Author: Flávio M. M. Mota, Neander M. Heming, and Gabriela Alves-Ferreira
Date: 2023-10-10

# divraster-vignette

#### Flávio M. M. Mota, Neander M. Heming, and Gabriela Alves-Ferreira

#### 2023-10-10

- 1 Introduction
- 2 Alpha diversity
  - 2.1 Alpha examples
    - 2.1.1 Alpha TD
    - 2.1.2 Alpha FD
    - 2.1.3 Alpha PD
- 3 Standardized effect size (SES)
  - 3.1 SES examples
    - 3.1.1 SES FD
    - 3.1.2 SES PD
- 4 Beta diversity
  - 4.1 Beta examples
    - 4.1.1 Beta spatial TD
    - 4.1.2 Beta spatial FD
    - 4.1.3 Beta spatial PD
    - 4.1.4 Beta temporal TD
    - 4.1.5 Beta temporal FD
    - 4.1.6 Beta temporal PD
- 5 Traits average
  - 5.1 Traits average examples

## 1 Introduction

Macroecological studies have been increasingly utilized in the context of climate change, necessitating the use of tools to analyze large datasets. To examine and comprehend the intricate mechanisms that underlie species distributions and the structure of biological communities, a diverse array of metrics has been developed. These metrics encompass alpha and beta diversity patterns across taxonomic (TD), functional (FD), and phylogenetic (PD) dimensions. The package `divraster` addresses a current gap in this field by offering functions to calculate diversity metrics directly from rasters, eliminating the need for matrix transformations. This capability is especially valuable when dealing with extensive datasets, as matrices often impose memory constraints.

## 2 Alpha calculations

Alpha diversity calculations use a tree-based approach for taxonomic (TD), functional (FD), and phylogenetic (PD) diversity. In the FD calculation, a species traits matrix is converted into a distance matrix and clustered to produce a regional dendrogram (i.e. a dendrogram with all species in the raster stack) from which the total branch length is calculated. When calculating FD for each community (i.e. raster cell), the regional dendrogram is subsetted into a local dendrogram containing only the species present on the local community, and only the branch lengths connecting them are summed to represent the functional relationships of the species locally present. Similarly, in PD, the sum of branch lengths connecting species within a community represents their shared phylogenetic relationships and cumulative evolutionary history. Alpha TD can also be visualized using a tree diagram, where each species is directly connected to the root by an edge of unit length, reflecting the number of different taxa in the community (i.e. species richness) since all taxa are at the same level.

## 2.1 Alpha examples

## 2.1.1 Alpha TD

    # Loading data
    # Presence-absence SpatRaster
    bin1 <- terra::rast(system.file("extdata",
                                    "ref_frugivor.tif",
                                    package = "divraster"))
    bin2 <- terra::rast(system.file("extdata",
                                    "fut_frugivor.tif",
                                    package = "divraster"))

    # Change extension to process faster
    terra::ext(bin1)
    #> SpatExtent : -41.875, -38.75, -21.375, -13 (xmin, xmax, ymin, ymax)
    e <- c(-41, -39, -15, -13)
    bin1 <- terra::crop(bin1, e)
    bin2 <- terra::crop(bin2, e)

    # Species traits
    traits <- read.csv(system.file("extdata",
                                   "traits_frugivor.csv",
                                   package = "divraster"),
                       sep = ";",
                       row.names = 1)

    # Phylogenetic tree
    tree <- ape::read.tree(system.file("extdata",
                                       "tree_frugivor.tre",
                                       package = "divraster"))

    # Alpha TD calculation for scenario 1
    alpha.td <- divraster::spat.alpha(bin1)
    alpha.td
    #> class       : SpatRaster
    #> dimensions  : 16, 16, 1  (nrow, ncol, nlyr)
    #> resolution  : 0.125, 0.125  (x, y)
    #> extent      : -41, -39, -15, -13  (xmin, xmax, ymin, ymax)
    #> coord. ref. : lon/lat WGS 84 (EPSG:4326)
    #> source(s)   : memory
    #> name        : Alpha_TD
    #> min value   :        0
    #> max value   :       67
    terra::plot(alpha.td, main = paste0(names(alpha.td), "_sce1"))

