Author: Roozbeh Valavi, Jane Elith, José Lahoz-Monfort and Gurutzeta Guillera-Arroita
Date: 2024-05-23

# 2. Block cross-validation for species distribution modelling

#### Roozbeh Valavi, Jane Elith, José Lahoz-Monfort and Gurutzeta Guillera-Arroita

#### 2024-05-23

## Introduction

Species distribution models (SDMs) are widely used tools for predicting the potential distribution of a species based on environmental variables. However, it is crucial to evaluate the performance of these models to ensure their accuracy and reliability. One commonly used method for evaluating the performance of SDMs is block cross-validation (read more in Valavi et al. 2019 and the Tutorial 1). This approach allows for a more robust evaluation of the model as it accounts for spatial autocorrelation and other spatial dependencies (Roberts et al. 2017). This document illustrates how to utilize the `blockCV` package to evaluate the performance of SDMs using block cross-validation.

Two examples are provided: modelling using the `randomForest`, and `biomod2` packages.

Check new updates of `blockCV` in the tutorial 1- blockCV introduction: how to create block cross-validation folds.

Please cite `blockCV` by: Valavi R, Elith J, Lahoz-Monfort JJ, Guillera-Arroita G. blockCV: An R package for generating spatially or environmentally separated folds for k-fold cross-validation of species distribution models. Methods Ecol Evol. 2019; 10:225–232. doi: 10.1111/2041-210X.13107

## Reading and plotting data

The `blockCV` package contains the raw format of the following data:

- Raster covariates of Australia (`.tif`)
- Simulated species data (`.csv`)

These data are used to illustrate how the package is used. The raster data include several bioclimatic variables for Australia. The species data include presence-absence records (binary) of a simulated species.

To load the package raster data use:

    library(sf) # working with spatial vector data
    library(terra) # working with spatial raster data
    library(tmap) # plotting maps

    # load raster data
    # the pipe operator |> is available for R version 4.1 or higher
    rasters <- system.file("extdata/au/", package = "blockCV") |>
      list.files(full.names = TRUE) |>
      terra::rast()

The presence-absence species data include `243` presence points and `257` absence points.

    # load species presence-asence data and convert to sf
    points <- read.csv(system.file("extdata/", "species.csv", package = "blockCV"))
    head(points)

    ##            x        y occ
    ## 1  1313728.4 -2275453   0
    ## 2  1176795.0 -1916003   0
    ## 3 -1741599.3 -3927213   1
    ## 4  1099769.9 -4124055   1
    ## 5  1279495.1 -3901538   0
    ## 6   928603.1 -1342594   0

The appropriate format of species data for the `blockCV` package is simple features (from the `sf` package). The data is provide in GDA2020 / GA LCC coordinate reference system with `"EPSG:7845"` as defined by `crs = 7845`. We convert the `data.frame` to `sf` as follows:

    pa_data <- sf::st_as_sf(points, coords = c("x", "y"), crs = 7845)

Let’s plot the species data using `tmap` package:

    tm_shape(rasters[[1]]) +
      tm_raster(legend.show = FALSE, n = 30, palette = gray.colors(10)) +
      tm_shape(pa_data) +
      tm_dots(col = "occ", style = "cat", size = 0.1)

# Generating block CV folds

Here, we generate two CV strategies, one k-fold CV using `cv_spatial` and one LOO CV using `cv_nndm`. See more options and configurations in the Tutorial 1 - introduction to `blockCV`.

    library(blockCV)

Creating spatial blocks:

    scv1 <- cv_spatial(
      x = pa_data,
      column = "occ", # the response column (binary or multi-class)
      r = rasters,
      k = 5, # number of folds
      size = 360000, # size of the blocks in metres
      selection = "random", # random blocks-to-fold
      iteration = 50, # find evenly dispersed folds
      progress = FALSE, # turn off progress bar
      biomod2 = TRUE, # also create folds for biomod2
      raster_colors = terrain.colors(10, rev = TRUE) # options from cv_plot for a better colour contrast
    )

    ##
    ##   train_0 train_1 test_0 test_1
    ## 1     204     166     53     77
    ## 2     209     218     48     25
    ## 3     214     187     43     56
    ## 4     200     191     57     52
    ## 5     201     210     56     33

