Community Assembly and Turnover

Overview

Understanding how communities change across space requires tools that quantify turnover at different scales. spacc provides three complementary approaches:

Beta distance-decay: How does compositional similarity decay with distance?
Zeta diversity: How does the number of shared species change with the number of sites compared?
SES null models: Are observed patterns different from random expectations?

Data setup

library(spacc)
set.seed(123)

n_sites <- 60
coords <- data.frame(
  x = runif(n_sites, 0, 100),
  y = runif(n_sites, 0, 100)
)

# Spatially structured community:
# species occurrence probability decays with distance from species' "center"
n_species <- 25
species <- matrix(0, nrow = n_sites, ncol = n_species)
centers_x <- runif(n_species, 0, 100)
centers_y <- runif(n_species, 0, 100)

for (sp in seq_len(n_species)) {
  dists <- sqrt((coords$x - centers_x[sp])^2 + (coords$y - centers_y[sp])^2)
  prob <- exp(-dists / 30)
  species[, sp] <- rpois(n_sites, lambda = prob * 3)
}
colnames(species) <- paste0("sp", seq_len(n_species))

# Build accumulation curve (used later for SES null models)
sac <- spacc(species, coords, n_seeds = 10, progress = FALSE)

Beta distance-decay

The betaDecay() function fits models to the relationship between compositional dissimilarity and geographic distance:

decay <- betaDecay(species, coords)
#> ℹ Computing distance matrix
#> ℹ Computing 1,770 pairwise dissimilarities (sorensen)
#> ℹ Fitting decay models
#> ✔ Done
plot(decay)

summary(decay)
#> $n_sites
#> [1] 60
#> 
#> $n_pairs
#> [1] 1770
#> 
#> $distance_range
#> [1]   2.133552 122.675695
#> 
#> $dissimilarity_range
#> [1] 0.1351351 1.0000000
#> 
#> $mean_dissimilarity
#> [1] 0.5569438
#> 
#> $coefficients
#>                    model         a           b        AIC
#> a            exponential 0.6639603 0.008131670 -1925.4191
#> (Intercept)        power 0.2005184 0.256130232   481.6219
#> (Intercept)1      linear 0.3656503 0.003674776 -1943.9352
#> 
#> $best_model
#> [1] "linear"
#> 
#> $half_life
#> [1] 85.24045
#> 
#> $index
#> [1] "sorensen"

Zeta diversity

Zeta diversity measures the number of species shared among exactly \(\zeta\) sites. The rate of decline from \(\zeta_1\) to higher orders indicates whether turnover is driven by common or rare species:

zd <- zetaDiversity(species, coords, orders = 1:10, n_samples = 50)
#> ℹ Computing distance matrix
#> ℹ Computing zeta diversity (orders 1-10, knn)
#> ✔ Done
plot(zd)

The ratio plot reveals whether turnover follows an exponential (stochastic) or power-law (niche-driven) pattern:

plot(zd, type = "ratio")

SES null models

Standardized effect sizes compare observed diversity patterns against null expectations. A positive SES indicates higher diversity than expected (overdispersion); negative SES indicates clustering.

result <- ses(sac, species, coords,
              null_model = "curveball", n_perm = 19,
              progress = FALSE)
print(result)
#> Standardized Effect Size (SES)
#> ------------------------------------ 
#> Input class: spacc
#> Metric: richness
#> Null model: curveball (19 permutations)
#> SES range: [-5.62, 0.47]
#> Mean SES: -0.51
#> Significant (p < 0.05): 0 / 60 values (0%)

plot(result, type = "curve")

The histogram shows the distribution of SES values across accumulation steps:

plot(result, type = "histogram")

Combining the three approaches

These tools answer complementary questions:

Approach	Question	Key output
Distance-decay	How fast does similarity decline?	Decay rate, half-distance
Zeta diversity	Common vs. rare species turnover?	Decline ratio, power/exp fit
SES null models	Is the pattern non-random?	SES values, p-values

Together they provide a comprehensive view of community assembly mechanisms operating in the study region.

References

Baselga, A. (2010). Partitioning the turnover and nestedness components of beta diversity. Global Ecology and Biogeography, 19, 134-143.
Hui, C. & McGeoch, M.A. (2014). Zeta diversity as a concept and metric that unifies incidence-based biodiversity patterns. American Naturalist, 184, 684-694.
Strona, G., Nappo, D., Boccacci, F., Fattorini, S. & San-Miguel-Ayanz, J. (2014). A fast and unbiased procedure to randomize ecological binary matrices with fixed row and column totals. Nature Communications, 5, 4114.

Gilles Colling