    # Alpha TD calculation for scenario 2
    alpha.td2 <- divraster::spat.alpha(bin2)
    alpha.td2
    #> class       : SpatRaster
    #> dimensions  : 16, 16, 1  (nrow, ncol, nlyr)
    #> resolution  : 0.125, 0.125  (x, y)
    #> extent      : -41, -39, -15, -13  (xmin, xmax, ymin, ymax)
    #> coord. ref. : lon/lat WGS 84 (EPSG:4326)
    #> source(s)   : memory
    #> name        : Alpha_TD
    #> min value   :        0
    #> max value   :       65
    terra::plot(alpha.td2, main = paste0(names(alpha.td2), "_sce2"))

    # Difference in Alpha TD between scenarios
    alpha.td2-alpha.td
    #> class       : SpatRaster
    #> dimensions  : 16, 16, 1  (nrow, ncol, nlyr)
    #> resolution  : 0.125, 0.125  (x, y)
    #> extent      : -41, -39, -15, -13  (xmin, xmax, ymin, ymax)
    #> coord. ref. : lon/lat WGS 84 (EPSG:4326)
    #> source(s)   : memory
    #> name        : Alpha_TD
    #> min value   :      -18
    #> max value   :        0
    terra::plot(alpha.td2-alpha.td, main = "Delta Alpha TD")

The alpha taxonomic diversity in the first scenario ranges from 0 to 67, and in the second scenario, it ranges from 0 to 65, with higher values concentrated towards the north in both cases. When comparing the two scenarios, subtracting the second from the first reveals greater species losses (n = 18) towards the south.

## 2.1.2 Alpha FD

    alpha.fd <- divraster::spat.alpha(bin1, traits)
    alpha.fd
    #> class       : SpatRaster
    #> dimensions  : 16, 16, 1  (nrow, ncol, nlyr)
    #> resolution  : 0.125, 0.125  (x, y)
    #> extent      : -41, -39, -15, -13  (xmin, xmax, ymin, ymax)
    #> coord. ref. : lon/lat WGS 84 (EPSG:4326)
    #> source(s)   : memory
    #> name        : Alpha_FD
    #> min value   : 3.723151
    #> max value   : 4.378846
    terra::plot(alpha.fd, main = names(alpha.fd))

The alpha functional diversity for the first scenario ranges from 3.7 to 4.4, with higher values concentrated towards the north, indicating greater functional diversity.

## 2.1.3 Alpha PD

    # Alpha PD calculation
    alpha.pd <- divraster::spat.alpha(bin1, tree)
    alpha.pd
    #> class       : SpatRaster
    #> dimensions  : 16, 16, 1  (nrow, ncol, nlyr)
    #> resolution  : 0.125, 0.125  (x, y)
    #> extent      : -41, -39, -15, -13  (xmin, xmax, ymin, ymax)
    #> coord. ref. : lon/lat WGS 84 (EPSG:4326)
    #> source(s)   : memory
    #> name        : Alpha_PD
    #> min value   : 1523.921
    #> max value   : 1859.668
    terra::plot(alpha.pd, main = names(alpha.pd))

The alpha phylogenetic diversity for the first scenario ranges from 1524 to 1860, with higher values concentrated towards the north, indicating greater phylogenetic diversity.

## 3 Standardized effect size (SES)

SES is often used in ecological studies to measure the magnitude of difference between observed and randomized patterns generated by null models, expressed in standard deviation units. We calculate SES using the `SESraster` package, which currently offers six community randomization methods. The basic randomization methods include: keeping the richness constant and randomizing the position of the species within each raster cell (site), keeping range size constant and randomizing the position of species presences in space (species), and randomizing by both site and species simultaneously (both). A positive SES indicates that the observed functional/phylogenetic diversity is higher than expected solely based on species richness (taxonomic diversity), whereas a negative SES indicates the opposite.

## 3.1 SES examples

## 3.1.1 SES FD

    # SES FD calculation
    ses.fd <- divraster::spat.rand(x = bin1,
                                   tree = traits,
                                   aleats = 3,
                                   random = "site")
    ses.fd
    #> class       : SpatRaster
    #> dimensions  : 16, 16, 4  (nrow, ncol, nlyr)
    #> resolution  : 0.125, 0.125  (x, y)
    #> extent      : -41, -39, -15, -13  (xmin, xmax, ymin, ymax)
    #> coord. ref. : lon/lat WGS 84 (EPSG:4326)
    #> source(s)   : memory
    #> names       :  Mean_FD,       SD_FD, Observed_FD,     SES_FD
    #> min values  : 3.746346, 0.001949611,    3.723151, -13.824157
    #> max values  : 4.428789, 0.186786901,    4.378846,   6.079558
    terra::plot(ses.fd, main = names(ses.fd))

The SES indicates that the majority of the areas have values close to 0, suggesting that functional diversity does not significantly differ from the expected change. However, one community is projected to be functionally dispersed (SES_FD = 31), while another community is projected to be functionally clustered (SES_FD = -39). This indicates an increase and decrease in functional diversity within these communities from scenarios 1 to 2, respectively.

