nullmalli

Nullmalli, or null model, is a reference model used to assess whether patterns observed in data differ from what would be expected under a defined random process or baseline conditions. It formalizes a hypothetical data-generating mechanism that preserves certain properties while randomizing others, allowing researchers to test specific hypotheses about structure or association.

A null model is typically constructed by generating many simulated datasets under a prescribed set of constraints. The choice of constraints defines what counts as “random” with respect to the question at hand. Common approaches include randomizing data while keeping margins fixed (for example, preserving row or column totals in a presence–absence matrix) or preserving structural features such as the degree sequence in a network. Different null models define different reference expectations, leading to different null distributions for the statistic of interest.

Applications span several fields. In ecology, null models test whether species co-occurrence patterns are more or less aggregated than expected by chance. In network science, they are used to evaluate whether observed connectivity or motif frequencies exceed what would occur under random wiring (as in Erdős–Rényi models) or under the constraint of a fixed degree sequence (the configuration model). In genomics and time-series analysis, permutations or shuffles of data serve as nulls to assess significance of correlations or periodicities.

Interpretation relies on comparing the observed statistic to the null distribution to obtain a p-value or confidence interval. A key caveat is that the null model reflects the researcher’s assumptions; mis-specification can lead to misleading conclusions.