On the consistent and scalable detection of spatial patterns

Detecting spatial patterns is fundamental to scientific discovery, yet current methods lack statistical consensus and face computational barriers when applied to large-scale spatial omics datasets. We unify major approaches through a single quadratic form and derive general consistency conditions. We reveal that several widely used methods, including Moran’s I, are inconsistent, and propose scalable corrections. The resulting test enables robust pattern detection across millions of spatial locations and single-cell lineage-tracing datasets.

💡 Research Summary

The paper addresses a critical gap in spatial omics analysis: the lack of statistically sound, scalable methods for detecting spatially variable genes (SVGs) across millions of spatial locations. The authors first demonstrate that a wide range of existing approaches—including Moran’s I, Hotspot, fixed‑effect models, linear mixed models, generalized linear mixed models, and non‑parametric dependence tests—can all be expressed as a quadratic form Qₙ = zᵀKz, where z is a standardized vector of observations and K encodes spatial relationships. This unifying “Q‑test” framework reveals a common limitation: all such tests are only sensitive to mean‑shift alternatives (i.e., changes in E