## 3.1.2 SES PD

    # SES PD calculation
    ses.pd <- divraster::spat.rand(x = bin1,
                                   tree = tree,
                                   aleats = 3,
                                   random = "site")
    ses.pd
    #> class       : SpatRaster
    #> dimensions  : 16, 16, 4  (nrow, ncol, nlyr)
    #> resolution  : 0.125, 0.125  (x, y)
    #> extent      : -41, -39, -15, -13  (xmin, xmax, ymin, ymax)
    #> coord. ref. : lon/lat WGS 84 (EPSG:4326)
    #> source(s)   : memory
    #> names       :  Mean_PD,      SD_PD, Observed_PD,    SES_PD
    #> min values  : 1573.836,  0.5760814,    1623.451, -28.19974
    #> max values  : 1875.329, 82.6070674,    1880.676,  14.05786
    terra::plot(ses.pd, main = names(ses.pd))

Similarly, the SES for phylogenetic diversity does not differ from what is expected by chance, with most communities presenting values close to 0. However, one community is projected to be phylogenetically dispersed (SES_PD = 10), while another community is projected to be phylogenetically clustered (SES_FD = -15). This indicates an increase and decrease in phylogenetic diversity within these communities from scenarios 1 to 2, respectively.

## 4 Beta diversity

Beta diversity captures variations in species composition between different communities. When examining a community in comparison to its neighboring ones, it is referred to as spatial beta diversity. On the other hand, when assessing changes within the same community over different time periods, it is termed temporal beta diversity. Beta diversity can further be partitioned into two components: “replacement” and “richness differences”. The former accounts for the substitution of one species with another, while the latter encompasses discrepancies in the total number of species (e.g. species gain or loss). In addition, since Btotal represents the sum of Brepl and Brich components, the proportion of Brepl/Btotal (Bratio) can be calculated, with values close to 0 indicating the predominance of Brich and values close to 1 indicating the predominance of Brepl. Moreover, the concept of beta diversity extends to functional (FD) and phylogenetic diversity (PD), using the same framework as taxonomic diversity (TD). In the context of TD, higher beta diversity represents higher dissimilarities in species composition between communities. In contrast, for FD, it indicates higher dissimilarities in functional traits, and for PD, it reflects higher dissimilarities in phylogenetic relationships of species between communities.

## 4.1 Beta examples

## 4.1.1 Beta spatial TD

    # Beta spatial TD calculation
    beta.td <- divraster::spat.beta(bin1)
    beta.td
    #> class       : SpatRaster
    #> dimensions  : 16, 16, 4  (nrow, ncol, nlyr)
    #> resolution  : 0.125, 0.125  (x, y)
    #> extent      : -41, -39, -15, -13  (xmin, xmax, ymin, ymax)
    #> coord. ref. : lon/lat WGS 84 (EPSG:4326)
    #> source(s)   : memory
    #> names       :   Btotal_TD,   Brepl_TD,    Brich_TD, Bratio_TD
    #> min values  : 0.006060606, 0.00000000, 0.004264392, 0.0000000
    #> max values  : 0.109409606, 0.03638009, 0.103181683, 0.7259259
    terra::plot(beta.td, main = names(beta.td))

Spatial beta diversity for TD indicates a slight change in species composition towards the south, as evidenced by the small values of Btotal (~0.1). The predominant component contributing to this change is the richness difference (Brich), suggesting that dissimilarities between each community (i.e. pixel) and its neighbors are primarily due to the loss or gain of species. The Bratio also indicates the predominance of Birch component in most communities.

