Null Models for Categorical and Continuous Community Matrices

Provides null model algorithms for categorical and quantitative community ecology data. Extends classic binary null models (e.g., 'curveball', 'swap') to work with categorical data. Provides a stratified randomization framework for continuous data.

nullcat

nullcat provides null model algorithms for categorical and quantitative community ecology data. It extends classic binary null models (e.g., curveball, swap) to work with categorical data, and introduces a stratified randomization framework for continuous data that addresses limitations in existing methods for randomizing quantitative and count data.

Installation

# Install stable version from CRAN:
install.packages("nullcat")

# Or dev version from GitHub:
# install.packages("remotes")
remotes::install_github("matthewkling/nullcat")

Quick start

Categorical null models

Generalize binary null models to matrices where cells contain integers representing discrete categories:

library(nullcat)

# Create a categorical matrix
set.seed(123)
cat_matrix <- matrix(sample(1:4, 20*10, replace = TRUE), nrow = 20)

# Randomize using curvecat (preserves row & column category multisets)
randomized <- curvecat(cat_matrix, n_iter = 1000)

# Verify margins are preserved
all.equal(sort(cat_matrix[1,]), sort(randomized[1,]))
#> [1] TRUE
all.equal(sort(cat_matrix[,1]), sort(randomized[,1]))
#> [1] TRUE

Available algorithms: curvecat(), swapcat(), tswapcat(), r0cat(), c0cat()

Quantitative null models

Apply stratified randomization to continuous community data:

# Create a quantitative community matrix
set.seed(456)
comm <- matrix(rexp(50 * 30, rate = 0.5), nrow = 50)

# Stratified randomization with 5 strata
rand1 <- quantize(comm, n_strata = 5, n_iter = 2000)

# Preserve row value multisets (row sums maintained)
rand2 <- quantize(comm, n_strata = 5, fixed = "row", n_iter = 2000)
all.equal(rowSums(comm), rowSums(rand2))
#> [1] TRUE

Spatially constrained null models

Weight pair selection by spatial proximity, trait similarity, or any pairwise measure:

set.seed(789)
x <- matrix(sample(1:4, 200, replace = TRUE), nrow = 20)

# Site coordinates and distance-decay weights
coords <- cbind(runif(20), runif(20))
W <- exp(-as.matrix(dist(coords)) / 0.3)

# Nearby sites exchange tokens more frequently
x_spatial <- curvecat(x, n_iter = 2000, wt_row = W)

# Weight both margins simultaneously (Gibbs-like alternating)
W_col <- exp(-as.matrix(dist(cbind(runif(10), runif(10)))) / 0.3)
x_dual <- curvecat(x, n_iter = 2000, wt_row = W, wt_col = W_col)