Single-cell gene expression distributions measured by single-cell RNA-sequencing (scRNA-seq) often display complex differences between samples. These differences are biologically meaningful but cannot be identified using standard methods for differential expression.


Here, we derive and implement a flexible and fast differential distribution testing procedure based on the 2-Wasserstein distance. Our method is able to detect any type of difference in distribution between conditions. To interpret distributional differences, we decompose the 2-Wasserstein distance into terms that capture the relative contribution of changes in mean, variance and shape to the overall difference. Finally, we derive mathematical generalizations that allow our method to be used in a broad range of disciplines other than scRNA-seq or bioinformatics.

Availability and implementation

Our methods are implemented in the R/Bioconductor package waddR, which is freely available at, along with documentation and examples.

Supplementary information

Supplementary data are available at Bioinformatics online.

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