## 4.1.2 Beta spatial FD

    # Beta spatial FD calculation
    beta.fd <- divraster::spat.beta(bin1, traits)
    beta.fd
    #> class       : SpatRaster
    #> dimensions  : 16, 16, 4  (nrow, ncol, nlyr)
    #> resolution  : 0.125, 0.125  (x, y)
    #> extent      : -41, -39, -15, -13  (xmin, xmax, ymin, ymax)
    #> coord. ref. : lon/lat WGS 84 (EPSG:4326)
    #> source(s)   : memory
    #> names       :    Btotal_FD,   Brepl_FD,     Brich_FD, Bratio_FD
    #> min values  : 0.0004245858, 0.00000000, 0.0004245858,  0.000000
    #> max values  : 0.0793045655, 0.01846139, 0.0793045655,  0.756675
    terra::plot(beta.fd, main = names(beta.fd))

Similarly, spatial beta diversity for FD indicates a slight change in functional traits composition towards the south, as evidenced by the small values of Btotal (~0.08). The predominant component contributing to this little change is the richness difference (Brich), suggesting that dissimilarities between each community (i.e. pixel) and its neighbors are primarily due to the loss or gain of functional traits. The Bratio also indicates the predominance of Birch component in most communities.

## 4.1.3 Beta spatial PD

    # Beta spatial PD calculation
    beta.pd <- divraster::spat.beta(bin1, tree)
    beta.pd
    #> class       : SpatRaster
    #> dimensions  : 16, 16, 4  (nrow, ncol, nlyr)
    #> resolution  : 0.125, 0.125  (x, y)
    #> extent      : -41, -39, -15, -13  (xmin, xmax, ymin, ymax)
    #> coord. ref. : lon/lat WGS 84 (EPSG:4326)
    #> source(s)   : memory
    #> names       :   Btotal_PD,    Brepl_PD,    Brich_PD, Bratio_PD
    #> min values  : 0.002851805, 0.000000000, 0.001618621, 0.0000000
    #> max values  : 0.059656685, 0.008026876, 0.059656685, 0.8250616
    terra::plot(beta.pd, main = names(beta.pd))

The spatial beta diversity for PD indicates a slight change in the evolutionary history of communities towards the south. However this change is even lower compared to TD and FD, as evidenced by the smallest values of Btotal (~0.06). The predominant component contributing to this little change is also the richness difference (Brich), suggesting that dissimilarities between each community (i.e. pixel) and its neighbors are due to the loss or gain of evolutionary history. The Bratio also indicates the predominance of Birch component in most communities.

## 4.1.4 Beta temporal TD

    # Beta temporal TD calculation
    betatemp.td <- divraster::temp.beta(bin1, bin2)
    betatemp.td
    #> class       : SpatRaster
    #> dimensions  : 16, 16, 4  (nrow, ncol, nlyr)
    #> resolution  : 0.125, 0.125  (x, y)
    #> extent      : -41, -39, -15, -13  (xmin, xmax, ymin, ymax)
    #> coord. ref. : lon/lat WGS 84 (EPSG:4326)
    #> source(s)   : memory
    #> names       :  Btotal_TD,   Brepl_TD,   Brich_TD, Bratio_TD
    #> min values  : 0.02985075, 0.00000000, 0.02985075, 0.0000000
    #> max values  : 0.31578947, 0.09836066, 0.31578947, 0.6666667
    terra::plot(betatemp.td, main = names(betatemp.td))

The temporal beta diversity for TD indicates that future communities are expected to experience changes in their species composition, predominantly towards the south, with Btotal reaching approximately 0.3. The predominance of the Brich component suggests that these dissimilarities are attributed to gains or losses of species. The Bratio also indicates the predominance of Birch component in most communities.

## 4.1.5 Beta temporal FD

    # Beta temporal FD calculation
    betatemp.fd <- divraster::temp.beta(bin1, bin2, traits)
    betatemp.fd
    #> class       : SpatRaster
    #> dimensions  : 16, 16, 4  (nrow, ncol, nlyr)
    #> resolution  : 0.125, 0.125  (x, y)
    #> extent      : -41, -39, -15, -13  (xmin, xmax, ymin, ymax)
    #> coord. ref. : lon/lat WGS 84 (EPSG:4326)
    #> source(s)   : memory
    #> names       :  Btotal_FD,   Brepl_FD,   Brich_FD, Bratio_FD
    #> min values  : 0.01733908, 0.00000000, 0.01012696, 0.0000000
    #> max values  : 0.17193290, 0.03741327, 0.17193290, 0.6872465
    terra::plot(betatemp.fd, main = names(betatemp.fd))

The temporal beta diversity for FD indicates a less pronounced pattern compared to TD, with smaller values of Btotal, reaching a maximum of only 0.17. The Brich component is also predominant, suggesting that the small dissimilarities can be attributed to gains or losses of functional traits. The Bratio also indicates the predominance of Birch component in most communities.

