 32:369-373.

Valavi R, Elith J, Lahoz-Monfort JJ, Guillera-Arroita G (2021) Modelling species presence-only data with random forests. Ecography 44:1731-1742.

See also

sdm_maxent().

Examples

# Brown-throated sloth (Phillips et al. 2006)
data(bradypus, package = "maxnet")
# \donttest{
ens <- sdm_ensemble(bradypus$presence, bradypus[, c(2, 3, 5:15)],
  algorithms = c("maxent", "glm", "rf"), folds = 4, ntree = 200
)
ens
#> SDM ensemble of 3 algorithms: 116 presences, 1000 background points, 4 random
#> folds.
#> # A tibble: 3 × 5
#>   algorithm   auc   tss boyce weight
#>   <chr>     <dbl> <dbl> <dbl>  <dbl>
#> 1 maxent    0.883 0.657 0.876  0.374
#> 2 glm       0.828 0.552 0.788  0.264
#> 3 rf        0.894 0.647 0.891  0.363
# }