The Gold Standard of Ecology | Null Models, Species Co-Occurrence and Checkerboard Patterns

1. Write the null hypothesis before choosing software

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“Random co-occurrence” is not one model. Decide what would vary if the focal assembly process were absent while sampling structure, species frequencies or site richness remained as observed. A null may preserve each species’ occurrence total, each site’s richness, both margins or neither. Those constraints define the comparison and embody ecological assumptions; they are not merely technical settings.

2. Build an incidence matrix that represents comparable opportunities

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Rows should be comparable taxa and columns comparable sites, times or samples. Standardise survey effort or model detection before treating a zero as absence. Remove duplicate spatial units and explain decisions about rare species, empty sites and taxonomic aggregation. If sites differ strongly in area, habitat or accessibility, equiprobable placement is usually implausible unless those differences are incorporated into the null.

3. Understand what a checkerboard score measures

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For a pair of species, checkerboard units increase when each species occupies sites without the other. A matrix-level C-score averages pairwise segregation across species pairs. A high value can indicate less co-occurrence than expected under a specified null; a low value can indicate aggregation. The number has no universal scale independent of row totals, site number and constraints, so comparisons need a simulated reference distribution or careful standardisation.

4. Choose constraints that match the sampling story

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Fixing row sums preserves observed species frequencies; fixing column sums preserves observed site richness. A fixed–fixed algorithm is conservative for many presence–absence problems but can condition on patterns partly created by the process of interest. Less constrained algorithms may inflate false positives when common species and rich sites are redistributed unrealistically. Run justified alternatives and explain what each treats as nuisance structure.

5. Generate and diagnose the null distribution

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Use enough randomisations for the desired tail resolution and verify that the algorithm explores the allowed matrix space rather than producing duplicates or biased swaps. Compare the observed metric with the simulated distribution using a prespecified tail, standardised effect size and Monte Carlo probability. Inspect null means, variances and convergence. A small probability attached to a poorly mixed or ecologically impossible null is not evidence of assembly rules.

6. Worked example: six insects across eight ponds

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Two predatory insects each occur in four of eight ponds but never together, producing many checkerboard units. Under an equiprobable-site null, the segregation is extreme. Field records show that four ponds are permanent and four dry seasonally: one insect occurs only in permanent water and the other only in temporary pools. A habitat-constrained null makes the pattern ordinary. The matrix contained non-random structure, but environmental sorting—not necessarily competition—explains it.

7. Separate pattern from process

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Competition, shared predators, dispersal barriers, habitat filtering, historical biogeography and detection error can all alter co-occurrence. Segregation is compatible with competition but is not a unique signature. Aggregation can reflect facilitation or merely shared habitat. Add environmental covariates, spatial structure, traits, experiments or longitudinal evidence before assigning mechanism. Null-model analysis detects departure from a reference, not the cause of departure.

8. Changed-context transfer check: microbial samples through time

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In repeated microbiome samples, columns are time points nested within hosts rather than independent sites. The transferable question remains what structure the null should preserve. Randomising across all columns destroys host identity, temporal autocorrelation and sequencing-depth differences. A defensible analysis constrains permutations within relevant strata or uses a model designed for repeated compositional data; a classic island-style checkerboard null does not transfer unchanged.

9. Know the common misconceptions

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A non-significant result does not prove random assembly, especially with few sites or rare species. A significant C-score does not prove competitive exclusion. Fixing both margins does not automatically make a null correct, and more randomisations cannot repair a wrong hypothesis. Pairwise tests create multiplicity, while a community-wide statistic can hide a small set of influential pairs. Presence–absence also discards abundance and uncertainty.

10. Audit the matrix, algorithm and ecological claim

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Publish the cleaned incidence matrix, sampling effort, exclusion rules, environmental strata, metric formula, algorithm name, constraints, number of simulations, random seed and software version. Repeat analyses with plausible treatments of rare taxa, site weights, spatial blocks and alternative nulls. Plot influential species pairs and sites. The strongest conclusion is the one that survives defensible reference models and remains modest about mechanism.

11. Frequently asked questions

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Is a checkerboard pair two species that never co-occur? In the strict pattern, yes, while the C-score measures degrees of segregation. Which null model is best? The one whose constraints match the ecological question and sampling design; no algorithm is universally best. Should rare species be removed? Only by a prespecified rule with sensitivity checks. Can null models show competition? They can identify patterns consistent with it, not establish it alone.

12. The gold standard makes randomness explicit

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Null models are useful because they force an investigator to state what “by chance” means. The gold standard keeps the incidence data, constraints, metric and ecological interpretation separate, checks algorithm performance and challenges results with plausible alternatives. A checkerboard pattern becomes credible evidence of non-random co-occurrence only relative to a transparent reference—and remains one step short of a causal mechanism.