Fit Sloan Neutral Community Model (SNCM)

The function implements the Sloan Neutral Community Model which predicts the occurrence frequency of taxa based on their relative abundance in the source pool and a migration parameter (m). It compares the neutral model against binomial and Poisson null models using various statistical measures.

Usage

sncm.fit(spp, pool = NULL, stats = TRUE, taxon = NULL)

Arguments

spp: A matrix or data frame where rows represent communities (samples) and columns represent species/taxa. Values should be abundances or counts.
pool: Optional. A matrix or data frame representing the source pool for calculating relative abundances. If NULL, the source pool is calculated from the spp matrix. Default is NULL.
stats: Logical. If TRUE, returns fit statistics including AIC, BIC, R-squared, and RMSE for model comparison. If FALSE, returns predicted vs. observed frequencies with confidence intervals. Default is TRUE.
taxon: Optional. A data frame containing taxonomic information to merge with results when stats = FALSE. Should have row names matching species names. Default is NULL.

Value

If stats = TRUE, returns a data frame with model fit statistics including:

m: Migration rate parameter from NLS fit
m.ci: Confidence interval for m parameter
m.mle: Migration rate from maximum likelihood estimation
maxLL, binoLL, poisLL: Log-likelihood values for SNCM, binomial, and Poisson models
Rsqr, Rsqr.bino, Rsqr.pois: R-squared values for each model
RMSE, RMSE.bino, RMSE.pois: Root mean squared error for each model
AIC, BIC: Information criteria for model selection
N: Average number of individuals per community
Samples: Number of samples/communities
Richness: Number of taxa analyzed
Detect: Detection limit (1/N)

If stats = FALSE, returns a data frame with observed and predicted frequencies along with confidence intervals for visualization.

Details

The model assumes neutral processes govern community assembly. Three models are compared: SNCM (beta distribution), binomial null model, and Poisson null model.

References

Sloan WT, Lunn M, Woodcock S, Head IM, Nee S, Curtis TP. (2006) Quantifying the roles of immigration and chance in shaping prokaryote community structure. Environ Microbiol. 8(4):732-40. doi:10.1111/j.1462-2920.2005.00956.x

Examples

# Generate community data
set.seed(42)
n_samples <- 100
n_species <- 80

# Log-normal abundances
mean_abund <- rlnorm(n_species, meanlog = 2, sdlog = 1.5)
# Simulate community matrix with multinomial sampling
spp_data <- t(sapply(seq_len(n_samples), function(i) {
  rmultinom(
    1,
    size = sample(500:2000, 1),
    prob = mean_abund / sum(mean_abund)
  )[, 1]
}))
colnames(spp_data) <- paste0("Species_", seq_len(n_species))

fit_stats <- sncm.fit(spp_data, stats = TRUE)
#> Waiting for profiling to be done...
#> Warning: SNCM `stats::dnorm()` produced a warning during MLE: NaNs produced
#> Warning: SNCM `stats::pbeta()` produced a warning during MLE: NaNs produced
#> Warning: Binomial model `stats::dnorm()` produced a warning during MLE: NaNs produced
#> Warning: Poisson model `stats::dnorm()` produced a warning during MLE: NaNs produced
#> ℹ Neutral model fitting:
#> • Average individuals per community (N): 1264.75
#> • Binomial model using rounded N: 1265
#> • Poisson model using N: 1264.75
#> • Maximum likelihood estimation using N: 1264.75, and starting parameters: mu =
#>   0, sigma = 0.1
predictions <- sncm.fit(spp_data, stats = FALSE)
#> Waiting for profiling to be done...
#> Warning: SNCM `stats::dnorm()` produced a warning during MLE: NaNs produced
#> Warning: SNCM `stats::pbeta()` produced a warning during MLE: NaNs produced
#> Warning: Binomial model `stats::dnorm()` produced a warning during MLE: NaNs produced
#> Warning: Poisson model `stats::dnorm()` produced a warning during MLE: NaNs produced
#> ℹ Neutral model fitting:
#> • Average individuals per community (N): 1264.75
#> • Binomial model using rounded N: 1265
#> • Poisson model using N: 1264.75
#> • Maximum likelihood estimation using N: 1264.75, and starting parameters: mu =
#>   0, sigma = 0.1