## 4.1.6 Beta temporal PD

    # Beta temporal PD calculation
    betatemp.pd <- divraster::temp.beta(bin1, bin2, tree)
    betatemp.pd
    #> class       : SpatRaster
    #> dimensions  : 16, 16, 4  (nrow, ncol, nlyr)
    #> resolution  : 0.125, 0.125  (x, y)
    #> extent      : -41, -39, -15, -13  (xmin, xmax, ymin, ymax)
    #> coord. ref. : lon/lat WGS 84 (EPSG:4326)
    #> source(s)   : memory
    #> names       : Btotal_PD,  Brepl_PD,    Brich_PD, Bratio_PD
    #> min values  : 0.0120217, 0.0000000, 0.009533166, 0.0000000
    #> max values  : 0.1792291, 0.0394096, 0.179229119, 0.7759122
    terra::plot(betatemp.pd, main = names(betatemp.pd))

Likewise, the temporal beta diversity for PD indicates a less pronounced pattern compared to TD, with smaller values of Btotal, reaching a maximum of only 0.18. The Brich component is also predominant, suggesting that the small dissimilarities can be attributed to gains or losses of evolutionary history. The Bratio also indicates the predominance of Birch component in most communities.

## 5 Traits average

Calculating the average traits of species for each climate scenario enables the evaluation of species traits that contribute the most to the loss of suitable habitat. Unlike functional diversity, which combines functional traits into an index, this approach provides direct insight into spatial variations in average traits. This information can complement the data necessary for delineating conservation priority areas, as shifts in average traits—whether increasing or decreasing—indicate the potential loss of species with specific features. This is of particular significance given that functional traits are closely tied to the ecological services provided by species.

## 5.1 Traits average examples

    # Average traits calculation
    # Scenario 1
    avg.traits1 <- divraster::spat.trait(bin1, traits)
    avg.traits1[[4]]
    #> class       : SpatRaster
    #> dimensions  : 16, 16, 1  (nrow, ncol, nlyr)
    #> resolution  : 0.125, 0.125  (x, y)
    #> extent      : -41, -39, -15, -13  (xmin, xmax, ymin, ymax)
    #> coord. ref. : lon/lat WGS 84 (EPSG:4326)
    #> source(s)   : memory
    #> name        : Beak.Depth
    #> min value   :   8.526923
    #> max value   :   9.601515
    terra::plot(avg.traits1[[4]], main = paste0(names(avg.traits1[[4]]), "_sce1"))

    # Scenario 2
    avg.traits2 <- divraster::spat.trait(bin2, traits)
    avg.traits2[[4]]
    #> class       : SpatRaster
    #> dimensions  : 16, 16, 1  (nrow, ncol, nlyr)
    #> resolution  : 0.125, 0.125  (x, y)
    #> extent      : -41, -39, -15, -13  (xmin, xmax, ymin, ymax)
    #> coord. ref. : lon/lat WGS 84 (EPSG:4326)
    #> source(s)   : memory
    #> name        : Beak.Depth
    #> min value   :   8.786792
    #> max value   :   9.942308
    terra::plot(avg.traits2[[4]], main = paste0(names(avg.traits2[[4]]), "_sce2"))

    # Percentage of change
    change.traits <- (avg.traits2 - avg.traits1) / avg.traits1 * 100
    change.traits[[4]]
    #> class       : SpatRaster
    #> dimensions  : 16, 16, 1  (nrow, ncol, nlyr)
    #> resolution  : 0.125, 0.125  (x, y)
    #> extent      : -41, -39, -15, -13  (xmin, xmax, ymin, ymax)
    #> coord. ref. : lon/lat WGS 84 (EPSG:4326)
    #> source(s)   : memory
    #> name        : Beak.Depth
    #> min value   :  -4.495893
    #> max value   :  13.541296
    terra::plot(change.traits[[4]], main = paste0(names(change.traits[[4]]), "_%"))

The average beak depth in the first scenario ranges from 8.5 to 9.6, while in the second scenario, it ranges from 8.8 to 9.9. Beak depth increased by 13.5% in the southern region but decreased by 4.5% in the central region. The earlier analysis indicated a prevalence of species loss, implying that the rise in average beak depth in the second scenario can be attributed to the decline of species with smaller beak depths. Conversely, the reduction in beak size can be attributed to the decline of species with larger beak depths.