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bioRxiv · 10.64898/2026.08.10.743911

Covariance Nonstationarity is Evident in Spatial Transcriptomics and Provides a New Categorization of Spatially Varying Genes

Velidi, P.·Wei, Z.·Nathoo, F.
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Abstract

Gaussian process models underlie many spatial transcriptomics tools but typically assume stationary covariance. Covariance non-stationarity has long been recognized in spatial statistics as an important feature of spatial data, yet it has received little attention in spatial transcriptomics. We show that this omission is consequential: covariance non-stationarity is substantially evident across spatial transcriptomic datasets and alters the characterization of spatially varying genes. While typically ignored, non-stationarity of spatial covariance in gene expression may correspond to tissue heterogeneity or cell aggregates. Across 12 Visium datasets, we use approximate Bayes factors from R-INLA to compare stationary and non-stationary Mat'ern covariance functions. Evidence for covariance non-stationarity appears in 3% to 50% of genes across tissue samples. We find that gene sets associated with immune, cytokine, and other effector functions are enriched among genes favoring non-stationary spatial covariance. Covariance stationarity is therefore not a benign technical simplification in spatial transcriptomics; it is frequently violated, the violation is biologically structured, and it changes the definition and classification of spatially varying genes.

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Velidi, P., Wei, Z., Nathoo, F.. 2026-08-18. Covariance Nonstationarity is Evident in Spatial Transcriptomics and Provides a New Categorization of Spatially Varying Genes. https://doi.org/10.64898/2026.08.10.743911

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