# Cross-mapping biodiversity metrics across spaces

#### Bruno Vilela

#### 2025-07-07

## Overview

This vignette demonstrates cross-mapping of biodiversity metrics between environmental, geographic, and attribute (trait) spaces using `letsR`. We:

1. Build an environmental-space PAM from Phyllomedusa data;
2. Compute per-cell descriptors in environmental space;
3. Summarize those descriptors to species level; and
4. Project (cross-map) a chosen environmental metric into geographic and attribute spaces via the package connectors.

## Data and environmental PAM (example with Phyllomedusa)

First we create a geographic and environmental PAM as described in previous articles.

    library(letsR)

    # Occurrences and climate
    data("Phyllomedusa"); data("prec"); data("temp")
    prec <- terra::unwrap(prec); temp <- terra::unwrap(temp)

    # Geographic PAM (keep empty cells)
    PAM  <- lets.presab(Phyllomedusa, remove.cells = FALSE)

    # Keep terrestrial landmasses for plotting and binning consistency
    wrld_simpl <- get(utils::data("wrld_simpl", package = "letsR"))
    PAM <- lets.pamcrop(PAM, terra::vect(wrld_simpl))

    # Environmental variables matrix (per geographic cell)
    envs <- lets.addvar(PAM, c(temp, prec), onlyvar = TRUE)
    colnames(envs) <- c("Temperature", "Precipitation")

    # Environmental-space PAM (envPAM)
    env_obj <- lets.envpam(PAM, envs, n_bins = 30, remove.cells = FALSE)

    # Plot
    lets.plot.envpam(env_obj, world = TRUE)

## Environmental descriptors per environmental cell

    # Compute env-space descriptors (centrality, border, isolation, etc.)
    env_cells <- lets.envcells(env_obj, perc = 0.2)

    head(env_cells)
    #>   Cell_env Frequency Area Isolation (Min.) Isolation (1st Qu.)
    #> 1        1         0   NA               NA                  NA
    #> 2        2         0   NA               NA                  NA
    #> 3        3         0   NA               NA                  NA
    #> 4        4         0   NA               NA                  NA
    #> 5        5         0   NA               NA                  NA
    #> 6        6         0   NA               NA                  NA
    #>   Isolation (Median) Isolation (Mean) Isolation (3rd Qu.) Isolation (Max.)
    #> 1                 NA               NA                  NA               NA
    #> 2                 NA               NA                  NA               NA
    #> 3                 NA               NA                  NA               NA
    #> 4                 NA               NA                  NA               NA
    #> 5                 NA               NA                  NA               NA
    #> 6                 NA               NA                  NA               NA
    #>   Weighted Mean Distance to midpoint Mean Distance to midpoint
    #> 1                          -3.730908                 -3.457246
    #> 2                          -3.646836                 -3.382386
    #> 3                          -3.564523                 -3.309862
    #> 4                          -3.484092                 -3.239832
    #> 5                          -3.405677                 -3.172460
    #> 6                          -3.329421                 -3.107918
    #>   Minimum Zero Distance Minimum 20% Zero Distance Distance to MCP border
    #> 1                     0                 0.9362266                      0
    #> 2                     0                 0.8700119                      0
    #> 3                     0                 0.8136812                      0
    #> 4                     0                 0.7676179                      0
    #> 5                     0                 0.7323872                      0
    #> 6                     0                 0.7068043                      0
    #>   Frequency Weighted Distance
    #> 1                    3.800462
    #> 2                    3.718461
    #> 3                    3.638213
    #> 4                    3.559825
    #> 5                    3.483411
    #> 6                    3.409092

Summarize those per-cell descriptors to species level by aggregating across the environmental cells each species occupies:

    # Species-level summaries (e.g., mean across occupied env cells)
    env_by_species <- lets.summaryze.cells(env_obj, env_cells, func = mean)

