Spatial Analysis: Endemism, Fragmentation, and SAR

Overview

spacc includes tools for conservation-oriented spatial analyses: endemism-area curves, fragmentation effects on species richness (SFAR), and sampling-effort correction for species-area relationships (SESARS).

Data Setup

library(spacc)

set.seed(42)
n_sites <- 80
n_species <- 40

coords <- data.frame(
  x = runif(n_sites, 0, 100),
  y = runif(n_sites, 0, 100)
)

# Species with varying range sizes (some endemic, some widespread)
species <- matrix(0L, n_sites, n_species)
for (sp in seq_len(n_species)) {
  cx <- runif(1, 10, 90)
  cy <- runif(1, 10, 90)
  # First 10 species are narrow-ranged (endemics)
  spread <- if (sp <= 10) 0.005 else 0.001
  prob <- exp(-spread * ((coords$x - cx)^2 + (coords$y - cy)^2))
  species[, sp] <- rbinom(n_sites, 1, prob)
}
colnames(species) <- paste0("sp", seq_len(n_species))

Endemism-Area Curves

spaccEndemism() tracks how many species are endemic (restricted) to the set of sites visited so far. As the sampled area expands, the number of endemic species initially rises then falls as widespread species are encountered:

end <- spaccEndemism(species, coords, n_seeds = 20, progress = FALSE)
end
#> spacc endemism: 80 sites, 40 species, 20 seeds
#> Final mean endemism: 40.0 species (100% of total)

plot(end)

Endemism-area curve showing endemic species as area expands.

The endemism curve is informative for identifying irreplaceable sites — areas where unique species would be lost if not protected.

Species-Fragmented Area Relationship (SFAR)

sfar() fits the SFAR model (Hanski et al. 2013), which quantifies how habitat fragmentation (number of fragments) reduces species richness beyond what area loss alone predicts:

\[\log(S) = c + z \cdot \log(A) + f \cdot \log(n)\]

where \(S\) is species richness, \(A\) is total area, \(n\) is number of fragments, and \(f\) is the fragmentation exponent.

# First create a spacc object
sac <- spacc(species, coords, n_seeds = 20, progress = FALSE)

# Define patch assignments (e.g., from k-means clustering)
set.seed(123)
patches <- kmeans(coords, centers = 5)$cluster

# Fit SFAR model
sfar_fit <- sfar(sac, patches)
sfar_fit
#> SFAR: Species-Fragmented Area Relationship
#> -------------------------------------------- 
#> Fragments: 5
#> R-squared: 0.985
#> 
#> Model: S = 7.74 * A^0.300 * n^(--0.248)
#> Fragmentation effect (f): -0.248
#>   No additional fragmentation penalty detected

plot(sfar_fit)

Species-Fragmented Area Relationship.

A negative fragmentation exponent \(f\) indicates that splitting habitat into more fragments reduces species richness beyond the area effect.

Sampling-Effort Corrected SAR (SESARS)

sesars() fits a species-area relationship corrected for variation in sampling effort across sites, avoiding the bias that arises when species-poor areas are also under-sampled:

\[\log(S) = c + z \cdot \log(A) + e \cdot \log(E)\]

# Simulate varying sampling effort per site
effort <- rpois(n_sites, 10) + 1

# Fit SESARS model using the spacc object from above
sesars_fit <- sesars(sac, effort)
sesars_fit
#> SESARS: Sampling Effort Species-Area Relationship
#> ------------------------------------------------ 
#> Model: power
#> R-squared: 0.996
#> 
#> Coefficients:
#>   log_c       z       w 
#>  4.2099  2.2586 -1.5486 
#> 
#> Interpretation: S = 67.35 * A^2.259 * E^-1.549

plot(sesars_fit)

Sampling-effort corrected SAR.

Per-Site Metrics for Spatial Prioritisation

spaccMetrics() computes accumulation metrics from every site as a starting point. This reveals spatial variation in diversity accumulation rates, useful for conservation planning:

met <- spaccMetrics(species, coords,
                    metrics = c("slope_10", "half_richness", "auc"),
                    progress = FALSE)

plot(met, metric = "slope_10", type = "heatmap")

Spatial heatmap of initial accumulation slope.

Sites with steep initial slopes represent areas where many species are concentrated — potential biodiversity hotspots.

Spatial Subsampling

subsample() reduces spatial autocorrelation when preparing data for macroecological analyses:

# Grid-based thinning
keep <- subsample(coords, method = "grid", cell_size = 20)
length(keep)
#> [1] 24

# Compare thinned vs full SAC
sac_full <- spacc(species, coords, n_seeds = 20, progress = FALSE)
sac_thin <- spacc(species[keep, ], coords[keep, ], n_seeds = 20, progress = FALSE)
combined <- c(full = sac_full, thinned = sac_thin)

plot(combined)

Effect of spatial thinning on SAC.

References

Hanski, I., Zurita, G.A., Bellocq, M.I. & Rybicki, J. (2013). Species-fragmented area relationship. Proceedings of the National Academy of Sciences, 110, 12715-12720.
Aiello-Lammens, M.E., Boria, R.A., Radosavljevic, A., et al. (2015). spThin: an R package for spatial thinning. Ecography, 38, 541-545.

Gilles Colling

2026-03-06