Now, let’s create LOO CV folds with nearest neighbour distance matching (NNDM; Milà et al. 2022) algorithm. To run `cv_nndm`, you need a measure of spatial autocorrelation present in your data. This can be done wither by 1) fitting a model and use it’s residual to calculate spatial autocorrelation, or 2) use the autocorrelation of response variable for it (Milà et al, 2022; Roberts et al. 2017). Here, we calculate spatial autocorrelation range in the response using the `cv_spatial_autocor` function.

    range <- cv_spatial_autocor(
      x = pa_data, # species data
      column = "occ", # column storing presence-absence records (0s and 1s)
      plot = FALSE
    )

    range$range

    ## [1] 362036

So the range of spatial autocorrelation is roughly `360` kilometres.

    scv2 <- cv_nndm(
      x = pa_data,
      column = "occ",
      r = rasters,
      size = 360000, # range of spatial autocorrelation
      num_sample = 10000, # number of samples of prediction points
      sampling = "regular", # sampling methods; it can be random as well
      min_train = 0.1, # minimum portion to keep in each train fold
      plot = TRUE
    )

    ##     train_0         train_1          test_0          test_1
    ##  Min.   :210.0   Min.   :145.0   Min.   :0.000   Min.   :0.000
    ##  Mean   :244.4   Mean   :221.5   Mean   :0.514   Mean   :0.486
    ##  Max.   :257.0   Max.   :243.0   Max.   :1.000   Max.   :1.000

You can visualise the generated folds of both methods using `cv_plot` function. Here is three folds from the `cv_nndm` object:

    # see the number of folds in scv2 object
    scv2$k

    ## [1] 500

    cv_plot(
      cv = scv2, # cv object
      x = pa_data, # species spatial data
      num_plots = c(1, 10, 100) # three of folds to plot
    )

## Evaluating SDMs with block cross-validation: examples

In this section, we show how to use the folds generated by `blockCV` in the previous sections for the evaluation of SDMs constructed on the species data available in the package. The `blockCV` stores training and testing folds in three different formats. The common format for all three blocking strategies is a list of the indices of observations in each fold. For `cv_spatial` and `cv_cluster` (but not `cv_buffer` and `cv_nndm`), the folds are also stored in a matrix format suitable for the `biomod2` package and a vector of fold’s number for each observation. This is equal to the number of observation in species spatial data. These three formats are stored in the cv objects as `folds_list`, `biomod_table` and `folds_ids` respectively.

### Using `blockCV` with Random Forest model

Folds generated by `cv_nndm` function are used here (a training and testing fold for each record) to show how to use folds from this function (the `cv_buffer` is also similar to this approach) for evaluation species distribution models.

Note that with `cv_nndm` using presence-absence data (and any other type of data except for presence-background data when `presence_bg = TRUE` is used), there is only one point in each testing fold, and therefore AUC cannot be calculated for each fold separately. Instead, the value of each point is first predicted to the testing point (of each fold), and then a unique AUC is calculated for the full set of predictions.

    # loading the libraries
    library(randomForest)
    library(precrec)

    # extract the raster values for the species points as a dataframe
    model_data <- terra::extract(rasters, pa_data, df = TRUE, ID = FALSE)
    # adding species column to the dataframe
    model_data$occ <- as.factor(pa_data$occ)
    head(model_data)

    # extract the fold indices from buffering object
    # created in the previous section
    # the folds_list works for all four blocking strategies
    folds <- scv2$folds_list

    # create a data.frame to store the prediction of each fold (record)
    test_table <- pa_data
    test_table$preds <- NA

    for(k in seq_len(length(folds))){
      # extracting the training and testing indices
      # this way works with folds_list list (but not folds_ids)
      trainSet <- unlist(folds[[k]][1]) # training set indices; first element
      testSet <- unlist(folds[[k]][2]) # testing set indices; second element
      rf <- randomForest(occ ~ ., model_data[trainSet, ], ntree = 500) # model fitting on training set
      test_table$preds[testSet] <- predict(rf, model_data[testSet, ], type = "prob")[,2] # predict the test set
    }

    # calculate Area Under the ROC and PR curves and plot the result
    precrec_obj <- evalmod(scores = test_table$preds, labels = test_table$occ)
    auc(precrec_obj)

    ##   modnames dsids curvetypes      aucs
    ## 1       m1     1        ROC 0.8798258
    ## 2       m1     1        PRC 0.8734455

Plot the curves:

    library(ggplot2)

    autoplot(precrec_obj)

### Using `blockCV` in `biomod2` package

Package `biomod2` (Thuiller et al., 2017) is a commonly used platform for modelling species distributions in an ensemble framework. In this example, we show how to use `blockCV` folds in `biomod2`. In this example, the folds generated by `cv_spatial` is used to evaluate three modelling methods implemented in `biomod2`. The `CV.user.table` can be generated by both `cv_spatial` and `cv_cluster` functions and it is stored as `biomod_table` in their output objects (note: in the older versions of the `biomod2` package, the argument `data.split.table` was used for external CV folds. This has now changed to `CV.user.table` that also requires `CV.strategy = "user.defined"` and new column names. See the example below).