    head(env_by_species)
    #>                    Species Frequency         Area Isolation (Min.)
    #> 1    Phyllomedusa araguari   9.00000  99942160705         97052.27
    #> 2 Phyllomedusa atelopoides  25.38889 310216725731        109736.78
    #> 3      Phyllomedusa ayeaye  11.50000 129979311887         99631.44
    #> 4      Phyllomedusa azurea  11.59091 137178852573        130717.35
    #> 5     Phyllomedusa bahiana  11.91667 142112800724        136522.70
    #> 6      Phyllomedusa baltea  19.00000 233017982880        110574.31
    #>   Isolation (1st Qu.) Isolation (Median) Isolation (Mean) Isolation (3rd Qu.)
    #> 1            494018.8           767952.4         747035.8            923841.2
    #> 2            593524.1          1109618.7        1175110.9           1714363.8
    #> 3            384047.4           599271.8         667315.7            851729.1
    #> 4            462970.6          1391519.0        1328709.9           2016286.4
    #> 5            463613.5          1492534.7        1354451.4           2121714.6
    #> 6            611182.1          1019632.7        1201164.4           1896221.5
    #>   Isolation (Max.) Weighted Mean Distance to midpoint Mean Distance to midpoint
    #> 1          1500329                         -0.3188860                -0.1627780
    #> 2          3008424                         -0.6007348                -1.0114155
    #> 3          1725300                         -0.3310414                -0.1608610
    #> 4          3035828                         -0.4455612                -0.7009224
    #> 5          2999208                         -0.4520640                -0.6818815
    #> 6          2950964                         -0.6779813                -1.0585809
    #>   Minimum Zero Distance Minimum 20% Zero Distance Distance to MCP border
    #> 1             0.2581989                 0.9296124              0.2581989
    #> 2             0.3258642                 1.0476293              0.3258642
    #> 3             0.3116736                 0.9521703              0.3116736
    #> 4             0.3197515                 1.2125076              0.3197515
    #> 5             0.2641105                 1.2398626              0.2641105
    #> 6             0.2581989                 0.9893314              0.2581989
    #>   Frequency Weighted Distance
    #> 1                   0.7555036
    #> 2                   0.7967939
    #> 3                   0.7590072
    #> 4                   0.7875067
    #> 5                   0.7752855
    #> 6                   0.8278369

We will use one metric from `env_by_species`(for example, “Weighted Mean Distance to midpoint”) for cross-mapping.

## Attribute-space PAM for Phyllomedusa species

We create a trait grid (attribute space) by simulating two quantitative traits for the species present in our PAM. (Replace with real traits if available.)

    set.seed(123)
    sp_vec   <- env_by_species$Species                    # species present in PAM
    n_sp     <- length(sp_vec)
    trait_a  <- rnorm(n_sp)
    trait_b  <- trait_a * 0.2 + rnorm(n_sp)               # correlated trait

    attr_df  <- data.frame(Species = sp_vec,
                           trait_a  = trait_a,
                           trait_b  = trait_b)

    # Attribute-space PAM (AttrPAM)
    attr_obj <- lets.attrpam(attr_df, n_bins = 5)

    # Richness map in attribute space
    lets.plot.attrpam(attr_obj)

## Cross-mapping an environmental metric into geographic and attribute spaces

### A. Into geographic space

Project environmental metric to geography:

    # Align env-cell descriptors to the order of geographic rows
    env_cells_geo <- env_cells[ env_obj$Presence_and_Absence_Matrix_geo[, 1], ]

    # Template = geographic richness raster
    map_richatt2 <- env_obj$Geo_Richness_Raster
    terra::values(map_richatt2) <- NA

    # Fill geographic cells with the env-space metric (species-level NOT needed here)
    terra::values(map_richatt2)[ env_obj$Presence_and_Absence_Matrix_geo[, 2] ] <-
      env_cells_geo$`Weighted Mean Distance to midpoint`

    # Palette and plot
    colfunc <- grDevices::colorRampPalette(c("#fff5f0", "#fb6a4a", "#67000d"))
    plot(map_richatt2, col = colfunc(200), box = FALSE, axes = FALSE,
         main = "Env centrality (env-space) mapped to geography")

### B. Into attribute space

Map the same environmental metric (species-level) into the attribute grid:

    met_env <- env_by_species$`Weighted Mean Distance to midpoint`
    sp_names <- env_by_species$Species

    attr_map <- lets.maplizer.attr(attr_obj, y = met_env, z = sp_names, func = mean)

    # Visualize
    lets.plot.attrpam(attr_map, mar = c(4,4,4,4))

These projections reveal how a descriptor computed in environmental space (centrality) distributes across geographic communities and trait space.

## Cross-mapping attribute metrics back to geography

You can compute attribute-space descriptors with `lets.attrcells(attr_obj, ...)`, summarize them to species with `lets.summarizer.cells(attr_obj, ...)`, and then project those species-level metrics to geographic or environmental spaces using `lets.maplizer(...)` or `lets.maplizer.env(...)`.

    # Attribute-space descriptors per cell
    attr_cells <- lets.attrcells(attr_obj, perc = 0.2)

    # Species-level summaries of attribute-space descriptors
    attr_by_species <- lets.summaryze.cells(attr_obj, attr_cells, func = mean)

    # Example: map an attribute-space centrality back to geography
    met_attr <- attr_by_species$`Weighted Mean Distance to midpoint`
    geo_from_attr <- lets.maplizer(PAM, y = met_attr, z = attr_by_species$Species, ras = TRUE)

    plot(geo_from_attr$Raster, main = "Attr centrality mapped to geography", col = colfunc(200))