Fast Spatial Species Accumulation Curves

High-performance spatial species accumulation curves using fixed-focus spatially constrained rarefaction, nearest-centroid expansion, and nearest-neighbor walks with a C++ backend for speed. Supports Hill numbers (q=0,1,2), beta diversity partitioning (turnover/nestedness) at site and pooled resolution, coverage-based rarefaction and extrapolation of alpha and beta diversity, phylogenetic diversity (PD; Faith's PD, EvoHeritage, mean pairwise distance, mean nearest taxon distance), functional diversity accumulation including aggregated functional diversity and intraspecific trait variation, phylogenetic and functional redundancy, interaction network accumulation, diversity-area relationships (DAR), endemism-area curves, sampling-effort correction and fragmentation analysis, species-area relationship (SAR) models based on extreme value theory (EVT), and area-based richness extrapolation via the total-species curve. Total richness is also estimated from frequency counts, including the accumulation rate curve estimator and an estimator for sites sampled without replacement, and shift-and-rotate null models test the position of a sampling design. Multiple starting points (seeds) provide uncertainty quantification. Methods are described in Chao et al. (2014) , Baselga (2010) , Chao and Jost (2012) , Faith (1992) , Ma (2018) , Borda-de-Agua et al. (2025) , Hanski et al. (2013) , Jost (2007) , Ugland et al. (2003) , Chao et al. (2023) , Chiu (2023) , Chiu et al. (2023) , Rosindell et al. (2024) , Wojcik et al. (2024) , Ridder et al. (2024) , Jones et al. (2025) , and Shestopaloff (2025) .

spacc

species accumulating in the neighbourhood

Spatial species accumulation curves built by fixed-focus expansion in C++.

Sample a focal point in continuous space, rank every sampling unit by its distance from that point, then count new species along the ranking. spacc repeats this from many focal points (Rcpp/RcppParallel backend), so the curve carries a confidence ribbon showing how richness depends on where expansion begins. The classical curve in vegan::specaccum() shuffles sites in random order, without using their spatial arrangement. spacc reproduces that random-order curve and adds the spatial one, so you can read the gap between them.

Installation

install.packages("spacc")            # CRAN

install.packages("pak")              # development version
pak::pak("gcol33/spacc")

Quick start

library(spacc)

coords  <- data.frame(x = runif(100), y = runif(100))
species <- matrix(rbinom(100 * 50, 1, 0.3), nrow = 100)

# spatial accumulation around continuous focal points
sac <- spacc(species, coords, method = "knn", n_seeds = 100)
plot(sac)

Spatial order, not random order

vegan::specaccum() accumulates sites in random or collector order, so geography drops out. spacc() keeps it: each curve expands around a continuous focal point, and the spread across focal points is the spatial signal. Run both and compare them directly.

sac        <- spacc(species, coords, method = "knn",    n_seeds = 100)
sac_random <- spacc(species, coords, method = "random", n_seeds = 100)

comp <- compare(sac, sac_random)   # permutation, bootstrap, or AUC test
plot(comp)

Seven expansion methods are available: knn (fixed-focus spatially constrained rarefaction), kncn (nearest-centroid expansion), nn_walk (a greedy nearest-neighbour traversal), gaussian and cone (distance- and direction-weighted growth), random (the classical null), and collector (data order). Geographic coordinates use distance = "haversine" with no projection step.

By default, continuous focal points are sampled uniformly from the convex hull of the eligible sites. Pass an sf polygon through focal_domain when the study boundary is known, or pass exact coordinates through focal_points for reproducible focal definitions.

Backend selection

The nn_walk and kncn methods pick a nearest-neighbour backend by site count, overridable with backend. Fixed-focus knn ranks distances directly.

sac <- spacc(species, coords_lonlat, distance = "haversine", n_seeds = 50)
sac <- spacc(species, coords, backend = "kdtree", n_seeds = 50)

Diversity beyond richness

Accumulation works for more than species counts. Each function carries the spatial ordering through to a different diversity measure, with map = TRUE and as_sf() for GIS output.

• spaccHill(): Hill numbers (q = 0, 1, 2) along the accumulation, extending the iNEXT framework to spatial order.
• spaccBeta(): beta diversity with turnover and nestedness components (Baselga 2010).
• spaccCoverage(): coverage-based rarefaction via the Good-Turing estimator (Chao & Jost 2012).
• spaccPhylo() / spaccFunc(): phylogenetic (MPD, MNTD) and functional (FDis, FRic) accumulation.
• alphaDiversity() / gammaDiversity() / diversityPartition(): local, regional, and alpha-beta-gamma decomposition (Jost 2007).

hill <- spaccHill(species, coords, q = c(0, 1, 2), n_seeds = 50, map = TRUE)
plot(hill)                       # accumulation curves
plot(hill, type = "map", q = 0)  # per-site richness map

beta <- spaccBeta(species, coords, index = "sorensen", n_seeds = 50)
plot(beta, partition = TRUE)     # turnover vs nestedness

Grouped and spatiotemporal accumulation

Split species into groups (native vs alien, families, any factor) and accumulate each under the same spatial site ordering, or add a temporal axis to weight space against time.

# same spatial ordering, separate curve per group
sac_grouped <- spacc(species, coords, groups = status, seed = 42)
plot(sac_grouped, facet = TRUE)

# sites sampled across years: weighted space-time distance
sac_st <- spacc(species, coords, method = "nn_walk",
                time = site_years, w_space = 1, w_time = 0.5)

Fitting and standardizing

• extrapolate(): asymptotic richness models (Michaelis-Menten, Lomolino, Weibull, logistic, EVT).
• compare(): permutation, bootstrap, or AUC tests between curves.
• rarefy() / subsample(): rarefaction to common effort, spatial subsampling.
• coleman() / mao_tau() / spatialRarefaction(): analytical (non-simulation) curves.
• as_spacc(): bring an existing vegan::specaccum() object into the same plotting and comparison machinery.

Documentation

• Getting Started
• Diversity Accumulation
• Extrapolation
• Spatial Analysis
• Community Assembly
• Richness Estimation
• Rarefaction
• Methods and Algorithms
• Function Reference

Support

"Software is like sex: it's better when it's free." — Linus Torvalds

I'm a PhD student who builds R packages in my free time because I believe good tools should be free and open. I started these projects for my own work and figured others might find them useful too.

If this package saved you some time, buying me a coffee is a nice way to say thanks. It helps with my coffee addiction.

License

MIT (see the LICENSE.md file)

Citation

@Manual{spacc,
  author = {Gilles Colling},
  title  = {spacc: Fast Spatial Species Accumulation Curves},
  year   = {2026},
  url    = {https://CRAN.R-project.org/package=spacc}
}