    # loading the library
    library(biomod2)

    # extract the raster values for the species points as a dataframe
    raster_values <- terra::extract(rasters, pa_data, df = TRUE, ID = FALSE)

    # 1. Formatting Data
    biomod_data <- BIOMOD_FormatingData(resp.var = pa_data$occ,
                                        expl.var = raster_values,
                                        resp.xy = sf::st_coordinates(pa_data),
                                        resp.name = "occ",
                                        na.rm = TRUE)

    # 2. Defining the folds for CV.user.table
    # note that biomod_table should be used here not folds
    # use generated folds from cv_spatial in previous section
    spatial_cv_folds <- scv1$biomod_table
    # the new update of the package biomod2 (v4.2-3 <) requires the names to be as below
    colnames(spatial_cv_folds) <- paste0("_allData_RUN", 1:ncol(spatial_cv_folds))

    # 3. Defining Models Options; using default options here. You can use your own settting here.
    biomod_options <- bm_ModelingOptions(data.type = "binary", strategy = "bigboss")

    # 4. Model fitting
    biomod_model_out <- BIOMOD_Modeling(biomod_data,
                                        models = c('GLM','MARS','GBM'),
                                        CV.strategy = "user.defined",
                                        CV.user.table   = spatial_cv_folds,
                                        OPT.user = biomod_options,
                                        var.import = 0,
                                        metric.eval = c('ROC'),
                                        do.full.models = TRUE)

    # 5. Model evaluation
    biomod_model_eval <- get_evaluations(biomod_model_out)
    biomod_model_eval[c("run", "algo", "metric.eval", "calibration", "validation")]

    ##     run algo metric.eval calibration validation
    ## 1  RUN1  GLM         ROC       0.921      0.878
    ## 2  RUN1 MARS         ROC       0.927      0.868
    ## 3  RUN1  GBM         ROC       0.972      0.914
    ## 4  RUN2  GLM         ROC       0.911      0.952
    ## 5  RUN2 MARS         ROC       0.916      0.941
    ## 6  RUN2  GBM         ROC       0.970      0.928
    ## 7  RUN3  GLM         ROC       0.921      0.889
    ## 8  RUN3 MARS         ROC       0.926      0.886
    ## 9  RUN3  GBM         ROC       0.974      0.899
    ## 10 RUN4  GLM         ROC       0.934      0.808
    ## 11 RUN4 MARS         ROC       0.941      0.833
    ## 12 RUN4  GBM         ROC       0.976      0.836
    ## 13 RUN5  GLM         ROC       0.906      0.934
    ## 14 RUN5 MARS         ROC       0.917      0.871
    ## 15 RUN5  GBM         ROC       0.973      0.886

The `validation` column shows the result of spatial cross-validation and each RUN is a CV fold.

## References:

- C. Milà, J. Mateu, E. Pebesma, and H. Meyer, Nearest Neighbour Distance Matching Leave-One-Out Cross-Validation for map validation, Methods in Ecology and Evolution (2022).

- Roberts, D.R., Bahn, V., Ciuti, S., Boyce, M.S., Elith, J., Guillera-Arroita, G., Hauenstein, S., Lahoz-Monfort, J.J., Schröder, B., Thuiller, W., others, 2017. Cross-validation strategies for data with temporal, spatial, hierarchical, or phylogenetic structure. Ecography. 40: 913-929.

- Thuiller W, Georges D, Guéguen M, Engler R, Breiner F, Lafourcade B, Patin R, Blancheteau H (2024). biomod2: Ensemble Platform for Species Distribution Modeling. R package version 4.2-5. https://CRAN.R-project.org/package=biomod2.

- Valavi R, Elith J, Lahoz-Monfort JJ, Guillera-Arroita G. blockCV: An R package for generating spatially or environmentally separated folds for k-fold cross-validation of species distribution models. Methods Ecol Evol. 2019; 10:225–232. doi: 10.1111/2041-210X.13107